Effect of the transformation of the magnetic structure of a FeBO<Subscript>3</Subscript>:Mg crystal on its magnetooptical anisotropy

The field dependence of the magnetic linear birefringence (MLB) in easy-plane weak FeBO₃:Mg ferromagnet has been investigated. It is found that MLB nonmonotonically (stepwise) tends to a constant value with an increase in magnetic field at low temperatures. This feature of MLB in FeBO₃:Mg is related to the transformation of the crystal magnetic structure during magnetization.     

Modulated magnetic structure of weak rhombohedral ferromagnets α-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>:Ga and FeBO<Subscript>3</Subscript>:Mg

The effect of diamagnetic impurities on the stability of the homogeneous magnetic state of rhombohedral antiferromagnets with weak ferromagnetism (α-Fe₂O₃:Ga and FeBO₃:Mg) is studied experimentally. It is shown that the application of an external magnetic field in the basal plane in the crystals under study in a certain temperature range induces a magnetic superstructure along the hard magnetization axis, which can be presented in the form of a ripplon phase with the azimuth of the local ferromagnetism vector oscillating about the direction of the field. The preferred orientation of the discovered modulated structures relative to crystallographic directions in the basal plane of α-Fe₂O₃:Ga and FeBO₃:Mg is studied, and the dependence of the spatial period of the superstructure on the applied magnetic field and temperature is analyzed. The magnetic-field-induced transition of the studied crystals from a homogeneous to an inhomogeneous magnetic state is described phenomenologically on the basis of the thermodynamic potential with gradient terms. In the discussion of physical reasons for magnetic order parameter modulation in weak ferromagnetic doped with diamagnetic ions, preference is given to the mechanism associated with the emergence of uniaxial magnetic centers with a random distribution of azimuths of easy axes in the basal plane of the crystal in the vicinity of impurities. A model describing the formation of a modulated magnetic state in α-Fe₂O₃:Ga and FeBO₃:Mg is proposed, according to which the competition between magnetoanisotropic and Zeeman interactions in the inhomogeneous magnetic phase of these crystals leads to periodic deviations in the direction of the local ferromagnetism vector from the direction of magnetization.     

Orientational phase transition into a modulated magnetic state in the weak ferromagnet FeBO<Subscript>3</Subscript>: Mg

The transition from a homogeneous into a modulated magnetic state in the easy-plane weak ferromagnet FeBO₃: Mg is studied by a magnetooptic method. At T < 135 K, the application of a magnetic field in the basal plane of the crystal is shown to excite the modulation of its magnetic order parameter, which manifests itself in a periodic deviation of the local ferromagnetism vector from the magnetization direction. The conditions for the existence of a modulated magnetic superstructure in FeBO₃: Mg are studied, and its preferred orientation in the basal plane of the crystal is analyzed. A magnetic H-T phase diagram that shows the boundaries between the homogeneous and inhomogeneous magnetic states of this weak ferromagnet is constructed. The modulation period and the azimuthal angle specifying the local ferromagnetism vector direction in the structure are studied as a function of temperature and magnetic field. The results obtained are discussed in terms of the theory of magnetic ripple using the model of anisotropic magnetic centers appearing in a crystal doped by magnesium ions.     

Effect of diamagnetic impurities on the magnetic susceptibility of iron borate

The low-frequency magnetic susceptibility of a FeBO₃ single crystal doped with diamagnetic Mg ions was measured by a magnetooptical method. It is shown that the introduction of Mg ions into the composition of this easy-plane weak ferromagnet results in the appearance, at low temperatures, of a strong in-plane magnetocrystalline anisotropy and also causes a marked difference between the field dependences of the magnetic susceptibility measured in magnetic fields applied along different directions in the basal plane of the crystal. The revealed specific features of the field dependence of the magnetic susceptibility of the crystal studied are associated with the transformation of its magnetic structure during magnetization.     

Structure of the inhomogeneous magnetic state of an FeBO<Subscript>3</Subscript>: Mg easy-plane weak ferromagnet

The magnetic linear birefringence of an FeBO₃: Mg ferromagnetic crystal is investigated as a function of the magnetic field strength, the magnetic field orientation, and the coordinates. The structure of the inhomogeneous magnetic phase of this weak ferromagnet is determined by analyzing the experimental results obtained. It is shown that, in an inhomogeneous magnetic state, the ferromagnetic moment does not deviate from the basal plane of the crystal and the angle of its deviation from the direction of the applied magnetic field is described by a one-dimensional harmonic function of the spatial coordinate along the axis of magnetization.     

Effect of infrared illumination on the modulated magnetic structure of the weak ferromagnet FeBO<Subscript>3</Subscript>: Mg

The effect of unpolarized white light on the period and conditions of the existence of the modulated magnetic structure of the FeBO₃: Mg single crystal, which is formed in this easy-plane weak ferromagnet in the low-temperature range during technical magnetization, has been investigated experimentally. It has been revealed that the degree of light action on the magnetic state of the crystal depends on both the irradiation duration and the orientation of the ferromagnetic vector during illumination. It has been established that light with wavelengths in the range 0.8 μm < λ < 0.9 μm has a maximum effect on the parameters of the modulated magnetic structure formed in the FeBO₃: Mg single crystal. The results obtained have been interpreted in the framework of the “magnetic ripple” theory using the model of photosensitivity of anisotropic magnetic centers associated with the presence of Mg impurity ions in the composition of the crystal.     

Photoinduced changes in the space-modulated magnetic order of a FeBO<Subscript>3</Subscript>:Mg single crystal

An effect of nonpolarized white light on the modulated magnetic structure of a FeBO₃:Mg single crystal, which arises in this light-plane weak ferromagnet in the low temperature range during technical magnetization, has been revealed. It has been found that the degree of the light action on the magnetic state of FeBO₃:Mg depends both on its duration and on the orientation of the spontaneous magnetization vector M of the crystal during illumination. Interpretation of the results obtained has been performed in the context of the “magnetic ripple” theory on the assumption that the absorbed light induces additional uniaxial magnetic anisotropy in the easy plane of the crystal and that the anisotropy axis is collinear to the vector M during illumination.     

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 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.     

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.     

Magnetic Ordering Dependence on Iron Ions Distribution in Cu<Subscript>2</Subscript>FeBO<Subscript>5</Subscript> Ludwigite

A comparative analysis of the copper and iron ions bonds exchange energies was conducted for various variants of orderings and distributions of iron ions among crystallographic positions in ludwigite Cu₂FeBO₅. Analysis showed that the exchange bonds of iron ions play a key role in the formation of magnetic order. The magnetic ordering strongly depends on the distribution of iron ions among the positions. In the case when the Fe³⁺ is in the same position as in Fe₃BO₅, the most favorable magnetic structure is similar to the magnetic structure of ludwigite Fe₃BO₅. In other cases, the type of magnetic ordering is different.     

Modulated magnetic structure in quasi-one-dimensional clinopyroxene NaFeGe<Subscript>2</Subscript>O<Subscript>6</Subscript>

The magnetic structure of the NaFeGe₂O₆ monoclinic compound has been experimentally investigated using the elastic scattering of neutrons. At a temperature of 1.6 K, an incommensurate magnetic structure has been observed in the form of an antiferromagnetic helix formed by a pairs of the spins of the Fe³⁺ ions with helical modulation in the ac plane of the crystal lattice. The wave vector of the magnetic structure has been determined and its temperature behavior has been studied. The analysis of the temperature dependences of the specific heat and susceptibility, as well as the isotherms of the field dependence of the magnetization, has revealed the existence of not only the order-disorder magnetic phase transition at the point T _N = 13 K, but also an additional magnetic phase transition at the point T _c = 11.5 K, which is assumingly an orientation phase transition.     

Magnetic linear birefringence in Yb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> gallate garnet

The magnetic linear birefringence and the magnetic susceptibility of Yb₃Ga₅O₁₂ gallate garnet was investigated experimentally in the temperature range 78–295 K. It was shown that, in this temperature range, the magnetic linear birefringence of the garnet studied depends linearly on inverse temperature 1/T. The magnitude of this effect is determined only by the part of the crystal magnetization that is due to the difference in the thermal population of the ground state of the Yb³⁺ ion rather than the total magnetization. The results obtained are interpreted within the microscopic theory. According to this theory, the magnetic linear birefringence is determined by the quadrupole moment of the magnetoactive ion, which is induced by an external magnetic field.     

Magnetic-field-induced orientational phase transition in a nonuniformly stressed iron borate single crystal

Spatially nonuniform magnetic anisotropy was induced in the basal plane of an iron borate (FeBO₃) single crystal by applying low-symmetry stresses. The effect of nonuniform magnetic anisotropy on the magnetic state of this weak ferromagnet was studied by magnetooptic methods. It is revealed that, when a nonuniformly stressed FeBO₃ crystal is magnetized in the basal plane along a certain direction (depending on the symmetry of the applied stress), a transition from a uniform to a spatially modulated magnetic state occurs, which is not observed in the crystal in the absence of stresses. The modulated magnetic phase of the crystal can be represented as a static spin wave linearly polarized in the basal plane, with the azimuth of the weak-ferromagnetism vector oscillating about the direction of the mean magnetization. The temperature and field dependences of the spatial period of the modulated magnetic structure and the amplitude of oscillations of the ferromagnetism vector are studied, and the temperature dependence of the field range over which the modulated phase exists in the nonuniformly stressed FeBO₃ crystal is found. The results are discussed in terms of the phenomenological theory of magnetic phase transformations. It is shown that the theoretical model used consistently describes all the experimental results of the study of the noncollinear magnetic phase of the nonuniformly stressed FeBO₃ crystal.     

Low-temperature magnetic behavior of the rare-earth cobaltites GdCoO<Subscript>3</Subscript> and SmCoO<Subscript>3</Subscript>

The temperature and magnetic field dependences of the static magnetization of the polycrystalline rare-earth cobaltites GdCoO₃ and SmCoO₃ have been measured. It is shown that, below room temperature, the magnetization of both compounds derives primarily from the rare-earth ion paramagnetism. The GdCoO₃ and SmCoO₃ compounds have been found to differ substantially in magnetic behavior, which can be traced to differences in their electronic shell structures. The magnetic behavior of GdCoO₃ is close to that of an array of free Gd³⁺ ions, whereas in SmCoO₃ the deviation from the free-ion properties is very large because of the Sm³⁺ ground state being crystal-field split. Van Vleck magnetic susceptibility measurements of SmCoO₃ suggest that the splitting is ～10 K.     

Phase transitions in FeBO<Subscript>3</Subscript> under pressure: DFT + DMFT study

We present a theoretical study of spectral, magnetic, and structural properties of the iron borate FeBO₃. Within the DFT + DMFT method combining density functional theory with dynamical mean-field theory FeBO₃ was investigated under pressures up to 70 GPa at 300 K. We found that FeBO₃ is an insulator with a gap of 2.0 eV with antiferromagnetic ordering at ambient pressure in agreement with experiments. In our calculations, we showed that Fe ions in FeBO₃ undergo a high-spin to low-spin transition under pressure with change from antiferromagnetic to paramagnetic state, and demonstrate that the spin and magnetic transitions occur simultaneously with an isostructural transition at 50.4 GPa with the volume collapse of 13%.     

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 properties of BiFe<Subscript>0.93</Subscript>Mn<Subscript>0.07</Subscript>O<Subscript>3</Subscript> powders obtained by ultrasonic spray pyrolysis

Samples of BiFe_0.93Mn_0.07O₃ with different specific surface area were synthesized for the first time by ultrasonic spray pyrolysis. The resulting powders consist of porous particles of a spherical shape of medium size ~0.5 μm and have record values of residual magnetization and coercive force. It is found that the magnetic properties of the porous powder particles are determined by the distortion of the crystal lattice and the presence of uncompensated magnetic moments of iron ions on the surface.     

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.     

Special features of linear magnetic birefringence in an α-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>:Ga single crystal

Experimental investigations of the field dependence of the linear magnetic birefringence (LMB) in an α-Fe₂O₃:Ga single crystal are presented. It is established that during crystal magnetization in the basal plane near directions perpendicular to the С₂ axes in the region of magnetic field saturation, the LMB changes nonmonotonically. The observed special feature of the field LMB dependence is due to the reorganization of the magnetic α-Fe₂O₃:Ga structure during magnetization.