Klaus-Dieter Usadel

Domain state model for exchange bias

Monte Carlo simulations of a system consisting of a ferromagnetic layer exchange coupled to a diluted antiferromagnetic layer described by a classical spin model show a strong dependence of the exchange bias on the degree of dilution in agreement with recent experimental observations on Co/CoO bilayers. These simulations reveal that diluting the antiferromagnet leads to the formation of domains in the volume of the antiferromagnet carrying a remanent surplus magnetization which causes and controls exchange bias. To further support this domain state model for exchange bias we study, in the present article, the dependence of the bias field on the thickness of the antiferromagnetic layer. It is shown that the bias field strongly increases with increasing film thickness and eventually goes over a maximum before it levels out for large thicknesses. These findings are in full agreement with experiments.

Asymmetric Reversal Modes in Ferromagnetic/Antiferromagnetic Multilayers

Experimentally an asymmetry of the reversal modes has been found in certain exchange bias systems. From a numerical investigation of the domain state model evidence is gained that this effect depends on the angle between the easy axis of the antiferromagnet and the applied magnetic field. Depending on this angle the ferromagnet reverses either symmetrically, e.g., by a coherent rotation on both sides of the loop, or the reversal is asymmetric with a nonuniform reversal mode for the ascending branch, which may even yield a zero perpendicular magnetization.

Domain wall mobility in nanowires : Transverse versus vortex walls

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of 1/ a 2 . PACS number~s!: 75.10.Hk, 75.40.Mg, 75.60.Ch Arrays of magnetic nanowires are possible candidates for patterned magnetic storage media. 1,2 For these nanowires and also for other future magnetoelectronic devices the understanding of domain wall motion and mobility is important for the controlled switching of the nanostructure. In a recent experiment, the velocity of a domain wall in a NiFe/Cu/NiFe trilayer was investigated using the giant magneto-resistance ~GMR! effect. 3 The measured velocities were compared with the Landau-Lifshitz formula for domain wall motion. 4 This comparison was used to determine the damping constant of the trilayer, a quantity that is usually not known a priori. However, several formulas for the velocity of a domain wall can be found in the literature 4‐8 which are derived in different limits and all in ~quasi-! one-dimensional models, neglecting the possible influence of nonuniform spin structures within the domain wall. Thus the question arises in how far these formulas are applicable to real three-dimensional domain structures. To shed some light onto this problem, we numerically investigate the domain wall mobility in nanowires starting from a three-dimensional local spin model. In the following we consider a classical spin model with energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field. Such a spin model for the description of magnetic nanostructures 9 can be justified following different lines: on the one hand, it is the classical limit of a quantum-mechanical, localized spin model; on the other hand, it might be interpreted as the discretized version of a micromagnetic continuum model, where the charge distribution for a single cell of the discretized lattice is approximated by a point dipole. For certain magnetic systems their description in terms of a lattice of magnetic moments may even be based on the mesoscopic structure of the material, especially when a particulate medium is described. However, our intention is not to describe a particular material but to investigate a general model Hamiltonian, which is

Exact ground-state properties of disordered Ising systems

Exact ground states are calculated with an integer optimization algorithm for two- and three-dimensional site-diluted Ising antiferromagnets in a field ~DAFF! and random field Ising ferromagnets ~RFIM!, the latter with Gaussian- and bimodal-distributed random fields. We investigate the structure and the size distribution of the domains of the ground state and compare it to earlier results from Monte Carlo ~MC! simulations for finite temperature. Although DAFF and RFIM are thought to be in the same universality class we found differences between these systems as far as the distribution of domain sizes is concerned. In the limit of strong disorder for the DAFF in two and three dimensions the ground states consist of domains with a broad size distribution that can be described by a power law with exponential cutoff. For the RFIM this is only true in two dimensions while in three dimensions above the critical field where long-range order breaks down the system consists of two infinite interpenetrating domains of up and down spins—the system is in a two-domain state. For DAFF and RFIM the structure of the domains of finite size is fractal and the fractal dimensions for the DAFF and the RFIM agree within our numerical accuracy supporting that DAFF and RFIM are in the same universality class. Also, the DAFF ground-state properties agree with earlier results from MC simulations in the whole whereas there are essential differences between our exact ground-state calculations and earlier MC simulations for the RFIM which suggested that there are differences between the fractality of domains in RFIM and DAFF. Additionally, we show that for the case of higher disorder there are strong deviations from Imry-Ma-type arguments for RFIM and DAFF in two and three dimensions.

Monte-Carlo study of the reorientation transition in Heisenberg models with dipole interactions

Abstract We simulated the classical two-dimensional anisotropic Heisenberg model with full long range dipole interaction with an algorithm especially designed for long range models. The results show strong evidence for a first order reorientation transition at a temperature T R T C for appropriate parameters of the model Hamiltonian.

REORIENTATION TRANSITION OF ULTRATHIN FERROMAGNETIC FILMS

We demonstrate that the reorientation transition from out-of-plane to in-plane magnetization with decreasing temperature as observed experimentally in Ni films on Cu(001) can be explained on a microscopic basis. Using a combination of mean-field theory and perturbation theory, we derive an analytic expression for the temperature-dependent anisotropy. The reduced magnetization in the film surface at finite temperatures plays a crucial role for this transition as with increasing temperature the influence of the uniaxial anisotropies is reduced at the surface and is enhanced inside the film.

Numerical determination of the avalanche exponents of the Bak-Tang-Wiesenfeld model

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration, and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.

Modeling exchange bias microscopically

Abstract Exchange bias is a horizontal shift of the hysteresis loop observed for a ferromagnetic layer in contact with an antiferromagnetic layer. Since exchange bias is related to the spin structure of the antiferromagnet, for its fundamental understanding a detailed knowledge of the physics of the antiferromagnetic layer is inevitable. A model is investigated where domains are formed in the volume of the AFM stabilized by dilution. These domains become frozen during the initial cooling procedure carrying a remanent net magnetization which causes and controls exchange bias. Varying the anisotropy of the antiferromagnet, we find a non-trivial dependence of the exchange bias on the anisotropy of the antiferromagnet.

Anisotropy of ultrathin ferromagnetic films and the spin reorientation transition

The influence of uniaxial anisotropy and the dipole interaction on the direction of the magnetization of ultrathin ferromagnetic films in the ground state is studied. The ground-state energy can be expressed in terms of anisotropy constants which are calculated in detail as a function of the system parameters and the film thickness. In particular noncollinear spin arrangements are taken into account. Conditions for the appearance of a spin reorientation transition are given and analytic results for the width of the canted phase and its shift in applied magnetic fields associated with this transition are derived.

DENSITY FLUCTUATIONS AND PHASE TRANSITION IN THE NAGEL-SCHRECKENBERG TRAFFIC FLOW MODEL

We consider the transition of the Nagel-Schreckenberg traffic flow model from the free flow regime to the jammed regime. We examine the inhomogeneous character of the system by introducing a new method of analysis which is based on the local density distribution. We investigated the characteristic fluctuations in the steady state and present the phase diagram of the system.