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.     

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.     

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.     

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.     

Peculiarities in the magnetic,magnetoelectric, and magnetoelastic properties of SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

Results of a complex investigation of the magnetic, magnetoelectric, and magnetoelastic properties of a SmFe₃(BO₃)₄ single crystal are presented. Samarium iron borate is similar to another easy-plane iron borate, NdFe₃(BO₃)₄, in that it possesses a large value of the magnetic-field-induced polarization (about 500 μC/m²), the sign of which changes when the field direction is changed between axes a and b of the crystal. However, the temperature dependence of the magnetic susceptibility and the field dependence of polarization and magnetostriction of the two compounds are significantly different, which is explained by the weak effect of external magnetic field on the ground-state multiplet of samarium ion, which is characterized by an extremely small value of its g-factor.     

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.     

Magnetostriction of Hexagonal HoMnO<Subscript>3</Subscript> and YMnO<Subscript>3</Subscript> Single Crystals

We report on the magnetostriction of hexagonal HoMnO₃ and YMnO₃ single crystals in a wide range of applied magnetic fields (up to H = 14 T) at all possible combinations of the mutual orientations of magnetic field H and magnetostriction ΔL/L. The measured ΔL/L(H, T) data agree well with the magnetic phase diagram of the HoMnO₃ single crystal reported previously by other authors. It is shown that the nonmonotonic behavior of magnetostriction of the HoMnO₃ crystal is caused by the Ho³⁺ ion; the magnetic moment of the Mn³⁺ ion parallel to the hexagonal crystal axis. The anomalies established from the magnetostriction measurements of HoMnO₃ are consistent with the phase diagram of these compounds. For the isostructural YMnO₃ single crystal with a nonmagnetic rare-earth ion, the ΔL/L(H, T) dependences are described well by a conventional quadratic law in a wide temperature range (4–100 K). In addition, the magnetostriction effect is qualitatively estimated with regard to the effect of the crystal electric field on the holmium ion.     

Quadratic magnetoelectric effect and the role of the magnetocaloric effect in the magnetoelectric properties of multiferroic BaMnF<Subscript>4</Subscript>

The magnetoelectric effects in BaMnF₄ in magnetic fields up to 250 kOe are experimentally studied and theoretically analyzed using the magnetic symmetry of the crystal. The presence of quadratic magnetoelectric effect tensor components that correspond to the electric polarization components along the b and c axes indicates triclinic distortions in the monoclinic symmetry of the crystal. The anomalous dependence of the magnetic field-induced polarization (P _a (H _b )) can be related to the pyroelectric effect caused by magnetocaloric heating of the crystal. The measured torque curves point to a 9° deviation of the spin orientation from the b axis.     

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.     

Specificity of magnetoelectric effects in a new GdMnO<Subscript>3</Subscript> magnetic ferroelectric

A complex study of the magnetic, electric, magnetoelectric, and magnetoelastic properties of GdMnO₃ single crystals has been performed in the low-temperature region in strong pulsed magnetic fields up to 200 kOe. An anomaly of the dielectric constant along the a axis of a crystal has been found at 20 K, where a transition from an incommensurate modulated phase to a canted antiferromagnetic phase, as well as electric polarization along the a and b axes of the crystal induced by the magnetic field H‖ b (H_cr ～ 40 kOe), is observed. Upon cooling the crystal in an electric field, the magnetic-field-induced electric polarization changes its sign depending on the sign of the electric field. The occurrence of the electric polarization is accompanied by anisotropic magnetostriction, which points to a correlation between the magnetoelectric and magnetoelastic properties. Based on these results, it has been stated that GdMnO₃ belongs to a new family of magnetoelectric materials with the perovskite structure.     

Magnetic state of the structural separated anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The results of neutron diffraction studies of the La_0.70Sr_0.30MnO_2.85 compound and its behavior in an external magnetic field are stated. It is established that in the 4–300 K temperature range, two structural perovskite phases coexist in the sample, which differ in symmetry (groups R[`3]cR\bar 3c and I4/mcm). The reason for the phase separation is the clustering of oxygen vacancies. The temperature (4–300 K) and field (0–140 kOe) dependences of the specific magnetic moment are measured. It is found that in zero external field, the magnetic state of La_0.70Sr_0.30MnO_2.85 is a cluster spin glass, which is the result of frustration of Mn³⁺-O-Mn³⁺ exchange interactions. An increase in external magnetic field up to 10 kOe leads to fragmentation of ferromagnetic clusters and then to an increase in the degree of polarization of local spins of manganese and the emergence of long-range ferromagnetic order. With increasing magnetic field up to 140 kOe, the magnetic ordering temperature reaches 160 K. The causes of the structural and magnetic phase separation of this composition and formation mechanism of its spin-glass magnetic state are analyzed.     

Magnetic and structural phase transitions in YMn<Subscript>2</Subscript>O<Subscript>5</Subscript> ferromagnetoelectric crystals induced by a strong magnetic field

Magnetic, magnetoelectric, and magnetoelastic properties of YMn₂O₅ ferromagnetoelectric single-crystals are investigated in strong pulsed magnetic fields of up to 250 kOe and in static magnetic fields of up to 12 kOe. It is found that, in YMn₂O₅ at T < T_N=42 K, a transverse weakly ferromagnetic moment of σ ₀=0.8 G cm³/g exists that is oriented along axis a and is attributed to the magnetoelectric interaction. When a magnetic field is directed along axis b, which is likely to be the axis of antiferromagnetism, a spin-flop transition is observed that is accompanied by jumps in magnetostriction and electric polarization. When a magnetic field is directed along axis a, the temperature of ferroelectric transition shifts from 20 to 25 K at H≈200 kOe. A theoretical analysis of the experimental results is given within phenomenological theory with regard to the fact that a YMn₂O₅ compound belongs to noncollinear antiferromagnetic crystals even in the exchange approximation.     

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.     

Influence of magnetic ordering on electronic structure of Tb<Superscript>3+</Superscript> ion in TbFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal

Optical absorption spectra of trigonal crystal TbFe₃(BO₃)₄ have been studied in the region of ⁷F₆ → ⁵D₄ transition in Tb³⁺ ion depending on temperature (2–220 K) and on magnetic field (0–60 kOe). Splitting of the Tb³⁺ excited states, both under the influence of the external magnetic field and effective exchange field of the Fe-sublattice, have been determined. Landé factors of the excited states have been found. Stepwise splitting of one of the absorption lines has been discovered in the region of the Fe-sublattice magnetic ordering temperature. This is shown to be due to the abrupt change of equilibrium geometry of the local Tb³⁺ ion environment only in the excited state of the Tb³⁺ ion. In general, the magnetic ordering is accompanied by temperature variations of the Tb³⁺ local environment in the excited states. The crystal field splitting components have been identified. In particular, it has been shown that the ground state (in D ₃ symmetry approximation) consists of two close singlet states of A ₁ and A ₂ type, which are split and magnetized by effective exchange field of the Fe-sublattice. Orientations of magnetic moments of the excited electronic states relative to that of the ground state have been experimentally determined in the magnetically ordered state of the crystal. A pronounced shift of one of absorption lines has been observed in the vicinity of the TbFe₃(BO₃)₄ structural phase transition. The temperature interval of coexistence of the phases is about 3 K.     

Field-induced magnetic transition in a mixed rare-earth aluminum garnet Er<Subscript>2</Subscript>HoAl<Subscript>5</Subscript>O<Subscript>12</Subscript>

The temperature dependence of the ac magnetic susceptibility of a single-crystal mixed rare-earth garnet Er₂HoAl₅O₁₂ has been investigated within the range from 1.8 to 300 K in a zero constant field and in applied bias fields of up to 9 T. In the absence of a constant magnetic field the magnetic susceptibility followed the Curie–Weiss law. The application of a constant magnetic field caused a magnetic phase transition, the temperature of which increased with increasing magnetic field. The temperature of the maximum of the ac magnetic susceptibility, which is a characteristic of the phase transition, did not show a noticeable dependence on the frequency of the alternating magnetic field.     

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.     

Polarization modes in the Ba<Subscript>2</Subscript>Mg<Subscript>2</Subscript>Fe1<Subscript>2</Subscript>O<Subscript>22</Subscript> multiferroic

The spectra of complex permittivity of a Ba₂Mg₂Fe₁₂O₂₂ single crystal belonging to the family of Y-type hexaferrites have been measured over a wide temperature range (10–300 K) with the aim of determining the dynamic parameters of the phonon and magnetic subsystems in the terahertz and infrared frequency ranges (3–4500 cm⁻¹). A factor-group analysis of the vibrational modes has been performed, and the results obtained have been compared with the experimentally observed resonances. The oscillator parameters of all nineteen phonon modes of E _u symmetry, which are allowed by the symmetry of the Ba₂Mg₂Fe₁₂O₂₂ crystal lattice, have been calculated. It has been found that, at temperatures below 195 and 50 K, the spectral response exhibits new absorption lines due to magnetic excitations.     

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.     

Features of low-temperature thermal expansion of n-type Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> single crystals in magnetic field

Tensometric study of n-type Bi₂Se₃ single crystals in dc magnetic fields to 6 T in a temperature range of 7–23 K detected a weak negative thermal expansion (NTE) in the basal plane. The NTE increases with the field strength and depends on its orientation with respect to the trigonal c axis. In a magnetic field of 6 T, parallel to the c axis, the linear NTE coefficient reaches ?7 · 10^?7 K^?1, and a minimum sample length is reached at a temperature of 13 K, where a Hall carrier concentration maximum is also detected. The found magnetoelastic anomaly can be associated with the topological insulator state.     

Elastic,magnetic, and magnetoelectric properties of the CaBaCo<Subscript>4</Subscript>O<Subscript>7</Subscript> multiferroic

The structural, elastic, magnetic, and magnetoelectric properties of the CaBaCo₄O₇ multiferroic are experimentally studied and compared with the properties of the related YBaCo₄O₇ cobaltite, where Y³⁺ ions substitute for Ca²⁺ ions. Unlike the frustrated YBaCo₄O₇ magnet, the softening of Young’s modulus and the hysteresis in the ΔE(T)/E ₀ curve of ferrimagnetic CaBaCo₄O₇ in the paramagnetic region are weak, and the anomaly during the magnetic transition increases by almost an order of magnitude. This difference can point to different characters of the development of a long-range magnetic order in these two cobaltites. The distortion of the crystal structure that removes the frustrations of exchange interactions is found to correlate with the magnetic behavior of the cobaltites under study. The magnetization curves of the Ca cobaltite have two steps below 15 K, which can point to the presence of a metastable state in a high magnetic field. The study of the longitudinal and transverse magnetoelectric effects in a pulsed magnetic field demonstrates that their magnitudes are maximal near T _C and change their character from linear to quadratic during passage through this temperature.