Evidence for critical fluctuations in Bloch walls near their disordering temperature

Kötzler, J.; Garanin, D. A.; Hartl, Martin; Jahn, L.

doi:10.1103/physrevlett.71.177

Cited by 36 publications

(41 citation statements)

References 13 publications

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“…These results are consistent with measurements of the domain wall mobility in YIG crystals close to T c (Ref. 20) and with recent atomistic simulations.…”

Section: Landau-lifshltz-bloch Equationsupporting

confidence: 92%

Towards multiscale modeling of magnetic materials: Simulations of FePt

et al. 2008

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The established methods for the numerical evaluation of magnetic material properties exist only in certain limits, including first-principles methods, spin models, and micromagnetics. In the present paper, we introduce a multiscale modeling approach, bridging the gaps between the three approaches above. The goal is to describe thermodynamic equilibrium and nonequilibrium properties of magnetic materials on length scales up to micrometers, starting from first principles. In the first step, we model, as an example, bulk FePt in the ordered Llo phase by using an effective, classical spin Hamiltonian that was constructed earlier on the basis of firstprinciples methods. The next step is to simulate this spin model by using the stochastic Landau-LifshitzGilbert equation. The temperature dependent micromagnetic parameters, which are evaluated with these atomistic simulations, are consequently used to develop a many macrospin micromagnetic approach, based on the Landau-Lifshitz-Bloch equation. As an example, we calculate the magnetization dynamics following a picosecond heat pulse resembling pump-probe experiments.

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“…These results are consistent with measurements of the domain wall mobility in YIG crystals close to T c (Ref. 20) and with recent atomistic simulations.…”

Section: Landau-lifshltz-bloch Equationsupporting

confidence: 92%

Towards multiscale modeling of magnetic materials: Simulations of FePt

et al. 2008

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“…The deviations of the LLB dynamics from the LL dynamics should be pronounced at high temperatures, especially close to the Curie temperature T c . The validity of this approach has been confirmed by the measurements of the domain-wall mobility in crystals of Ba-and Sr-hexaferrites close to T c [9].Since the proposal of the heat-assisted magnetic recording (HAMR) [10] the problem of high-temperature thermal magnetization dynamics has become of large practical importance. The basic idea of HAMR is to write bits of information at elevated temperature (close to the Curie temperature, where the switching field is small) and store the information at room temperature.…”

mentioning

confidence: 93%

Thermal fluctuations and longitudinal relaxation of single-domain magnetic particles at elevated temperatures

2004

Self Cite

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We present numerical and analytical results for the swiching times of magnetic nanoparticles with uniaxial anisotropy at elevated temperatures, including the vicinity of Tc. The consideration is based in the Landau-Lifshitz-Bloch equation that includes the relaxation of the magnetization magnitude M . The resulting switching times are shorter than those following from the naive Landau-Lifshitz equation due to (i) additional barrier lowering because of the reduction of M at the barrier and (ii) critical divergence of the damping parameters.PACS numbers: 75.50. Tt, 75.40.Mg, 75.60.Nt, 75.50.Ss The theory of thermal fluctuations of small magnetic particles is one of the fundamental issues of modern micromagnetics. The conditions at which the particle becomes superparamagnetic define the thermal stability of the magnetized state and, therefore, is also valuable for technological application such as magnetic recording [1]. The basis of the theory has been introduced by Brown [2] who suggested to include thermal fluctuations into the Landau-Lifshitz (LL) dynamical equation as formal random fields whose properties are defined by the equilibrium solution of the correspondent Fokker-Planck (FP) equation. He also derived the Arrhenius-Néel formula to describe the relaxation rate in the axially symmetric case of single-domain particles which was lately generalized to the presence of external field [3,4]. Since the paper of Chantrell and Lyberatos [5], this Langevin-dynamics approach of Brown has been brought to numerical micromagnetics to model the thermal properties of an ensemble of interacting particles and, more generally, of ferromagnetic materials, interpreting the micromagnetic discretization elements as small particles. Generally speaking, the LL equation used in these simulations is a lowtemperature approximation only. Recently a generalized Landau-Lifshitz-Bloch (LLB) equation for a ferromagnet [6,8] was derived which is valid for all temperatures and includes the longitudinal relaxation. The deviations of the LLB dynamics from the LL dynamics should be pronounced at high temperatures, especially close to the Curie temperature T c . The validity of this approach has been confirmed by the measurements of the domain-wall mobility in crystals of Ba-and Sr-hexaferrites close to T c [9].Since the proposal of the heat-assisted magnetic recording (HAMR) [10] the problem of high-temperature thermal magnetization dynamics has become of large practical importance. The basic idea of HAMR is to write bits of information at elevated temperature (close to the Curie temperature, where the switching field is small) and store the information at room temperature. To achieve a significant areal density advantage, the use of high-anisotropy intermetallics such as Ll 0 FePt has been suggested [11]. Therefore, from both fundamental and applied points of view it is necessary to consider the micromagnetics of small particles (or magnetic grains) at elevated temperatures. The straightforward approach [12] uses the formalism of the sta...

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“…Using this approach, Bulaevskii and Ginzburg [3] predicted a phase transition between the Bloch walls and the Ising-like walls at temperatures slightly below T c . Much later this phase transition was observed experimentally [4,5] using the theoretical results for the mobility of domain walls in this regime [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…That is, for the magnetization to overcome the barrier, it is easier to change its magnitude than its direction. This is a phenomenon of the same kind as the phase transition in ferromagnets between the Ising-like domain walls in the vicinity of T c (the magnetization changes its magnitude and is everywhere directed along the z axis) and the Bloch walls at lower temperatures [3,4].…”

Section: Free Energy Of a Magnetic Particlementioning

confidence: 99%

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

Kachkachi¹,

Garanin

2001

Physica A: Statistical Mechanics and its Applications

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We derive a free energy for weakly anisotropic ferromagnets which is valid in the whole range of temperature and interpolates between the micromagnetic energy at zero temperature and the Landau free energy near the Curie point T c . This free energy takes into account the change of the magnetization length due to thermal effects, in particular, in the inhomogeneous states. As an illustration, we study the thermal effect on the Stoner-Wohlfarth curve and hysteresis loop of a ferromagnetic nanoparticle assuming that it is in a single-domain state. Within this model, the saddle point of the particle's free energy, as well as the metastability boundary, are due to the change in the magnetization length sufficiently close to T c , as opposed to the usual homogeneous rotation process at lower temperatures.

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Evidence for critical fluctuations in Bloch walls near their disordering temperature

Cited by 36 publications

References 13 publications

Towards multiscale modeling of magnetic materials: Simulations of FePt

Towards multiscale modeling of magnetic materials: Simulations of FePt

Thermal fluctuations and longitudinal relaxation of single-domain magnetic particles at elevated temperatures

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

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