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.     

Magnetic properties of the rare-earth ferroborate SmFe3(BO3)4

The magnetic properties of trigonal antiferromagnet SmFe₃(BO₃)₄ are studied experimentally and theoretically. The measured characteristics are considered in terms of a theoretical approach based on the molecular field approximation and a crystal field model for a rare-earth ion. The temperature dependences of the initial magnetic susceptibility and the field and temperature dependences of magnetization in fields up to 5 T are described, and the anomaly in the magnetization curve for B ⊥ c near 1 T, which points to a first-order phase transition, is analyzed.     

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 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.     

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.     

Giant magnetoresistance of PbSnTe:In films in the space-charge-limited current regime: Angular features and effect of the surface

In the space-charge-limited current regime at T = 4.2 K, the magnetoresistance of PbSnTe:In/(111)BaF₂ films has been studied at various mutual orientation of the magnetic field B (up to 4 T), electric field E (up to ~10³ V/cm), and normal to the surface n. At B ‖ n, the reduction of the current reaches a factor of ~10⁵, whereas at B ‖ E, the current increases by a factor of ~10³. The angular dependences of the magnetoresistance have been studied at the “rotation” of B in three different planes. The angular dependences of the magnetoresistance for the plane corresponding to the orientation B ⊥ E exhibit local maxima near the orientations B ⊥ n, at which charge carriers are deflected by the magnetic field to one of the boundaries of the film. At the deviation to the free surface, the half-width of maxima is several degrees. At the deviation to the interface with the substrate, the half-width of maxima is about an order of magnitude larger and their amplitude is one or two orders of magnitude smaller. Possible mechanisms of giant positive and negative magnetoresistance, as well as the effect of the boundaries of the film on the angular dependences of the magnetoresistance, have been discussed.     

Field Confinement Energy at a Nonlinear Interface between Nonlinear Defocusing Media

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS₃ on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T₀ ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T₀. The negative magnetoresistance (at B ∥ c) below T₀ is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

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.     

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.     

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.     

Spatial dispersion in polariton spectra of CuGaS2 crystals

The unmodulated and wavelength-modulated reflectivity spectra of CuGaS₂ crystals for the polarization E ‖ c, k ⊥ c at 77 and 8 K have been studied. The states n=1, 2, and 3 of A excitons and n=1 and 2 of B and C excitons are established. The luminescence spectra from the surface at k ‖ c and k ⊥ c are obtained. The fine structure of the reflectivity spectra of excitons are analyzed with due regard for the normal and oblique incidence of light onto the crystal surface. The main parameters of the A, B, and C excitonic series are determined such as the energies of the longitudinal and transverse excitons Γ₄ (E ‖ c) for states n=1 and 2, the longitudinal and the transverse mass of excitons in CuGaS 2, and the effective masses of electrons (m _c1*) and holes (m _v1*, m _v2*, m _v3*). It is shown that the mass m _v1* in the upper valence band at k ‖ c equals (0.7–0.8)m ₀ and at k ⊥ c, 1.87m ₀.     

Domain structure in centroantisymmetric antiferromagnets

The domain structure of an antiferromagnet whose magnetic-symmetry group contains a center of antisymmetry is studied theoretically. The magnetoelectric effect and weak ferromagnetism are shown to coexist in a domain wall. It is established that when the inhomogeneous magnetic moment interacts with a sufficiently strong magnetic field H ‖ C ₃, a multidomain state with an odd number of 180° domain walls becomes energetically favorable. The critical field for the transition from a single-domain state to a multidomain state is found. It is shown that domain reversal occurs when the magnetic field H is reversed.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

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.     

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.     

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.     

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.