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 Sm0.7Ho0.3Fe3(BO3)4

The magnetic properties of a ferroborate single crystal of substituted composition Sm_0.7H_0.3Fe₃(BO₃)₄ with competing Sm-Fe and Ho-Fe exchange interactions are studied. The measured properties and effects are interpreted in terms of a general theoretical approach based on the molecular field approximation and calculations using the crystal field model for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the temperature range 2?C300 K, the anomalies in the magnetization curves for B ?? c and B ?? c in fields lower than 1.2 T, and the field and temperature dependences of magnetization in fields lower than 9 T are described. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined during the interpretation of the experimental data.     

Magnetic properties of the Nd0.95Dy0.05Fe3(BO3)4 ferroborate with small substitution in the rare-earth element subsystem

The magnetic properties of a substituted Nd_0.95Dy_0.05Fe₃(BO₃)₄ ferroborate single crystal with competing Nd-Fe and Dy-Fe exchange interactions are studied experimentally and theoretically. A spontaneous spin-reorientation transition is detected near T = 4.3 K, and anomalies are observed in the low-temperature magnetization curves along trigonal axis c and in basal plane ab. The measured properties and the detected effects are interpreted in terms of a general theoretical approach, which is based on the molecular field approximation and crystal field calculations for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the range 2–300 K, the anomalies in the magnetization curves for B ‖ c and B ⊥ c in fields up to 1.5 T, and the field and temperature dependences of magnetization in fields up to 9 T are described. The effect of small substitution in the rare-earth subsystem on the magnetic properties is analyzed. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined from the experimental data.     

Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

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.     

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.     

High-frequency properties of KNiPO<Subscript>4</Subscript> in alternating magnetic and electric fields

The dependences of the antiferromagnetic resonance frequencies on the constant magnetic field H and constant electric field E are calculated for a KNiPO₄ crystal with spontaneous electric polarization and antiferromagnetic order. It is demonstrated that the KNiPO₄ crystal is characterized by an exchange-enhanced effect of the electric field E on the antiferromagnetic resonance frequencies. This effect is not revealed in the magnetoelectric materials studied earlier. It is established that oscillations of both magnetization and electric polarization exhibit resonance response at antiferromagnetic resonance frequencies. The expressions for these responses in alternating magnetic and electric fields are presented.     

The microwave absorption of high-T c superconducting thin film samples

The experimental and theoretical investigations of microwave losses (ML) in HTSC thin films are carried out. It is shown theoretically that ML in the maximum of the magnetic componentB ₁ are essentially larger than those in the maximum of the electric componentE ₁. This is because eddy currents make much more substantial contribution to ML as compared to conventional conductivity currents. The consequence of this is the angular dependence of ML with respect to theB ₁ field direction which was experimentally observed. The angular dependences of ML with respect to theB ₀ field direction for both low and highB ₀ values were also investigated. The majority of experimental data can be well explained within the mixed model which predicts the existence of a critical state in inter- and intragranular Josephson medium.     

Effect of constant magnetic field on the microhardness of LiIO3 single crystals

The microhardness of LiIO₃ crystals is found to decrease after action of a constant magnetic field B. The maximum change in the microhardness is observed within an hour after the magnetic treatment. Then, the microhardness demonstrates a gradual relaxation return to the initial value. The change in the microhardness is dependent on the orientation of magnetic inductance vector with respect to the polar axis. The effect is pronounced at B ⊥ [0001] and is absent at B ‖ [0001]. The sensitivity of the microhardness of LiIO₃ to a constant magnetic field has a threshold character: the effect appears at the magnetic induction higher than 1 T, increases quickly, and reaches the saturation even at 1.3 T. The reversibility of the magnetically induced decrease in the microhardness has been justified: the effect is exactly reproduced during repeated tests after two weeks. The study of the crystals doped with chromium shows that the increase in the Cr concentration enhances the magnetoplastic effect in LiIO₃, i.e., favors the softening of the material after the magnetic treatment.     

Modulated magnetic structure of a nonuniformly stressed FeBO3 single crystal

The magnetization of a nonuniformly stressed FeBO₃ crystal along any of the two specific directions in the basal plane (the easy plane) at a temperature of T < 140 K in a magnetic field exceeding the threshold value H ₀ is found to lead to a transition of the crystal from the uniform magnetic state to the spatially modulated one. The modulated magnetic phase arising under these conditions exists in a certain temperature-dependent field range H ₀ ≤ H ≤ H _c and is representable in the form of a static spin wave that is linearly polarized in the easy plane of the crystal and has a wave vector k oriented at an angle of ～30° to the magnetization axis. The field, temperature, and orientation dependences of k are investigated. A physical mechanism is proposed to explain the modulation of the magnetic order parameter of the crystal under study. The results obtained are discussed in terms of the magnetic ripple theory.     

Crossover effects in scheelite DyLiF4

The Zeeman effect, magnetization, and differential susceptibility of a DyLiF₄ crystal in a pulsed magnetic field are studied experimentally and theoretically. It is found that Dy³⁺ ion levels in DyLiF₄ approach each other and a crossover occurs in a magnetic field H ‖ [001], which leads to a smearing of peaks in the differential magnetic susceptibility dM/dH and to inflection points in the magnetization curves M(H) at low temperatures. It is demonstrated that magnetic anomalies that accompany the crossover in DyLiF₄ in a field H ‖[001] are sensitive to the electronic structure of the Dy³⁺ ion. Therefore, these anomalies can be used to refine the crystal-field parameters. The effects of variations in the crystal field and temperature and of a deviation of the direction of the magnetic field from the symmetry axis on the magnitude and character of the magnetic anomalies associated with the crossover are investigated. The crystal field and crossover effects in the scheelite structure are compared with those in the zircon structure.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Analysis of the spin splitting of maxima of quantum oscillations of the resistivity of n-Bi-Sb semiconductor alloys in a magnetic field parallel to the bisector axis

In samples of semiconductor alloys n-Bi_0.93Sb_0.07 with different electron concentrations (n ₁ = 8 × 10¹⁵ cm^?3, n ₂ = 1.2 × 10¹⁷ cm^?3, and n ₃ = 1.9 × 10¹⁸ cm^?3), dependences of the electrical resistivity on magnetic fields up to 45 T parallel to the current and the bisector axis (H ‖ C ₁ ‖ j) have been measured at temperatures of 1.5, 4.5, and 10 K. The obtained dependences ρ₂₂(H) demonstrate quantum oscillations of the resistivity (Shubnikov-de Haas effect), and, in high magnetic fields, there is a resistivity maximum far away from other maxima. On assumption that this maximum is related to the spin-split Landau level N = 0^? for electrons of the main ellipsoid, the spin-splitting parameters are calculated for electrons of the main ellipsoid: γ₁ = 0.87, γ₂ = 0.8, and γ₃ = 0.73. Using these values, the oscillation maxima can be reliably related to the numbers of split Landau levels for electrons of the main and secondary ellipsoids. The dependences of the resistivity ρ₁₁ and the Hall coefficient R _31.2 on magnetic field have been measured in a transverse magnetic field at H ‖ C ₁ and j ‖ C ₂ on the sample with the electron concentration n ₄ = 1.4 × 10¹⁷ cm^?3. Using similar analysis, the spin-splitting parameter is found to be γ₄ = 0.85, which is close to the value of γ₂ = 0.8 obtained for the sample with close electron concentration (n ₂ = 1.2 × 10¹⁷ cm^?3) during the measurements in a longitudinal magnetic field. The quantum oscillation maxima of Hall coefficient R _31.2 are shifted to the range of high magnetic fields as compared to the quantum oscillation maxima of resistivity ρ₁₁.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Magnetic anisotropy of the VBO<Subscript>3</Subscript> and CrBO<Subscript>3</Subscript> transition-metal borates

Temperature and field dependences of the magnetization of VBO₃ and CrBO₃ single crystals with the magnetic field applied parallel and perpendicular to the (111) basal plane were measured. VBO₃ was found to have a considerable uniaxial anisotropy with a field H_a≈6.25 T. CrBO₃ was shown to exhibit not only uniaxial but also hexagonal anisotropy. The experimental anisotropy constants were estimated, and their temperature dependences are presented.     

Effect of electric field on NMR spectra in centroantisymmetric antiferromagnets

A symmetry approach is used to study the influence of electric field E on the NMR frequency spectrum of antiferromagnets of the rhombohedral (Cr₂O₃) and tetragonal (e.g., the Fe₂TeO₆ trirutiles) systems exhibiting a linear magnetoelectric (ME) effect. The latter originates from the presence in their magnetic structure of an antisymmetry center $\bar 1'$ . It is shown that besides the trivial effect of E on the NMR frequency through the total magnetization induced by the ME phenomenon, there also exists an independent mechanism of a direct action of electric field on the local field at the nuclei, which can, in particular, produce an additional NMR frequency splitting. The dependence of this effect on the exchange magnetic structure and orientational state is considered.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.