Surface effects in nanoparticles: application to maghemite -Fe O

We present a microscopic model for nanoparticles, of the maghemite (-Fe₂O₃) type, and perform classical Monte Carlo simulations of their magnetic properties. On account of M?ssbauer spectroscopy and high-field magnetisation results, we consider a particle as composed of a core and a surface shell of constant thickness. The magnetic state in the particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions and bulk and surface anisotropy. We consider the case of ellipsoidal (or spherical) particles with free boundaries at the surface. Using a surface shell of constant thickness ( nm) we vary the particle size and study the effect of surface magnetic disorder on the thermal and spatial behaviors of the net magnetisation of the particle. We study the shift in the surface “critical region” for different surface-to-core ratios of the exchange coupling constants. It is also shown that the profile of the local magnetisation exhibits strong temperature dependence, and that surface anisotropy is responsible for the non saturation of the magnetisation at low temperatures. Received 1 September 1999 and Received in final form 3 November 1999     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

Switching of vortex polarization in 2D easy-plane magnets by magnetic fields

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation. Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: juan.zagorodny@uni-bayreuth.de     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Phase transitions in the mixed Ashkin-Teller model

By using a mean-field approximation (MFA) and Monte-Carlo (MC) simulations, we have studied the effect on the phase diagrams of mixed spins ( and S =1) in the Ashkin-Teller model (ATM) on a hypercubic lattice. By varying the strength describing the four spin interaction and the single ion potential, we have obtained by these two methods quite rich phase diagrams with several multicritical points. This model exhibits a new partially ordered phase which does not exist neither in the spin-1/2 ATM nor in the spin-1 ATM. While MFA yields phase diagrams which are sometimes qualitatively incorrect, accurate results are obtained from MC simulations. From the critical exponents which have been calculated using finite-size scaling ideas, we have shown that all phase transitions are Ising-like except for the paramagnetic-Baxter critical surface on which the critical exponents vary continuously, by varying only the strength of the coupling interaction independently of the value of the single ion potential. Received 5 July 1999 and Received in final form 4 July 2000     

Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of at small T,H: and , where D=3 is the number of spin components, J ₀=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)). Received 20 March 2000     

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 12 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which consistently covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram. Received 23 April 2001     

Ising magnets with mobile defects

Motivated by recent experiments on cuprates with low-dimensional magnetic interactions, a new class of two-dimensional Ising models with short-range interactions and mobile defects is introduced and studied. The non-magnetic defects form lines, which, as temperature increases, first meander and then become unstable. Using Monte Carlo simulations and analytical low- and high-temperature considerations, the instability of the defect stripes is monitored for various microscopic and thermodynamic quantities in detail for a minimal model, assuming some of the couplings to be indefinitely strong. The robustness of the findings against weakening the interactions is discussed as well. Received 22 August 2002 / Received in final form 4 October 2002 Published online 19 November 2002     

New geometries associated with the nonlinear Schrödinger equation

We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schr?dinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation = ×, ( = 1). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained. Received 5 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: radha@imsc.ernet.in     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Dynamic spin-glass behavior in a disorder-free,two-component model of quantum frustrated magnets

Motivated by the observation of a spin-glass transition in almost disorder-free Kagome antiferromagnets, and by the specific form of the effective low-energy model of the S = 1/2, trimerized Kagome antiferromagnet, we investigate the possibility to obtain a spin-glass behavior in two-component, disorder-free models. We concentrate on a toy-model, a modified Ashkin-Teller model in a magnetic field that couples only to one species of spins, for which we prove that a dynamic spin-glass behavior occurs. The dynamics of the magnetization is closely related to that of the underlying Ising model in zero field in which spins and pseudo-spins are intimately coupled. The spin-glass like history dependence of the magnetization is a consequence of the ageing of the underlying Ising model. Received 21 September 2001 and Received in final form 16 January 2002     

The glassy phase of Gallager codes

Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q _EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes. Received 9 April 2001     

Cycloidal vortex motion in easy-plane ferromagnets due to interaction with spin waves

The dynamics of a non-planar vortex in a two-dimensional easy-plane ferromagnet of finite size is studied. Spin dynamics simulations show small cycloidal oscillations of the vortex around its mean path. In contrast to an earlier phenomenological theory we give a physical explanation: The oscillations occur due to the interaction of the vortex with coherent spin waves which are excited by this vortex at the moment when it starts to move, in order to conserve the total energy and angular momentum. The calculation of these quantities yields the frequencies and amplitudes of the cycloidal oscillations in good agreement with the simulation data. Received 9 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: franz.mertens@uni-bayreuth.de     

Solitons in the spin-Peierls compound CuGeO <Subscript>3</Subscript>

We calculate the excitation gap, the soliton energy, and the soliton density at finite temperature, of the spin-1/2 one dimensional antiferromagnet coupled to phonons, using a self-consistent harmonic approximation, and the thermal-Green function technique. The spin degrees of freedom are represented by the phase Hamiltonian with the help of the boson representation of the spinless fermions. We estimate the critical field H_c above which begins the incommensurate phase. We also present a theoretical calculation for the specific heat in this phase. We use CuGeO₃ as an example of a compound where our theory could be applied. Received 22 October 2002 / Received in final form 21 January 2003 Published online 14 March 2003     

The spin-1/2 anisotropic Heisenberg-chain in longitudinal aaand transversal magnetic fields: a DMRG study

Using the density matrix renormalization group technique, we evaluate the low-energy spectrum (ground state and first excited states) of the anisotropic antiferromagnetic spin-one-half chain under magnetic fields. We study both homogeneous longitudinal and transversal fields as well as the influence of a transversal staggered field on the opening of a spin-gap. We find that only a staggered transversal field opens a substantial gap. Received 16 April 2002 / Received in final form 4 July 2002 Published online 17 September 2002     

The CPA solution of the anomalous Lyapunov exponent for disordered binary chains

The Coherent Potential Approximation (CPA) self-consistent equation is calculated for a binary disordered chain introducing a simple transformation. The transformation reduces the CPA equation to a cubic polynomial whose complex roots are related to the Green function and their relation to the complex Lyapunov exponent is also established. This solution fruitfully captures essential aspects of the well-known anomalous scaling behaviors in a different and advantageous way. It is found that the anomalous behavior is strongly effected by the nature of these roots. A small disorder expansion is carried out for comparison with the previous weak disorder calculations. We found that the CPA reproduced the anomalous behavior of the exact calculations. Received 22 April 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: avgin@bornova.ege.edu.tr     

Temperature fluctuations for a finite system of classical spin-1/2 particles

For sufficiently large but finite N independent spin-1/2 paramagnets in a constant magnetic field, the orientation of every spin has the same probability to be parallel or anti-parallel to that of the magnetic field. In our statistical ensemble treatment, all fundamental thermodynamic quantities fluctuate, including the entropy and temperature, and all fluctuations are gradually vanishing as the temperature itself approaches zero. Our approach presents a remedy of infinite temperature fluctuations and reproduces other reasonable results that are given by standard theory.     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999