Spin State of the Co³⁺ Ions in the Layered TbBaCo₂O_5.5 Cobaltite in the Metal–Insulator Transition Range

Abstract

A scheme is proposed to describe the spin state of the Co³⁺ ions in the layered TbBaCo₂O_5.5 cobaltite near the metal–insulator transition. The spin state of the Co³⁺ ions in the metallic phase corresponds to a mixture of the HS($t_{{2g}}^{4}$$e_{g}^{2}$, S = 2) and LS($t_{{2g}}^{6}$$e_{g}^{0}$, S = 0) states taken at approximately the same proportion. The transition into a nonmetallic state occurs due to the transformation of the HS state into the LS state in octahedra and part of the LS state into the IS($t_{{2g}}^{5}$$e_{g}^{1}$, S = 1) state in pyramids (near T_C ~ 280 K). The proposed scheme agrees with the well-known structural data obtained for the TbBaCo₂O_5.5 cobaltites. As follows from volumetric and linear expansion, the transition takes place over a wide temperature range T ≈ T_MI ± 50 K. The study of thermal expansion shows that an LS/IS state is retained down to T = 80 K.

INTRODUCTION

Interest in the ordered layered RBaCo₂O_{5 + δ} cobalt oxides is mainly caused by the detection of colossal magnetoresistance (MR) in hole lanthanum manganites [1, 2]. Although they do not exhibit the magnetoresistance properties comparable with those of hole manganites, they attract great attention due to their unusual magnetic and electrical properties and phase transitions [3–15]. The driving force of the cation ordering in the R_{1 –x}Ba_xCoO_{3 – δ} perovskites at x = 0.5 is the significant difference between the radii of the R³⁺ and Ba³⁺ rare-earth ions, which leads to cation ordering in the form of alternating layers with rare-earth (R) and alkali metal (Ba) ions. The layered RBaCo₂O_{5 + δ} cobaltites have a perovskite crystal structure, in which RO and BaO layers alternate with CoO₂ layers located normal to axis c. They are strongly anisotropic because of their layered structure [3, 11]. Depending on the oxygen content 0 ≤ δ ≤ 1, the valence state of cobalt changes from Co²⁺ to Co⁴⁺, and Co ions have different oxygen environment (octahedra or pyramids with a square base). RBaCo₂O_5.5 only contains Co³⁺ ions, which are located in the crystal lattice of the same number of CoO₆ octahedra and square CoO₅ pyramids, and the oxygen pyramids and octahedra surrounding Co³⁺ ions are ordered [2].

The unusual electron, magnetic, and structural transitions in RBaCo₂O_{5 + δ}, δ ≈ 0.5, are of particular interest. The following sequential transitions were detected in them: metal–insulator (MI), paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM) transitions [1–15]. In contrast to manganites, the MI transition in cobaltites is not related to magnetic ordering, which results from the magnetically active (antiferromagnetic) character of the RMnO₃ matrix in the case of manganites and the weakly magnetic (paramagnetic) behavior of RCoO₃ in the case of cobaltites (as the nature of magnetoresistance). Colossal magnetoresistance is promoted by the presence of FM clusters in an AFM matrix. The FM clusters in hole manganites are coupled to an AFM matrix by an exchange interaction, which causes an increase in the cluster size and a high MR [16, 17]. The increase in the magnetic cluster (polaron) size with decreasing temperature or in a magnetic field is explained by the unusual transport properties of layered manganites, namely, metal–nonmetal transition and higher MR [18]. A weakly magnetic cobaltite matrix exhibits cluster coalescence [19] and a low MR. The properties of the matrix cause the following new phenomena for layered cobalt oxides: a unidirectional electrical resistance anisotropy, exchange bias [20, 21], and the absence of exchange bias in MR hole manganites.

The physics of layered cobaltites is determined by the complex interaction between the charge, spin, orbital, and lattice degrees of freedom [1–5, 22]. The MI transition is accompanied by anomalous changes in the lattice parameters, the average cobalt–oxygen distance d(Co–O) in octahedra and pyramids [4, 6, 12, 13], and effective paramagnetic moment μ_eff [1, 2], which are determined by changes in the spin states of Co³⁺. Depending on the relation between the energies of intraatomic exchange and the crystal field, the Co³⁺ ions can be in a low-, intermediate-, or high-spin state. The differences between the spin-state energies in many cobaltites are small and can easily be overcome by temperature changes, which lead to transformation of the spin state of Co and unusual structural and phase transitions (including MI transition) [22].

At present, there is no agreement regarding the spin state of Co³⁺ and the origin of the MI transition in the layered RBaCo₂O_5.5 cobaltites. The spin state of the Co³⁺ ions in the relatively simple LaCoO₃ compound is still unclear and has been the subject of controversy since the 1960s. The situation in the rare-earth layered RBaCo₂O_{5 + δ} cobaltites at δ ≈ 0.5 is more complex. First, unlike LaCoO₃, the Co³⁺ ions in these compounds can be in two different oxygen environment positions (octahedral, pyramidal). Second, the Co³⁺ ions can also be in the following three different spin states: high-spin (HS, S = 2), intermediate-spin (IS, S = 1), and low-spin (LS, S = 0) states. In addition, the magnetic properties of the RBaCo₂O_{5 + δ} cobaltites depend on a paramagnetic R³⁺ ion [3, 4]. Depending on the type of rare-earth ion, this contribution can be significant, which substantially affects the spin moment of Co³⁺ determined from magnetic measurements.

The authors of the first works [1, 2] assumed that the Co³⁺ ions are in an LS/IS state at low temperatures and evolve to the HS state in both polyhedra at above transition temperature T_MI [1, 2]. According to the soft X-ray absorption and the photoelectron spectroscopy of GdBaCo₂O_5.5, the HS state of the Co³⁺ ions is also retained at T < T_MI [23]. The analysis [24] of the X-ray absorption spectra of TbBaCo₂O_5.5 did not detect a change in the spin state of the Co³⁺ ions at T_MI. The Mössbauer spectroscopy of TbBaCo₂O_5.5 [25] suggests the IS → HS transition for the cobalt ions in octahedra and the retained HS state for cobalt in pyramids when temperature increases [25]. Thus, the data obtained are conflicting.

Magnetic methods are most widely used to determine the spin state of Co³⁺ [1, 2]. The complexity of the magnetic methods applied for this purpose is the problem of separating the contribution of the Co³⁺ ions from the PM contribution of rare-earth R³⁺ ions. Moreover, magnetization studies cannot determine the oxygen environment (octahedral or pyramidal) of the Co³⁺ ions. The authors of [4, 7] tried to determine the oxygen environment and the spin state of the Co³⁺ ions using magnetic and structural data. The structural data [4] obtained for GdBaCo₂O_5.5 revealed elongated octahedra and compressed pyramids in the metallic phase. Since the ionic radius of Co³⁺ increases with the spin state, these results could be interpreted as an increase in the spin state of the Co³⁺ ions in the octahedra and a decrease in the spin state in the pyramids. However, the spin state of the Co³⁺ ions in GdBaCo₂O_5.5 is LS/IS below T_MI and HS/IS above T_MI [7], which is in conflict with the structural data [7]. The authors of [4] suppose that the transition into a metallic state is due to a change in the LS state of the Co³⁺ ions to the HS state only in the octahedra without changing the IS state in the pyramids. The same conclusions about the spin state of the Co³⁺ ions in PrBaCo₂O_5.5 were made without regard for the PM contribution of the Pr³⁺ ions [13]. The authors think that the compression of pyramids can be attributed to either the steric effect or the formation of metallic bonds [4, 13]. This model has received wide acceptance, and many researchers use this model of the MI transition in RBaCo₂O_5.5.

However, the authors of [26] were doubtful of the reliability of the conclusions [4] regarding the spin state Co³⁺, since the method of determining the PM contribution of the Gd³⁺ ions that was used in [7] is incorrect (see below). Moreover, the magnetizations of samples [7] were anomalous high as compared to the data in [2, 8]. A method of determining the PM contribution of the Gd³⁺ ions was proposed in [26]. The studies [26] of the magnetization of GdBaCo₂O_5.5 as a function of temperature and magnetic field showed that the PM contribution of the Gd³⁺ ion almost coincided with the contribution of a free Gd³⁺ ion. As follows from the refined PM contribution of the Gd³⁺ ions, the Co³⁺ ions in GdBaCo₂O_5 + δ at δ ≈ 0.5 are still in the LS/IS state below T_MI and transform into the HS/LS state above T_MI [26]. The transition into the metallic state of GdBaCo₂O_5.5 takes place when the spin state of the Co³⁺ ions increases in the octahedra (LS–HS transition) and decreases in the pyramids (IS–LS transition). These conclusions agree with the structural data obtained by synchrotron X-ray diffraction of GdBaCo₂O_5.5 [4].

The purpose of this work is to determine the spin state of the Co³⁺ ions in the layered TbBaCo₂O_{5 + δ} cobaltite at δ ≈ 0.5. Although the magnetic properties of TbBaCo₂O_5.5 were extensively studied and the neutron and X-ray diffraction measurements were performed in many works, there are no unambiguous conclusions regarding the spin state of Co³⁺ in this compound in the MI transition range [2, 5, 6, 15, 23–25, 27]. This situation is mainly caused by the fact that the conclusions were drawn using the magnetic data that do not take into account the PM contribution of the Tb³⁺ ions [2, 5]. The spin state of the Co³⁺ ions in TbBaCo₂O_5.5 in this work is determined with allowance for the PM contribution of the Tb³⁺ ions. As follows from our data, the spin states of the Co³⁺ ions in TbBaCo₂O_5.5 and GdBaCo₂O_5.5 near the MI transition are identical. The Co³⁺ ions are in the LS/IS state below T_MI and in the HS/LS state above T_MI. The transition to the quasimetallic state occurs when the LS state changes to the HS state in octahedra and IS states to LS states in pyramids in the temperature range T ≈ T_MI ± 50 K. This assumption explains the increase in the cobalt–oxygen distance d(Co–O) in the octahedra and its decrease in the pyramids in TbBaCo₂O_5.5 [6] because of the changes in the ionic radii of the Co³⁺ ions induced by changes in their spin state during transition into the metallic phase.

EXPERIMENTAL

Polycrystalline TbBaCo₂O_{5 + δ} samples were synthesized from Tb₄O₇ (99.99% purity), Co₃O₄ (analytical grade), and BaCO₃ (special purity grade) powders using solid-phase reactions. The powders taken in the necessary proportion were ground, pressed in pellets, and sintered at 1150°C for 24 h, and the pellets were then cooled to room temperature at a rate of 1 K/min. Oxygen content δ was determined by reducing a sample in a hydrogen atmosphere. The samples were single-phase with δ = 0.38 and had an orthorhombic structure (space group Pmmm, no. 47) with unit cell parameters a = 3.869(5) Å, b = 7.815(4) Å, and c = 7.515(5) Å. These results agree with the data in [28]. To change the oxygen content, we annealed the pellets in sealed ampules at a pressure of 5 atm. The Ag₂O compound was as an oxygen source. The linear expansion coefficient was determined using an ULVAC-SINKU RIKO (Japan) quartz dilatometer in the temperature range 77–550 K in the dynamic mode at the rate of change of temperature of 2 K/min. The magnetization was determined on an MPMS-5XL (Quantum Design) device at T = 10–400 K and on a 7407 VSM (Lake Shore) vibrating-sample magnetometer at T = 280–500 K at the Center for Collective Use of the Institute of Metal Physics.

RESULTS AND DISCUSSION

Figure 1 shows the temperature dependence of the magnetization M(T) of the TbBaCo₂O_5.47(2) polycrystal in a magnetic field H = 1 kOe. When the temperature decreases below the Curie temperature (T_C = 279 ± 2 K), the magnetization increases sharply, reaches its maximum at T_max ≈ 263 ± 1 K, and decreases sharply at T ~ 220 K. Based on neutron diffraction investigations, the authors of [27] explained this behavior of M(T) in the TbBaCo₂O_5.50 polycrystal by the formation of a canted FM structure below T_C and its further transition into a noncollinear AFM state. Researchers usually suppose that the transition into the AFM state takes place at T = T_max, although magnetization is retained within 30–40 K. A gradual transition from a canted FM state into a noncollinear AFM state is likely to occur in the temperature range from T = T_max ~ 260 K to T_N ~ 200 K (Fig. 1). The right inset to Fig. 1 shows the temperature dependences of saturation magnetization M_S, which were obtained extrapolation of M(H) to 50 kOe, and the magnetizations at 50 kOe (PM contribution of the Tb³⁺ ions was subtracted) at T = 300–200 K. M_S is seen to decrease below T_max and the FM state exists in a narrow temperature range T ≈ 220–280 K. The increase in the magnetization below T = 200 K is explained the PM contribution of the Tb³⁺ ion (Fig. 1, solid line).

Fig. 1.

(Color online) Temperature dependences of the magnetization of TbBaCo₂O_5.47 (symbols 1) and the paramagnetic contribution of Tb³⁺ ions (solid line 2) at H = 1 kOe (see text). (left onset) Temperature dependence of the paramagnetic susceptibility at low temperatures. (right inset) temperature dependence of the saturation magnetization M_S and the magnetization of a TbBaCo₂O_5.47 polycrystal at H = 50 kOe.

At low temperatures in the range T = 10–60 K, the paramagnetic susceptibility of the sample (left-side inset to Fig. 1) is described by the Curie–Weiss law with a paramagnetic temperature θ_PM ≈ –11 K and an effective magnetic moment μ_eff ≈ 8.3μ_B, which differs from the moment expected for a free Tb³⁺ ion (μ_eff = 9.72μ_B),

$$\chi \sim \mu _{{{\text{eff}}}}^{2}{\text{/}}(T - {{\theta }_{{PM}}}).$$

(1)

Rare-earth ion compounds are known to be Van Vleck paramagnets, and their paramagnetic properties are described by the Curie–Weiss law with μ_eff of a free ion [29, Chapter 9]. A negative value θ_PM < 0 characterizes the presence of AFM interactions and agrees with the AFM ordering of the Tb³⁺ ions in TbBaCo₂O_5.5 below θ_N = 3.44 K [15].

At present, the influence of the PM contribution of R³⁺ ions on the magnetic properties of RBaCo₂O_{5 + δ} is poorly understood. This contribution was not taken into account in [1, 2, 5, 8, 11, 13, 14, 30], and the authors of [3, 10, 15, 31] assumed that the contribution of R³⁺ ions coincides with the contribution of a free ion. In [4, 7], the contribution of the Gd³⁺ ion was determined using the results of studying the PM susceptibility of GdBaCo₂O_5.5 at low temperatures,

$${{\chi }_{{{\text{G}}{{{\text{d}}}^{{3 + }}}}}}\,[{\text{emu/g/Oe}}] = 1.92 \times {{10}^{{ - 2}}}{\text{/}}(T + 0.4).$$

(2)

This method is inaccurate, since the effective moment depends on the presence of magnetic ions [29]. The value of μ_eff in Eq. (2), which differs from the moment of a free Gd³⁺ ion, is caused by the influence of Co ions, as in our experiment for the Tb³⁺ ion (inset to Fig. 1), since the PM susceptibility is determined by the contribution of Co and R³⁺ ions.

To determine the PM contribution of the Gd³⁺ ions, we [26] proposed to use the saturation of magnetization M(H) in a magnetic field at low temperatures. It was preliminarily shown that the contribution of the Co ions to the magnetization of GdBaCo₂O_5.5 at T = 10 K is low and the field dependence of magnetization at T = 10 K is described by a Brillouin function with the parameters characteristic of the free Gd³⁺ ion at θ_PM = –1.4 K,

$$M = {{N}_{{\text{A}}}}g{{\mu }_{{\text{B}}}}J{{B}_{S}}(x),$$

(3)

where B_S(x) is the Brillouin function, N_A is Avogadro’s number, x = gμ_BJH/k(T – θ_PM), g is the Landé factor, μ_B is the Bohr magneton, J is the total magnetic moment, H is the magnetic field, and k is the Boltzmann constant.¹ At x ≪ 1, from Eq. (3) the PM contribution of the Gd³⁺ ions is [26]

$${{\chi }_{{{\text{G}}{{{\text{d}}}^{{3 + }}}}}}\,[{\text{emu/g/Oe}}] = 1.57 \times {{10}^{{ - 2}}}{\text{/}}(T + 1.4).$$

(4)

Using the method proposed in [26], we determine the PM contribution of the Tb³⁺ ions using the results of studying the magnetization of TbBaCo₂O_5.47 in the range T = 10–150 K. The symbols in Fig. 2a show the experimental magnetization M(H) of the TbBaCo₂O_5.47 polycrystal at T = 10 K. Unlike GdBaCo₂O_5.52 [26], the M(H) dependence of the sample at T = 10 K is not described by Eq. (3) for the parameters of the Tb³⁺ ion at any values of θ_PM (Fig. 2a; solid lines 1, 2). The M(H) curves at T = 10 K are explained by the fact that TbBaCo₂O_5.47 at T = 10 K is not a pure paramagnet, since temperature T = 10 K is close to the AFM ordering temperature (θ_N = 3.44 K) of the Tb³⁺ ions [15], in contrast to GdBaCo₂O_5.5, in which ordering of the Gd³⁺ ions above T = 1.7 K was not detected [3, 4, 10].

Fig. 2.

Field dependences of the magnetization of a TbBaCo₂O_5.47 polycrystal at T = (a) 10 and (b) 20–150 K. (symbols) Experiment and (solid lines) calculation.

The symbols in Fig. 2b show the experimental values of M(H) at T = 20–150 K, which are determined by the total contribution of the Tb³⁺, Co³⁺, and 2–3% Co²⁺ ions. The magnetization M(H) determined at T = 10–150 K demonstrates that the PM susceptibility of the Co ions tends to decrease with decreasing temperature (as in GdBaCo₂O_{5 + δ} [26]), which is characteristic of AFM at T ≪ T_AFM [29]. Our estimates demonstrate that the contribution of the cobalt ions to the magnetization at T = 20 K is at most 0.2μ_B. At 20–50 K, the contribution of the Tb³⁺ ion is satisfactorily described by Eq. (3) with Tb³⁺ ion parameters J = 6, g = 1.5, and θ_PM = –(8 ± 2) K. At T = 75–150 K, the calculated values of M(H) bounded by the contribution of the Co³⁺ ions deviate slightly from the experimental values (Fig. 2b). The contribution of the Tb³⁺ ions to the paramagnetic susceptibility is determined by the following expression derived from Eq. (3) at x ≪ 1 (T > 300 K and H ~ 10 kOe):

$$\chi \,[{\text{emu/mol/Oe}}] = {{C}_{M}}{\text{/}}(T - {{\theta }_{{PM}}})\,[{\text{K}}],$$

(5)

where C_M = N_A$\mu _{{\text{B}}}^{2}\mu _{{{\text{eff}}}}^{2}$/3k = 11.82 is the Curie constant for the Tb³⁺ ion [32].

In a wide temperature range of 300–10 K, the PM susceptibility of plain GdCoO₃ [33, 34] and TbCoO₃ [35] is described by Eq. (5) with the parameters of free Gd³⁺ and Tb³⁺ ions, which indirectly supports our conclusions. Line 2 in Fig. 1 shows the PM contribution of the Tb³⁺ ions at H = 1 kOe. Our estimates demonstrate that the contribution of the Tb³⁺ ions to the magnetization of TbBaCo₂O_5.5 above T_MI is predominant and the contribution of the Co³⁺ ions accounts for less than 14% of the total magnetization, which is almost half that in GdBaCo₂O_5.5 [26].

Figure 3 depicts the temperature dependence of the electrical resistivity of TbBaCo₂O_5.52 at T = 100–400 K, which is typical of layered cobaltites [1, 2]. It has a semiconductor character: ρ(T) decreases monotonically with increasing temperature and, in the temperature range 100–250 K, is described by the activation expression

$$\rho (T)\sim \exp ( - \Delta E{\text{/}}kT)$$

with an activation energy ΔE ≈ 40 meV. An inflection point in the electrical resistivity is observed in the AFM–FM transition range (T ≈ 200–250 K). This inflection point shifts in a magnetic field toward low temperatures. An unusually high (for cobaltites) magnetoresistance

$$\begin{gathered} {\text{M}}{{{\text{R}}}_{0}} = [\rho (H = 15\,{\text{kOe}}) \\ \, - \rho (H = 0)]{\text{/}}\rho (H = 0) \approx - 12\% \\ \end{gathered} $$

is observed in the same temperature range (Fig. 3, bottom insets). Analogous behavior of ρ(T) and MR₀ was detected in GdBaCo₂O_5.5 [4, 26]. These results are explained by the fact that the carrier mobility in the AFM state is lower than that in the FM state and that a magnetic field widens the temperature range of the FM state toward low temperatures and narrows the range of the AFM state [4]. Below T ≈ T_C ≈ 280 K, the linear dependence lnρ ~ 1/T changes and ρ(T) decreases sharply; at T = 330–338 K, an electrical resistivity jump takes place, which is thought to be related to a change in the spin state of Co³⁺ (Fig. 3, top inset). Above T_MI ≈ 338 K, the electrical resistivity of the sample weakly depends on temperature, ρ ~ 2 × 10^–3 Ω cm (Fig. 3, top inset). The sign of the electrical resistivity derivative dρ/dT remains negative, which indicates a semiconductor character of ρ(T) in the temperature range up to 400 K.

Fig. 3.

(Color online) Temperature dependence of the electrical resistivity ρ(T) of a TbBaCo₂O_5.52 polycrystal. (top inset) ρ(T) near T_MI ~ 338 K. (bottom insets): (1) ρ(T) in the AFM–FM transition range at H = (solid line) 0 and (symbols) 15 kOe and (2) temperature dependence of the magnetoresistance at H = 15 kOe.

Figure 4 (left axis) shows the temperature dependence of the experimental PM susceptibility $\chi _{{\exp }}^{{ - 1}}$(T) of the TbBaCo₂O_5.52 sample measured in a magnetic field H = 10 kOe. The $\chi _{{\exp }}^{{ - 1}}$(T) dependence is linear in the range T = 500–350 K, a small jump is observed below T_MI ≈ 340 K, and the $\chi _{{\exp }}^{{ - 1}}$(T) is then obviously nonlinear. The value estimated according to the Curie–Weiss law (μ_eff/Co ≈ 7.55μ_B) is close to the data in [5] and is too high to be attributed to the spin state of Co³⁺. To separate the contribution of the Co³⁺ ions from the total magnetization of the sample, we used Eq. (5) to subtract the contribution of the Tb³⁺ ions and recalculated χ^–1(T) for the cobalt ions (Fig. 4, right axis). The contribution of the Tb³⁺ ions increases the values of χ^–1(T) in the metallic phase more than sixfold. In the temperature range 500–380 K, inverse susceptibility χ^–1(T) linearly depends on temperature. The nonlinear part of χ^–1(T) is observed below T ≈ 380 K: χ^–1(T) changes slowly down to T ≈ 350 K, χ^–1(T) jumps in the range T_MI ≈ 345–335 K, and χ^–1(T) decreases monotonically and nonlinearly when temperature decreases further. A similar change in the slope of χ^–1(T) near T_MI was detected in EuBaCo₂O_{5 + δ} crystals (see Fig. 2 in [1]). In the temperature range 500–380 K, the PM susceptibility is described by the Curie–Weiss law with a Néel temperature θ_N = ‒(155 ± 10 K) and μ_eff/Co = 3.28 ± 0.1μ_B; below T_MI in the narrow range 325–280 K, μ_eff/Co = 1.40 ± 0.05μ_B and θ_C = 283 ± 2 K are used (Fig. 4b; solid lines μ_eff and θ_C(θ_N)).

Fig. 4.

(Color online) (a): (1) Temperature dependence of the paramagnetic susceptibility $\chi _{{\exp }}^{{ - 1}}$(T) of a TbBaCo₂O_5.52 polycrystal (left axis) and (2) χ^–1(T) with subtracted contribution of the Tb³⁺ ion (right axis). (b) Temperature dependences of (solid line 1) effective moment μ_eff/Co and (solid line2) temperature θ_C(θ_N); (symbols and dashed line) differential values $\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$/Co and θ_C(θ_N).

No linear segment is detected in the χ^–1(T) dependence in the temperature range 380–280 K, which means that the transition is accompanied by changes in μ_eff(T) with temperature. To test this assumption, we separated linear segments in χ^–1(T) in the temperature range 300–400 K and determined the differential values of μ_eff and θ_C(θ_N) by the Curie–Weiss law for each segment. The symbols in Fig. 4b show the temperature dependences of the differential values of $\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$ and θ_C(θ_N) thus determined. The MI transition is seen to occur over a wide temperature range (280–380 K): from the maximum (μ_eff/Co = 3.28 ± 0.10μ_B) at T = 500–380 K to the minimum ($\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$/Co ≈ 0.5μ_B) at T_MI ≈ 340 K upon an increase to $\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$/Co ≈ 1.6μ_B at T ~ 280 K. The behavior of θ_C(T) is analogous: θ_C increases gradually from θ_N ≈ –150 K to θ_C ~ +320 K in the range T ≈ 400–340 K and then decreases weakly to θ_C ≈ +280 K. The values of μ_eff and $\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$ coincide in the range of the linear behavior of χ^–1(T).

In the metallic state (T = 400–500 K), the value μ_eff/Co ≈ 3.28 ± 0.10μ_B corresponds best of all to a mixture of the HS($t_{{2g}}^{4}$$e_{g}^{2}$, S = 2) and LS($t_{{2g}}^{6}$$e_{g}^{0}$, S = 0) states with μ_eff/Co = 3.43μ_B taken at the proportion 1 : 1 among all possible states of the Co³⁺ ions (Fig. 4b). Below T_MI near T_C (T = 280–325 K), the value μ_eff/Co = 1.40 ± 0.05μ_B means that only up to one-fourth of the Co³⁺ ions are in the IS($t_{{2g}}^{5}$$e_{g}^{1}$, S = 1) state and the remaining ions are in the LS state. The predominance of the fraction of the LS state near T_MI in TbBaCo₂O_5.5 was also detected in [15]. The X-ray and neutron diffraction studies [6, 27] also predicted the existence of an LS/IS state of the Co³⁺ ions below T_MI.

Our magnetic data did not allow us to determine the type of oxygen environment of the Co³⁺ ions. The structural investigations [27] of TbBaCo₂O_5.5 revealed an increase in the oxygen–cobalt bond length d(Co–O) in the octahedra and a decrease in this length in the pyramids in the metallic phase, which can be interpreted as an increase in the ionic radius of Co³⁺ in the octahedra and its decrease in the pyramids. Based on our magnetic data and the structural data in [27], we conclude that the transition into a nonmetallic state is caused by the transition of the HS state into the LS state in the octahedra, as in GdBaCo₂O_5.5 [26]. In the pyramids, only part (about one-fourth) of the Co³⁺ ions transform from the LS to the IS state, and the remaining ions are still in the LS state (at T ≈ T_C).

A mixture of Co³⁺ ions with an approximately identical proportion of the IS and LS states is assumed to exist in GdBaCo₂O_5.5 below T_MI [1, 2, 4, 7, 13]. This is partly true: this assumption is likely to be correct for temperatures T ≪ T_MI [3, 10]. The spontaneous magnetization of GdBaCo₂O_5.5 without a twinned structure that was determined by extrapolation of the magnetization from high fields increases gradually upon cooling from M_S ~ 0.3μ_B/Co at T = T_C ≈ 280 K to M_S ~ 0.6μ_B/Co at T ≈ 200 K (see Figs. 22 and 24 in [3]). At T = 1.8 K, it reaches M_S ~ 1μ_B/Co in a magnetic field higher than 300 kOe, which corresponds to the ratio 1 : 1 of the LS/IS states of Co³⁺ at T → 0 [10]. Upon cooling below T_C ≈ 270 K, the spontaneous magnetization of GdBaCo₂O_5.5 with a twinned structure increases gradually to M_S ~ 0.5μ_B/Co at T = 78 K (see Fig. 3 in [10]). Half of the IS (S = 1) spins is parallel to an applied field due to the twinned structure of the crystal and the other half is opposite the field, which leads to the saturation moment M_S ~ 0.5μ_B/Co [3, 10].

As is seen in the inset to Fig. 1, the spontaneous magnetization increases gradually from M_S ~ 0.11μ_B/Co at T = T_C ≈ 280 K to M_S ~ 0.23μ_B/Co at T ≈ 260 K. Actually, M_S ~ 0.11μ_B/Co at T = 280 K corresponds to the LS/IS state of the Co³⁺ ions at the ratio 0.7 : 0.3 for T ≈ 280 K, which was obtained above from fitting χ^–1(T) by the Curie–Weiss law. However, the maximum value (M_S ~ 0.45μ_B/Co) is significantly lower than the expected value (about 1μ_B/Co) for the LS/IS state at the ratio 1 : 1 because of the twinned and noncollinear FM structure of the TbBaCo₂O_5.52 crystal.

Therefore, the spin state of Co³⁺ as a function of the type of rare-earth ion R³⁺ is of interest. Using the well-known results on the PM susceptibility of the RBaCo₂O_5.5 (R = Pr, Nd, Sm, Gd, Tb, Dy, Ho) cobaltites [1, 2, 7, 11–14], we estimated possible spin states of the Co³⁺ ions near the MI transition with allowance for the PM contribution of the R³⁺ ions. For simplicity, the PM contribution was assumed to coincide with the contribution of a free R³⁺ ion [3]. Using these estimates, we can assume that the Co³⁺ ions in all these cobaltites below T_MI are in an IS/LS state. The Co³⁺ ions in the metallic phase in all cobaltites except for those with R = Ho and Pr are in an HS/LS state.²

Anomalous lattice expansion is detected along with the spin transition (Fig. 5). The thermal expansion was measured on a TbBaCo_1.96O_{5 + δ} single crystal along three directions in a 3 × 3 × 2.5 mm³ parallelepiped. One parallelepiped axis is perpendicular to axis c and coincides with the [120] growth direction, and two other axes are directed along axis c.

Fig. 5.

(Color online) Temperature dependence of the volumetric expansion ΔV/V of a TbBaCo₂O_{5 + δ} single crystal. (insets) Temperature dependences of the linear expansion ΔL/L (along and across axis c, upon heating and cooling) at T_MI and linear thermal expansion coefficient α(T) along the [120] direction.

The symbols in Fig. 5 show the temperature dependence of the volumetric expansion ΔV/V near T ≈ T_MI ± 100 K. The volumetric expansion coefficient α_V(T) = 1/V ⋅ dV/dT in the metallic phase (400–500 K) is higher than that in the dielectric phase (T < T_C), 3.9 × 10^–5 and 3.2 × 10^–5 K^–1, respectively. The deviations of ΔV/V(T) from the linear dependence of the lattice (solid lines) take place at T ≈ T_MI ± 40 K and are indicated by arrows. The nonmonotonic (S-like) change in the lattice volume ΔV/V(T) at the transition range is noteworthy: the lattice volume decreases upon heating above T ≈ 300 K, increases sharply at T ≈ T_MI ± 10 K, and then again decreases. The linear expansion ΔL/L(T) near T_MI also exhibits nonmonotonic (S-like) behavior (Fig. 5, top inset). An analogy between ΔV/V(T) and $\mu _{{{\text{eff}}}}^{{{\text{diff}}}}$(T) in Fig. 4b is visible. The results of thermal expansion are likely to reflect the fact of different temperature changes in the spin states of the Co³⁺ ions in different polyhedra near the MI transition. The linear expansion ΔL/L(T) has an anisotropic character (Fig. 5, left inset). During the transition into the metallic state, the lattice expands along axis c and is compressed along [120] normal to axis c. The lattice expansion ΔL/L(T) along axis c, the lattice compression normal to axis c, and the increase in the volume ΔV/V during the transition into the metallic phase agree qualitatively with the neutron diffraction data in [5, 6]. The linear and volumetric expansion curves plotted upon heating and cooling exhibit hysteretic behavior, supporting the fact that the MI transformation is a first-order phase transition.

The temperature dependence of the linear thermal expansion coefficient α(T) = 1/L ⋅ dL/dT of TbBaCo_1.96O_{5 + δ} has a well-pronounced peak at T = T_MI ≈ 338–340 K and a weak anomaly at T_N ≈ 190 K (Fig. 5, bottom inset). A good correlation between the linear thermal expansion coefficient α(T) and the effective magnetic moment μ_eff(T) is clearly visible (Fig. 4b). Coefficient α(T) deviates from the linear temperature dependence (solid lines) induced by thermal lattice expansion in the range T ≈ 380–290 K, i.e., the temperature range of changing the spin state of Co³⁺.

The α(T) anomaly at T_N ≈ 190 K is smaller than α(T) at T_MI by almost two orders of magnitude, which excludes the possibility of its explanation by changing the spin state of the Co³⁺ ions near this temperature. Allowing for the magnetic data (Fig. 1), we assume that this anomaly can be caused by magnetostriction phenomena during the transition from a canted FM state to a noncollinear AFM state. The thermal expansion of TbBaCo_1.96O_{5 + δ} confirms the retention of the LS/IS state of the Co³⁺ ions at low temperatures down to at least T = 80 K.

Extrapolating the thermal expansion of nickel below and above the transition temperature, we estimated the increase in the unit cell volume during the MI transition at ΔV/V ≈ 2 × 10^–4 at T_MI. Approximately the same value of ΔV/V was obtained for a GdBaCo₂O_5.5 polycrystal [36]. Volume increment ΔV/V near T_MI demonstrates that the transition into a metallic state is accompanied by an increase in the spin state of the Co³⁺ ions. The results of studying the thermal expansion of a TbBaCo_1.96O_{5 + δ} single crystal support the fact that the spin state of Co³⁺ changes over a wide temperature range T ≈ T_MI ± (40–50) K. The physical properties, such as ρ(T) (Fig. 3), χ^–1(T) (Fig. 4), α(T), ΔL/L, and ΔV/V (Fig. 5), change sharply only in a narrow temperature range T = T_MI ± 10 K, where χ^–1(T) and μ_eff change jumpwise.

CONCLUSIONS

Magnetic and structural investigations are the main methods for determining the spin state of the Co³⁺ ions in the layered RBaCo₂O_5.5 cobaltites near the MI transition. However, unambiguous conclusions regarding the spin state of the Co³⁺ ions cannot always be drawn using the results of these investigations, which is mainly caused by the fact that conclusions were usually based on the magnetic data that incorrectly took into account the PM contribution of the R³⁺ ions. In this work, we studied the magnetization of TbBaCo₂O_5.5 over a wide temperature range and found that the PM contribution of the Tb³⁺ ions was determined by the Curie–Weiss law with the parameters of a free Tb³⁺ ion at θ_PM = –8 ± 2 K. The spin states of the Co³⁺ ions in TbBaCo₂O_5.5 and GdBaCo₂O_5.5 were found to be identical with allowance for the PM contribution of the Tb³⁺ ions. The Co³⁺ ions are in an HS/LS state above T_MI and in an LS/IS state below T_MI. The transition into a metallic state takes place when the Co³⁺ ions in the octahedra transform from the LS to the HS state and the Co³⁺ ions in the pyramids transform from the IS to the LS state, according to the structural data indicating expansion of the octahedra and compression of the pyramids. As follows form the data obtained for volumetric and linear expansion, the MI transition occurs over a wide temperature range T ≈ T_MI ± (40–50) K when the spins state of the Co³⁺ changes. The hysteretic behavior of the volumetric and linear expansion demonstrates that the MI transition in the compound under study is a first-order phase transition. Thermal expansion data indicate that the LS/IS state of the Co³⁺ ions is retained down to T = 80 K.

NOTE ADDED IN PROOF (FEBRUARY 13, 2020)

In conclusion, we note that the authors of [5, 12, 37, 38] considered the role of orbital ordering in the metal–insulator transition in layered cobaltites. Neutron diffraction of TbBaCo₂O_5 + δ at δ = 0.5 [37] and X‑ray diffraction of GdBaCo₂O_5.5 [38] demonstrate that the spin states of the Co³⁺ ions differ in the low-temperature phase and they are located in two different octahedra and two different pyramids because of orbital ordering. It is assumed that, in the low-temperature TbBaCo₂O_5 + δ at δ = 0.5 and T = 260 K, the Co³⁺ ions in octahedra are in the LS state and half the ions in pyramids is in the HS state and the other half is in the LS state [37]. The increase in μ_eff/Co approximately from 0.5μ_B to 1.5μ_B when temperature decreases from T_MI to T_C in both TbBaCo₂O_5 + δ at δ ≈ 0.5 (see Fig. 4) and GdBaCo₂O_5 + δ at δ ≈ 0.5 (see Fig. 5 in [26]) is thought to be caused by an increase in the fraction of the IS state from a few percent to 20–25% in the IS/LS state of the pyramids. The same μ_eff/Co(T) results could also be interpreted as an increase in the fraction of HS in the HS/LS state of the pyramids; the only difference is that the fraction of HS states would be approximately half as much. In the orbital ordering model approximation, the transition into the low-temperature insulator state occurs from the HS into the LS state of the Co³⁺ ions in octahedra. In pyramids, half the Co³⁺ ions is retained in the LS state and the other half should transform into the HS state. This model is in conflict with our data and the well-known data [15] on measuring the paramagnetic susceptibility, since the effective moment in the low-temperature phase should be twice as large, about μ_eff/Co ≈ 2.5μ_B. On the other hand, the authors of [15] state that the magnetic moment per Co³⁺ ion increases from 1.22μ_B to 2.8μ_B when the magnetic field increases from 1 to 50 kOe. The substantiation of the proposed model and, in particular, the presence of the HS state in the low-temperature phase need additional investigations.