Antiferromagnetic resonance and magnetic anisotropy in single crystals of the YFe3(BO3)4-GdFe3(BO3)4 system

The antiferromagnetic resonance in single crystals of the YFe₃(BO₃)₄-GdFe₃(BO₃)₄ system is studied in the frequency range 25–140 GHz and the temperature range 4.2–50.0 K. It is established that the YFe₃(BO₃)₄ crystal containing only the magnetic subsystem of Fe³⁺ ions is an antiferromagnet with an easy anisotropy plane. The temperature dependences of the gaps in the antiferromagnetic resonance spectra of GdFe₃(BO₃)₄ and Y _x Gd_{1 ? x} Fe₃(BO₃)₄ are used to calculate the contributions of the Fe³⁺ and Gd³⁺ subsystems to the magnetic anisotropy of these crystals. The contributions are found to be close in magnitude and have opposite signs. This leads to a relatively weak uniaxial anisotropy field in the crystals under investigation. Since the exchange interaction between the Gd³⁺ and Fe³⁺ ions magnetizes the magnetic subsystem of gadolinium, both subsystems start to contribute simultaneously at the Néel temperature of the iron subsystem.     

Magnetization and specific heat of DyFe3(BO3)4 single crystal

We present thermodynamic and magnetic studies of single crystalline DyFe₃(BO₃)₄. The data indicate an easy axis antiferromagnetic order below T_N~ 38 K which we attribute to the Fe subsystem. The Dy subsystem remains paramagnetic down to the lowest investigated temperatures of 2 K, but it is polarized by the Fe spins due to a f-d interaction. External magnetic field leads to a spin-flop transition in the iron subsystem as well as to superposed magnetization in the Dy subsystem. The repopulation of two low-lying Kramers doublets in Dy³⁺ ions results in well defined Schottky anomalies in specific heat and magnetization.     

Effects of the interaction between R and Fe modes of the magnetic resonance in RFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> rare-earth iron borates

Resonance modes that are due to magnetic excitations in the exchange-coupled subsystems of rare-earth ions (R = Nd³⁺, Sm³⁺, and Gd³⁺) and Fe³⁺ ions have been detected in submillimeter transmission spectra (0.1–0.6 THz) of RFe₃(BO₃)₄ iron borate-multiferroic single crystals. The strong interaction between spin oscillations of the Fe and R subsystems has been revealed, which determines the behavior of the modes depending on the anisotropy of the exchange splitting of the ground doublet of the R ion. It has been shown that the intensities of coupled modes (contributions to the magnetic permeability) depend strongly on the difference between the g factors of Fe and R ions. This dependence makes it possible to determine the sign of the latter g factor. In particular, a noticeable intensity of exchange Nd modes in NdFe₃(BO₃)₄ is due to an increase in their contribution at g _{⊥, ‖}^Nd < 0, while in GdFe₃(BO₃)₄ with g _Gd ≈ g _Fe ≈ 2, the Fe and Gd contributions compensate each other and the exchange (Gd) mode is not observed. In spite of the weak interaction of Sm ions with the magnetic field, SmFe₃(BO₃)₄ exhibits resonance modes, which are attributed to the excitation of Sm ions through the Fe subsystem.     

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.     

Infrared absorption spectra of a Nd0.5Ho0.5Fe3(BO3)4 crystal

Infrared absorption spectra of a Nd_0.5Ho_0.5Fe₃(BO₃)₄ crystal in the spectral range of 30–1700 cm^–1 have been measured at temperatures from 6 to 300 K. The experimental spectra have been analyzed based on the semiempirical calculation of the lattice dynamics and the analysis of correlation diagrams of borate complexes. No changes associated with structural phase transitions have been detected in the temperature range of measurements; the effect of magnetic ordering on the infrared absorption spectra has not been observed.     

Cascade of phase transitions in GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Cascade of phase transitions in GdFe₃(BO₃)₄ at 156, 37, and 9 K has been detected by specific heat measurements and further studied by Raman scattering and Nd³⁺ spectroscopic probe method. A weakly first-order structural phase transition at 156 K is followed by a second-order antiferromagnetic ordering phase transition at 37 K and a first-order spin-reorientational phase transition at 9 K.     

Magnetic-resonance and thermophysical studies of the magnetic phase diagram for a GdFe<Subscript>2.1</Subscript>Ga<Subscript>0.9</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystal

The antiferromagnetic resonance, heat capacity, magnetic properties, and magnetic phase diagram of a GdFe₃(BO₃)₄ crystal in which some of the iron ions were substituted by diamagnetic gallium ions have been investigated. It has been found that the Neél temperature upon diamagnetic substitution decreased to 17 K compared to 38 K in the unsubstituted crystal. The effective exchange and anisotropy fields for GdFe_2.1Ga_0.9(BO₃)₄ have been estimated from the field dependences of magnetization and resonance measurements. The magnetic phase diagram of the crystal has been constructed from magnetic and resonance measurements. In GdFe_2.1Ga_0.9(BO₃)₄, there is no spontaneous reorientation and, in the absence of a magnetic field, the crystal remains an easy-axis one in the entire domain of magnetic ordering. The critical field of the reorientation transition to an induced easy-plane state in a magnetic field along the trigonal axis has been found to increase compared to that in the unsubstituted crystal.     

Vibrational spectra and elastic,piezoelectric, and magnetoelectric properties of HoFe3(BO3)4 and HoAl3(BO3)4 crystals

Raman spectra of light are obtained for HoFe₃(BO₃)₄ and HoAl₃(BO₃)₄ crystals at various temperatures and are used for determining the frequencies of crystal lattice vibrations at the center of the Brillouin zone. It is also found that the HoFe₃(BO₃)₄ crystal exhibits a phase transition at T _c ≈ 366 K. The magnetoelectric effect in the paramagnetic phase of these compounds is studied experimentally. The lattice vibration frequencies, elastic and piezoelectric moduli, Born dynamic charges, and the high-frequency permittivity are calculated using the density functional method. A peculiar behavior of the transverse acoustic vibration branch is observed in the Γ → Z direction of the Brillouin zone of the HoFe₃(BO₃)₄ crystal. The electric polarization induced by an external field is estimated using the calculated values of piezoelectric moduli and experimental values of magnetostriction.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

Nature of optical properties of GdFe3(BO3)4 and GdFe2.1Ga0.9(BO3)4 crystals and other 3d5 antiferromagnets

Influence of the partial substitution of paramagnetic Fe³⁺ ions by diamagnetic Ga³⁺ ions in the trigonal crystal GdFe₃ (BO₃)₄ on its optical and magnetic properties is studied and discussed in connection with problems common for all antiferromagnets containing 3d ⁵ ions. Polarized optical absorption spectra and linear birefringence of GdFe₃ (BO₃)₄ and GdFe_2.1Ga_0.9 (BO₃)₄ single crystals have been measured in the temperature range 85–293 K. Specific heat temperature dependence (2–300 K) and structure of GdFe_2.1Ga_0.9 (BO₃)₄ crystal have been also studied. As a result of substitution of 30% Fe to Ga the Neel temperature diminishes from 38 till 16 K, the strong absorption band edge shifts on 860 cm^-1 (0.11 eV) to higher energy and the d-d transitions intensity decreases substantially larger than the Fe concentration does. Strong absorption band edge is shown to be due to Mott-Hubbard transitions. Correlation between position of the strong absorption band edge and the Neel temperature of antiferromagnets has been revealed. Properties of the doubly forbidden d-d transitions in the studied crystals and in other antiferromagnets are explained within the framework of the model of the exchange-vibronic pair absorption, which is theoretically analyzed in detail. The model permitted us to determine the connection between parameters of d-d absorption bands (intensity, width and their temperature dependences), on the one hand, and the exchange, spin-orbit and electron-lattice interactions, on the other hand.     

Spectroscopic investigation of rare-earth chromium borates RCr3(BO3)4 (R = Nd, Sm)

The optical absorption spectra of single crystals of neodymium and samarium chromium borates are studied. A magnetic phase transition in NdCr₃(BO₃)₄ (at T _c = 8 ± 1 K) and SmCr₃(BO₃)₄ (at T _c = 5 ± 1 K) is observed. The effective magnetic field acting on the Nd³⁺ ion from the side of the ordered magnetic subsystem of chromium is estimated.     

Heat capacity of YAl3(BO3)4 in the range of 329–1051 K

Single-crystalline YAl₃(BO₃)₄ is grown by spontaneous crystallization from a RAl₃(BO₃)₄-based solution-melt. The heat capacity in the temperature range of 329–1051 K is measured by differential scanning calorimetry. The thermodynamic functions of the YAl₃(BO₃)₄ solid compound are determined.     

Features of the magnetic and magnetoelectric properties of HoAl3(BO3)4

The main features of the magnetic and record magnetoelectric properties of a HoAl₃(BO₃)₄ aluminoborate single crystal have been studied experimentally and theoretically. It has been found that the electric polarization that was previously detected in HoAl₃(BO₃)₄ and is record for multiferroics is significantly larger, ΔP _ba (B _a ) ≈ ?5240 μC/m², with an increase in the magnetic field to 9 T at T = 5 K. The measured magnetic properties and revealed features have been interpreted within a united theoretical approach based on the molecular field approximation and on calculations in the crystal field model for a rare-earth ion. The experimental temperature (from 3 to 300 K) and field (up to 9 T) dependences of the magnetization have been described. The parameters of the crystal field of trigonal symmetry for a Ho³⁺ ion in HoAl₃(BO₃)₄ have been determined from the interpretation of the experimental data.     

CW laser action in acentric NdAl3(BO3)4 and KNdP4O12

We report low-threshold, room-temperature, cw lasing in two new high-Nd-concentration materials, NdAl₃(BO₃)₄ and KNdP₄O₁₂, the first ones with acentric space groups. For both materials, thresholds below 1 mW and slope power conversion efficiencies exceeding 20% have been measured. Fluorescence spectra and lifetimes have been measured in Nd_xGd_1?xAl₃(BO₃)₄ and Nd_xGd_1?xP₄O₁₂.     

High-temperature heat capacity of YFe3(BO3)4

The molar heat capacity of YFe₃(BO₃)₄ has been measured using differential scanning calorimetry in the temperature range 339–1086 K. It has been found that the dependence C _p = f(T) exhibits an extremum at a temperature of 401 K due to the structural transition.     

Magnetoelectric and magnetoelastic interactions in NdFe3(BO3)4 multiferroics

Complex experimental and theoretical investigations of the magnetic, magnetoelectric, and magnetoelastic properties of neodymium iron borate NdFe₃(BO₃)₄ along various crystallographic directions have been carried out in strong pulsed magnetic fields up to 230 kOe in a temperature range of 4.2–50 K. It has been found that neodymium iron borate, as well as gadolinium iron borate, is a multiferroic. It has a much larger (above 300 μC/m²) electric polarization controlled by the magnetic field and giant quadratic magnetoelectric effect. The exchange field between the rare-earth and iron subsystems (～50 kOe) has been determined for the first time from experimental data. The theoretical analysis based on the magnetic symmetry and quantum properties of the Nd ion in the crystal provides an explanation of the unusual behavior of the magnetoelectric and magnetoelastic properties of neodymium iron borate in strong magnetic fields and correlation observed between them.     

High-temperature heat capacity of TbFe3(BO3)4

The molar heat capacity of TbFe₃(BO₃)₄ in the temperature range of 346–1041 K has been measured by differential scanning calorimetry. It has been found that the C _p = f(T) curve does not show extremes. The thermodynamic properties of the oxide compound have been determined from the experimental data.     

Magnetic properties of the rare-earth ferroborate SmFe3(BO3)4

The magnetic properties of trigonal antiferromagnet SmFe₃(BO₃)₄ are studied experimentally and theoretically. The measured characteristics are considered in terms of a theoretical approach based on the molecular field approximation and a crystal field model for a rare-earth ion. The temperature dependences of the initial magnetic susceptibility and the field and temperature dependences of magnetization in fields up to 5 T are described, and the anomaly in the magnetization curve for B ⊥ c near 1 T, which points to a first-order phase transition, is analyzed.     

Hydrothermal synthesis and magnetic studies of transition metal nocerites M3(BO3)F3 (M=Fe,Co, Ni)

Polycrystalline samples of M₃(BO₃)F₃ (M=Fe, Co, Ni), isostructural with nocerite Mg₃(BO₃)(OH,F)₃, have been prepared in supercritical hydrothermal conditions. These compounds represent with boracites, M₃B₇O₁₃F (M=Mg, Cr, Mn, Fe, Co, Zn), the only transition metal fluoride borates known to date. Co₃(BO₃)F₃ and Ni₃(BO₃)F₃ are antiferromagnetic with T_N=17(2) and 40(2) K, respectively. Spin-flop transitions at B_C1=4.0 T and B_C2=7.5 T occur at 1.6 K in Co₃(BO₃)F₃, while a parasitic ferromagnetism (0.02 μ_B/Ni²⁺ at 1.6 K) appears below T_N in Ni₃(BO₃)F₃. The magnetic structures consist of three spin sub-lattices of double rutile-type ferromagnetic chains.     

Magnetic and Magnetodielectric Properties of Ho<Subscript>0.5</Subscript>Nd<Subscript>0.5</Subscript>Fe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The magnetic and magnetodielectric properties of Ho_0.5Nd_0.5Fe₃(BO₃)₄ ferroborate with the competing Ho–Fe and Nd–Fe exchange couplings have been experimentally and theoretically investigated. Step anomalies in the magnetization curves at the spin-reorientation transition induced by the magnetic field B ║ c have been found. The spontaneous spin-reorientation transition temperature T_SR ≈ 8 K has been refined. The measured magnetic properties and observed features are interpreted using a single theoretical approach based on the molecular field approximation and calculations within the crystal field model of the rare-earth ion. Interpretation of the experimental data includes determination of the crystal field parameters for Ho³⁺ and Nd³⁺ ions in Ho_0.5Nd_0.5Fe₃(BO₃)₄ and parameters of the Ho–Fe and Nd–Fe exchange couplings.