Random textures of the order parameter of superfluid 3He-B in aerogel

A phenomenological scheme of the observed properties of superfluid ³He in aerogel is proposed in the spirit of the Ginzburg-Landau theory. The effect of the aerogel on the order parameter is described by the random tensor field η_jl(r). The tensor field exerts a considerable disorienting effect on the order parameter in the A phase of ³He, but virtually unaffects the orientation of the order parameter in the B phase in zero magnetic field. The change in the texture of the order parameter emerging in the B phase in aerogel in a magnetic field is considered. It is shown that the mean square of the angle between the magnetic field direction and the anisotropy axis of the B phase is proportional to the third power of the magnetic field strength. The fluctuations of the direction of the magnetic anisotropy axis of ³He-B are correlated over the familiar “healing length”, which is inversely proportional to the field strength and has a macroscopic scale.     

Low-temperature stability limit of the coherent spin precession in <Superscript>3</Superscript>He-B

It has been shown that the instability of uniform spin precession in the bulk of the ³He-B superfluid phase is due to the joint action of the anisotropy of the velocities of spin waves and dipole interaction. In the leading approximation in the ratio of the Leggett frequency to the Larmor frequency, the growth increments of the amplitudes of spin waves for all of the possible decay channels have been found. The maximum increment has been determined for all of the angles of spin deviation from the equilibrium orientation. The minimum temperature to which precession is stable has been estimated.     

Spin transport in the Néel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice

We analyze and compare the effect of spatial and spin anisotropy on spin conductivity in a two dimensional S = 1/2 Heisenberg quantum magnet on a square lattice. We explore the model in both the Néel antiferromagnetic (AF) phase and the collinear antiferromagnetic (CAF) phase. We find that in contrast to the effects of spin anisotropy in the Heisenberg model, spatial anisotropy in the AF phase does not suppress the zero temperature regular part of the spin conductivity in the zero frequency limit–rather it enhances it. In the CAF phase (within the non-interacting approximation), the zero frequency spin conductivity has a finite value, which is suppressed as the spatial anisotropy parameter is increased. Furthermore, the CAF phase displays a spike in the spin conductivity not seen in the AF phase. We also explore the finite temperature effects on the Drude weight in the AF phase (within the collisionless approximation). We find that enhancing spatial anisotropy increases the Drude weight value and increasing spin anisotropy decreases the Drude weight value. Based on these studies, we conclude that antiferromagnets with spatial anisotropy are better spin conductors than those with spin anisotropy at both zero and finite temperatures.     

Quantum HeisenbergS=1/2 spin glass with ferromagnetic coupling and random Dzyaloshinskii-Moriya interactions

By means of the generalized static replica symmetric spin glass theory, a quantum HeisenbergS=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J ₀). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.     

On the room temperature multiferroic BiFeO<Subscript>3</Subscript>: magnetic,dielectric and thermal properties

Magnetic dc susceptibility between 1.5 and 800 K, ac susceptibility and magnetization, thermodynamic properties, temperature dependence of radio and audio-wave dielectric constants and conductivity, contact-free dielectric constants at mm-wavelengths, as well as ferroelectric polarization are reported for single crystalline BiFeO₃. A well developed anomaly in the magnetic susceptibility signals the onset of antiferromagnetic order close to 635 K. Beside this anomaly no further indications of phase or glass transitions are indicated in the magnetic dc and ac susceptibilities down to the lowest temperatures. The heat capacity has been measured from 2 K up to room temperature and significant contributions from magnon excitations have been detected. From the low-temperature heat capacity an anisotropy gap of the magnon modes of the order of 6 meV has been determined. The dielectric constants measured in standard two-point configuration are dominated by Maxwell-Wagner like effects for temperatures T > 300 K and frequencies below 1 MHz. At lower temperatures the temperature dependence of the dielectric constant and loss reveals no anomalies outside the experimental errors, indicating neither phase transitions nor strong spin phonon coupling. The temperature dependence of the dielectric constant was measured contact free at microwave frequencies. At room temperature the dielectric constant has an intrinsic value of 53. The loss is substantial and strongly frequency dependent indicating the predominance of hopping conductivity. Finally, in small thin samples we were able to measure the ferroelectric polarization between 10 and 200 K. The saturation polarization is of the order of 40 μC/cm², comparable to reports in literature.     

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

We review the normal and superconducting state properties of the unconventional triplet superconductor Sr₂RuO₄ with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru d‐orbitals and a strong magnetic anisotropy occurs (χ^+‐ < χ^zz) due to spin‐orbit coupling. The latter results mainly from different values of the g‐factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation‐induced Cooper‐pairing scenario in application to Sr₂RuO₄ we show how p‐wave Cooper‐pairing with line nodes between neighboring RuO₂‐planes may occur. We also discuss the open issues in Sr₂RuO₄ like the influence of magnetic and non‐magnetic impurities on the superconducting and normal state of Sr₂RuO₄. It is clear that the physics of triplet superconductivity in Sr₂RuO₄ is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy‐fermion systems exhibiting spin fluctuations.     

Orbital glass and spin glass states of <Superscript>3</Superscript>He-A in aerogel

Glass states of superfluid A-like phase of ³He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vector Ηthe orbital glass (OG). The phases differ by the spin structure: the spin nematic vector \(\hat d\) can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal ³He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation is applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.     

Ferromagnetic resonance in the Cr1/3NbS2 helical magnet

The high-frequency spin excitations in the Cr_1/3NbS₂ helical magnet have been investigated. The contributions of the uniform and Goldstone modes of the spin precession have been determined. It has been shown that the resonant field of the uniform mode is determined by the uniaxial magnetocrystalline anisotropy. Final values of the energy and the resonant field of the Goldstone mode are determined by the sixth-order magnetocrystalline anisotropy in the basal plane.     

Diffuse X-ray scattering and nanoclusters in the Hg2Br2 model ferroelastics

Diffuse maxima are revealed and studied for the first time in the x-ray scattering patterns of Hg₂Br₂ single crystals. These maxima originate from clusters of the orthorhombic phase due to the phase transition in the paraphase tetragonal matrix. The nucleation and growth of clusters are initiated by spatiotemporal fluctuations of the order parameter corresponding to the soft transverse acoustic mode at X points of the Brillouin zone boundary. Information on the behavior of the susceptibility and correlation length with variations in temperature and on the shape and anisotropy of the clusters is obtained, and the critical exponents are determined.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Nuclear resonance measurements of CePd2Ga3

CePd₂Ga₃, a Kondo lattice exhibiting ferromagnetic order below T _C = 6.3 K, has been studied using Ga NMR technique. Measurements of the magnetic susceptibility on an oriented sample proved the strong anisotropy of this quantity, whose major component is in the basal plane. From the analysis of NMR spectra of differently oriented samples, the quadrupole parameters and the temperature-dependent anisotropic Knight-shift have been determined. While the anisotropy of the susceptibility can sufficiently account for the axial anisotropy of the ⁷¹Ga Knight shift, the in-plane anisotropy of the shift points towards dipolar effects enhanced by hybridization of the Ce-4f and Ga-s electrons.     

Order parameters in lanthanum gallate lightly doped with manganese and paramagnetic resonance

The Cr³⁺ centers have been revealed, transitions at room temperature have been identified, and spin Hamiltonian parameters have been determined for the Cr³⁺ and Fe³⁺ triclinic centers in lanthanum gallate lightly doped with manganese. The principal axes of the fourth-rank fine-structure tensor for the Fe³⁺ triclinic centers have been established and used to determine the order parameters, i.e., the angles of rotation of oxygen octahedra of lanthanum gallate with respect to the perovskite structure. The order parameter in the rhombohedral phase has been estimated.     

13C and 1H nuclear spin lattice magnetic relaxation in undoped polyacetylene

Pulsed NMR spin lattice relaxation measurements on ¹³C and ¹H nuclei in undoped trans-polyacetylene have been carried out between 6 and 295 K. The results indicate that the spin lattice relaxation is due to equilibrium fluctuations of the orientational order parameter for the protons while the carbon relaxation can be attributed to their coupling to paramagnetic impurities. In this temperature range no contribution of solitons has been detected in the relaxation mechanisms.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Random anisotropy in ising spin glass

The theory of Ghatak and Sherrington for the Ising spin glass with uniform uniaxial anisotropy has been extended for the random uniaxial anisotropy (RUA). The magnitude of the RUA is assumed to fluctuate randomly with gaussian probability distribution. The susceptibility and the specific heat have been calculated for a system of spin one and zero mean values of the anisotropy and the exchange interaction. It is found that the random fluctuations of the anisotropy produce a cusp in the susceptibility and a broad maximum in the specific heat.     

Diffuse x-ray scattering in the Hg2I2 model incipient ferroelastics

This paper reports the first detection and study of diffuse maxima in x-ray scattering in Hg₂I₂ incipient ferroelastics. These maxima originate from the formation of clusters of the incipient orthorhombic phase in the paraelastic tetragonal matrix. The nucleation and growth of the clusters are caused by spatial and temporal fluctuations of the order parameter (which correspond to the TA soft mode at the X point of the Brillouin zone edge) and are induced by the incipient phase transition. Information is obtained on the temperature behavior of the susceptibility and correlation length and on the shape and anisotropy of clusters, and the critical indices are determined.     

Spin dynamics in LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> and NaCu<Subscript>2</Subscript>O<Subscript>2</Subscript> low-dimensional helical magnets

Comprehensive NMR investigation of low-frequency spin dynamics of LiCu₂O₂ (LCO) and NaCu₂O₂ (NCO) low-dimensional helical magnets in the paramagnetic state has been carried out for the first time. Temperature dependences of the spin–lattice relaxation rate and anisotropy on various LCO/NCO nuclei have been determined at various orientations of single crystals in an external magnetic field. The spatial asymmetry of spin fluctuations in LCO multiferroic has been discovered. The quantitative analysis of the anisotropy of spin–lattice relaxation in LCO/NCO has allowed estimating the contributions of individual neighboring Cu²⁺ ions to the transferred hyperfine field on Li⁺(Na⁺) ions.     

Magnetization and configurational anisotropy in magnetic clusters: Monte Carlo simulation

Based on the Monte Carlo simulation, the magnetic properties of the clusters, e.g. magnetization, Curie temperature, hysteresis, coercivity, natural angle and energy distribution etc., have been calculated. It has been found that, for the pure ferromagnetic cluster, the T^3/2 Bloch law is well satisfied at low temperature (T < 0.5 T_C) and B_sur is equal to 3 B_bulk. Meanwhile, there are clear indications that B increases drastically with the reducing atomic number Nwhich is consistent with the experimental facts. The results have been evalucted using the Bloch exponent law in the approximate crystalline approximation. It has also been demonstrated that the size dependence of the Curie temperature can be described by finite-size scaling theory. The investigation of the hysteresis and the spin configurations in different magnetization processes reveals the existence of an easy magnetization direction and anisotropy. The thermal coercivity for the clusters with zero and finite uniaxial anisotropy matches the experimental results well. The simulated results for the natural angle and energy distribution in the clusters prove further the existence of the configurational anisotropy in the clusters. It has been discussed that the natural angle and energy distribution influence the hysteresis of a cluster.Received: 10 September 2003, Published online: 15 March 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.40.Mg Numerical simulation studies - 75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

Dipolar anisotropy in quasi-2D honeycomb antiferromagnet MnPS<Subscript>3</Subscript>

The nature of the anisotropy in magnetic systems which show isotropic Heisenberg exchange is crucial in determining their magnetic properties. This is particularly true in low-dimensional systems in which the very existence of long-range order depends on the anisotropy. The honeycomb lattice MnPS₃ system has been studied as an example of a magnetically quasi-two-dimensional system of unusual symmetry. In this paper the effect of the dipole-dipole interaction in MnPS₃ on the magnetic ordering is explored through modelling. It is found that the dipolar anisotropy can explain the spin directions both in zero field and above the spin flop phase transition, but it is important that real rather than idealised atomic coordinates are used; this latter consideration is significant because in performing theoretical calculations, it may sometimes be assumed that small deviations away from the ideal can be ignored, but in truth they determine key aspects of the behaviour.     

Magnetic properties of magnetoactive spin clusters

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([…] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter.