The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets
Open accessAbstract
A macroscopic equation of motion for the magnetization of a ferromagnet at elevated temperatures should contain both transverse and longitudinal relaxation terms and interpolate between the Landau-Lifshitz equation at low temperatures and the Bloch equation at high temperatures. It is shown that for the classical model where spin-bath interactions are described by stochastic Langevin fields and spin-spin interactions are treated within the mean-field approximation (MFA), such a ``Landau-Lifshitz-Bloch'' (LLB) equation can be derived exactly from the Fokker-Planck equation, if the external conditions change slowly enough. For weakly anisotropic ferromagnets within the MFA the LLB equation can be written in a macroscopic form based on the free-energy functional interpolating between the Landau free energy near ${\mathrm{T}}_{\mathrm{C}}$ and the ``micromagnetic'' free energy, which neglects changes of the magnetization magnitude |M|, at low temperatures.
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Citations
Cites
Theory of dynamic critical phenomena
Hohenberg, P. C., & Halperin, B. I. (1977) · Reviews of Modern Physics · doi:10.1103/revmodphys.49.435 · Cited by 6,891
Quantum Field Theory and Critical Phenomena
Zinn-Justin, J. (2002) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198509233.001.0001 · Cited by 5,116
Thermal Fluctuations of a Single-Domain Particle
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Critical dynamics of ferromagnets in 6−ε dimensions: General discussion and detailed calculation
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Generalized equation of motion for a ferromagnet
Garanin, D. A. (1991) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(91)90395-s · Cited by 120
Self-citationIntegral relaxation time of single-domain ferromagnetic particles
Garanin, D. A. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.54.3250 · Cited by 116
Self-citationExact analytic formula for the correlation time of a single-domain ferromagnetic particle
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Dynamics of an ensemble of single-domain magnetic particles
Garanin, D. A., Ishchenko, V. V., & Panina, L. V. (1990) · Theoretical and Mathematical Physics · doi:10.1007/bf01079045 · Cited by 95
Self-citationSelf-consistent Gaussian approximation for classical spin systems: Thermodynamics
Garanin, D. A. (1996) · Physical review. B, Condensed matter · doi:10.1103/physrevb.53.11593 · Cited by 72
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Cited by
Atomistic spin model simulations of magnetic nanomaterials
Evans, R. F. L., Fan, W. J., Chureemart, P., Ostler, T. A., Ellis, M. O. A., & Chantrell, R. W. (2014) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/26/10/103202 · Cited by 886
Langevin-dynamics study of the dynamical properties of small magnetic particles
García-Palacios, J. L., & Lázaro, F. J. (1998) · Physical Review B · doi:10.1103/physrevb.58.14937 · Cited by 675
Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons
Braun, H.-B. (2012) · Advances in Physics · doi:10.1080/00018732.2012.663070 · Cited by 421
Perspective: Ultrafast magnetism and THz spintronics
Walowski, J., & Münzenberg, M. (2016) · Journal of Applied Physics · doi:10.1063/1.4958846 · Cited by 386
Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys
Kirilyuk, A., Kimel, A. V., & Rasing, T. (2013) · Reports on Progress in Physics · doi:10.1088/0034-4885/76/2/026501 · Cited by 360
Metadata
- Authors
- Garanin, D. A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1997-02-01
- Volume
- 55
- Issue
- 5
- Pages
- 3050-3057
- ISSN
- 0163-1829 (ISSN-L)
- 1095-3795
- OpenAlex
- W2026126039
- Cited by
- 428
- References
- 9
- FWCI
- 2.20
- Type
- journal article
- Language
- en
- Open access
- green
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- Garanin, D. A. (1997). Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets. Physical Review B. https://doi.org/10.1103/physrevb.55.3050
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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