Magnetoelectric and magnetoelastic properties of easy-plane ferroborates with a small ionic radius

The magnetic, magnetoelectric, and magnetoelastic properties of RFe₃(BO₃)₄ ferroborates are studied. The measurement of the field dependences of the magnetoelectric polarization along the a axis in holmium ferroborate and in the mixed composition Ho_0.5Sm_0.5Fe₃(BO₃)₄ revealed the following dependences for easy-plane ferroborates: (a) the longitudinal and transverse magnetoelectric effects have the opposite signs and (b) magnetically induced polarization changes its sign in a field close to the field of exchange between rare-earth and iron ions. These dependences agree well with theoretical predictions based on the symmetry of the compounds. The relatively low f-d exchange field in holmium ferroborate (about 20 kOe), which magnetizes the rare-earth subsystem, causes smaller polarization jumps (about 30 ??C/m²) in fields lower than 10 kOe as compared to the jumps in other easy-plane ferroborates (R = Sm, Nd). The increase in the electric polarization induced in HoFe₃(BO₃)₄ in magnetic fields higher than 100 kOe (200?C300 ??C/m²) is found to be significantly smaller than in neodymium ferroborate, which indicates a substantial dependence of the magnetoelectric effects on the electronic structure of a rare-earth ion.     

Magnetostriction in the rare-earth ferroborates RFe3(BO3)4, R=Pr and Tb

Recent experimental data for magnetostriction in the rare-earth (RE) ferroborates RFe₃(BO₃)₄ with R=Pr and Tb are discussed from a theoretical point of view. Multipole moments of RE ions are calculated in the framework of a crystal-field model for the RE ion and the molecular-field approximation. Quadrupole approximation is shown to be sufficient for interpretation of data for longitudinal magnetostriction at the magnetic field along the trigonal axis. Parameters of PrFe₃(BO₃)₄ are deduced when accounting for the experimental magnetization curves that manifest a spin-flop transition.     

Antiferromagnetic resonance and dielectric properties of rare-earth ferroborates in the submillimeter frequency range

The magnetoresonance and dielectric properties of a number of crystals of a new family of multiferroics, namely, rare-earth ferroborates RFe₃(BO₃)₄ (R = Y, Eu, Pr, Tb, Tb_0.25Er_0.75), are studied in the sub-millimeter frequency range (ν = 3–20 cm⁻¹). Ferroborates with R = Y, Tb, and Eu exhibit permittivity jumps at temperatures of 375, 198, and 58 K, respectively, which are caused by the R32 → P3₁21 phase transition. Antiferromagnetic resonance (AFMR) modes in the subsystem of Fe³⁺ ions are detected in the range of anti-ferromagnetic ordering (T < T _N = 30–40 K) in all ferroborates that have either an easy-plane (Y, Eu) or easy-axis (Pr, Tb, Tb_0.25Er_0.75) magnetic structure. The AFMR frequencies are found to depend strongly on the magnetic anisotropy of a rare-earth ion and its exchange interaction with the Fe subsystem, which determine the type of magnetic structure and the sign and magnitude of an effective anisotropy constant. The basic parameters of the magnetic interactions in these ferroborates are found, and the magnetoelectric contribution to AFMR is analyzed.     

Contribution of the multipole polarization to the elastic constants in fluorite structure crystals

Numerical calculations are presented for the contribution of the multipole polarization to the elastic constants in fluorite structure crystals. The multipole polarizability is calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The elastic constants are significantly affected by the multipole polarization of the ions. The contributions of the multipole polarization of the ions to the elastic constant C₁₁, C₁₂, and C₄₄ are about 25%, 40% and 20% of the experimental values, respectively. The calculated values of the deviation from the Cauchy relation are in good agreement with the experimental values.     

Effect of a Rare-Earth Ion on the Structural Instability in RFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> Crystals

The dynamics of the crystal lattice of RFe₃(BO₃)₄ (R = Pr, Nd, Sm, Gd, Tb, Dy, and Ho) compounds in the high-symmetry R32 phase has been calculated. Significant changes in spectra of compounds with various rare-earth ions have been obtained only near the edge Λ point of the Brillouin zone (qΛ = 1/3(?2b₁ + b₂ + b₃, where b₁, b₂, and b₃ are the reciprocal lattice vectors) for acoustic oscillation branches. A decrease in the frequency of an acoustic mode at the point Λ has been revealed in all studied compounds. This frequency depends on the type of rare-earth ion and decreases from a compound with Pr to a compound with Ho down to imaginary values. Such a behavior of the frequency of the unstable acoustic mode is in good agreement with experimental data on the dependence of the temperature of the R32 → P3₁21 structural phase transition on the type of rare-earth ion in ferroborates.     

Influence of the ground state of the Pr<Superscript>3+</Superscript> ion on magnetic and magnetoelectric properties of the PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe₃(BO₃)₄ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below T _N = 32 K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial (l ∥ c), while, in a strong magnetic field H ∥ c (H _cr ～ 43 kOe at T = 4.2 K), a Fe³⁺ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an H-T phase diagram. The contribution of the Pr³⁺ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.     

Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

EPR of Er3+, Nd3+, and Ce3+ ions in YAlO3 single crystals

EPR spectra of the Er³⁺, Nd³⁺, and Ce³⁺ ions substituting for the Y³⁺ ion in the YAlO₃ yttrium orthoaluminate lattice are studied. The EPR spectra of these rare-earth ions are described by a spin Hamiltonian of rhombic symmetry with an effective spin S=1/2. The principal values of the g tensors were determined from an analysis of the angular dependences of the EPR spectra. The orientation of the local magnetic axes of paramagnetic centers relative to the YAlO₃ crystallographic directions are shown to depend on the actual rare-earth species. The EPR spectra exhibit a hyperfine structure due to the ¹⁶⁷Er, ¹⁴³Nd, and ¹⁴⁵Nd odd isotopes, which permitted unambiguous identification of these spectra. The hyperfine coupling constants for the odd erbium and neodymium isotopes are determined.     

Interaction between the magnetic moments of the 3d and the 4f electrons in manganite, probed by Ga substitution

The substitution of Ga for Mn in manganite Nd_0.6Dy_0.1Sr_0.3MnO₃ with a ferromagnetic (FM) ground state has been performed to study the influence of the Mn-sublattice magnetic ordering on the magnetic rare-earth sublattice. It is found that the substitution of Mn³⁺ with Ga³⁺ ions results in a sharp decrease of T_C, reflecting the reduction of the double-exchange interactions strength J_Mn-Mn. At the same time, a depinning effect of the rare-earth magnetic moment has been observed. This behavior unambiguously proves that the exchange interaction between Mn and rare-earth ions J_Mn-R strongly influences the rare-earth magnetic ordering at temperatures below T_C and stabilizes the rare-earth magnetic ground state.     

Crystal field effect on the magnetic moment's direction of rare earth ions with low point symmetry in r4co3 (r = Tb, Ho, Dy, Er, Tm) compounds

Neutron diffraction measurements, made on powder samples, show that Ho₄Co₃ and Er₄Co₃ intermetallic compounds are ferrimagnetic at 4.2 K. The magnetic moments of the 2 holmium sites are 8.7 and 2.1 μ_B and those of the erbium sites are equal to 8.7 and 8.1μ_B. The cobal⁺ magnetic moment is 0.2μ_B for both compounds. The easy magnetization direction lies on the hexagonal plane for Ho₄Co₃ while for Er₄Co₃ there are 2 anisotropy directions. Exchange interactions between rare-earth ions of both sites are very weak compared with the total crystal field splitting of the ground state multiplet J. The crystal field parameters are calculated and the magnitude and direction of the rare-earth magnetic moments in each site is determined.     

The magnetoelastic contribution to thermal expansion of rare-earth metal scheelites RLiF<Subscript>4</Subscript> (R = Tb-Yb)

The paper presents systematic experimental and theoretical studies of thermal expansion for rare-earth metal scheelites RLiF₄ (R = Tb-Ho, Tm, and Lu). Pronounced thermal expansion anomalies were observed. The magnetoelastic contributions were determined taking into account corrections for changes in the phonon contribution in the RLiF₄ series according to the Debye thermal expansion model. The calculated multipole moments of various orders for various rare-earth metal ions were compared to analyze the applicability of the quadrupole approximation to totally symmetric modes in the scheelite structure. For some ions (Ho and Tm), the magnetoelastic contributions to thermal expansion could not be described by the temperature dependences of their quadrupole moments, that is, multipole moments made considerable contributions. The totally symmetric magnetoelastic coefficients for the scheelite structure were determined from the experimental data on magnetoelastic contributions. These coefficients were compared with those for the zircon structure.     

Crystal fields of hexameric rare-earth clusters in fluorites

In solid solutions of alkaline-and rare-earth fluorides with a fluorite structure, ions of most elements of the rare-earth (RE) row form hexameric clusters that assimilate the minor component of the solid solutions (fluorine) and build it into the cubic fluorite lattice without changing its shape. An analysis of the EPR spectra of paramagnetic RE ions (Er³⁺, Tm³⁺, Yb³⁺) in clusters of diamagnetic ions (Lu³⁺, Y³⁺) confirms their hexagonal structure, which was established when studying the superstructures of the compounds under study. In such a cluster, a RE ion is in a nearly tetragonal crystal field, with the parameters of this field differing radically from those of single cubic and tetragonal RE centers in crystals with a fluorite structure. In particular, this field causes high (close to limiting) values of the g_∥ factors of the ground states of the paramagnetic RE ions. Computer simulation is used to determine the atomic structure of a hexameric cluster in MF₂ crystals (M = Ca, Sr, Ba). The crystal field and energy spectrum of Er³⁺, Tm³⁺, and Yb³⁺ ions in such clusters are calculated, and the spectroscopic parameters of the ground states of these ions are determined. The calculations confirm the earlier assumption that the unusual EPR spectra of nonstoichiometric fluorite phases are related to RE ions in hexameric clusters.     

Intensity of the <Emphasis Type="Italic">f-f</Emphasis> transitions of Nd<Superscript>3+</Superscript>, Er<Superscript>3+</Superscript>, and Tm<Superscript>3+</Superscript> rare-earth ions in calcium niobium gallium garnet crystals

This paper reports on the results of the investigation into the intensities of the f-f transitions of Nd³⁺, Er³⁺, and Tm³⁺ ions in calcium niobium gallium garnet (CNGG) crystals. The values of the oscillator strengths and line strengths obtained for hypersensitive transitions and the intensity parameters Ω _t of the rare-earth ions in the CNGG crystals are compared with the corresponding quantities for crystals of other garnets and some oxide and fluoride crystals. The assumption is made that an increase in the oscillator strengths and line strengths for the hypersensitive transitions and the intensity parameters Ω₂ of the Nd, Er, and Tm ions in the CNGG crystals as compared to those for crystals of other garnets is associated with the specific features revealed in the crystal structure of the calcium niobium gallium garnet, in particular, with the lowering of the symmetry of the positions occupied by rare-earth ions in the crystal structure.     

Magnetic structure of geometrically frustrated compound Co2Cl(OH)3 determined by proton NMR

The magnetic structure of a geometrically frustrated system Co₂Cl(OH)₃ is determined by comparing the observed proton NMR spectrum with numerical calculations based on various magnetic models. The best fit is obtained with a model that the magnetic moments of Co²⁺ ions in the triangular plane are parallel to the principal axis of local crystal field and those of Co²⁺ ions in the kagome lattice plane are randomly disordered in the a-b plane, which nearly bisects the angle between the principal axis of the local field and a line pointing towards the body center of the tetrahedron. The coexistence of the ferromagnetic order in the triangular plane and the random disorder in the kagome plane is consistent with the results of measurements by Zheng et al. However, the magnetic moments of Co²⁺ ions are not directed towards the body center of the tetrahedron as characteristic in the “spin ice” magnetic structure. Furthermore, the Co²⁺ ions in the triangular plane have a smaller magnitude of magnetic moment than those in the kagome plane. Thus, our result suggests that the transition metal compound Co₂Cl(OH)₃ is different from the “spin ice” in magnetic structure, although it is similar to rare-earth pyrochlores in crystal structure.     

On the crystalline field of rare-earth ions in the cubic intermetallic compound: YSb

Resolved fine structure spliting of Gd in YSb yields a fourth order crystalline field parameter b₄ = (29±3)G. A correlation between b₄ and the crystalline field experienced by other rare-earth ions in the same host is demonstrated.     

EPR of Yb3+ ions in Ba1−xLaxF2+x mixed crystals

Electron paramagnetic resonance (EPR) spectra of impurity Yb³⁺ ions (about 0.1 at.%) in mixed crystals BaF₂(1-x) plus LaF₃(x) have been investigated for different values of the concentrationx at a frequency of about 9.5 GHz by both continuous-wave (CW) EPR and electron spin echo methods. A spectrum of trigonal symmetry with a complex hyperfine structure is observed in “pure” BaF₂:Yb³⁺ (x=0). Upon admixture of small amounts of LaF₃ (x=0.001), additional EPR lines arise with intensities increasing with the increase ofx up to 0.005. These lines are attributed to trigonal centers including two rare-earth ions and two compensating fluorine ions. A further increase ofx results in a decrease of the total EPR spectrum intensity, and atx≥0.05 the CW resonance becomes practically unobservable. This may be due to the formation of rare-earth ion clusters with paramagnetic Yb³⁺ ions occurring in domains with a disordered structure of surroundings resulting in very broad EPR lines, which cannot be registered by CW EPR. Indeed, very broad (not less than 1 KG) EPR lines were observed by the electron spin echo method for concentrationsx<-0.02.     

Magnetic and thermal properties of single-crystal NdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The neodymium ferroborate NdFe₃(BO₃)₄ undergoes an antiferromagnetic transition at T _N = 30 K, which manifests itself as a λ-type anomaly in the temperature dependence of the specific heat C and as inflection points in the temperature dependences of the magnetic susceptibility χ measured at various directions of an applied magnetic field with respect to the crystallographic axes of the sample. Magnetic ordering occurs only in the subsystem of Fe³⁺ ions, whereas the subsystem of Nd³⁺ ions remains polarized by the magnetic field of the iron subsystem. A change in the population of the levels of the ground Kramers doublet of neodymium ions manifests itself as Schottky-type anomalies in the C(T) and χ(T) dependences at low temperatures. At low temperatures, the magnetic properties of single-crystal NdFe₃(BO₃)₄ are substantially anisotropic, which is determined by the anisotropic contribution of the rare-earth subsystem to the magnetization. The experimental data obtained are used to propose a model for the magnetic structure of NdFe₃(BO₃)₄.     

Magnetization,magnetoelectric polarization,and specific heat of HoGa3(BO3)4

A comprehensive experimental and theoretical study of magnetic, magnetoelectric, thermal, and spectroscopic characteristics of HoGa₃(BO₃)₄ gallium borate single crystals has been performed. A large magnetoelectric effect exceeding its values found in all iron and aluminum borates except HoAl₃(BO₃)₄ has been observed. The magnetoelectric polarization of HoGa₃(BO₃)₄ equals ΔP _ba (B _a ) ≈ ?1020 μC/m² at T = 5 K in a magnetic field of 9 T. The theoretical treatment based on the crystal field model for rare-earth ions provides a unified approach for the consistent interpretation of all measured characteristics. The crystal-field parameters are determined. The temperature (in the 3–300 K range) and magnetic field (up to 9 T) dependences of the magnetization, the Schottky anomaly in the temperature dependence of the specific heat, and its shift in the field B ‖ c are described. To compare the thermal properties of HoGa₃(BO₃)₄ with those of HoAl₃(BO₃)₄ exhibiting record values of the polarization, the specific heat of HoAl₃(BO₃)₄ at various B values and the temperature dependence of the polarization ΔP _b (T) in the applied magnetic field of 9 T have been measured.     

Magnetoelectric interactions in rare-earth ferroborates

Magnetic-field-induced phase transitions in single crystals of the rare-earth ferroborates GdFe₃(BO₃)₄ and NdFe₃(BO₃)₄ have been studied by measuring magnetoelectric dependences and torque curves. These phase transitions can serve as one of the possible mechanisms for magnetic control of electric polarization. Magnetic phase transitions in GdFe₃(BO₃)₄ are analyzed theoretically.     

Contribution of Co3+ ions to the high-temperature magnetic and electrical properties of GdCoO3

The temperature dependence of the static magnetization of polycrystalline rare-earth cobaltite GdCoO₃ is measured in the temperature range 2?C800 K. The magnetic behaviors of GdCoO₃ and Gd³⁺ are found to be different at temperatures above room temperature, which is caused by the appearance of a contribution from Co³⁺ ions at high temperatures. The temperature dependence of the magnetic susceptibility of GdCoO₃ is determined by the magnetization of rare-earth gadolinium ions and the additional paramagnetic contribution induced by the thermally excited magnetic terms of Co³⁺ ions. The LDA + GTB method is used to calculate the electronic structure of GdCoO₃ in the temperature range 0?C300 K with allowance for strong electron correlations. The energy spectrum of GdCoO₃ is found to have intragap states that decrease the dielectric gap width with increasing temperature.