Bloch-wall phase transition in the spherical model

Garanin, D. A.

doi:10.1088/0305-4470/29/10/014

Cited by 14 publications

(23 citation statements)

References 40 publications

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“…A more involved approach taking into account spin-wave effects for an exactly solvable model confirms the concomitant increase of thermal effects on the variation of the magnetization length, as was explicitly shown for domain walls in Ref. [12].…”

Section: Hysteresis Loopssupporting

confidence: 75%

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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Section: Hysteresis Loopssupporting

confidence: 75%

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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“…which describes within the MFA both the homogeneous state and such configurations as domain walls with account of thermal effects (see, e.g., Ref. 26 and references therein).…”

Section: Llb Equation For Ferromagnetsmentioning

confidence: 99%

Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets

1997

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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 LandauLifshitz 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 "LandauLifshitz-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 TC and the "micromagnetic" free energy, which neglects changes of the magnetization magnitude |M|, at low temperatures. [S0163-1829(97)

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“…(The definition of G i can be found in Ref. [5]; here it is nonessential.) In the film geometry, it is convenient to use the Fourier representation in d ′ = d − 1 translationally invariant dimensions parallel to the surface and the site representation in the dth dimension.…”

Section: Basic Equations and Their Solutionmentioning

confidence: 99%

Ordering in magnetic films with surface anisotropy

Garanin

1999

J. Phys. A: Math. Gen.

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Effects of the surface exchange anisotropy on ordering of ferromagnetic films are studied for the exactly solvable classical spin-vector model with D → ∞ components. For small surface anisotropy η ′ s ≪ 1 (defined relative to the exchange interaction), the shift of Tc in a film consisting of N ≫ 1 layers behaves as T bulk, which is realized for the model with a bulk anisotropy η ′ ≪ 1 in the range N η ′1/2 > ∼ 1, never appears for the model with the pure surface anisotropy. Here for N exp(−1/η ′ s ) > ∼ 1 in three dimensions, film orders at a temperature above T bulk c (the surface phase transition). In the semi-infinite geometry, the surface phase transition occurs for whatever small values of η ′ s (i.e., the special phase transition corresponds to T bulk c ) in dimensions three and lower.. The possibility of this effect, which is absent in the mean field approximation (MFA), can be seen from the following simple arguments. The isotropic large-D model orders at T bulk c = J 0 /(DW d ), where J 0 is the zero Fourier component of the exchange interaction and W d ≡ P d (1) [see Eq. (2.21)] is the Watson integral containing the information on the lattice dimensionality and structure. On the other hand, the Curie temperature of the monolayer with the (surface) anisotropy of the extreme Ising type, η s = 0 (i.e., η ′ s = 1), is T c (1) = (d ′ /d)J 0 /D. For the simple cubic lattice one has W 3 = 1.51639, so that the Curie temperature of the anisotropic monolayer slightly exceeds the isotropic bulk Curie temperature. That is, the lack of interacting neighbours at the surface can be compensated for by a stronger suppression of T bulk c due to long-wavelength fluctuations making contribution to W d . It is clear that the bilayer has a substantially higher value of T c than the monolayer, and that in dimensions lower than 3 the bulk Curie temperature is suppressed even stronger. For the continuous-dimension model introduced in Ref.[6], one has W 3.0 = 1.719324 and W 2.5 = 2.527059. In two dimensions

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Bloch-wall phase transition in the spherical model

Cited by 14 publications

References 40 publications

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets

Ordering in magnetic films with surface anisotropy

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