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.     

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.     

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.     

Incommensurate helical magnetic order in LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript> quasi-one-dimensional compounds

The results of the measurements of the ^{6, 7}Li and ²³Na nuclear magnetic resonance (NMR) and ^{63, 65}Cu nuclear quadrupole resonance in LiCu₂O₂ and NaCu₂O₂ quasi-one-dimensional compounds with a spin chains in the paramagnetic and magnetically ordered states are presented. The shape of the NMR line below T _c = 24 and 13 K for LiCu₂O₂ and NaCu₂O₂, respectively, is characteristic of the incommensurate static modulation of the local magnetic field matching with the incommensurate spiral modulation of the magnetic moments. The differences in the shape of the NMR spectra of ²³Na and ⁷Li are discussed in terms of the features of the crystal structure of LiCu₂O₂ and NaCu₂O₂.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.     

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.     

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.     

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.     

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.     

Effect of an external magnetic field and a trapped magnetic flux on the current-voltage characteristics of a granular high-temperature superconductor YBa2Cu3O7−δ

A comparative study of the current-voltage characteristics of the high-temperature ceramic superconductor YBa₂Cu₃O_～6.95 at T = 77.3 K is performed over wide ranges of external magnetic fields H _ext and “treatment” fields H _treat. It is found that the field dependences of the parameters a and j _c involved in the exponential equation E = a(j ? j _c)^v describing the current-voltage characteristics depend substantially on the method used for applying the magnetic field, whereas the exponent v ～ 2 depends on neither the method of application nor on the magnetic field strength. The field dependence of the trapped magnetic field H _trap is determined.     

States of cobalt fluoride in a strong magnetic field

The behavior of the magnetic subsystem of cobalt fluoride is investigated in a strong magnetic field oriented in an arbitrary direction in space. In the case where the magnetic field is out of the planes passing through the easiest magnetization axis A and the axis [100] ‖ X or through the easiest magnetization axis A and the axis [010] ‖ Y, it follows from the derived system of equations that the antiferromagnetic vector l does not change direction to be align with the basal plane, provided the magnetic field has a nonzero component along the A axis. It is demonstrated that the antiferromagnetic vector l becomes parallel to the basal plane only when the magnetic field is perpendicular to the A axis. The case of the magnetic field directed parallel to the [110] axis is examined thoroughly. The critical value of the magnetic field is determined at which the antiferromagnetic vector l becomes parallel to the basal plane and perpendicular to the external magnetic field H for H _⊥ → ∞.     

Magnetization reversal dynamics in La0.65Sr0.28Mn1.07O3 ceramics and NixZn1−x Fe2O4 nickel-zinc ferrite placed in complicated pulsating fields

The magnetization reversal dynamics in La_0.65Sr_0.28Mn_1.07O₃ ceramics and Ni_xZn_1?x Fe₂O₄ nickel-zinc ferrite placed in a magnetic field is studied experimentally. The field is a superposition of quasi-static field H, rf field h _ω cosωt, and low-frequency field h _ΩcosΩt with H ∥ h _ω ∥ h _Ω. The low-frequency response is found to be nonlinear in h _Ω. A procedure discriminating between the linear and nonlinear components of this response is proposed. Unlike the linear component, the nonlinear component is an essentially anharmonic function of time. The results are analyzed in detail using the high-frequency and low-frequency magnetization reversal curves of the materials.     

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.     

Pair correlations in a ferromagnetic colloid

We discuss some properties of the equation of state and of the static correlations for spherical ferromagnetic grains, at thermal equilibrium, in a passive fluid. At high external fieldsH, low concentrations, and not too high temperatures, the grains tend to formchains along the directions ofH. In zero field (but otherwise identical conditions), some chains are still present but oriented at random and in competition with closed rings and clusters. Various experimental methods which could give information on these chain structures are listed.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.     

Helical magnetic structure in a quasi-one-dimensional LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> multiferroic crystal according to <Superscript>63,65</Superscript>Cu NMR studies

The NMR spectra of ⁶³Cu and ⁶⁵Cu natural copper isotopes in a LiCu₂O₂ multiferroic single crystal compound have been measured above and below the temperature of magnetic phase transition (T _c = 23 K) in zero magnetic field and in applied magnetic field H ₀ = 94 kOe parallel to the c axis of the crystal. In LiCu₂O₂ below T _c, a complicated helical magnetic structure with the magnetic moment of copper ions Cu²⁺ varying along the chain according to the harmonic law with the wave vector being incommensurate to the crystal lattice constants has been revealed. The experimental results have been successfully interpreted using the model based on the planar helical magnetic structure. It has been found that the plane of rotation for Cu²⁺ magnetic moments in LiCu₂O₂ does not coincide at H ₀ = 0 with the ab plane. The high magnetic field (H ₀ = 94 kOe) applied along the c axis of the single crystal does not affect the spatial orientation of the plane of rotation.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Antiferromagnetic resonance in CuB2O4 single crystal

The frequency-field, temperature, and angular dependences of the antiferromagnetic resonance parameters for the tetragonal CuB₂O₄ single crystal are studied in the frequency range 2.6–80 GHz and at temperatures of 4.2–30 K. The results obtained confirm the fact that, in the high-temperature state in the range 10–21 K, this compound is an easy-plane weak ferromagnet. The temperature dependence of the Dzyaloshinski field is determined. An abrupt change observed in the frequency-field dependence of the magnetic resonance at T=4.2 K and H ⊥ C ₄ indicates the transition to the weak ferromagnetic state induced by the external field H _⊥. The phase diagram for CuB₂O₄ is constructed on the H _⊥-T coordinates. It is demonstrated that, in the low-temperature state, the magnetic moments of copper ions remain in the basal plane, but the weak ferromagnetism is absent.