Molecular Magnetism of Metal Complexes and Light-Induced Phase Transitions

Abstract

One of the most attractive research in the field of molecular solids is multifunctional molecular magnets coupled with spin, charge and photon, and single-molecular magnet/single-chain magnet toward spintronics. In this chapter, we focus on the molecular magnetism and its related light-induced phase transitions from the viewpoint of Mössbauer spectroscopy. In the Sect. 6.1, the outline of this chapter is described. In the Sect. 6.2, static and dynamic spin crossover phenomena between the high-spin and low-spin states, and the spin frustration system induced by dynamic spin crossover phenomena for [Mn^IIFe^III(C₂O₃S)₃] complex are described. In the Sect. 6.3, metal complexes showing charge transfer phase transitions such as Prussian blue analogous complexes and [Fe^IIFe^III(C₂O₂S₂)₃] complexes and their photo-induced phase transitions are described. In the Sect. 6.4, various kinds of molecular magnets including single molecular chain magnets are described.

6.1 Introduction

Transition-metal complexes consist of transition-metal elements and various kinds of ligands with the ability to control the structural dimensionality, which have produced wide variety of magnetic materials such as low-dimensional magnets, photo-induced magnets, single-molecule magnets (SMMs) and so forth, which have stimulated the theory of molecular magnetism. Thus, the development of advanced magnetic materials and the theory of molecular magnetism have mutually stimulated each other. Especially, the discoveries of light induced excited state spin trapping (LIESST) for spin crossover system (1984), SMM of [Mn₁₂] cluster complex (1993), and photo-induced ferrimagnet of Prussian blue analogous complex (1996) have significantly expanded the field of molecular magnetism. These recent topics of molecular magnetism are reviewed in the following excellent books [1].

In this chapter, we focus on the molecular magnetism and its related light-induced phase transitions from the viewpoint of Mössbauer spectroscopy. Among various kinds of molecular compounds, in the case of transition-metal complexes whose spin states are situated in the spin crossover region, new types of synergetic phenomena coupled with spin and charge are expected. Based on this viewpoint, we have synthesized organic–inorganic hybrid systems, A[Fe^IIFe^IIIX₃] [A = (C_nH_2n+1)₄N, spiropyran, etc.; X = dto (C₂O₂S₂), mto (C₂O₃S), tto (C₂OS₃)] and have found novel multifunctional phenomena coupled with spin, charge and photon [2].

In general, the Fe^III site coordinated by six S atoms is in the low spin (LS) state, while that coordinated by six O atoms is in the high spin (HS) state. Therefore, the spin state of Fe^III coordinated by three S atoms and three O atoms is expected to be situated in the spin crossover region. Based on this viewpoint, we have synthesized (C₆H₅)₄P[Zn^IIFe^III(mto)₃] consisting of Fe^IIIO₃S₃ and Zn^IIO₆ octahedra, and the ⁵⁷Fe Mössbauer spectroscopy and the electron spin resonance (ESR) revealed the dynamic spin equilibrium phenomenon occurs at the Fe^IIIO₃S₃ site in which the HS and LS states exchange alternately in the time scale of 10⁻¹⁰ < τ < 10⁻⁷ s [3]. On the other hand, in the case of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] consisting of Fe^IIIO₃S₃ and Mn^IIO₆, there exists a dynamic spin equilibrium (τ < 10⁻⁷ s) between the HS and LS states at the Fe^IIIO₃S₃ site, which induces the frustration of internal magnetic field between the ferromagnetic and antiferromagnetic interactions at the Mn^IIO₆ site. Owing to the frustration of internal magnetic field at the Mn^II site caused by the rapid spin equilibrium at the Fe^III site, (C₆H₅)₄P[Mn^IIFe^III(mto)₃] undergoes the successive magnetic phase transitions at 30 and 23 K.

In the case of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃], in addition to the ferromagnetic phase transition, a spin-entropy driven charge transfer phase transition (CTPT) takes place, in which the electrons of Avogadro’s constant transfer between the Fe^II and Fe^III sites [4]. At the CTPT, the Fe valence state is dynamically fluctuated, which was revealed by means of muon spin relaxation (μSR) [5]. The CTPT and the ferromagnetic phase transition strongly depend on the honeycomb ring size in [Fe^IIFe^III(dto)₃]_∞ [6]. The increase of counter-cation size expands the honeycomb ring, which stabilizes and destabilizes the high temperature phase (HTP) and the low temperature phase (LTP), respectively. In order to control the ferromagnetic properties and the CTPT by means of light irradiation, we have synthesized a photo-responsive organic–inorganic hybrid system, (SP-Me)[Fe^IIFe^III(dto)₃] (SP = spiropyran), and discovered that the photo-isomerization of intercalated SP-Me by UV light irradiation induces the CTPT from the LTP to the HTP in the two-dimensional [Fe^IIFe^III(dto)₃] layer and the change of T_C from 5 to 22 K, by means of magnetization measurement and ⁵⁷Fe Mössbauer spectroscopy [7].

In the Sect. 6.4, we show various kinds of molecular magnets such as SMMs including transition-metal clusters, low-coordinated Fe complexes, and single-chain magnets (SCMs) with easy-plane anisotropy.

6.2 Spin Crossover Phenomena

6.2.1 Static and Dynamic Spin Crossover Phenomena

Octahedral transition-metal complexes with d⁴–d⁷ configurations have a possibility of spin crossover transition between the LS and HS states in the ground state. If the ligand field splitting energy is smaller than the spin-pairing energy in the d orbitals, the d electrons occupy the t_2g (d_xy, d_yz, d_zx) and the e_g $({\text{d}}_{{x^{2}}-{y^{2}}}, {\text{d}}_{z^{2}})$ orbitals being followed by Hund’s rule, in which the spin configuration shows the maximum spin multiplicity (HS state). On the other hand, if the ligand field splitting energy is larger than the spin-pairing energy, Hund’s rule is broken down, in which the spin configuration shows the minimum spin multiplicity (LS state). Therefore, the ground state of the transition metal ion with dⁿ (n = 4–7) is ruled by the competition between ligand field splitting energy and spin-pairing energy in the d electrons, which is schematically shown in Fig. 6.1.

Fig. 6.1

Spin arrangements in the ground states for dⁿ (n = 4–7) configuration with octahedral symmetry

The energy diagram for dⁿ system called Tanabe–Sugano diagram is the most effective tool to analyze the competition between the HS and LS states as the ground state [8]. The Tanabe–Sugano diagram exhibits the energies of multiplets for 3dⁿ (n = 2–8) system as a function of the ratio of ligand field (Dq) to the Racah parameter (B) representing the strength of Coulomb interaction between 3d electrons. In the case of 3dⁿ (n = 4–7), if the ground energies of HS and LS states are close to each other, the system has a possibility to convert the spin states between the HS and LS states by external perturbations such as heat, applied pressure or light irradiation. Such the HS–LS conversion is called spin crossover phenomenon.

The spin crossover phenomenon was observed for the first time by L. Cambi et al. in 1930s for tris(dithiocarbamato)iron(III) complexes, Fe^III(S₂CNR₂)₃ (R = n-C₄H₉, iso-C₄H₉, etc.) [9]. In this system, as shown in Fig. 6.2, the Fe^III ion is coordinated by six S atoms. According to L. Cambi et al., the magnetic susceptibilities of Fe^III(S₂CNR₂)₃ significantly change depending on temperature caused by the gradual LS (S = 1/2)−HS (S = 5/2) transition, which is shown in Fig. 6.3. If the spin conversion between the LS (S = 1/2) and HS (S = 5/2) states is slower than the time scale (τ = 10⁻⁷ s) of ⁵⁷Fe Mössbauer spectroscopy, two kinds of quadrupole doublets corresponding to the HS and LS states should be clearly distinguished. On the other hand, if the spin conversion is faster than 10⁻⁷ s, an averaged quadrupole doublet should be observed. In the case of Fe^III(S₂CNR₂)₃ (R = C₂H₅), as shown in Fig. 6.4, the ⁵⁷Fe Mössbauer spectrum exhibits a broad quadrupole doublet in the temperature range of the gradual LS (S = 1/2) ↔ HS (S = 5/2) transition, which shows that the rapid spin equilibrium between the HS and LS states is realized in the time scale of τ < 10⁻⁷ s [10]. Until now, various kinds of Fe^III complexes consisting of Fe^IIIS₆, Fe^IIIO₃S₃, or Fe^IIIN₄O₂ octahedra exhibiting rapid spin equilibrium phenomena have been reported [11].

Fig. 6.2

Molecular structure of Fe^III(S₂CNR₂)₃ (R = n-C_nH_2n+1, etc.)

Fig. 6.3

(Reprinted from [9(c)]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA)

Inverse magnetic susceptibilities as a function of temperature for Fe^III(S₂CNR₂)₃ (R = n-C_nH_2n+1, etc.).

Fig. 6.4

Copyright 1987 American Chemical Society

⁵⁷Fe Mössbauer spectra of Fe^III(S₂CNR₂)₃ (R = C₂H₅) at various temperatures. Reprinted with permission from [10].

Thirty years after the discovery of spin-crossover phenomenon for Fe^III(S₂CNR₂)₃, W.A. Baker et al. reported the spin-crossover phase transition for [Fe^II(phen)₂X₂] (phen = 1,10-phenanthroline, X = NCS or NCSe) [12]. In [Fe^II(phen)₂(NCS)₂], the Fe^II ion is coordinated by six N atoms of phen and NCS molecules, and this complex undergoes the first-order LS (¹A_1g, S = 0)−HS (⁵T_2g, S = 2) transition at 176 K with a small thermal hysteresis. Since the discovery of the spin-crossover phase transition for [Fe^II(phen)₂X₂] (X = NCS, NCSe), various kinds of spin crossover complexes have been reported for Cr^II (3d⁴), Mn^III (3d⁴), Mn^II (3d⁵), Fe^III (3d⁵), Fe^II (3d⁶), Co^III (3d⁶), and Co^II (3d⁷) complexes [13,14,15], in which most of them are Fe^II (3d⁶) and Fe^III (3d⁵) complexes.

The spin-crossover phenomena have attracted much attention since the discovery of the light-induced spin transition for [Fe^II(ptz)₆](BF₄)₂ (ptz = 1-propyltetrazole) in 1984 [16(b)]. This complex exhibits a sharp spin transition at 135 K with a remarkable change of color [16(a)]. The color in the LS state is purple, while that in the HS state is colorless. S. Decurtins, P. Gütlich, et al. discovered a persistent light-induced HS state for [Fe^II(ptz)₆](BF₄)₂ when they measured the optical absorption spectra at 8 K with white light including the spin-allowed absorption region ($^{1} {\text{A}}_{{1{\text{g}}}} ( {{\text{t}}_{{2{\text{g}}}}^{6} } ) \to^{1} {\text{T}}_{{1{\text{g}}}} ,^{1} {\text{T}}_{{2{\text{g}}}}( {{\text{t}}_{{2{\text{g}}}}^{5} {\text{e}}_{\text{g}} } )$ transitions), in which the purple color was completely “bleached” and the colorless remained unchanged as long as the temperature was kept below 50 K [16(c)]. This light-induced spin-crossover phenomenon was named LIESST (Light Induced Excited Spin State Trapping) by them. The trapping ⁵T_2g state of the lowest HS state could also be optically pumped back to the ¹A_1g ground state via intermediate triplet states $^{3} {\text{T}}_{{1{\text{g}}}} ,^{3} {\text{T}}_{{2{\text{g}}}} ( {{\text{t}}_{{2{\text{g}}}}^{5} {\text{e}}_{\text{g}} } )$ by the light irradiation corresponding to the ⁵T_2g → ⁵E_g transition, which was called reverse-LIESST. The discovery of LIESST and reverse-LIESST have attracted much attention from the viewpoint of photonic molecular devices, and various kinds of spin crossover complexes showing LIESST have been developed mainly for Fe^II and Fe^III complexes [17]. Figure 6.5 shows the schematic demonstration of the erasable optical recording based on the LIESST and reverse-LIESST for [Fe^II(ptz)₆](BF₄)₂.

Fig. 6.5

Schematic demonstration of the erasable optical recording based on the LIESST and reverse-LIESST for [Fe^II(ptz)₆](BF₄)₂

6.2.2 Dynamic Spin Crossover Phenomena of A[M^IIFe^III(mto)₃] (A = Counter Cation; M = Zn, Cd; mto = C₂O₃S)

In this section, we focus on the spin crossover phenomenon of Fe^III coordinated by three S atoms and three O atoms, Fe^IIIO₃S₃. In general, the Fe^III site coordinated by six S atoms tends to be in the LS state $({\text{t}}_{{2{\text{g}}}}^{5} ,S = 1/2)$, while the Fe^III site coordinated by six O atoms is in the HS state $({\text{t}}_{{2{\text{g}}}}^{3} {\text{e}}_{\text{g}}^{2} ,S = 5/2)$. Therefore, the spin state of Fe^IIIO₃S₃ has a possibility to exhibit the spin-crossover phenomenon between the LS and HS states, which is schematically shown in Fig. 6.6.

Fig. 6.6

Spin states of the Fe^III sites for [Fe^III(ox)₃], [Fe^III(dto)₃], and [Fe^III(mto)₃]

As a matter of fact, in the case of tris(monothio-β-diketonato)iron(III) complexes, the LS (S = 1/2) and HS (S = 5/2) states coexist between 300 and 80 K, and two kinds of quadrupole doublets corresponding to the LS and HS states are clearly distinguished in the ⁵⁷Fe Mössbauer spectra, in which the component of LS state increases with decreasing temperature from 300 to 80 K [18]. In the case of tris(monothiocarbamato)iron(III) complexes, on the other hand, the rapid spin equilibrium occurs in which the HS and LS states exchange in the time scale of less than 10⁻⁷ s [19]. In this case, an averaged quadrupole doublet between the HS and LS states is observed. However, the rapid spin equilibrium phenomenon has not yet been found for assembled metal complex systems. For this viewpoint, in order to search the rapid spin equilibrium phenomenon for assembled metal complex system including Fe^IIIO₃S₃ site, we have synthesized (C₆H₅)₄P[M^IIFe^III(mto)₃] (M = Mn, Zn) consisting of the Fe^IIIO₃S₃ and M^IIO₆ sites and investigated the spin state of the Fe^IIIO₃S₃ site [3].

Based on the crystal structure of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] analyzed by the single-crystal X-ray diffraction [20], the Rietveld analysis was performed for the powder X-ray diffraction pattern of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] at room temperature. In this complex, the Mn^II and Fe^III ions are alternately arrayed by the bridging ligand, mto, which forms the honeycomb network structure of [Mn^IIFe^III(mto)₃]. The (C₆H₅)₄P⁺ layer is intercalated between two adjacent [Mn^IIFe^III(mto)₃] layers.

In the case of (n-C₄H₉)₄N[Zn^IIFe^III(ox)₃] with a similar structure of (C₆H₅)₄P[Zn^IIFe^III(mto)₃], the χT value (= 4.22 cm³ K mol⁻¹) is almost constant between 300 and 4.2 K, whose value is regarded as the spin-only χT value (4.375 cm³ K mol⁻¹) of the HS state (S = 5/2) for Fe^III [21]. On the other hand, the χT value for (C₆H₅)₄P[Zn^IIFe^III(mto)₃] decreases from 3.60 (at 300 K) to 2.66 cm³ K mol⁻¹ (at 4.2 K) [3]. Therefore, the χT value of (C₆H₅)₄P[Zn^IIFe^III(mto)₃] is considered to be situated in the middle value between those of the HS and LS states for Fe^III.

Figure 6.7a shows the X-band ESR spectra for (C₆H₅)₄P[Zn^IIFe^III(mto)₃] at 300, 77 and 10 K, in which the ESR signals corresponding to the HS and LS states of Fe^III site are clearly distinguished at about 300 mT (g ≈ 2.05) and 150 mT (g ≈ 4.25), respectively. The ESR intensity ratio of the LS state to the HS state increases with decreasing temperature, which is consistent with the temperature dependence of χ_MT. Therefore, these results imply that the spin state of Fe^IIIO₃S₃ in (C₆H₅)₄P[Zn^IIFe^III(mto)₃] is the spin equilibrium between the HS and LS states, and the HS and LS states are clearly distinguished under the time scale (10⁻¹⁰ s) of X-band ESR spectroscopy. Figure 6.7b shows the ⁵⁷Fe Mössbauer spectra of (C₆H₅)₄P[Zn^IIFe^III(mto)₃] at 300, 77 and 10 K, where only one quadrupole doublet of Fe^III appears in spite of the coexistence of HS and LS states in the ESR signal between 300 and 10 K. Therefore, the ⁵⁷Fe Mössbauer spectra of (C₆H₅)₄P[Zn^IIFe^III(mto)₃] indicates the rapid spin equilibrium at the Fe^III site whose time scale is faster than that (10⁻⁷ s) of the ⁵⁷Fe Mössbauer spectroscopy. The relaxation process between the HS and LS states at the Fe^IIIO₃S₃ site is considered to be a tunneling process. The time scale of spin equilibrium at the Fe^III site in (C₆H₅)₄P[Zn^IIFe^III(mto)₃] is estimated at 10⁻¹⁰ < τ < 10⁻⁷ s. The tunneling probability for a non-radiative multi-phonon process from a given vibrational levels, m of the HS state and m′ of the LS state is given by the following equation [22],

Fig. 6.7

Reprinted with permission from [3]. Copyright 2010 the Chemical Society of Japan

a X-band ESR spectra, and b ⁵⁷Fe Mössbauer spectra for (C₆H₅)₄P[Zn^IIFe^III(mto)₃] at various temperatures.

$$W_{mm'} = \frac{2\pi }{{\hbar^{2} \omega }}\beta_{\text{HL}}^{2} \left| { < \chi_{m'} } \right|\chi_{m} > |^{2} \delta \left( {E_{{m^{\prime}}} , E_{m} } \right),$$

(6.1)

where the electronic coupling matrix element β_HL = < ψ_LS|H_SO|ψ_HS > is the second order spin-orbit coupling, ℏω is the energy of metal-ligand vibration, δ(E_m′, E_m) is the delta function ensuring energy conservation, |<χ_m′|χ_m>|² is the Franck–Condon factor of the overlap of the vibrational functions between the HS state (χ_m) and LS state (χ_m′). At T ≈ 0 K, since the vibrational ground state of the HS state is populated, the relaxation rate constant between the HS and LS states is expressed as follows [22],

$$k_{\text{HL}} ( {T} \approx 0 ) = \frac{2\pi }{{\hbar^{2} \omega }}\beta_{\text{HL}}^{2} \left| { < \chi_{n} } \right|\chi_{0} > |^{2} , \qquad n = \frac{{\Delta E_{\text{HL}}^{0} }}{\hbar \omega },$$

(6.2)

where |<χ_n|χ₀>|² is expressed as follows,

$$\left| { < \chi_{n} } \right|\chi_{0} > |^{2} = \frac{{S^{n} e^{ - S} }}{n!},\, \qquad S = \frac{{\frac{1}{2}f\Delta Q_{\text{HL}}^{2} }}{\hbar \omega },$$

(6.3)

where S is the Huang-Rhys factor [23], ΔQ_HL is the difference of horizontal displacement between the HS and LS potential wells in the metal-ligand coordinate geometry, and f is the force constant. According to Eqs. (6.2) and (6.3), with decreasing the Huang–Rhys factor, the Frank–Condon factor increases, which increases the relaxation rate constant between the HS and LS states. In general, the ΔQ_HL of spin crossover Fe^III complex is shorter than that of Fe^II complex. Indeed, the change in the Fe^II–ligand distance due to the HS–LS transition is 0.16–0.21 Å, while that in the Fe^III–ligand distance is about 0.12 Å [24], which is the reason why the rapid spin equilibrium phenomenon has been found for Fe^III complexes consisting of Fe^IIIS₆, Fe^IIIO₃S₃, or Fe^IIIN₄O₂ octahedra.

6.2.3 Spin Frustration Induced by Dynamic Spin Crossover Phenomena for A[Mn^IIFe^III(mto)₃]

In the case of mto bridged hetero-metal complex system, [Mn^IIFe^III(mto)₃] consisting of Mn^IIO₆ and Fe^IIIO₃S₃ octahedra, the spin states of the Mn^II and Fe^III sites are considered to be HS state (S = 5/2) and the spin equilibrium state of HS (S = 5/2) ↔ LS (S = 1/2), respectively. If the spin state of Fe^III site is LS state (S = 1/2), there exist four potential exchange interactions (J_P) and one kinetic exchange interaction (J_K) between the Fe^III and Mn^II sites. The sum of the potential exchange interaction is considered to be stronger than the kinetic exchange interaction, which is responsible for the ferromagnetic ordering. In connection with this, the following should be mentioned. The ferromagnetic ordering of (n-C₃H₇)₄N[Mn^IIFe^III(dto)₃] with Mn^II (S = 5/2) and Fe^III (S = 1/2) has been reported [25], in which the Curie temperature (T_C) and the Weiss temperature (θ) were estimated at 4 and 10 K, respectively, from the analysis of magnetization and magnetic susceptibility. On the other hand, if the spin state of Fe^III site is HS state (S = 5/2), there exist five J_K between the Fe^III and Mn^II sites, which are considered to be stronger than the potential exchange interactions between the Fe^III and Mn^II sites. Indeed, the ferrimagnetic ordering of (n-C_nH_2n+1)₄N[Mn^IIFe^III(ox)₃] with Mn^II (S = 5/2) and Fe^III (S = 5/2) has been reported [26], in which T_N was estimated at 27–28 K.

Therefore, if the spin state of the Fe^III site in the [Mn^IIFe^III(mto)₃] system behaves as the dynamic spin equilibrium phenomenon, the internal magnetic field at the Mn^II site should be frustrated between the ferromagnetic and antiferromagnetic interactions, which is schematically shown in Fig. 6.8.

Fig. 6.8

Schematic representation of the relationship between the rapid spin equilibrium of the Fe^III site and the dynamic frustration of internal magnetic field at the Mn^II site in [Mn^IIFe^III(mto)₃]

Based on this viewpoint, we have synthesized (C₆H₅)₄P[Mn^IIFe^III(mto)₃] and investigated the magnetic properties [27]. Figure 6.9 shows the temperature dependence of the magnetization and ac magnetic susceptibility for (C₆H₅)₄P[Mn^IIFe^III(mto)₃]. As shown in Fig. 6.9a, with decreasing temperature, the field cooled magnetization (FCM) remarkably increases just below 30 K, then slightly increases below 23 K. In the heating process, the remnant magnetization (RM) disappears at 30 K. On the other hand, both of the real (χ′) and imaginary (χ″) parts of ac magnetic susceptibility exhibit a steep peak at 23 K indicating a magnetic phase transition, which is shown in Fig. 6.9b, c. Therefore, it is obvious that (C₆H₅)₄P[Mn^IIFe^III(mto)₃] undergoes two successive magnetic phase transitions at 30 and 23 K. As shown in Fig. 6.10, the ⁵⁷Fe Mössbauer spectra of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] imply that the spin state at the Fe^III site is still paramagnetic between 30 and 24 K. Then, both of the Mn^II and Fe^III spins are eventually ordered at 23 K. In this manner, it is concluded that the successive magnetic phase transitions at 30 and 23 K for (C₆H₅)₄P[Mn^IIFe^III(mto)₃] are induced by the rapid spin equilibrium at the Fe^III site.

Fig. 6.9

a Magnetization, b in-phase ac magnetic susceptibility (χ′), and c out-phase ac magnetic susceptibility (χ″) of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] as a function of temperature. FCM: field-cooled magnetization, ZFCM: zero-field-cooled magnetization, RM: remnant magnetization. FCM and ZFCM were measured at 3.0 mT. The ac magnetic susceptibility measurements were performed under the ac magnetic field of 0.3 mT and the frequency between 20 and 1000 Hz

Fig. 6.10

⁵⁷Fe Mössbauer spectra of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] at 30, 22 and 10 K

Taking account of the temperature dependences of the magnetization, ac magnetic susceptibility, and ⁵⁷Fe Mössbauer spectra for (C₆H₅)₄P[Mn^IIFe^III(mto)₃], the Gibbs energies of the A, B and C phases as a function of temperature for (C₆H₅)₄P[Mn^IIFe^III(mto)₃] are schematically represented in Fig. 6.11, in which the A, B and C phases are defined as follows,

Fig. 6.11

Schematic Gibbs energies of the A, B and C phases as a function of temperature for (C₆H₅)₄P[Mn^IIFe^III(mto)₃]. G(A), G(B) and G(C) indicate the Gibbs energies for the A, B and C phases, respectively. Phase A: The spins at the Mn^II and Fe^III sites are paramagnetic, Phase B: The spin at the Mn^II site is ordered, while that at the Fe^III site is still paramagnetic, Phase C: Both of the spins at the Mn^II and Fe^III sites are ordered

Phase A:

The spins at the Mn^II and Fe^III sites are paramagnetic.

Phase B:

The spin at the Mn^II site is ordered, while that at the Fe^III site is still paramagnetic.

Phase C:

Both of the spins at the Mn^II and Fe^III sites are ordered.

As shown in Fig. 6.11, with decreasing temperature, the first magnetic phase transition from the phase A to the phase B takes place at 30 K, then the second magnetic phase transition from the phase B to the phase C takes place at 23 K.

6.3 Mixed-Valence System and Charger Transfer Phase Transition

6.3.1 Classification of Mixed-Valence System

Mixed-valence compounds, defined as compounds containing an element with more than one oxidation state, are classified into three groups according to the Robin–Day classification [28],

Class I:

Compounds whose valence states occupy different crystallographic sites and are too distant from each other to allow the electronic interaction between the mixed-valence states.

Class II:

Compounds in which an electron exchange between the different valence states takes place as a thermally activated process. The inter-valence charge transfer (IVCT) between different valence states is observable in optical absorption spectra.

Class III(A):

Compounds in which valence electrons are delocalized between atoms within discrete polynuclear ions.

Class III(B):

Compounds in which valence electrons are delocalized between identically crystallographic sites.

6.3.2 Prussian Blue and Its Analogues Salts Showing Photo-Induced Magnetism

Among these mixed-valence compounds, the boundary compounds between the class II and III are the leading candidates exhibiting field-responsive multifunctional properties coupled with transport, optical or magnetic properties. In this section, we describe the characteristic properties of Prussian blue and its analogous compounds as an example.

Prussian blue has a three dimensional network structure with an alternating array of Fe^II and Fe^III ions through CN bridges [29], which is schematically shown in Fig. 6.12a. The spin state of the Fe^II site coordinated by six C atoms is LS (S = 0) state, and that of the Fe^III site coordinated by six N atoms is HS (S = 5/2) state. Prussian blue has a broad strong IVCT band at around 730 nm, which is responsible for the deep blue pigment. Figure 6.12b shows “The Great Wave off Kanagawa” painted by Hokusai, in which Prussian blue was used as a deep blue pigment.

Fig. 6.12

a Schematic representation of the crystal structure of ${\text{Fe}}_{4}^{\text{III}} \left[ {{\text{Fe}}^{\text{II}} \left( {\text{CN}} \right)_{6} } \right]_{3}$. b “The Great Wave off Kanagawa” painted by Hokusai, in which Prussian blue was used as deep blue pigment

The soluble Prussian blue, KFe^IIFe^III(CN)₆, is obtained by adding Fe³⁺ to the aqueous solution of K₄[Fe^II(CN)₆], as following scheme, Fe³⁺(aq) + K⁺(aq) + [Fe^II(CN)₆]⁴⁻(aq) → KFe^IIFe^III(CN)₆(s). On the other hand, by adding Fe²⁺ to the aqueous solution of K₃[Fe^III(CN)₆], KFe^IIFe^III(CN)₆ called Turnbull’s blue is also obtained as follows, Fe²⁺(aq) + K⁺(aq) + [Fe^III(CN)₆]³⁻(aq) → KFe^IIFe^III(CN)₆(s). A long historical debate had continued in relation to Prussian blue and Turnbull’s blue, whether Prussian blue obtained by mixing the solutions of ferric compound and ferrocyanide, and Turnbull’s blue obtained by mixing the solutions of ferrous compound and ferricyanide, are the same compound or not? This problem was solved by means of ⁵⁷Fe Mössbauer spectroscopy in 1968 [30]. According to the ⁵⁷Fe Mössbauer spectroscopy, Prussian blue and Turnbull’s blue are essentially the same compound, in spite of the different synthesis processes. Figure 6.13 shows the ⁵⁷Fe Mössbauer spectra for the soluble Prussian blue, insoluble Prussian blue, and Turnbull’s blue in the ferromagnetic ordered phase (T_C = 5.5 K) at 1.6 K [30]. These spectra show the superposition of a central peak corresponding to the LS state (S = 0) of Fe^II coordinated by six C atoms and six magnetically split branches corresponding to the HS state (S = 5/2) of Fe^III coordinated by six N atoms. The estimated internal magnetic fields of Fe^III (S = 5/2) at 1.6 K were estimated at 53.6 ± 2, 54.1 ± 2 and 54.3 ± 2 T for the soluble Prussian blue, insoluble Prussian blue and Turnbull’s blue, respectively.

Fig. 6.13

Reprinted from [30], with the permission of AIP Publishing

⁵⁷Fe Mössbauer spectra of a soluble Prussian blue, b insoluble Prussian blue and c Turnbull’s blue at 1.6 K.

In connection with Turnbull’s blue, the following should be noted. As shown in Fig. 6.14, in the precipitation process of Turnbull’s blue by adding ⁵⁷Fe²⁺ to the aqueous solution of K₃[Fe^III(CN)₆], an electron of ⁵⁷Fe²⁺ transfers to the Fe^III site in [Fe^III(CN)₆]³⁻ and Turnbull’s blue, KFe^{II 57}Fe^III(CN)₆, is precipitated [31].

Fig. 6.14

Formation process of Turnbull’s blue

In connection with Prussian blue, one of the most fascinating phenomena is the photo-induced magnetism of Prussian blue analogues by means of IVCT. In 1996, O. Sato, K. Hashimoto, et al. first reported a photo-induced ferrimagnetic phase for K_0.2Co_1.4[Fe(CN)₆]·6.9H₂O [32] and K_0.4Co_1.3[Fe^II(CN)₆]·5H₂O [33]. In the case of ${\text{K}}_{{0.4}} {\text{Co}}_{{0.3}}^{{{\text{II}}}} {\text{Co}}^{{{\text{III}}}} [{\text{Fe}}^{{{\text{II}}}} \left( {{\text{CN}}} \right)_{6} ]{\cdot}5{\text{H}}_{2} {\text{O}}$, the electronic state of the Fe–CN–Co framework before light irradiation is ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{6} {\text{e}}_{\text{g}}^{0} ,S = 0} ){ {-} \text{CN} {-}\text{Co}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{6} {\text{e}}_{\text{g}}^{0} ,S = 0} )$ at 5 K. Visible light (λ = 500–750 nm) irradiation at 5 K induces the IVCT, forming the excited state of ${\text{Fe}}^{\text{III}}( {{\text{t}}_{{2{\text{g}}}}^{5} {\text{e}}_{\text{g}}^{0} ,S = 1/2} ){ {-}\text{CN} {-}\text{Co}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{6} {\text{e}}_{\text{g}}^{0} ,S = 1/2})$. Subsequently, this excited state relaxes to the meta-stable state of ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{5} {\text{e}}_{\text{g}}^{0} ,S = 1/2} ){{-}\text{CN}{-}\text{Co}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{5} {\text{e}}_{\text{g}}^{0} ,S = 3/2})$. While the compound before light irradiation is paramagnetic, that after the visible light irradiation exhibits a meta-stable ferrimagnetic phase, which can be reconverted to the initial phase by near-IR light (λ = 1319 nm) irradiation or a thermal treatment [33]. Since then, not only Prussian blue analogues but also various CN-bridged compounds exhibiting photo-induced magnetism have been reported [34]. In addition to the photo-induced magnetism, since the discovery of thermally induced charge-transfer induced spin transition (CTIST) for Na_0.4Co_1.3[Fe(CN)₆]·5H₂O in 1997 [35], several Prussian blue analogues and CN-bridged compounds exhibiting thermally induced CTIST or CTPT have been reported [36].

Figure 6.15 shows the photo-induced ferrimagnetic transition for Rb_0.66Co_1.25[Fe(CN)₆]·4.3H₂O by using IVCT [37]. While ${\text{Rb}}_{0.66} {\text{Co}}_{1.25} \left[ {{\text{Fe}}\left( {\text{CN}} \right)_{6} } \right] {\cdot} 4.3{\text{H}}_{2} {\text{O}}$ before the light irradiation is paramagnetic in the whole temperature region, that after the light irradiation corresponding to the IVCT (500–750 nm) exhibits a meta-stable ferrimagnetic phase with T_N = 22 K.

Fig. 6.15

Reprinted with permission from [37]. Copyright 1999 American Chemical Society

Field-cooled magnetization (FCM) curves for Rb_0.66Co_1.25 [Fe(CN)₆]·4.3H₂O before and after light irradiation (hν) at H = 0.5 T. ○: before light irradiation, •: after light irradiation, ×: after thermal treatment (Δ) at 150 K.

Figure 6.16 shows the ⁵⁷Fe Mössbauer spectra before and after the light irradiation corresponding to the IVCT (500–750 nm) at 25 K [37]. Before the light irradiation, the single peak with IS = 0.02 ± 0.01 mm/s and QS = 0.15 ± 0.01 mm/s is assigned to the LS state (S = 0) of Fe^II. After the light irradiation at 25 K, the single peak corresponding to the LS state of Fe^II was significantly reduced and a new doublet with IS = 0.09 ± 0.01 mm/s and QS = 1.13 ± 0.01 mm/s assigned to the LS state (S = 1/2) of Fe^III. As a result of the light-induced CT from the Fe^II site to the Co^III site, ${\text{Rb}}_{0.66} {\text{Co}}_{1.25} \left[ {{\text{Fe}}\left( {\text{CN}} \right)_{6} } \right] {\cdot} 4.3{\text{H}}_{2} {\text{O}}$ was converted from the paramagnet to the ferrimagnet with T_N = 22 K, which is schematically shown in Fig. 6.17.

Fig. 6.16

⁵⁷Fe Mössbauer spectra of Rb_0.66Co_1.25 [Fe(CN)₆]·4.3H₂O before and after the light irradiation of 500–750 nm at 25 K [37]

Fig. 6.17

Schematic representation of the photo-induced magnet for Rb_0.66Co_1.25 [Fe(CN)₆]·4.3H₂O

6.3.3 Mixed-Valence System, A[Fe^IIFe^III (dto)₃] (A = Counter Cation; dto = C₂O₂S₂), and the Charge Transfer Phase Transition

Among various kinds of multifunctional compounds, in the case of mixed-valence system whose spin states are situated in the spin crossover region, it is expected that new types of synergetic phenomena induced by both of spin and charge appear between different metal ions in order to minimize the Gibbs energy. Based on this viewpoint, we have developed a ferromagnetic organic–inorganic hybrid system, A[Fe^IIFe^III(dto)₃] (A = (n-C_nH_2n+1)₄N, spiropyran, etc.), and investigated their synergetic properties coupled with spin, charge and photon [4]. The single-crystal X-ray structural analysis of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] reveals the existence of the honeycomb network structure of [Fe^IIFe^III(dto)₃], and the (n-C₃H₇)₄N⁺ layer is intercalated between two adjacent [Fe^IIFe^III(dto)₃] layers [20], whose structure is common for A[M^IIM′^IIIX₃] (A = cation, X = ox, dto, mto).

In order to investigate the electronic properties and the valence states of Fe^II and Fe^III of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] by means of ⁵⁷Fe Mössbauer spectroscopy, we employed ⁵⁷Fe enriched complexes, (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] and (n-C₃H₇)₄N[Fe^{II 57}Fe^III(dto)₃], in which Fe^II or Fe^III was substituted with ⁵⁷Fe (96%) [38]. In the case of (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃], a solution of ⁵⁷FeCl₂·4H₂O and (n-C₃H₇)₄NBr in a methanol/water mixture was added to a solution of KBa[Fe^III(dto)₃], then black powdered crystals of (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] were precipitated. (n-C₃H₇)₄N[Fe^{II 57}Fe^III(dto)₃] was also obtained by using FeCl₂·4H₂O, (n-C₃H₇)₄NBr and KBa[⁵⁷Fe^III(dto)₃]. Figure 6.18 shows the ⁵⁷Fe Mössbauer spectra of (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] and (n-C₃H₇)₄N[Fe^{II 57}Fe^III(dto)₃] at 200 and 60 K. In the case of the ⁵⁷Fe Mössbauer spectra of (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] at 200 K, the dominant doublet (74.5% area) with IS = 1.18 mm s⁻¹ and QS = 1.36 mm s⁻¹ is assigned to the ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{4} {\text{e}}_{\text{g}}^{2} ,S = 2} )$ site coordinated by six O atoms. These values of IS and QS are quite similar to those (IS = 1.18 mm s⁻¹, QS = 1.26 mm s⁻¹) of the ⁵⁷Fe Mössbauer spectrum for the ${\text{Fe}}^{\text{II}}( {{\text{t}}_{{2{\text{g}}}}^{4} {\text{e}}_{\text{g}}^{2} ,S = 2} )$ site in (n-C₄H₉)₄N[Fe^IICr^III(ox)₃] [39]. As shown in Fig. 6.18, the line profile of the ⁵⁷Fe Mössbauer spectra of (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] dramatically changes between 200 and 60 K. The intensity of the dominant doublet corresponding to the Fe^II (S = 2) site decreases and a new doublet with IS = 0.55 mm s⁻¹ and QS = 0.91 mm s⁻¹ appears. The IS and QS values of the new doublet are quite similar to those (IS = 0.49 mm s⁻¹, QS = 0.68 mm s⁻¹) of the ⁵⁷Fe Mössbauer spectrum for the ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{3} {\text{e}}_{\text{g}}^{2} ,S = 5/2} )$ site in (n-C₄H₉)₄N[Ni^IIFe^III(ox)₃] at 78 K [40]. On the other hand, in the case of (n-C₃H₇)₄N[Fe^{II 57}Fe^III(dto)₃] at 200 K, the dominant doublet with IS = 0.33 mm s⁻¹ and QS = 0.36 mm s⁻¹ is assigned to the ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{5} ,S = 1/2} )$ site coordinated by six S atoms. These values of IS and QS are quite similar to those (IS = 0.33 mm s⁻¹, QS = 0.35 mm s⁻¹ at 196 K) for the ${\text{Fe}}^{\text{III}}( {{\text{t}}_{{2{\text{g}}}}^{5} ,S = 1/2})$ site coordinated by six S atoms in KBa[Fe^III(dto)₃] [41]. On the other hand, the dominant doublet with IS = 0.41 mm s⁻¹ and QS = 0.51 mm s⁻¹ at 60 K is assigned to the ${\text{Fe}}^{\text{II}}( {{\text{t}}_{{2{\text{g}}}}^{6} ,S = 0} )$ site coordinated by six S atoms. These IS and QS values are quite similar to those (IS = 0.41 mm s⁻¹, QS = 0.64 mms⁻¹ at 77 K) for the ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{6} ,S = 0} )$ site coordinated by six S atoms in pyrite (FeS₂) [42]. In this manner, we have elucidated the CTPT for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] by means of ⁵⁷Fe Mössbauer spectroscopy.

Fig. 6.18

⁵⁷Fe Mössbauer spectra below and above the CTPT (T_CT ≈ 120 K) for (n-C₃H₇)₄N[⁵⁷Fe^IIFe^III(dto)₃] and (n-C₃H₇)₄N[Fe^{II 57}Fe^III(dto)₃], and the schematic representation of CTPT. The HT phase (T > T_CT) and LT phase (T < T_CT) indicate the high temperature phase with ${\text{Fe}}^{\text{III}} {\text{S}}_{6} ( {t_{{2{\text{g}}}}^{5} } ) - {\text{Fe}}^{\text{II}} {\text{O}}_{6} ( {t_{{2{\text{g}}}}^{4} e_{\text{g}}^{2} } )$ and the low temperature phase with ${\text{Fe}}^{\text{II}} {\text{S}}_{6} ( {t_{{2{\text{g}}}}^{6} } ) - {\text{Fe}}^{\text{III}} {\text{O}}_{6} ( {t_{{2{\text{g}}}}^{3} e_{\text{g}}^{2} } )$, respectively

As mentioned above, (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] undergoes the CTPT between 200 and 60 K. In order to determine the critical temperature (T_CT) of CTPT, ⁵⁷Fe Mössbauer spectroscopy was carried out in the temperature range between 130 and 90 K. As shown in Fig. 6.19, the HT phase with Fe^IIO₆ (S = 2)–Fe^IIIS₆ (S = 1/2) and the LT phase with Fe^IIS₆ (S = 0)–Fe^IIIO₆ (S = 5/2) are clearly distinguished in the vicinity of CTPT, which implies that the frequency of electron transfer between the Fe^II and Fe^III sites at the CTPT is at least slower than the time scale (10⁻⁷ s) of ⁵⁷Fe Mössbauer spectroscopy. When the temperature decreases from 130 to 90 K, the fractions of HT and LT phases decreases and increases, respectively. The crossing point between the HT phase and LT phase components is about 122 K, which is consistent with the critical temperature (122.4 K) of CTPT determined by the heat capacity [43].

Fig. 6.19

⁵⁷Fe Mössbauer spectra of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] in the vicinity of CTPT (T_CT = 122 K). A: Fe^III (S = 1/2), B: Fe^II (S = 2), C: Fe^II (S = 0), D: Fe^III (S = 5/2)

In order to confirm the direct evidence of charge transfer between the Fe^II and Fe^III sites in (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃], the electrical resistivity was measured along the parallel and perpendicular directions to the [Fe^II Fe^III(dto)₃] layer under several applied pressures [44]. At 0.5 GPa, (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] behaves as a semiconductor as shown in Fig. 6.20. Above 0.9 GPa, on the other hand, both of the intra- and inter-layer resistivities show an anomalous drop with thermal hysteresis due to the CTPT. The intra-layer resistivity as a function of temperature at 0.9 GPa exhibits a plateau in the middle range of hysteresis loop, while an abrupt drop of resistivity appears in the inter-layer resistivity. Similar behavior appears at 1.5 GPa except for the temperature shift of the hysteresis loop. The temperature of hysteresis loop increases with increasing applied pressure, which is consistent with that of the magnetic susceptibility under applied pressures [45]. The activation energies at 0, 0.9 and 1.5 GPa are 1700, 1400 and 1200 K, respectively. The anomalous drop in the resistivity as a function of temperature is attributed to the electron transfer between the t_2g orbitals of the Fe^II and Fe^III sites in the temperature region of CTPT.

Fig. 6.20

Reprinted from [44], Copyright 2003, with permission from Elsevier

Temperature dependence of a intra-layer and b inter-layer electrical resistivities of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] under several applied pressures. Arrows denote the direction of heating or cooling process.

6.3.4 Dynamics of Charge Transfer Phase Transition in A[Fe^IIFe^III (dto)₃] by Means of Muon Spectroscopy

Muon spin relaxation (μSR) is one of the most powerful methods to investigate the magnitude, distribution or fluctuation of internal magnetic field. Therefore, the μSR technique has been applied to the study of magnetic phase transitions, various kinds of spin frustrations, superconducting phenomena and so forth [46]. The asymmetry parameter of μSR is defined as A(t) = [N_B(t) − N_F(t)]/[N_B(t) + N_F(t)], in which N_F(t) and N_B(t) are the total muon events of the forward and backward counters in the muon beam line, respectively. The initial asymmetry, A(0), is defined as the asymmetry at t = 0. In order to analyze the time spectra of A(t), the following function with two components was used [46],

$$A_{0} G_{Z} \left( {\Delta ,H_{\text{LF}} ,t} \right)\exp ( - \lambda_{0} t) + A_{1} \exp ( - \lambda_{1} t)$$

(6.4)

where A₀ and A₁ are the initial asymmetries of the slow and fast relaxation components, λ₀ and λ₁ are the respective muon spin depolarization rates. G_Z(Δ, H_LF, t) is the static Kubo–Toyabe function [47]. Δ/γ_μ is the distribution width of the nuclear-dipole fields at the muon sites, and γ_μ is the gyromagnetic ratio of muon spin. H_LF is the longitudinal magnetic field. Figure 6.21 shows the time scale and the schematic representation of muon spectroscopy.

Fig. 6.21

Schematic representation of muon spectroscopy and its time scale

Figure 6.22 shows the time dependence of the asymmetry parameter, A(t) = [N_B(t) − N_F(t)]/[N_B(t) + N_F(t)] of μSR for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] at various temperatures under zero-field [5]. From the analysis of time spectra of μSR by using Eq. (6.4), we obtained the depolarization rate (λ₀) as a function of temperature for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃].

Fig. 6.22

Reprinted figure with permission from [5]. Copyright 2008 by the American Physical Society

Time dependence of the asymmetry parameter, A(t) = [N_B(t) − N_F(t)]/[N_B(t) + N_F(t)] of μSR for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] at several temperatures under zero-field [5].

Figure 6.23 shows the depolarization rate (λ₀) of muon spin as a function of temperature under various longitudinal magnetic fields for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3, 5). In the case of n = 3, an anomalous enhancement of depolarization rate appears at around 80 K. This anomalous peak decreases with increasing the longitudinal field, and eventually disappears at about 10 mT (= 100 Oe). In the case of n = 5, on the other hand, any anomalous peak does not appear between 200 and 40 K. Therefore, the anomalous enhancement of depolarization rate at around 80 K for n = 3 is attributed to the frequency of electron transfer between the Fe^II and Fe^III sites at the CTPT, which induces the fluctuating internal magnetic field at the muon site.

Fig. 6.23

Reprinted figure with permission from [5]. Copyright 2008 by the American Physical Society

Temperature and longitudinal-field dependence of the muon spin depolarization rate, λ₀, for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] and (n-C₅H₁₁)₄N[Fe^IIFe^III(dto)₃]. 1 Oe = 0.1 mT. The solid lines are guides for eye.

As shown in Fig. 6.23, the depolarization rates for n = 3 and n = 5 decrease with increasing longitudinal field up to 10 mT and become almost constant above 10 mT. The constant value increases with decreasing temperature from 200 to 40 K, which suggests the existence of two components. One component is easily suppressed by 10 mT, while the other component remains even at 400 mT (= 4000 Oe). The former component implies that there is a weak and slowly fluctuating internal magnetic field at the muon site, which is easily masked by 10 mT, which is attributed to the fluctuating component of nuclear dipoles such as MnSi [48]. On the other hand, considering that the latter component increases with decreasing temperature and similar values of the depolarization rate are observed for n = 3 and 5 in the same temperature region, which implies that the latter component is attributed to the dipole field due to the fluctuation of paramagnetic Fe spins.

As for the anomalous enhancement of the depolarization rate of muon spin induced by the CTPT, we extract the difference of depolarization rate between those of n = 3 and 5 to analyze the frequency of electron transfer between the Fe^II and Fe^III sites at the CTPT. The longitudinal field dependence of this subtracted depolarization rate at 80 K is plotted in Fig. 6.24. By using the Redfield equation [49] for the longitudinal field (H_LF) dependence of the subtracted depolarization rate (λ_CT) between n = 3 and 5, we determined the correlation time of muon spins (τ_c) and the amplitude of fluctuating internal magnetic field (H_loc) at the muon site, respectively. The Redfield equation is expressed as follows,

Fig. 6.24

Reprinted figure with permission from [5]. Copyright 2008 by the American Physical Society

Subtracted depolarization rate (λ_CT) between n = 3 and 5 as a function of applied longitudinal magnetic field for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] at 80 K in the cooling process. The solid line shows the best fit of the Redfield equation. 1 Oe = 0.1 mT.

$$\lambda_{\text{CT}} = \frac{{2\gamma_{\mu }^{2} H_{\text{loc}}^{2} \tau_{\text{c}} }}{{1 + \gamma_{\mu }^{2} H_{\text{LF}}^{2} \tau_{\text{c}}^{2} }}$$

(6.5)

where γ_μ is the gyromagnetic ratio of muon spin. These parameters at several temperatures are summarized in Table 6.1 [5].

Table 6.1 Parameters obtained by fitting the Redfield equation to the subtracted depolarization rate (λ_CT) between n = 3 and 5 for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] [5]

The frequency of the additional internal field at the muon site induced by the CTPT, which is given as ν = 1/τ_c, is the order of 0.1 MHz as the maximum value at 80 K and zero at 60 K [5]. The magnitude of H_loc is between 0.19 and 0.40 mT, which is larger than that of nuclear dipole field (~0.1 mT). These results imply the fluctuation of electron transfer between the Fe^II and Fe^III sites at the CTPT, which is schematically shown in Fig. 6.25. The time scale of τ_c is consistent with the result of the ⁵⁷Fe Mössbauer measurement. The fluctuation of electron transfer between the Fe^II and Fe^III sites induced by the CTPT for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] is responsible for the anomalous drop with thermal hysteresis in the electrical resistivity at the CTPT.

Fig. 6.25

Schematic representation of the valence fluctuation between the Fe^II and Fe^III sites at the CTPT for (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃]

6.3.5 Size Effect of Intercalated Cation on the Charge Transfer Phase Transition and Ferromagnetism for A[Fe^IIFe^III (dto)₃]

Figure 6.26 shows the ⁵⁷Fe Mössbauer spectra at 200, 77 and 4 K for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6) [50]. At 200 K, the line profiles of all the complexes are quite similar to each other, where two quadrupole doublets (A and B) mainly exist. The wider doublet (B) is assigned to the Fe^II (S = 2) site coordinated by six O atoms. The IS and QS of (B) fall in the range of 1.05–1.17 mm s⁻¹ and 1.20–1.69 mm s⁻¹, respectively. On the other hand, the narrower doublet (A) with IS = 0.29–0.35 mm s⁻¹ and QS = 0.38–0.56 mm s⁻¹ is assigned to the Fe^{IIIS = 1/2) site coordinated by six S atoms.}

Fig. 6.26

Reprinted with permission from [50]. Copyright 2012 Mössbauer Effect Data Center

⁵⁷Fe Mössbauer spectra of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6) at 200 K, 77 K and 4 K. A: Fe^III (S = 1/2), B: Fe^II (S = 2), C: Fe^II (S = 0), D: Fe^III (S = 5/2) [50].

In the cases of n = 3 and 4, with decreasing temperature from 200 to 77 K, the ⁵⁷Fe Mössbauer spectra corresponding to the HTP decrease by about 80%. Instead of these spectra, two doublets (C and D) appear. The doublet (C) with IS = 0.43–0.46 mm s⁻¹ and QS = 0.35–0.41 mm s⁻¹ is assigned to the Fe^II (S = 0) site coordinated by six S atoms. On the other hand, the doublet (D) with IS = 0.54–0.55 mm s⁻¹and QS = 0.89–0.92 mm s⁻¹ is assigned to the Fe^III (S = 5/2) site coordinated by six O atoms. At 4 K, a central strong doublet (C) with IS = 0.43–0.45 mm s⁻¹and QS = 0.39–0.46 mm s⁻¹, and a sextet (D) divided from –8 to +8 mm s⁻¹ with a large hyperfine field of H_int = ~45.0 T are observed in the spectra of n = 3 and 4. The former can be assigned to the diamagnetic state of Fe^II (S = 0) and the latter is typical of the magnetically ordered state of Fe^III (S = 5/2). From the analysis of ⁵⁷Fe Mössbauer spectra for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃], it is obvious that the charge transfer between the Fe^II and Fe^III sites takes place between 200 and 77 K for n = 3 and 4. At 4 K, in addition to the ⁵⁷Fe Mössbauer spectra corresponding to the Fe^II (S = 0) and Fe^III (S = 5/2) sites, the sextets of the Fe^II (S = 2) and Fe^III (S = 1/2) sites corresponding to the HTP are also required as the relative area of ca. 15% (for n = 3) or 30% (for n = 4). In the case of n = 4, two ferromagnetic phases with T_C = 7 and 13 K are clearly observed in the magnetization measurement, being consistent with the large area of the HTP at 4 K in the ⁵⁷Fe Mössbauer spectra.

The ⁵⁷Fe Mössbauer spectra in the ferromagnetic phases for n = 5 and 6 are completely different from those for n = 3 and 4. In the cases of n = 5 and 6, the CTPT does not take place, so that the spectra of n = 5 and 6 at 4 K can be assigned to the Fe^II (S = 2) and Fe^III (S = 1/2) sites in the magnetically ordered phase. The sextets of the Fe^III (S = 1/2) sites have relatively large H_int of 24.6 T (for n = 5) and 24.8 T (for n = 6) at 4 K, while the Fe^II (S = 2) sites have relatively small H_int of 7.3 T (for n = 5) and 9.9 T (for n = 6).

Figure 6.27 shows the ⁵⁷Fe Mössbauer spectra for (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3 and 5) in the magnetically ordered phase. In the case of n = 3, the LTP with Fe^IIS₆ (S = 0)–Fe^IIIO₆ (S = 5/2) undergoes the ferromagnetic transition with T_C = 7.1 K. In the case of n = 5, on the other hand, the HTP with Fe^IIO₆ (S = 2)–Fe^IIIS₆ (S = 1/2) undergoes the ferromagnetic transition with T_C = 19.5 K. As shown in Fig. 6.13, the ⁵⁷Fe Mössbauer spectrum of the ferromagnetically ordered state in Prussian blue is a very informative guide to the assignment of the ⁵⁷Fe Mössbauer spectra in magnetically ordered state for n = 3 and 4. In the case of Prussian blue, the spin state of the Fe^II site coordinated by six C atoms of cyanide ligands is the LS state $( {t_{{2{\text{g}}}}^{6} ,S = 0} )$, and that of the Fe^III site coordinated by six N atoms is the HS state $( {{\text{t}}_{{2{\text{g}}}}^{3} {\text{e}}_{\text{g}}^{2} ,S = 0} )$. The estimated H_int for ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{6} ,S = 0} )$ and ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{3} {\text{e}}_{\text{g}}^{2} ,S = 5/2} )$ in ${\text{Fe}}_{4}^{\text{III}} \left[ {{\text{Fe}}^{\text{II}} \left( {\text{CN}} \right)_{6} } \right]_{3}$ at 1.6 K are 0 and 54.0 T, respectively [30]. ⁵⁷Fe Mössbauer paramers of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6) are listed in Table 6.2.

Fig. 6.27

⁵⁷Fe Mössbauer spectra of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3 and 5) in the magnetically ordered phase

Table 6.2 ⁵⁷Fe Mössbauer parameters of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6)

In order to confirm the ferromagnetic phase transition, we investigated the magnetization as a function of temperature for n = 3–6, which is shown in Fig. 6.28. The Curie temperature were estimated at 7, (7 and 13), 19.5 and 23 K for n = 3, 4, 5, and 6, respectively, from the heat capacity measurements for n = 3 and 4, [2(b)] and from the analysis of Arrott plot for n = 5 and 6 [6]. In the case of n = 4, the coexisting LTP and HTP undergo the ferromagnetic phase transitions at 7 K and 13 K, respectively. The critical temperature of CTPT, the Curie temperature and Weiss temperature of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6) are summarized in Fig. 6.28.

Fig. 6.28

Magnetization of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (n = 3–6) as a function of temperature. FCM: field-cooled magnetization, ZFCM: zero-field-cooled magnetization, RM: remnant magnetization. FCM and ZFCM were measured at 3.0 mT. (= 30 Oe). T_C and θ denote the Curie temperature and Weiss temperature, respectively

6.3.6 New Type of Photo-Induced Magnetism Induced by the Photo-Isomerization of Intercalated Cation

As mentioned in 6.3.4, the CTPT and the ferromagnetic phase transition of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] remarkably depend on the size of intercalated cation, which implies a possibility to control the CTPT and the ferromagnetic phase transition in the $\left[ {{\text{Fe}}^{{{\text{II}}}} {\text{Fe}}^{{{\text{III}}}} \left( {{\text{dto}}} \right)_{3} } \right]_{\infty }^{ - }$ layer by means of a photo-isomerization of intercalated cation as well as a photo-induced IVCT. In organic–inorganic hybrid systems, it is effective to use an organic photochromic molecule for producing photo-switchable materials. On the basis of this strategy, we have synthesized (SP-R)[Fe^IIFe^III(dto)₃] (SP-R = cationic spiropyran, R = alkyl group) [7]. In general, the cationic spiropyran can be converted from the yellow-colored closed form (CF) to the red-colored open form (OF) under UV light irradiation (330–370 nm). The OF is usually less stable and returns to the CF thermally or photo-chemically (500–600 nm). This photo-isomerization is associated with a volume change of molecule, which is schematically shown in Fig. 6.29.

Fig. 6.29

Photochromic reaction of cationic spiropyran (SP-R)

Fig. 6.30

Reprinted with permission from [7(a)]. Copyright 2009 American Chemical Society

Optical absorption of (SP-Me)[Fe^IIFe^III(dto)₃] in a KBr pellet under a UV light irradiation and b visible-light irradiation at 70 K. UV light irradiation (350 nm with 40 mW cm⁻²) on the KBr pellet was performed at first. After the saturation of light-induced absorption spectra at around 550–600 nm, visible-light irradiation (white light with 600 mW cm⁻²) on the pellet was performed.

Figure 6.30 shows the change of absorption spectra for (SP-Me)[Fe^IIFe^III(dto)₃] in a KBr pellet under UV light irradiation (350 nm with 40 mW cm⁻²) at 70 K [7]. At 70 K, the absorption band between 550 and 600 nm corresponding to the π−π* transition of the OF is continuously enhanced with the increase of UV light irradiation time, meanwhile the initial black pellet changes to a deep purple pellet. After the UV light irradiation for 3 h, its intensity is almost saturated. The UV light induced OF in (SP-Me)[Fe^IIFe^III(dto)₃] is stable even at room temperature on dark condition. This absorption band almost disappears under visible light irradiation (white light, 600 mW cm⁻²) for 2 h. The photo-isomerization of cationic SP-Me from the CF to the OF by UV light irradiation and that from the OF to the CF by visible light irradiation reversibly occurs at 300 K as well as at 70 K [7].

Fig. 6.31

Reprinted with permission from [7(a)]. Copyright 2009 American Chemical Society

a–c Temperature dependence of the magnetization for (SP-Me)[Fe^IIFe^III(dto)₃] before and after the UV light irradiation (350 nm with 40 mW cm⁻²) for 2 and 4 h at 300 K. d Temperature dependence of the magnetization after the UV light irradiation for 5 h at 70 K. e Schematic representation of the photo-induced phase conversion from the phase (A) to the phase (B). T = 75 K denotes the CTPT.

Figure 6.31 shows the temperature dependence of the magnetization for (SP-Me)[Fe^IIFe^III(dto)₃] before and after the UV light irradiation at 300 and 77 K. As shown in Fig. 6.31, on the heating process, the FCM and RM curves decrease stepwise at about 7 K and disappears at about 25 K. On the other hand, the ZFCM curve has two maxima (5 K and 17 K) and a hump at 22 K. The LTP and HTP of (SP-Me)[Fe^IIFe^III(dto)₃] individually undergo the ferromagnetic phase transitions at 5 K and 22 K, respectively.

When the UV light (350 nm with 40 mW cm⁻²) is irradiated for 4 h at 300 K, the FCM and RM curves change from the stepwise magnetization curves to normal magnetization curves, and the peak of ZFCM at around 5 K disappears, being reflected by the disappearance of LTP. On the other hand, being reflected by the growth of HTP, the FCM and RM values between 5 and 22 K slightly increase after the UV light irradiation. These photo-induced effects can be explained as follows. The photo-isomerization of cationic SP-Me from CF to OF by UV irradiation leads to the expansion of its own volume, which expands the unit cell volume and destabilizes the LTP. The photo-induced phase conversion of (SP-Me)[Fe^IIFe^III(dto)₃] is schematically shown in Fig. 6.31e, where we name two phases, (A) and (B). Only in the phase (A), the CTPT takes place. Suppose that the UV light irradiation induces the transformation from the phase (A) to the phase (B), the LTP in the phase (A) is forced to convert into the HTP in the phase (B) by UV light irradiation below 95 K. In order to confirm the CTPT in [Fe^IIFe^III(dto)₃] induced by the photo-isomerization of spiropyran, we performed UV light irradiation at 70 K, which corresponds to the arrow of the left side in Fig. 6.31e. The FCM, RM, and ZFMC curves after UV light irradiation for 5 h at 70 K are shown in Fig. 6.31d. Indeed, the photo-induced change in the ferromagnetic property shows the same tendency as in the case of UV light irradiation for 2 h at 300 K. Therefore, It is concluded that the destabilization of LTP and the stabilization of HTP by the photo-isomerization of intercalated SP-Me⁺ below 70 K induces the CTPT in the [Fe^IIFe^III(dto)₃] layer.

Moreover, in order to prove the disappearance of LTP by UV light irradiation, we measured the ⁵⁷Fe Mössbauer spectra of (SP-Me)[Fe^IIFe^III(dto)₃] at 6 K before and after the UV light irradiation (350 nm with 40 mW cm⁻²) for 3 h at 300 K, which is shown in Fig. 6.32 [7(b)]. As shown in Fig. 6.32a, the ⁵⁷Fe Mössbauer spectra at 6 K before UV light irradiation shows two kinds of magnetically ordered states. The sextet with a large hyperfine field from −8 to +8 mm s⁻¹ is typical of the magnetically ordered spectrum of ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{3} {\text{e}}_{\text{g}}^{2} ,S = 5/2} )$ and the narrow quadrupole doublet at around 0.3 mm s⁻¹ is assigned to the diamagnetic ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{6} ,S = 0} )$, which indicates the magnetically ordered LTP. The magnetic sextets of ${\text{Fe}}^{\text{II}} ( {{\text{t}}_{{2{\text{g}}}}^{4} {\text{e}}_{\text{g}}^{2} ,S = 2} )$ and ${\text{Fe}}^{\text{III}} ( {{\text{t}}_{{2{\text{g}}}}^{5} ,S = 1/2} )$ corresponding to the HTP are also observed. However, as shown in Fig. 6.32b, after the UV light irradiation for 3 h at 300 K, the ⁵⁷Fe Mössbauer spectra corresponding to the LTP vanishes entirely at 6 K. In this way, the remarkable change of ⁵⁷Fe Mössbauer spectra derived from the UV light irradiation proves that the photo-isomerization of SP-Me⁺ in (SP-Me)[Fe^IIFe^III(dto)₃] induces the transformation from the phase (A) to the phase (B).

Fig. 6.32

Reprinted from [7(b)], Copyright 2009, with permission from Elsevier

⁵⁷Fe Mössbauer spectra of (SP-Me)[Fe^IIFe^III(dto)₃] at 6 K before and after UV light irradiation (350 nm with 40 mW cm⁻²) for 3 h at 300 K.

The photo-isomerization induced CTPT for (SP-Me)[Fe^IIFe^III(dto)₃] is illustrated in Fig. 6.33. This new type of synergetic phenomenon coupled with spin, charge and photon is triggered by the photo-isomerization of intercalated spiropyran from the CF to the OF, which seems to have a significant similarity with the first event for the perception of light in rhodopsin where the photo-isomerization of 11-cis-retinal to the all-trans-retinal induces a conformational change in opsin and activates the associated G protein and triggers a second messenger cascade [51].

Fig. 6.33

Reprinted with permission from [7(a)]. Copyright 2009 American Chemical Society

Schematic representation of the synergetic CTPT induced by the photo-isomerization of spiropyran in (SP-Me)[Fe^IIFe^III(dto)₃]. White and black colored circles represent the Fe^II and Fe^III sites, respectively.

6.4 Single-Molecule Magnets and Single-Chain Magnets

6.4.1 Single-Molecule Magnets of Transition-Metal Clusters

Mössbauer spectroscopy have been applied to various kinds of molecular magnets as well as classical inorganic bulk magnets. Molecular magnets include not only classical magnets showing a long-range magnetic order but also quantum molecular magnets such as SMMs and SCMs the latter of which resemble superparamagnetic compounds in magnetism. These molecular nanomagnets have a possibility for ultra-high density memory, spintronics, and quantum computing devices. However, thermal and quantum relaxation processes limit them to afford such an application. Therefore, it is much important to elucidate slow relaxation dynamics of magnetization in quantum magnets. Varied measurements with individual time windows (Fig. 6.21) have been applied to SMMs and SCMs in order to reveal such spin dynamics. Especially, Mössbauer spectroscopy is a powerful tool to investigate spin dynamics for target atoms even in the condition of zero field as well as applied dc magnetic fields.

The dodecanuclear mixed-valence manganese cluster, [Mn₁₂O₁₂(AcO)₁₆(H₂O)₄]·2AcOH·4H₂O (AcOH = acetic acid) abbreviated as [Mn₁₂]_ac (Fig. 6.34), is well known as the first SMM reported in 1993 [52], while the synthesis of [Mn₁₂]_ac had already been described in 1980 [53]. In the precedent papers, slow magnetization relaxation like superparamagnetic bahavior was revealed in ac susceptibility measurements [54, 55], accompanied by that the nature of the ground spin state is shown to be S_total = 10 by high-field electron paramagnetic resonance [54]. The relaxation time (τ) of magnetization was found to follow the Arrhenius law:

Fig. 6.34

Molecular structure of [Mn₁₂O₁₂(AcO)₁₆(H₂O)₄] ([Mn₁₂]_ac)

$$\left( {\omega = } \right)\frac{1}{\tau } = \frac{1}{{\tau_{0} }}\exp \left( { - \frac{\Delta }{{k_{\text{B}} T}}} \right),$$

(6.6)

where ω is the relaxation rate at the temperature of T, 1/τ₀ is the pre-exponential factor, Δ is the effective activation energy, and k_B is the Boltzmann constant. This temperature dependence is the characteristics of the thermally-activated relaxation process by Orbach mechanism. The Δ is corresponding to |D|S ²_z for an integer spin or |D|(S ²_z  − 1/4) for a half integer spin, where D represents the axial zero-field splitting parameter. For [Mn₁₂]_ac, the Arrhenius parameters were estimated as τ₀ = 2.1 × 10⁻⁷ s and Δ/k_B = 61 K [52], where the blocking temperature (T_B) was estimated as about 3 K for τ ~ 10² s. Actually, magnetic hysteresis in MH curves was found below 4 K. Subsequently, some succeeding reports demonstrated clear magnetization steps (Fig. 6.35) in the hysteresis loops [56,57,58]. They are the first observations of quantum tunnelling of magnetization (QTM). A step occurs at every 0.44–0.46 T in an equally -spaced manner. The QTM originates in the level crossing between negative and positive m_S states as shown in Fig. 6.36. For example, at zero field the pair of +m_S and −m_S levels degenerates, affording a fast relaxation of magnetization because of the QTM. By applying external magnetic field, a non-zero field mismatching the energies of the +m_S and −m_S levels breaks down the tunnel relaxation. Some applied fields again lead to the degeneration of the energy levels when the m_S = +S level corresponds to the m_S = −S + n level (n is an integer), resulting in a fast relaxation. The interval field of the magnetization steps approximates the value of −nD/gμ_B, giving the D value of ~0.60 K for [Mn₁₂]_ac. From the Arrhenius analysis, the D value is given as 0.61 K using Δ = |D|S ²_total (S_total = 10), indicating an excellent agreement of those estimated values.

Fig. 6.35

Reprinted by permission from Springer Nature: [58], Copyright 1996

Magnetization versus magnetic field (MH) curves at 1.77, 2.10, and 2.64 K for a single crystal (volume: 0.066 ± 0.008 mm³) of [Mn₁₂]_ac. The magnetic field was applied along the magnetization axis, which aligns with the longest crystal dimension.

Fig. 6.36

a Magnetic hysteresis curve and b–d double-well potentials with energy levels for a spin state of S for a single-molecule magnet having easy-axis magnetic anisotropy (D < 0). The levels of positive m_S states are localized in the right well and the negative ones in the left well. Applied dc fields (H) are b zero, c 0 < H < −D/gμ_B, and d −D/gμ_B. The QTM occurs when energy levels between the two wells come to the same level

The [Mn₁₂]_ac has diversified into various derivatives, and wide variety of spectroscopic measurements have been performed to probe their SMM characteristics such as ground and excited spin states, magnetic anisotropy, and QTM. No Mössbauer study has been reported for [Mn₁₂]_ac because of less applicability for Mn atoms. A one-electron reduced analog, [Fe(C₅H₅)₂][Mn₁₂O₁₂(O₂CC₆F₅)₁₆(H₂O)₄] (Fe(C₅H₅)₂ = ferrocenium cation), was reported by Kuroda et al. [59] to determine the relaxation of magnetization derived from the magnetic field of the [Mn₁₂]⁻ core via ⁵⁷Fe Mössbuaer spectra of the ferrocenium site. The complex showed the effective energy barrier (U_eff) of magnetization reversal estimated as 50 K. In ⁵⁷Fe Mössbauer spectra (Fig. 6.37) below 13.5 K, a broad magnetic hyperfine splitting was found, which is a proof of slow paramagnetic relaxation originating in the SMM behavior of the [Mn₁₂]⁻ unit.

Fig. 6.37

Reprinted with permission from [59]. Copyright 2001 American Chemical Society

Temperature-varied ⁵⁷Fe Mössbauer spectra of 11% ⁵⁷Fe-enriched [Fe(C₅H₅)₂][Mn₁₂O₁₂(O₂CC₆F₅)₁₆(H₂O)₄] sample [59].

The [Fe₄] [60, 61] and [Fe₈] [60, 62, 63] coordination clusters are representative SMMs, the chemical formulae of which represent as [Fe₄(OCH₃)₆(dpm)₆] (Hdpm = dipivaloylmethane) and [Fe₈O₂(OH)₁₂(tacn)₆]Br₈ (Fig. 6.38; tacn = 1,4,7-triazacyclononane), respectively. These typical SMMs have been examined by means of ⁵⁷Fe Mössbauer spectroscopy, which were well summarized in a preceding book [64].

Fig. 6.38

Molecular structure of [Fe₈O₂(OH)₁₂(tacn)₆]Br₈. The arrows represent the spin structure

The [Fe₈] complex consists of eight Fe^III ions to form the ground S_total = 10 state [65] and shows SMM behavior with frequency dependence of ac magnetic susceptibilities giving τ₀ = 1.9 × 10⁻⁷ s and Δ/k_B = 22.2 K [63]. The relaxation time of magnetization was first investigated by means of ⁵⁷Fe Mössbauer spectroscopy for a SMM. As shown in Fig. 6.39a, a clear magnetic sextet superimposed three six-line patterns was observed in the ⁵⁷Fe Mössbauer spectrum at 2 K also under the absence of an external field. On heating, the splitting collapses gradually and results in partially-resolved quadrupole doublets at 300 K. A simplified line shape model was applied to the Mössbauer spectra in order to compare the estimated relaxation time with the values deduced from the ac magnetic measurements. The τ values were reasonably evaluated as they are compatible with the Arrhenius law in the ln(τ) versus T⁻¹ plot of ac measurements.

Fig. 6.39

Reprinted with permission from [63]. Copyright 1987 EDP Sciences

⁵⁷Fe Mossbauer spectra of [Fe₈] a at 2 K in an applied field of 0.22 T and b at 300 K in zero field. The rake-like bar graphs represent three sextet patterns attributable to the three iron sites.

Very recently, the development of synchrotron techniques enables us to employ ⁵⁷Fe Mössbauer spectroscopy of a monolayer SMM grafted on a gold substrate. This technique was first applied to a monolayered sample containing a ⁵⁷Fe-enriched [Fe₄] moiety [66], revealing slow magnetization relaxation of the iron cluster at zero magnetic field. In the monolayer, individual Fe^III sites lay in different chemical environments due to structural deformations induced by the interaction with the substrate, although such a modification tenuously affected SMM behavior. The zero-field splitting parameter, D, was estimated as |D| = −0.49(6) K by fitting ⁵⁷Fe Mössbauer spectrum at the lowest temperature of 2.2 K, which is reduced compared to the typical values of ~−0.6 K for the [Fe₄] family.

6.4.2 Linear Two-Coordinate Fe^II and Fe^I Complexes

Linear two-coordinate Fe^II complexes have been recently developed in the viewpoint of remarkably slow magnetization relaxation to afford SMMs due to a large magnetic anisotropy. In particular, a species of SMM originated in magnetic anisotropy of a single metal ion are called single-ion magnets (SIMs). A representative two-coordinate Fe^II compound, [Fe(C(SiMe₃)₃)₂], has impressed with a huge internal hyperfine field of 152 T in ⁵⁷Fe Mössbauer spectra at 4.2 K on both chemists and physicists [66]. Such a giant magnetic anisotropy is attributable to the unquenched orbital angular momentum corresponding to the degenerate ${\text{d}_{xy}}-{\text{d}}_{x^{2}-y^{2}}$ orbital pair. The [Fe(C(SiMe₃)₃)₂] compound possesses the strictly linear C–Fe^II–C geometry in the crystal [67, 68], being free from the Renner–Teller effect leading to a reduction of the orbital contribution due to a break of the local D_∞h symmetry.

The ⁵⁷Fe Mossbauer spectrum at room temperature shows an asymmetric doublet with much broadening in order to a magnetic relaxation, where the IS of ~0.4 mm/s and the QS of 1.3 mm/s. The temperature-independent characteristics of quadrupole splitting is observed, indicating a large separation between the ground orbital states and the excited ones. Below about 50 K, the broad doublet becomes a well-resolved sextet, and then ends up with the sharp spectrum having overall hyperfine splitting of 48.8 mm s⁻¹ at 4.2 K. The result indicates slower magnetization relaxation than the Mössbuaer time scale (τ ~ 10⁻⁸ s). Magnetic hyperfine field, H_n, is estimated as 152 T. According to H_n = H_F + H_D + H_L, where H_F is the Fermi contact roughly determined by −12.7 × (2S) T [69] and H_D is the dipolar contribution, the value of the orbital contribution term, H_L, is estimated as 203 T when H_D is assumed to be zero.

In the precedent paper [70], saturation magnetization of this compound was reported to reach ~32,500 cm³ Oe mol⁻¹ (or 5.82 μ_B) at 1.85 K (for field-oriented sample), which is larger than the spin-only value (4 μ_B) that would be expected for the Fe^II ion with S = 2. After this preliminary study, the details of dynamic magnetization in the SIM compound have been examined by means of ac and dc magnetic property measurements and ab initio calculations [71], followed by the analysis of ⁵⁷Fe Mössbauer relaxation spectra [72]. Low-temperature saturation magnetization for a fixed sample of [Fe(C(SiMe₃)₃)₂] is of M_sat = 3.24 μ_B. This value is lower than the spin-only value of the HS Fe^II ion because of random orientation of strong anisotropic species. Actually, the χ_MT value at room temperature is 4.79 cm³ K mol⁻¹ (the effective magnetic moment: μ_eff = 6.19 μ_B), indicating strong anisotropy with a large g value of 2.53. At zero applied dc field, [Fe(C(SiMe₃)₃)₂] shows no slow relaxation of magnetization in ac magnetic susceptibility, indicating no SIM behavior. However, such a relaxation can be detectable by means of ⁵⁷Fe Mössbauer spectroscopy as shown in Fig. 6.40, and analysed using a relaxation model formalized by Dattagupta and Blume [73]. Relaxation time constant (τ) ranges from 2.5 × 10⁻⁷ to 1.2 × 10⁻¹⁰ s within the measuring temperature range of 5–295 K. From the analysis of Arrhenius plots, the physical parameters on quantum tunnelling and Orbach relaxation processes were extracted as τ ⁻¹_QTM  = 4.2(3) × 10⁶ s⁻¹ and U_eff = 178(9) and 553(68) cm⁻¹, respectively. Two obtained U_eff values correspond to the energy splitting from the ground M_J = ±4 to the first excited M_J = ±3 or the second excited M_J = ±2 doublets among the Stark sublevels of ⁵D₄. It should be mentioned that ac susceptibility measurements (τ < ~10⁴ s) cannot detect the magnetic relaxation for this system due to the fast QTM process (τ_QTM = 2.4 × 10⁻⁶ s) at the level crossing between the ground M_J = ±4 states under zero field. Applying a small dc field induced suppression of the level crossing between the M_J doublets, and thus magnetization dynamics was observable as a nonzero signal in the out-of-phase ac susceptibility (χ_M″). For Cole–Cole plots, the relaxation dynamics can be evaluated by using a generalized Debye model [74, 75]. Their results reveal clearly the field-induced SIM nature of [Fe(C(SiMe₃)₃)₂].

Fig. 6.40

Reprinted with permission from [72]. Copyright 2013 American Chemical Society

Temperature-varied ⁵⁷Fe Mössbauer spectra of [Fe(C(SiMe₃)₃)₂] at zero dc magnetic field. Solid lines are the best fit profiles of a relaxation model.

Following the pioneering compound, some of ca. 30 linear two-coordinate Fe^II complexes [76] have currently been investigated from the viewpoint of SIM behavior [71, 77, 78] as well as magnetization dynamics by using Mössbauer spectroscopy [78,79,80,81]. The development of linear two-coordinate metal complexes frequently needs the introduction of bulky ligands. A fused-ring 1,1,3,3,5,5,7,7-octa-R-substituted s-hydrindacene skeleton (Rind) is useful as a sterically-hindered ligand to isolate stably low-coordinated complexes [82]. Linear two-coordinate iron(II) complexes with various Rinds have been developed and investigated for an extremely large internal hyperfine field in the Mössbauer spectrum [78]. Owing to bulkiness of ligands, the crystal structure of Fe(Eind)₂ (Fig. 6.41; Eind denotes Rind of R = ethyl) adopts a highly linear two-coordination geometry with the C–Fe–C bond angles of 174.24(15)–177.73(13)°. The effective magnetic moment of 5.82 μ_B at 300 K exceeds the spin-only value of 4.90 μ_B estimated for a HS (S = 2) Fe^II species, indicating virtually unquenched orbital angular momentum on the 3d electrons of Fe^II.

Fig. 6.41

Reprinted with permission from [78]. Copyright 2016 the Chemical Society of Japan

(left) Crystal structure of Fe(Eind)₂ with 50% probability ellipsoids. Hydrogen atoms are omitted for clarity. (right) Arrhenius plot showing the temperature dependence of the relaxation time (τ). The solid line represents a data fit to the Arrhenius law.

Such a large contribution of angular momentum leads to slow magnetization reversal, which is detectable by means of ac magnetic measurements (about 10–1000 Hz) as well as ⁵⁷Fe Mössbauer spectroscopy. Without a dc magnetic field, no frequency dependence was observed in the ac magnetic susceptibilities, which is consistent with a broad signal derived from paramagnetic relaxation in the ⁵⁷Fe Mössbauer spectrum at 4.2 K. This Mössbauer result indicates that the relaxation time approaches the time scale of 10⁻⁹ s. The rapid relaxation is due to QTM. An applied dc field of 0.1 T suppressed the quantum tunnelling effectively, and consequently the spectrum split into a remarkably wide sextet with an internal hyperfine field of H_n = 140.3 T. The H_n value reached up to 143.1 T at an applied field of 3.0 T. The IS is 0.368(9) mm s⁻¹ and QS −1.706(13) mm s⁻¹. The QS value is rather negative, reflecting a larger electric field gradient at the iron(II) ion compared with that of [Fe(C(SiMe₃)₃)₂] showing QS = −1.08(1) to −1.27 mm s⁻¹. As with ⁵⁷Fe Mössbauer results, slow relaxation was observed in the χ_M″ versus frequency plots below 12 K in the ac frequency range of 5–1512 Hz with the applied dc field of 1200 Oe. The analysis of Arrhenius plots (Fig. 6.41) gave U_eff = 51.2(7) cm⁻¹. At lower temperatures (T < 10 K), a dominant relaxation process gradually changed from thermally-activated Orbach mechanism to direct and/or Raman ones before quantum tunnelling regime in the temperature range less than 3 K.

Very recently, the first two-coordinate Fe^I complex, [Fe^I(C(SiMe₃)₃)₂]⁻, was developed via the chemical reduction of [Fe^II(C(SiMe₃)₃)₂]⁰ using KC₈, and its excellent SIM behavior was reported [83]. This complex has a highly anisotropic S = 3/2 spin state that is regarded as a Kramers ion with the ground M_J = ±7/2 doublets. Single-crystal X-ray diffraction analysis revealed the almost perfectly linear structure with the C–Fe–C angle of 179.2(2)° [83]. Extremely slow magnetization relaxation to behave as SIM was observed in the absence of an applied dc field, resulting in a large magnetic hysteresis loop due to magnetic blocking below 4.5 K. The effective activation barrier of spin reversal is estimated as U_eff = 226(4) cm⁻¹ from ac susceptibility measurements, which is consistent with the value of U_eff = 246(3) cm⁻¹ evaluated by the analyses of ⁵⁷Fe Mössbauer relaxation spectra [72].

6.4.3 Single-Chain Magnets: Unique Chain Magnet with Easy-Plane Anisotropy

Although pure one-dimensional (1D) spin systems never show magnetic phase transition based on any long-range ordering at a finite temperature, they can afford to behave like a magnet below a blocking temperature in the case of the presence of strong uniaxial magnetic anisotropy. Such compounds are categorized as SCMs, where slow relaxation dynamics of magnetization follows the Arrhenius law [Eq. (6.6)]. Dynamics of spin reversal for Ising chain systems is formulated by Glauber [84], whose model manages to explain quantitatively experimental results for some tangible SCMs. There are currently some practical reviews for SCMs [85, 86], interpreting anisotropic Heisenberg model applicable to the real materials, based on Glauber dynamics of 1D Ising chain. The spin system can be described by the following Hamiltonian:

$$H = - 2J\mathop \sum \limits_{i = 1}^{L} S_{i} \cdot S_{i + 1} + D\mathop \sum \limits_{i = 1}^{L} S_{i}^{2} - g\mu_{\text{B}} H\mathop \sum \limits_{i = 1}^{L} S_{i}^{2} ,$$

(6.7)

where J is the exchange coupling constant between adjacent spins and L the effective chain length. In the case of |D/J| > 4/3 (Ising limit), the spin system can be considered to be pseudo-Ising chain as shown in Fig. 6.42. At finite temperatures, the thin domain walls are created with the energy barrier 2Δ_ξ = 8|J|S² if the system is regarded as the infinite chain with the small domain size (2ξ) compared to L (that is 2ξ < L, Fig. 6.42a). Additionally, each spin has an anisotropic energy of Δ_A = |D|S², and therefore the relaxation time can be described as follows,

Fig. 6.42

Schematic represents for spin reversal in a infinite and b finite Ising chain systems. The parameters of Δ_ξ and ξ denote the energy barrier of spin reversal and the correlation length (2ξ: the width of domain), respectively

$$\tau_{1} = \tau_{0} \exp \left( {\frac{{2\Delta_{\xi } + \Delta_{\text{A}} }}{{k_{\text{B}} T}}} \right) = \tau_{0} \exp \left( {\frac{{\left( {8J + \left| D \right|} \right)S^{2} }}{{k_{\text{B}} T}}} \right).$$

(6.8)

On cooling, ξ increases exponentially and gets comparable to L, which results in the occurrence of the finite size effect (Fig. 6.42b). In such a case, the formation energy of the domain is Δ_ξ = 4|J|S² due to the creation of the domain wall in only one side. Thus, the thermal activation energy can be estimated as (4J + |D|)S², and the dynamics of magnetization reversal obeys Eq. (6.9).

$$\tau_{2} = \tau_{0} \exp \left( {\frac{{\Delta_{\xi } + \Delta_{\text{A}} }}{{k_{\text{B}} T}}} \right) = \tau_{0} \exp \left( {\frac{{\left( {4J + \left| D \right|} \right)S^{2} }}{{k_{\text{B}} T}}} \right)$$

(6.9)

In 2001, a slow relaxation of magnetization like SMMs was observed in 1D spin systems. The first SCM is the metal-radical compound [Co(hfac)₂(NITPhOMe)] (Hhfac = hexafluoroacetylacetone, NITPhOMe = p-methoxyphenyl nitronyl nitroxide) [87]. This compound consists of the effective S = 1/2 spin of Co²⁺ (g_Co = 7.4) and the S = 1/2 spin of radical (g_R = 2) connected via an antiferromagnetic coupling (2J/k_B = −220 K for −2JΣS_Co·S_R). The ac measurements revealed frequency dependences of χ_M′ and χ_M″ below 17 K, indicating apparently a slow relaxation of magnetization. The relaxation time was perfectly accordance with the Arrhenius law, and the analysis gave the parameters of τ₀ = 3.0(2) × 10⁻¹¹ s and Δ/k_B = 154(2) K.

Almost coincidentally, a heterometallic chain [Mn₂(saltmen)₂Ni(pao)₂(py)₂] (ClO₄)₂ (H₂saltmen = N,N′-bis(salicylidene)tetramethylethylenediamine, Hpao = pyridine-2-aldoxime) was developed in 2002 [87], which is comprised of ferromagnetically-coupled S_T = 3 spin units to form an Ising-like chain. Varied magnetic analyses were performed to scrutinize Glauber dynamics for the compound [88, 89]. Below 6.5 K, the frequency dependence of χ_M′ and χ_M″ were clearly observed, and a semicircle in the Cole–Cole plot indicates a practical single relaxation process according to the Debye model. From a detailed Arrhenius plot, such a thermally-activated relaxation process switched in the vicinity of ~2.7 K (Fig. 6.43). The Arrhenius parameters of two relaxation manners were given as τ₀ = 5.5(1) × 10⁻¹¹ s, Δ₁/k_B = 72(1) K in a high-temperature region and τ₀ ~10⁻⁸ s, Δ₂/k_B ~55 K in a low-temperature one. The former is considered as the infinite chain regime according to Eq. (6.8), and the latter seems to obey Eq. (6.9) due to the finite size effect. The exchange coupling between the spin units was estimated as J/k_B = 0.77 K by means of dc magnetic measurements, while the anisotropy parameter of each unit was D/k_B = −2.5 K. The Δ₁ and Δ₂ are excellent consistent with the expected values of (8J + |D|)S ²_T (= 78 K) and (4J + |D|)S ²_T (= 50 K), respectively.

Fig. 6.43

Reprinted figure with permission from [89]. Copyright 2004 by the American Physical Society

Arrhenius plot of the relaxation time τ (logarithmic scale) versus 1/T. Inset graph is time-dependent magnetization relaxation at 3 K. Solid lines represent the best fits using the model for Glauber dynamics. Schematic view indicates the spin model consisting of S = 3 units connected by an inter-unit ferromagnetic coupling of J′.

Among various SCMs developed, there are few examples on Mössbauer relaxation study compared with an overwhelming number of ac susceptibility measurements. An alternating Fe^II–Fe^III chain compound, catena-[Fe^II(ClO₄)₂{Fe^III(bpca)₂}]ClO₄ (Hbpca = bis(2-pyridylcarbonyl)amine) as shown in Fig. 6.44, is one of representative SCMs, where ⁵⁷Fe Mössbauer and μSR spectroscopic measurements were performed to investigate the spin relaxation based on Glauber dynamics in the chain structure [90, 91]. The material can be described as a unique 1D Ising system composed of metal ions in the nature of easy-plane magnetic anisotropy (D > 0). In general, SMMs and SCMs prefer consisting of an easy-axis anisotropic (D < 0) metal ions in order to overcome a thermal relaxation of magnetization. However, the overall easy-axis anisotropy of the molecule can stem from the orthogonal arrangement of each metal ion with easy-plane anisotropy. In catena-[Fe^II(ClO₄)₂{Fe^III(bpca)₂}]ClO₄, the HS Fe^II ions have a octahedral coordination geometry with the axial bonds elongated. This situation can provides an easy-plane anisotropy (XY spin) in the equatorial plane. The XY spin of each Fe^II site is coupled antiferromagnetically with Fe^III (S = 1/2) spins in an alternately-twisted array of the easy-plane, which affords a net easy-axis anisotropy along the chain direction. This compound showed a slow magnetization relaxation in ac susceptibility, and activation energy U_eff/k_B of 27 K was estimated from the Arrhenius plot [90]. The U_eff value is smaller than the (8J + |D|)S² expected for pure Glauber dynamics theory, suggesting that the transverse magnetization of the Fe^II spins in the easy plane is responsible for the magnetic relaxation.

Fig. 6.44

Reprinted with permission from [90]. Copyright 2005 American Chemical Society

Crystal structure of the catena-[Fe^II(ClO₄)₂{Fe^III(bpca)₂}]ClO₄ (Hbpca = bis(2-pyridylcarbonyl)amine) and the spin alignment of Fe^II (S = 2)–Fe^III (S = 1/2) in the chain.

A short-range ordering was observed in ⁵⁷Fe Mössbauer spectroscopy as well as μSR spectroscopy [91]. The μSR technique is one of the methods to approach a ground magnetic state at zero field (ZF). The depolarization of spin-polarized muons was observed in ZF-μSR time spectra at 20 K, which are reproducible by using two Gaussian-type relaxations. On cooling down to 6 K, a gradual loss of the initial asymmetry was found, which was simultaneously followed by the enhancement of the relaxation rate for the fast depolarizing component. Below 6 K, the initial asymmetry became almost constant, and the relaxation rate declined rapidly after the divergence around 6 K. This behavior indicates a critical slowing down of magnetic fluctuation. No oscillation signal was observed in the decay spectra even at 0.3 K, indicating that the muon is located in a randomly distributed magnetic field.

The ⁵⁷Fe Mössbauer spectroscopy also accepts a short-range ordering nature of magnetic moment on the SCM compound (Fig. 6.45). Above 20 K, two doublets are observed, which are assignable as the HS Fe^II and LS Fe^III species. These paramagnetic signals turn into broadening before splitting into two magnetic sextet with a partially residual paramagnetic components below 7 K. The hyperfine fields were estimated at 19.2 T for Fe^II and 33.5 T for Fe^III.

Fig. 6.45

Reprinted with permission from [90]. Copyright 2005 American Chemical Society

Temperature-varied ⁵⁷Fe Mössbauer spectra of catena-[Fe^II(ClO₄)₂{Fe^III(bpca)₂}]ClO₄ a at 298 and 20 K, b at 7 and 3.7 K.

6.5 Conclusion

In this chapter, we have focused on the molecular magnetism and its related light-induced phase transitions from the viewpoint of Mössbauer spectroscopy. In the Sect. 6.2, we have described mainly the dynamic spin equilibrium phenomena for [M^IIFe^III(mto)₃] (M = Zn, Mn) complexes. In the case of (C₆H₅)₄P[Mn^IIFe^III(mto)₃] consisting of Fe^IIIO₃S₃ and Mn^IIO₆ octahedra, there exists a rapid spin equilibrium (τ < 10⁻⁷ s) between the HS and LS states at the Fe^IIIO₃S₃ site, which induces the fluctuation of internal magnetic field on the Mn^II site. Owing to the fluctuation of internal magnetic field caused by the rapid spin equilibrium, (C₆H₅)₄P[Mn^IIFe^III(mto)₃] undergoes the successive magnetic phase transitions at 30 and 23 K. In the Sect. 6.3, we have described the CTPT and the ferromagnetism of (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃]. At the CTPT, the electrons of Avogadro’s constant transfer between the Fe^II and Fe^III sites, and the Fe valence state is dynamically fluctuated with a frequency of about 0.1 MHz, which was confirmed by means of μSR. In order to control the ferromagnetism and the CTPT by means of photo-irradiation, we have synthesized a photo-responsive organic-inorganic hybrid system, (SP-Me)[Fe^IIFe^III(dto)₃], and discovered that the photo-isomerization of intercalated SP-Me by UV light irradiation induces the CTPT and the enhancement of the Curie temperature from 7 to 22 K. In the Sect. 6.4, we have described the spin dynamics of various kinds of molecular magnets such as SMMs with transition-metal clusters, SIMs with linear coordination, and SCMs with easy-plane anisotropy.