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.     

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.     

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.     

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.     

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.     

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.     

Anisotropy of magnetic properties of Sm<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript> single crystals

Anisotropy of the magnetic properties of Sm_0.55Sr_0.45MnO₃ single crystals has been studied. A significant increase in the antiferromagnetic component of magnetization in the case of orientation of an external magnetic field H close to the c axis has been found. Magnetization for a field lying in the ab plane seems typical of a ferromagnet. Anisotropy of susceptibility reaches 2.2 in weak fields and nearly vanishes at H > 1 T.     

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.     

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.     

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.     

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.     

Interrelation of anisotropy of magnetic properties and magnetodielectric effect in a Cu<Subscript>3</Subscript>B<Subscript>2</Subscript>O<Subscript>6</Subscript> single crystal

The effect of an external magnetic field on permittivity has been studied in a Cu₃B₂O₆ single crystal with a layered structure in the direction perpendicular to layers (bc-planes). It has been found that the appreciable magnetodielectric effect in the temperature range below the Néel temperature (≈10 K) takes place only at one magnetic field orientation H and one crystallographic direction, i.e., H || b. Such “selectivity” of the magnetodielectric effect correlates with the anisotropic behavior of magnetic properties of the crystal.     

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.     

Magnetic structure of the quasi-one-dimensional frustrated antiferromagnet LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> with Spin <Emphasis Type="Italic">S</Emphasis> = 1/2

The magnetic properties of LiCu₂O₂ single-crystal samples without twinning are investigated using electron spin resonance and nuclear magnetic resonance spectroscopy. The experimental results obtained are described in terms of the model of a planar spiral antiferromagnet for the orientation of the magnetic field H ‖ b or H ‖ c and the model of a collinear spin-modulated antiferromagnet for the orientation of the static magnetic field H ‖ a.     

Magnetic and electrical properties of Fe<Subscript>1.91</Subscript>V<Subscript>0.09</Subscript>BO<Subscript>4</Subscript> warwickite

We have performed a complex investigation of the structure and the magnetic and electrical properties of a warwickite single crystal with the composition Fe_1.91V_0.09BO₄. The results of Mössbauer measurements at T=300 K indicate that there exist “localized” (Fe²⁺, Fe³⁺) and “delocalized” (Fe_2.5+) states distributed over two crystallographically nonequivalent positions. The results of magnetic measurements show that warwickite is a P-type ferrimagnet below T=130 K. The material exhibits hopping conductivity involving strongly interacting electrons. The experimental data are analyzed in comparison to the properties of the initial (unsubstituted) Fe₂BO₄ warwickite. The entire body of data on the electric conductivity and magnetization are interpreted on a qualitative basis.     

High-temperature complex impedance and modulus spectroscopic studies of doped Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-BaTiO<Subscript>3</Subscript> ferroelectric ceramics

Lead-free Na_0.5Bi_0.5TiO₃ (NBT) and (1 ? x)Na_0.5Bi_0.5TiO₃ + xBaTiO₃ with x = 0.1 and 0.2 (where x = 0.1 and 0.2 are named as NBT1 and NBT2, respectively), (1 ? y)Na_0.5Bi_0.5TiO₃ + yBa_0.925Nd_0.05TiO₃ with y = 0.1 and 0.2 (where y = 0.1 and 0.2 are named as NBT3 and NBT4, respectively)-based relaxor ferroelectric ceramics were prepared using the sol-gel method. The crystal structure was investigated by X-ray diffraction (XRD) at room temperature (RT). The XRD patterns confirmed the presence of the rhombohedral phase in all the samples. The electrical properties of the present NBT-based samples were investigated by complex impedance and the modulus spectroscopy technique in the temperature range of RT–600 °C. The AC conductivity was found to increase with the substitution of Ba²⁺ ions to the NBT sample whereas it significantly decreased with the addition of Nd³⁺ ions. The more anion vacancies in Ba-added samples and the lower anion vacancies in Nd-added samples were found to be responsible for higher and lower conductivities, respectively.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

Causes of the Metamagnetism in a Disordered EuMn<Subscript>0.5</Subscript>Co<Subscript>0.5</Subscript>O<Subscript>3</Subscript> Perovskite

The magnetic properties of the EuMn_0.5Co_0.5O₃ perovskite synthesized under various conditions are studied in fields up to 140 kOe. The sample synthesized at T = 1500°C is shown to exhibit a metamagnetic phase transition, which is irreversible below T = 40 K, and the sample synthesized at T = 1200°C demonstrates the field dependence of magnetization that is typical of a ferromagnet. Both samples have T_C = 123 K and approximately the same magnetization in high magnetic fields. The metamagnetism is assumed to be related to a transition from a noncollinear ferromagnetic phase to a collinear phase, and the presence of clusters with ordered Co²⁺ and Mn⁴⁺ ions leads to ferromagnetism. The noncollinear phase is formed due to the competition between positive Co²⁺–Mn⁴⁺ and negative Mn⁴⁺–Mn⁴⁺ and Co²⁺–Co²⁺ interactions, which make almost the same contributions, and to the existence of a high magnetic anisotropy.     

Electrical resistivity and magnetotransport in La<Subscript>0.67</Subscript>Ba<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript> films asymmetrically biaxially compressed by an NdGaO<Subscript>3</Subscript>(001) substrate

The La_0.67Ba_0.33MnO₃(40 nm) films are quasi-coherently grown on an NdGaO₃(001) substrate with an orthorhombic unit cell distortion of ～1.4%. The biaxial compressive stresses generated during nucleation and growth lead to a decrease in the unit cell volume of the grown layers. This, in turn, results in a decrease (by ～35 K) in the temperature of the maximum in the dependence of the electrical resistivity ρ of the layers on the temperature. For T < 150 K, the electrical resistivity ρ of the films increases in proportion to ρ₂ T ^4.5 and the coefficient ρ₂ decreases almost linearly with increasing magnetic field H. The negative magnetoresistance (≈?0.17 for μ₀ H = 1 T) reaches a maximum at temperatures close to room temperature. The response of the electrical resistivity ρ of the La_0.67Ba_0.33MnO₃(40 nm) films to the magnetic field depends on the crystallographic direction of the film orientation and the angle between H and I (where I is the electric current through the film).     

On the Measurement of the Stiffness of Spin Waves in the Fe<Subscript>0.75</Subscript>Co<Subscript>0.25</Subscript>Si Helimagnet by the Small-Angle Neutron Scattering Method

The stiffness of spin waves in the Fe_0.75Co_0.25Si helimagnet with the Dzyaloshinskii–Moriya interaction in a state fully magnetized by an external field has been measured by the small-angle neutron scattering method. It has been shown that the dispersion of magnons in this state is anisotropic because the neutron scattering pattern consists of two circles for neutrons with obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field H and equal to the wave vector of the spiral ±k_s measured in inverse nanometers. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnitude of the magnetic field. It has been shown that the stiffness of spin waves A for the helimagnet is equal to 46.0 meV Ų at T = 0 K and decreases weakly (by 20%) with increasing temperature up to the critical value T_c = 38 K.