Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a^†b=Λ(N)$a^{†}b=\Lambda \left(N\right)$ or N=Λ⁻¹(a^†b)$N={\Lambda }^{-1}\left(a^{†}b\right)$, where N$N$, a^†$a^{†}$, and b$b$ denote the number, creation, and annihilation operators, i.e., N$N$ is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides the Bose–Einstein and Fermi–Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q$q$-deformation schemes. Our result shows that the statistical distributions corresponding to various q$q$-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q$q$. This result shows that the results given in much literature on the q$q$-deformation distribution are inaccurate or incomplete.     

Measurements of magnetostriction of paramagnetic Fe–Mo–Cu–B metallic glasses

Magnetostriction of amorphous Fe₇₉Mo₈Cu₁B₁₂, (Fe₁₂Co₁)₇₉Mo₈Cu₁B₁₂ and (Fe₉Co₁)₇₉Mo₈Cu₁B₁₂ prepared by planar flow casting was measured using a direct method. The results indicate that magnetostriction in parallel (_λ∥)$({\lambda }_{\parallel })$ and perpendicular (_λ⊥)$({\lambda }_{\perp })$ directions of applied magnetic field is linearly dependent on magnetic field. In order to determine the influences of chemical composition and the conditions of sample preparation the magnetostriction of pure BCC-Fe, Cu and Mo were also measured. Samples containing Co with Curie temperatures slightly above room temperatures were shown to exhibit a hybrid magnetostriction behaviour with both ferromagnetic and paramagnetic features.     

On the Riemannian geometry of Seiberg–Witten moduli spaces

We construct a natural L²$L^2$-metric on the perturbed Seiberg–Witten moduli spaces _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ of a compact 4-manifold M$M$, and we study the resulting Riemannian geometry of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$. We derive a formula which expresses the sectional curvature of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ in terms of the Green operators of the deformation complex of the Seiberg–Witten equations. In case M$M$ is simply connected, we construct a Riemannian metric on the Seiberg–Witten principal U(1)$U\left(1\right)$ bundle P→_Mμ+$\mathfrak{P}\to {\mathfrak{M}}_{{\mu }^{+}}$ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M$M$, the L²$L^2$-metric on _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ coincides with the natural Kähler metric on moduli spaces of vortices.     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

The phase diagram of a ferrimagnetic multilayer system with disordered interface layers

The critical and compensation behaviors of a ferrimagnetic multilayer system on a simple cubic structure consisting of L layer of spin-1/2 A atoms, L   layers of spin-1 B atoms and a disordered interface with two layers in between that is characterized by a random arrangement of A and B atoms of _APB1-P${\mathrm{A}}_P{\mathrm{B}}_{1-P}$ type in the first layer and _A1-PBP${\mathrm{A}}_{1-P}{\mathrm{B}}_P$ type in the second layer and a negative A–B coupling, are examined using the effective field theory based on a probability distribution technique. The effect of the probability p$p$, interactions, different anisotropy and the thickness L on the magnetic properties is examined. The obtained results show a number of characteristic features, such as the possibility of many compensation points.