Electron Paramagnetic Resonance of Cr³⁺ Ions in ABO₃ (A = Sc, In, Ga) Diamagnetic Crystals

Abstract

A magnetic resonance method is applied to the investigation of a number of isostructural diamagnetic compounds ABO₃ (A = Sc, In, and Ga) with small additions of Cr³⁺ ions (S = 3/2) sufficient to observe single-ion and pair spectra. It is shown that the resonance spectra for isolated Cr³⁺ ions can be described to a good accuracy by the ordinary axial spin Hamiltonian for 3d ions in octahedral oxygen environment. The parameters of the spin Hamiltonian are determined for single Cr³⁺ ion and Cr³⁺–Cr³⁺ pair. Lattice distorsions of the parent ABO₃ crystals caused by the Cr³⁺ impurities is discussed.

1 INTRODUCTION

Borates of transition metals with chemical formula ABO₃ (A = Fe, V, Cr, Ti) have attracted attention because of the variety of their physical properties that are manifested in this isostructural series of compounds [1]. However, a number of borates of 3d metals ABO₃, except for FeBO₃, remain poorly studied. For example, from among the whole series of 3d borates, magnetic anisotropy has been experimentally investigated to date only in FeBO₃ [2]. In the present study, we apply the electron paramagnetic resonance method to the experimental investigation of the anisotropic properties of Cr³⁺ ions in diamagnetic matrices of isostructural compounds of ABO₃ (A = Sc, In, Ga) borates. In this case, a Cr³⁺ ion was chosen due to the unusual magnetic properties of the isostructural crystal CrBO₃ [3]. For example, in [4] the authors showed that the magnetic properties of the CrBO₃ crystal can be described on the basis of a simple model of a collinear two-sublattice antiferromagnet with magnetic moments along a [111] axis. The authors of [3] suggested, on the basis of static magnetic measurements, that it is more probable that, on the contrary, the antiferromagnetism vector of CrBO₃ lies in a plane close to the base plane.

The present paper is the continuation of the investigations presented by us in [5]. In [5] only single ion spectra for A = In, Sc, and Lu were discussed and was pointed out the presence of a Cr³⁺–Cr³⁺ pair spectra. In this paper we present the new data of the Electron Spin Resonance (ESR) spectra of single Cr³⁺ ions in diamagnetic matrix GaBO₃ and pair spectra of Cr³⁺–Cr³⁺ ions were treated and discussed for A = Sc, In, Ga compounds.

2 MATERIALS AND METHODS

ABO₃ (A = Sc, In, Ga) crystals with small (about 5 at % of A) addition of Cr³⁺ ions were grown from the solution-melt with composition Cr₂O₃–M₂O₃–B₂O₃–(70PbO–30PbF₂ wt %). The detailed synthesis technology is described in [6]. In this technology, a Cr³⁺ ions substitute the A ions. We obtained single crystals in the form of thin plates with a size of 2 × 2 mm and thickness of about 0.1 mm with a smooth shining surface of light gray color. ABO₃ (A = Sc, In, Ga) isostructural crystals have a rhombohedral symmetry in space group R$\bar {3}$c, the point group symmetry of the A ion is (–3m). Parameters of the unit cell were determined by using X-ray Smart APEX II (Bruker) (Mo K_α radiation) installation at room temperature and are presented in Table 1 for Sc, In, Ga.

Table 1. Unit cell parameters of ABO₃ crystals

The C₃-axis of the crystal is normal to sample plate (the c-axis in Fig. 1). The A ions are located in the octahedrons formed by oxygen ions connected with boron ions by a strong covalent bond.

Fig. 1.

(Color online) Crystal structure of ABO₃.

In addition, there is a possibility for nearest Cr³⁺ ions to form a magnetically coupled pairs. The projection of the pair’s axes onto basal plane of the crystal is presented in Fig. 2. All pairs are magnetically equivalent. The Cr³⁺–Cr³⁺ distances and angles between C₃ axis of the crystal and pair axes are shown in Table 1.

Fig. 2.

(Color online) Projection of the axes of Cr³⁺ ions pairs onto basal plane of the crystal. Only Cr³⁺ ions are shown.

The electron paramagnetic resonance measurements were carried out on a Bruker Elexsys E-580 spectrometer operating at X-band at temperatures 300 and 77 K.

3 RESULTS

3.1 Single-Ion Spectra

In this chapter we present the experimental results for the single ion ESR spectra of Cr³⁺ ions obtained in ABO₃ (Sc, In, Ga) compounds. So far this paper is the continuation of the investigations presented by us in [5], let us consider more detailed only experimental data for the GaBO₃ crystal, that was not discussed previously.

The angular dependence of the resonance fields of the single Cr³⁺ ions transitions observed in the (ac) plane are shown in Fig. 3. The resonance spectra for isolated ions of Cr³⁺ can be described by the following axial spin Hamiltonian for 3d ions:

$$H = - {{g}_{{||}}}\beta {{H}_{z}}{{S}_{z}} - {{g}_{ \bot }}\beta ({{H}_{x}}{{S}_{x}} + {{H}_{y}}{{S}_{y}}) + DS_{z}^{2},$$

((1))

where D is the axial constant of the spin Hamiltonian, g_|| and g_⊥ are the values of the g-tensor for parallel and perpendicular orientations of the external magnetic field with respect to the C₃ axis of the crystal, β is the Bohr magneton, S_i and H_i are the projections of the spin of a Cr³⁺ ion and the external magnetic field to the C₃ axis of the crystal, and S = 3/2 is the spin of the Cr³⁺ ion. The experimental and theoretical spectra were fitted with the use of the XSophe software [8]. The results are presented in Table 2.

Fig. 3.

(Color online) Angular dependence of resonance fields of the ESR signals observed in GaBO₃ (ac) plane of the crystal. Dots represent experiment and solid curves—calculation (see Table 2).

Table 2. Parameters of the spin Hamiltonian (1) for an isolated Cr³⁺ ion in the ABO₃ matrix at room temperature

The values of the g-tensor obtained are nearly isotropic and correspond to appropriate values for d³ ions in the octahedral environment [9]. The spin-Hamiltonian constant D correlates with those in the earlier investigated compounds Al₂O₃ [10] and ZnGa₂O₄ [11, 12], in which the Cr³⁺ ion is also in an octahedral coordination. The D sign for Cr³⁺ ion in GaBO₃ was determined by comparison of the resonance lines intensities of M_S = 1/2 ↔ 3/2 and M_S = –1/2 ↔ –3/2 transitions at 300 and 77 K respectively as in [5].

As an example, Fig. 4 demonstrates the calculated schemes of energy levels of the Cr³⁺ ion in GaBO₃.

Fig. 4.

(Color online) Calculated schemes of energy levels of a Cr³⁺ ion in GaBO₃; (a) external magnetic field is parallel to the base plane of the crystal, and (b) external magnetic field is parallel to the C₃ axis.

3.2 Pair Spectra

In compounds with A = Sc, In, Ga the Cr³⁺–Cr³⁺ pair spectra were observed. The example of the pair spectra for ScBO₃ at room temperature is presented in Fig. 5. The intense line in the right and left sides corresponds to the single ion transitions.

Fig. 5.

The example of the Cr³⁺–Cr³⁺ pair spectra for ScBO₃ at room temperature in basal plane of the crystal.

Cr³⁺–Cr³⁺ pair forms by the nearest neighbors with the distances r = 3.7424, 3.774, and 3.5459 Å for A = Sc, In, and Ga compounds respectively (see Table 1). The angle between pair axes and C₃ axis of the crystals is equal approximately θ ≈ 47° for all compounds. When two Cr³⁺ ions interact to form a magnetically coupled pair, the spins (s) on each ion combine as vectors to produce a manifold of four spin states each characterized by a total spin quantum number S, which value varies from (s₁ + s₂), (s₁ + s₂ – 1) … to 0. Assuming that the energy intervals between these spin states are large compared with the other magnetic interactions, a separate spin Hamiltonian may be written for each spin state. In our case, it was possible to identify resonance spectra for pair multiplets with total spin S = 2 and 3 only. The angle dependencies of the resonance fields of the signals in basal plane of the crystals are shown in Figs. 6–8.

Fig. 6.

(Color online) Angle dependencies of the resonance fields in basal plane of the crystals for ScBO₃ crystal at room temperature. Dots—experiment, solid lines—fitted curves by using of spin Hamiltonian (2) with parameters from Table 3.

Fitting of the experimental spectra were carried out with XSophe program [8] and the spin Hamiltonian (2).

$$\begin{gathered} H = - {{g}_{{||}}}\beta {{H}_{z}}{{S}_{z}} - {{g}_{ \bot }}\beta ({{H}_{x}}{{S}_{x}} + {{H}_{y}}{{S}_{y}}) + {{D}_{S}}S_{z}^{2} \\ \, + {{E}_{S}}(S_{x}^{2} - S_{y}^{2}) + 1{\text{/}}60[B_{4}^{0}O_{4}^{0} + B_{4}^{2}O_{4}^{2} + B_{4}^{4}O_{4}^{4}], \\ \end{gathered} $$

((2))

where g_|| and g_⊥ are the values of the g-tensor for parallel and perpendicular orientations of the external magnetic field with respect to the C₃ axis of the crystal, β is the Bohr magneton. Spin operators $O_{4}^{0}$, $O_{4}^{2}$, and $O_{4}^{4}$ are mentioned in [13]. Third and fourth terms in (2) describe the value of the “fine” structure for the total spin S of pair’s multiplet and have the form [13]

$${{D}_{S}} = (3{{\alpha }_{S}}{{D}_{e}} + {{\beta }_{S}}{{D}_{c}}),\quad {{E}_{S}} = ({{\alpha }_{S}}{{E}_{e}} + {{\beta }_{S}}{{E}_{c}}),$$

((3))

where D_e, E_e are the dipole-dipole interaction constants (assuming isotropic exchange interaction) in point approximation, D_c, E_c—“single ion” multiplet terms and

$$\begin{gathered} {{\alpha }_{S}} = \frac{1}{2}\frac{{S(S + 1) + 4{{s}_{i}}({{s}_{i}} + 1)}}{{(2S - 1)(2S + 3)}}, \\ {{\beta }_{S}} = \frac{{3S(S + 1) - 3 - 4{{s}_{i}}({{s}_{i}} + 1)}}{{(2S - 1)(2S + 3)}}. \\ \end{gathered} $$

((4))

The N ↔ J symbols in Figs. 6–8 denote transitions between corresponding M_S numbers in pair multiplets. Note, that the real experimental spectrum for each crystal consists from three identical spectra from Figs. 6–8 corresponding to Cr³⁺–Cr³⁺ pairs rotated by 60 degrees in basal plane (see Fig. 2).

Fig. 7.

(Color online) Angle dependencies of the resonance fields in basal plane of the crystals for InBO₃ crystal at room temperature. Dots—experiment, solid lines—fitted curves by using of spin Hamiltonian (2) with parameters from Table 3.

Fig. 8.

(Color online) Angle dependencies of the resonance fields in basal plane of the crystals for GaBO₃ crystal at room temperature. Dots—experiment, solid lines—fitted curves by using of spin Hamiltonian (2) with parameters from Table 3.

The best fitting spin-Hamiltonian (2) values are presented in Table 3.

Table 3. Spin-Hamiltonian (2) values (cm^–1) for the Cr³⁺–Cr³⁺ pairs in ABO₃ crystals. The numbers in parentheses are the estimated errors in the last decimal place of the reported parameters. g_|| = 1.980 and g_⊥ = 1.982 for all crystals

4 DISCUSSION

Let us, firstly, discuss the experimental results for Cr³⁺–Cr³⁺ pairs in ABO₃ crystals. The D_e term can be obtained directly from D_{S = 2} value (Eq. (3)) since there is no lattice contribution (β = 0 for S = 2 (Eq. (4))). For a pair system which exhibits a nearly isotropic g-tensor the anisotropic zero-field term D_e is almost entirely due to dipole–dipole interaction. If the paramagnetic ions which form the pair are treated as point dipoles, the value of D_e can be calculated from the following expression. D_e = –g²β²/R³ (where R is the interionic separation). From the D_e (for S = 2) values observed for the Cr³⁺–Cr³⁺ pairs in ABO₃ a distances can be calculated for separation between two Cr³⁺ ions. The results are presented in Table 4. Note, that Cr³⁺–Cr³⁺ distance in pure CrBO₃ crystal is equal to 3.5535 Å [14].

Table 4. D_e values for the Cr³⁺–Cr³⁺ pairs in ABO₃ crystals

In Table 4R_theor is the interionic A³⁺–A³⁺ separation X-ray data from Table 1, $D_{e}^{{{\text{theor}}}}$ = –g²β²/$R_{{{\text{theor}}}}^{3}$, $D_{{S = 2}}^{{{\text{theor}}}}$ = 3/2$D_{e}^{{{\text{theor}}}}$, R_exp are the interionic Cr³⁺–Cr³⁺ distance values calculated from $D_{{S = 2}}^{{{\text{exp}}}}$. From Table 4 one can see the lattice distortions caused by the impurity Cr³⁺–Cr³⁺ pairs in the parent ABO₃ lattice. Figure 9 presents these distortions vs. interionic separation of the crystals.

Fig. 9.

Lattice distortion of the crystal caused by the Cr³⁺–Cr³⁺ pair (see Table 4). Here R_A–A is the interionic A³⁺–A³⁺ distances from Table 1.

One can notice a tendency: the smaller the interionic A³⁺–A³⁺ distances, the stronger the distortions. Moreover, the sign of distortion is changing at A³⁺–A³⁺ distance approximately equal to 3.7 Å.

From the Eq. (3) the D_c values can be found also ($D_{{S = 2}}^{{{\text{exp}}}}$ value was used) (see Table 5).

Table 5. D_c values for the Cr³⁺–Cr³⁺ pairs in ABO₃ crystals

It is seen, that D_c values are close enough to the axial constants D of the spin-Hamiltonian (1) for the single Cr³⁺ ion in ABO₃ crystals except for the GaBO₃. The reasonable origin of this difference for the GaBO₃ crystal may be explained if we take into account the strong lattice distortion observed for Cr³⁺–Cr³⁺ pair in GaBO₃.

Figure 10 shows the dependencies of the pair spin-Hamiltonian (2) term D_s on Cr³⁺–Cr³⁺ distance, calculated in Table 4.

Fig. 10.

D_{S = 2}—closed circles and D_{S = 3}—open circles vs. calculated Cr³⁺–Cr³⁺ pair distance for ABO₃ (A = In, Sc, Ga) crystals. R_exp is the real Cr³⁺–Cr³⁺ distance, determined in Table 4.

Now, let us consider the axial constant D of the single ion spin-Hamiltonian (1). Assuming the model of the point dipole and considering only six nearest oxygen ions (forming octahedral environment of Cr³⁺ ion) it is possible roughly to estimate the electric field gradient (EFG) for Cr³⁺ site using the X-ray data (Table 1). Obviously, the EFG value substantially determines the D value. Figure 11 presents D and c/a dependencies on EFG for ABO₃ (A = Ga, In, Sc, Lu) crystals.

Fig. 11.

D—open circles (axial constant of the single ion spin Hamiltonian (1)) and c/a—closed circles (lattice parameters) vs. EFG in ABO₃ (A = Ga, In, Sc, Lu) crystals. The straight line is guide for eyes only for open circles (In, Sc, Lu).

The general trend is an increase in EFG as the c/a ratio increases. At the same way, the absolute value of the axial constant D increases with the EFG growing except for Cr³⁺ ion in GaBO₃. This fact may be explained if we assume that the strong lattice distorsion observed for Cr³⁺–Cr³⁺ pair in GaBO₃ (see Fig. 9 and Table 4) may be implemented for single Cr³⁺ ion in GaBO₃ too. In this case, the EFG value calculated from X-ray data (Table 1) may sufficiently differs from the real one.

5 CONCLUSIONS

Single ion and pair spectra of Cr³⁺ ions in ABO₃ (A = Sc, In, Ga) diamagnetic crystals were explored by using electron paramagnetic resonance technique. Spin-Hamiltonian values for single ions and Cr³⁺–Cr³⁺ pairs at room temperature were determined. The lattice distortions of the parent ABO₃ (A = Sc, In, Ga), caused by Cr³⁺ impurity were discussed. This work will be prolonged by the pair’s resonance line intensities vs. temperature investigation in order to determine the signs and the values of the Cr³⁺–Cr³⁺ exchange integrals J.