Nowak, Ulrich

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#### Monte Carlo simulation of magnetization switching in a Heisenberg model for small ferromagnetic particles

1999, Hinzke, Denise, Nowak, Ulrich

Using Monte Carlo methods we investigate the thermally activated magnetization switching of small ferromagnetic particles driven by an external magnetic field. For low uniaxial anisotropy one expects that the spins rotate coherently while for sufficiently large anisotropy the reversal should be due to nucleation. The latter case has been investigated extensively by Monte Carlo simulation of corresponding Ising models. In order to study the crossover from coherent rotation to nucleation we use a specially adjusted update algorithm for the Monte Carlo simulation of a classical three-dimensional Heisenberg model with a finite uniaxial anisotropy. This special algorithm which uses a combined sampling can simulate different reversal mechanisms efficiently. It will be described in detail and its efficiency and physical validity will be discussed by a comparison with other common update-algorithms.

#### Magnetization switching in small ferromagnetic particles : Nucleation and coherent rotation

1999, Nowak, Ulrich, Hinzke, Denise

The mechanisms of thermally activated magnetization switching in small ferromagnetic particles driven by an external magnetic field are investigated. For low uniaxial anisotropy the spins rotate coherently while for sufficiently large uniaxial anisotropy they behave Ising-like, i.e., the switching then is due to nucleation. The crossover from coherent rotation to nucleation is studied for the classical three-dimensional Heisenberg model with uniaxial anisotropy by Monte Carlo simulations. From the temperature dependence of the metastable lifetime the energy barrier of a switching process can be determined. For the case of infinite anisotropy we compare numerical results from simulations of the Ising model with theoretical results for energy barriers for both, single- and multidroplet nucleation. The simulated barriers are in agreement with the theoretical predictions.

#### Modified Scaling Relation for the Random-Field Ising Model

1998, Nowak, Ulrich, Usadel, Klaus-Dieter, Esser, J.

We investigate the low-temperature critical behavior of the three-dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T â†’ 0 the usual scaling relations have to be modified as far as the exponent Î± of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to Î± + 2Î² + Î³ = 1, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three-dimensional random-field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite-size scaling analysis we calculate the critical exponents Î½ â‰ˆ 1.0, Î² â‰ˆ 0.05, Ó¯ â‰ˆ 2.9, Î³ â‰ˆ 1.5 and Î± â‰ˆ âˆ’0.55.

#### Domain dynamics of magnetic films with perpendicular anisotropy

1997, Nowak, Ulrich, Heimel, JÃ¶rg, Kleinefeld, Theo, Weller, Dieter

We study the magnetic properties of nanoscale magnetic films with large perpendicular anisotropy comparing polarization-microscopy measurements on Co28Pt72-alloy samples based on the magneto-optical Kerr effect with Monte Carlo simulations of a corresponding micromagnetic model. In our model the magnetic film is described in terms of single-domain magnetic grains interacting via exchange as well as via dipolar forces. Additionally, the model contains an energy barrier which has to be overcome in order to reverse a single cell and a coupling to an external magnetic field. Disorder is taken into account. We focus on the understanding of the dynamics especially the temperature and field dependence of the magnetization reversal process. The experimental and simulation results for hysteresis, the reversal mechanism, domain configurations during the reversal, and the time dependence of the magnetization are in very good qualitative agreement. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films the hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.

#### Universality in three dimensional random-field ground states

1999, Hartmann, Alexander K., Nowak, Ulrich

We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three dimensional diluted Ising antiferromagnet in an external field. These models are expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm and by a finite-size scaling analysis we calculate the critical exponents v, Î², and Î³. While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be significantly different.

#### Influence of the temperature on the depinning transition of driven interfaces

1998, Nowak, Ulrich, Usadel, Klaus-Dieter

We study the dynamics of a driven interface in a two-dimensional random-field Ising model close to the depinning transition at small but finite temperatures T using Glauber dynamics. A square lattice is considered with an interface initially in the (11)-direction. The drift velocity v is analyzed using finite-size scaling at T = 0 and additionally finite-temperature scaling close to the depinning transition. In both cases a perfect data collapse is obtained from which we deduce ÃŽÂ² approx 1/3 for the exponent which determines the dependence of v on the driving field, ÃŽÂ½ approx 1 for the exponent of the correlation length and ÃŽÂ´ approx 5 for the exponent which determines the dependence of v on T.

#### Magnetization switching in a Heisenberg model for small ferromagnetic particles

1998, Hinzke, Denise, Nowak, Ulrich

We investigate the thermally activated magnetization switching of small ferromagnetic particles driven by an external magnetic field. For low uniaxial anisotropy the spins can be expected to rotate coherently, while for sufficient large anisotropy they should behave Ising-like, i.e., the switching should then be due to nucleation. We study this crossover from coherent rotation to nucleation for a classical three-dimensional Heisenberg model with finite anisotropy. The crossover is influenced by the size of the particle, the strength of the driving magnetic field, and the anisotropy. We discuss the relevant energy barriers which have to be overcome during the switching, and find theoretical arguments which yield the energetically favorable reversal mechanisms for given values of the quantities above. The results are confirmed by Monte Carlo simulations of Heisenberg and Ising models.

#### Depinning transition and thermal fluctuations in the random-field Ising model

1999, Roters, Lars, Hucht, Alfred, LÃ¼beck, Sven, Nowak, Ulrich, Usadel, Klaus-Dieter

We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system. [S1063-651X(99)03011-1]

#### On the relaxation dynamics of diluted antiferromagnets

1998, Staats, Michael, Nowak, Ulrich, Usadel, Klaus-Dieter

The phase diagram of a diluted Ising antiferromagnet in an external magnetic field has a disordered phase for sufficiently large values of this field and for low temperatures, in which the system's equilibrium state is a domain state. We study the relaxation dynamics out of this state after switching off the magnetic field, for two- and three-dimensional diluted antiferromagnets using Monte Carlo Simulation techniques. We measure the decay of the initial magnetization carried by the domain state. The data can be described by a unique law for a wide range of temperatures, magnetic fields and dilutions in two and three dimensions.

#### Non-exponential relaxation in diluted antiferromagnets

1998, Staats, Michael, Nowak, Ulrich, Usadel, Klaus-Dieter

Dilute Ising antiferromagnets in a homogenous magnetic field have a disordered phase for sufficiently large values of the field and for low temperatures. Here, the system is in a domain state with a broad size-distribution of fractal domains. We study the relaxation dynamics of this domain state after removing the external field for two and three dimensions. Using Monte Carlo simulation techniques, we measure the decay of the remanent magnetization. Its temperature dependence can be understood as thermal activation. All data can be described by a unique generalized power law for a wide range of temperatures in two-and three-dimensions. The question of whether the exponent of the generalized power-law is universal remains open.