Magnetic properties of the Nd<Subscript>0.5</Subscript>Gd<Subscript>0.5</Subscript>Fe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystal

The magnetic properties of the Nd_0.5Gd_0.5Fe₃(BO₃)₄ single crystal have been studied in principal crystallographic directions in magnetic fields to 90 kG in the temperature range 2–300 K; in addition, the heat capacity has been measured in the range 2–300 K. It has been found that, below the Néel temperature T _N = 32 K down to 2 K, the single crystal exhibits an easy-plane antiferromagnetic structure. A hysteresis has been detected during magnetization of the crystal in the easy plane in fields of 1.0–3.5 kG, and a singularity has been found in the temperature dependence of the magnetic susceptibility in the easy plane at a temperature of 11 K in fields B < 1 kG. It has been shown that the singularity is due to appearance of the hysteresis. The origin of the magnetic properties of the crystal near the hysteresis has been discussed.     

Magnetic and magnetoelectric properties of the Tb<Subscript>0.75</Subscript>Ho<Subscript>0.25</Subscript>Fe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> ferroborate

Single crystals of the Tb_0.75Ho_0.25Fe₃(BO₃)₄ ferroborate have been grown by the group method from a solution–melt based on bismuth trimolybdate. The magnetic and magnetoelectric properties of the ferroborate single crystals have been investigated in the temperature range from 4.2 to 300 K and in magnetic fields up to 9 T. Magnetically, this material is an antiferromagnet with the Néel temperature T _N = 38.8 K and easy-axis anisotropy. The magnitude of the magnetoelectric polarization has been found to be more than 1.5–2.0 times greater than the sum of the polarizations induced by the magnetic field for the ferroborates TbFe₃(BO₃)₄ and HoFe₃(BO₃)₄ taken in the corresponding shares.     

Magnetic properties of DyFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The magnetic properties of an easy-axis trigonal DyFe₃(BO₃)₄ antiferromagnetic crystal have been theoretically studied. On this basis, recent experimental data [1] on the field and temperature dependences of magnetization and the temperature dependence of the initial magnetic susceptibility for three crystallographic directions in this antiferromagnet have been interpreted. The characteristics of the trigonal crystal field for the rare earth ion and the parameters of the Fe-Fe and Fe-Dy exchange interactions are determined. Limitations imposed by features of the magnetic characteristics (anisotropic magnetization in the three crystallographic directions, Schottky-type anomalies in the magnetic susceptibility, etc.) on the possible splitting of the ground-state multiplet in the crystal field and the splitting of the lowest doublet due to the f-d interaction for Dy³⁺ ions are established.     

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.     

Magnetic circular dichroism and optical absorption in TmAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The polarized spectra of absorption and magnetic circular dichroism in a TmAl₃(BO₃)₄ single crystal are studied in the region of ³ H ₆ → ³ F ₄, ³ H ₆ → ³ F ₃, and ³ H ₆ → ³ F ₂ electronic transitions in the Tm³⁺ ion. The structure of the spectra is interpreted qualitatively. It is shown that the magnetic circular dichroism of the ³ H ₆ → ³ F ₄ transition is determined by the contribution from the splitting of the ground state, whereas the magnetic circular dichroism of the ³ H ₆ → ³ F ₃ transition is governed by the contribution from the splitting of an excited state in a trigonal crystal field.     

Magnetic properties of an easy-plane trigonal NdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> antiferromagnet

The field and temperature dependences of magnetization and the temperature dependences of the initial magnetic susceptibility have been theoretically studied for three crystallographic directions in a trigonal NdFe₃(BO₃)₄ antiferromagnetic crystal. The calculations were performed using a molecular field approximation and a crystal field model for the rare-earth subsystem. The obtained theoretical expressions are applied to the interpretation of recent experimental data [1–4] on the magnetic properties of NdFe₃(BO₃)₄. The results of calculations show a good agreement with experiment. The proposed theory adequately describes (i) anomalies of the Schottky type in the temperature dependence of the magnetic susceptibility, (ii) nonlinear curves of magnetization in the basal plane in a magnetic field up to 1 T (showing evidence of the first-order phase transitions) and their evolution with the temperature, and (iii) the field and temperature dependences of magnetization in a magnetic field up to 9 T.     

Diode-pumped Nd<Superscript>3+</Superscript>:YAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> laser at 1338 nm

A high-power diode -pumped Nd³⁺:YAl₃(BO₃)₄ (Nd:YAB) laser emitting at 1338 nm is described. At the incident pump power of 9.8 W, as high as 734 mW of continuous-wave (CW) output power at 1338 nm is achieved. The slope efficiency with respect to the incident pump power was 9.0%. To the best of our knowledge, this is the first demonstration of such a laser system. The output power stability over 60 min is better than 2.6%. The laser beam quality M ² factor is 1.21.     

Magnetic and EPR studies of the EuFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystal

Magnetic and electron paramagnetic resonance (EPR) properties of EuFe₃(BO₃)₄ single crystals have been studied over the temperature range of 300–4.2 K and in a magnetic field up to 5 T. The temperature, field and orientation dependences of susceptibility, magnetization and EPR spectra are presented. An antiferromagnetic ordering of the Fe subsystem occurs at about 37 K. The easy direction of magnetization perpendicular to the c axis is determined by magnetic measurements. Below 10 K, we observe an increase of susceptibility connected with the polarization of the Eu sublattice by an effective exchange field of the ordered Fe magnetic subsystem. In a magnetic field perpendicular to the c axis, we have observed an increase of magnetization at T < 10 K in the applied magnetic field, which can be attributed to the appearance of the magnetic moment induced by the magnetic field applied in the basal plane. According to EPR measurements, the distance between the maximum and minimum of derivative of absorption line of the Lorentz type is equal to 319 Gs. The anisotropy of g-factor and linewidth is due to the influence of crystalline field of trigonal symmetry. The peculiarities of temperature dependence of both intensity and linewidth are caused by the influence of excited states of europium ion (Eu³⁺). It is supposed that the difference between the g-factors from EPR and the magnetic measurements is caused by exchange interaction between rare earth and Fe subsystems via anomalous Zeeman effect.     

Comparative Study of the Magnetoelectric Effect in HoAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> and HoGa<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> Single Crystals

The comparative study of the magnetoelectric properties and magnetostriction of HoGa₃(BO₃)₄ and HoAl₃(BO₃)₄ single crystals has been carried out. The investigated compounds exhibit qualitatively similar magnetodielectric and inverse magnetoelectric ME _E effects with the close absolute values, which is indicative of the weak effect of a nonmagnetic metal ion. On the contrary, the magnetostriction of the galloborate has been found to be threefold higher than that of the alumoborate. In addition, the difference between the qualitative behaviors of magnetostriction has been established: the magnetic-field dependence of magnetostriction for the alumoborate has the maximum near 70 kOe at T = 4.2 K, while the galloborate magnetostriction has no maximum and does not saturate in a field of 140 kOe.     

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.     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Magnetoelectric effects in gadolinium iron borate GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Magnetoelectric interactions have been investigated in a single crystal of gadolinium iron borate GdFe₃(BO₃)₄, whose macroscopic symmetry is characterized by the crystal class 32. Using the results of this study, the interplay of magnetic and electric orderings occurring in the system has been experimentally revealed and theoretically substantiated. The electric polarization and magnetostriction of this material that arise in spin-reorientation transitions induced by a magnetic field have been investigated experimentally. For H ‖ c and H ⊥ c, H-T phase diagrams have been constructed, and a strict correlation between the changes in the magnetoelectric and magnetoelastic properties in the observed phase transitions has been ascertained. A mechanism of specific noncollinear antiferroelectric ordering at the structural phase transition point was proposed to interpret the magnetoelectric behavior of the system within the framework of the symmetry approach in the entire temperature range. This ordering provides the conservation of the crystal class of the system when the temperature decreases to the antiferroelectric ordering point. The expressions that have been obtained for the magnetoelectric and magnetoelastic energy describe reasonably well the behavior of gadolinium iron borate observed experimentally.     

Magnetoelectric effect in ytterbium aluminum borate YbAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The anisotropic magnetoelectric properties of an ytterbium aluminum borate YbAl (BO single crystal having noncentrosymmetric crystal structure (space group R32) are studied, including the orientational, field, and temperature dependences of the polarization in magnetic fields up to 5 T in the temperature range of 2–300 K. It has been shown experimentally for the first time that the symmetry of the observed magnetoelectric effects exactly corresponds to the trigonal structure of the crystal and is characterized by two quadratic magnetoelectric constants. The polarization in the basal plane P _{a, b} is a quadratic function of the field at low fields and reaches 250–300 μC/m² in a field of 5 T at a temperature of 2 K, almost an order of magnitude exceeding the previously reported values. A theoretical model based on the spin Hamiltonian of the ground Kramers doublet of Yb³⁺ ions in the crystal field is proposed including magnetoelectric interactions allowed by the symmetry. This model makes it possible to quantitatively describe all observed magnetic and magnetoelectric properties of YbAl₃(BO₃)₄.     

Antiferromagnetic resonance and phase diagrams of gadolinium ferroborate GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Antiferromagnetic resonance in single crystals of rhombohedral gadolinium ferroborate GdFe₃(BO₃)₄ was studied. The frequency-field dependences of antiferromagnetic resonance over the frequency range 26–70 GHz and the temperature dependences of resonance parameters for magnetic fields oriented along the crystal axis and in the basal plane were determined. It was found that the iron subsystem, which can be treated as a two-sublattice antiferromagnet with anisotropy of the easy-plane type, experienced ordering at T=38 K. At temperatures below 20 K, the gadolinium subsystem with the opposite anisotropy sign strongly influenced the anisotropic properties of the crystal. This resulted in a spontaneous spin-reorientation transition from the easy-plane to the easy-axis state at 10 K. Below 10 K, magnetic field-induced transitions between the states were observed. Experimental phase diagrams on the temperature-magnetic field plane were constructed for fields oriented along the crystal axis and in the basal plane. A simple model was used to calculate the critical transition fields. The results were in close agreement with the experimental values measured at T=4.2 K for both field orientations.     

Optical absorption spectra and magnetic phase transitions in TbFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Optical absorption spectra of the trigonal crystal of TbFe₃(BO₃)₄ in the vicinity of the ⁷F₆ → ⁵D₄ transition in a Tb³⁺ ion were studied as a function of temperature (2–70 K) and magnetic field strength (0–60 kOe) at 2 K. The splitting of the excited states of Tb³⁺ due to both the magnetic ordering of iron and an external magnetic field was determined. Abrupt splitting of the absorption lines of Tb³⁺ at temperature T_N of the magnetic ordering of the subsystem of iron was revealed, suggesting that the nature of such splitting is not entirely magnetic.     

Structure and lattice dynamics of PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>: Ab initio calculation

The crystal structure and phonon spectrum of PrFe₃(BO₃)₄ are ab initio calculated in the context of the density functional theory. The ion coordinates in the unit cell of a crystal and the lattice parameters are evaluated from the calculations. The types and frequencies of the fundamental vibrations, as well as the line intensities of the IR spectrum, are determined. The elastic constants of the crystal are calculated. A “seed” frequency of the vibration strongly interacting with the electron excitation on the praseodymium ion is obtained for low-frequency A₂ mode. The calculated results are in agreement with the known experimental data.     

Infrared absorption spectra of pure and doped YAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystals

Several weak absorption bands have been observed in the optical absorption spectra of pure and rare-earth-doped YAl₃(BO₃)₄ single crystals in the 3350– 3650 cm⁻¹ wave number region. Two of them, peaking at about 3377 cm⁻¹ and 3580 cm⁻¹ in the 8 K spectra, appear in most of the samples. They are tentatively attributed to the stretching mode of OH⁻ ions incorporated in the crystal during the growth. An additional absorption band at about 5250 cm⁻¹ at 8 K has also been detected in almost all samples. The temperature and polarization dependences of these bands, and their possible origin, are discussed.     

Linear and nonlinear optical spectroscopy of gadolinium iron borate GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The optical spectra and the second-harmonic generation (SHG) are studied in a noncentrosymmetric GdFe₃(BO₃)₄ magnet. In the region of weak absorption (α～20–400 cm^?1) below ～3 eV, three absorption bands are distinguished, which can be unambiguously assigned to forbidden electronic transitions from the ground ⁶A₁ state of the Fe³⁺ ion to its excited states ⁴T₁(～1.4 eV), ⁴T₂(～2 eV), and ⁴A₁, ⁴E(～2.8 eV). Intense absorption begins in the region above 3 eV (α～2–4×10⁵ cm^?1), where two bands at ～4.0 and 4.8 eV are observed, which are caused by allowed electric dipole charge-transfer transitions. The spectral features of SHG in the 1.2–3.0-eV region are explained by a change in the SHG efficiency caused by a change in the phase mismatch. It is shown that in the weak absorption region, phase matching can be achieved for SHG.     

Spin reorientation effects in GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> induced by applied field and temperature

Magnetic properties of GdFe₃(BO₃)₄ single crystals were investigated by ⁵⁷Fe-Mössbauer spectroscopy and static magnetic measurements. In the ground state, the GdFe₃(BO₃)₄ crystal is an easy-axis compensated antiferromagnet, but the easy axis of iron moments does not coincide with the crystal C₃ axis, deviating from it by about 20°. The spontaneous and field-induced spin reorientation effects were observed and studied in detail. The specific directions of iron magnetic moments were determined for different temperatures and applied fields. Large values of the angle between the Fe³⁺ magnetic moments and the C₃ axis in the easy-axis phase and between Fe³⁺ moments and the a₂ axis in the easy-plane phase reveal the tilted antiferromagnetic structure.     

High-resolution spectroscopy of HoFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal: a study of phase transitions

The transmission spectra of HoFe₃(BO₃) multiferroic single crystals are studied by optical Fourier-transform spectroscopy at temperatures of 1.7–423 K in polarized light in the spectral range 500–10 000 cm^–1 with a resolution up to 0.1 cm^–1. A new first-order structural phase transition close to the second-order transition is recorded at T_c = 360 K by the appearance of a new phonon mode at 976 cm^–1. The reasons for considerable differences in T_c for different samples of holmium ferroborate are discussed. By temperature variations in the spectra of the f–f transitions in the Ho³⁺ ion, we studied two magnetic phase transitions, namely, magnetic ordering into an easy-plane structure as a second-order phase transition at T_N = 39 K and spin reorientation from the ab plane to the c axis as a first-order phase transition at T_SR = 4.7 ± 0.2 K. It is shown that erbium impurity in a concentration of 1 at % decreases the spin-reorientation transition temperature to T_SR = 4.0 K.