D. A. Garanin

QUANTUM-CLASSICAL ESCAPE-RATE TRANSITION OF A BIAXIAL SPIN SYSTEM WITH A LONGITUDINAL FIELD : A PERTURBATIVE APPROACH

The quantum-classical transition of the escape rate of the spin model cal H= -DS_z^2 - H_zS_z + B S_x^2 is investigated by a perturbative approach with respect to B [D. A. Garanin, J. Phys A {bf 24}, L61 (1991)]. The transition is first order for B<B_c(H_z), the boundary line going to zero as B_c/D ~ 1 - H_z/(2SD) in the strongly biased limit. The range of the first-order transition is thus larger than for the model cal H = -DS_z^2 - H_zS_z - H_x S_x studied earlier, where in the strongly biased case H_{xc}/(2SD) ~ [1-H_z/(2SD)]^{3/2}. The temperature of the quantum-classical transition, T_0, behaves linearly in the strongly biased case for both models: T_0 ~ 2SD - H_z.

Generalized equation of motion for a ferromagnet

We derive microscopically an equation of motion for a ferromagnetic substance at nonzero temperatures allowing for both transverse and longitudinal relaxation and generalizing the Landau-Lifshitz equation. The consideration starts from the density matrix equation for a quantum spin interacting with the environment, which is within about 7% accuracy reduced to the closed equation for the first moment of the distribution function — the magnetization. The latter interpolates between the Landau-Lifshitz equation (S ⪢ 1 and low temperatures) and the Bloch equation (S = 12 or high temperatures). For condensed magnetic media (i.e. a ferromagnet) one can replace in the spirit of the mean field theory the magnetic field by the molecular one containing the exchange field acting on a given magnetic ion from its neighbours, which results in a Landau-Lifshitz type equation of motion with a longitudinal relaxation term providing the Curie-Weiss static solution. Further we consider the mobility of a domain wall (DW) in a uniaxial ferromagnet at nonzero temperatures where the magnetization in the middle of the domain boundary is smaller than in the domains (the elliptic DW transforms to the linear one near Tc). It is shown that longitudinal relaxation plays a crucial role in DW dynamics in a wide range of high temperatures.

Dynamics of elliptic domain walls

With the use of the generalized Landau-Lifshitz-Bloch equation of motion for a ferromagnet at finite temperatures we investigate the dynamic properties of domain walls (DWs) taking into account their ellipticity, i.e., the deficit of the magnetization value M in the DW in comparison with that of the domains. The translational motion of elliptic DWs is accompanied by longitudinal relaxation, which governs the DW dynamics even in the case of small ellipticity, if the relaxation constants are small. The linear DW mobility μ calculated in the whole temperature range 0⩽T⩽Tc shows a singular behavior in the point T=T∗ where the elliptic DW restructures into a linear one. At low temperatures the calculated dependence of μ on the transverse field Hx is consistent with the experimental observations. The longitudinal relaxation mechanism of the DW damping switches off for the DW velocities υ≳υ0≈lΓ1 (l is the DW width, Γ1 is the longitudinal relaxation rate), and the dependence υ(H) may show a hysteresis. We also derive Slonczewski-like reduced equations of motion for the DW parameters with an additional equation for the magnetization deficit. With the use of these equations the stability of the stationary DW motion is investigated. It is shown that in some cases there are three separate stable sections of the curve υ(H). Finally, the dynamic susceptibility of a ferromagnetic sample due to the displacement of elliptic domain walls is calculated.

Quantum statistical metastability for a finite spin.

We study quantum-classical escape-rate transitions for uniaxial and biaxial models with finite spins

High temperature spin wave dynamics of the uniaxial antiferromagnets

S=10

Phase transitions in classical vector models

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Boundary and finite-size effects in small magnetic systems

{mathrm{Mn}}_{12}mathrm{Ac}

Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

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Tunneling of a large spin via hyperfine interactions.

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An equation of state of the Ising systems

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