147 research outputs found
Fokker-Planck and Landau-Lifshitz-Bloch Equations for Classical Ferromagnets
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 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 T_C and the
``micromagnetic'' free energy, which neglects changes of the magnetization
magnitude |{\bf M}|, at low temperatures.Comment: 9 pages, no figures, a small error correcte
Bloch-Wall Phase Transition in the Spherical Model
The temperature-induced second-order phase transition from Bloch to linear
(Ising-like) domain walls in uniaxial ferromagnets is investigated for the
model of D-component classical spin vectors in the limit D \to \infty. This
exactly soluble model is equivalent to the standard spherical model in the
homogeneous case, but deviates from it and is free from unphysical behavior in
a general inhomogeneous situation. It is shown that the thermal fluctuations of
the transverse magnetization in the wall (the Bloch-wall order parameter)
result in the diminishing of the wall transition temperature T_B in comparison
to its mean-field value, thus favouring the existence of linear walls. For
finite values of T_B an additional anisotropy in the basis plane x,y is
required; in purely uniaxial ferromagnets a domain wall behaves like a
2-dimensional system with a continuous spin symmetry and does not order into
the Bloch one.Comment: 16 pages, 2 figure
Quantum statistical metastability for a finite spin
We study quantum-classical escape-rate transitions for uniaxial and biaxial
models with finite spins S=10 (such as Mn_12Ac and Fe_8) and S=100 by a direct
numerical approach. At second-order transitions the level making a dominant
contribution into thermally assisted tunneling changes gradually with
temperature whereas at first-order transitions a group of levels is skipped.
For finite spins, the quasiclassical boundaries between first- and second-order
transitions are shifted, favoring a second-order transition: For Fe_8 in zero
field the transition should be first order according to a theory with S \to
\infty, but we show that there are no skipped levels at the transition.
Applying a field along the hard axis in Fe_8 makes transition the strongest
first order. For the same model with S=100 we confirmed the existence of a
region where a second-order transition is followed by a first-order transition
[X. Martines Hidalgo and E. M. Chudnovsky, J. Phys.: Condensed Matter (in
press)].Comment: 7 Phys. Rev. pages, 10 figures, submitted to PR
Landau-Zener-Stueckelberg effect in a model of interacting tunneling systems
The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting
tunneling particles is studied numerically and analytically. Each of N
tunneling particles interacts with each of the others with the same coupling J.
This problem maps onto that of the LZS effect for a large spin S=N/2. The
mean-field limit N=>\infty corresponds to the classical limit S=>\infty for the
effective spin. It is shown that the ferromagnetic coupling J>0 tends to
suppress the LZS transitions. For N=>\infty there is a critical value of J
above which the staying probability P does not go to zero in the slow sweep
limit, unlike the standard LZS effect. In the same limit for J>0 LZS
transitions are boosted and P=0 for a set of finite values of the sweep rate.
Various limiting cases such as strong and weak interaction, slow and fast sweep
are considered analytically. It is shown that the mean-field approach works
well for arbitrary N if the interaction J is weak.Comment: 13 PR pages, 15 Fig
The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field
The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical
magnets described by the -component vector model is calculated analytically
in the whole range of temperature and magnetic fields with the help of the 1/D
expansion. In the 1-st order in 1/D the theory reproduces with a good accuracy
the temperature dependence of the zero-field susceptibility of antiferromagnets
\chi with the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of the
exchange interaction) and describes for the first time the singular behavior of
\chi(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0}
\chi(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0}
\chi(H,T)=1/(2|J_0|)
Phase transition between quantum and classical regimes for the escape rate of a biaxial spin system
Employing the method of mapping the spin problem onto a particle one, we have
derived the particle Hamiltonian for a biaxial spin system with a transverse or
longitudinal magnetic field. Using the Hamiltonian and introducing the
parameter where (U_{min})
corresponds to the top (bottom) of the potential and is the energy of the
particle, we have studied the first- or second-order transition around the
crossover temperature between thermal and quantum regimes for the escape rate,
depending on the anisotropy constant and the external magnetic field. It is
shown that the phase boundary separating the first- and second-order transition
and its crossover temperature are greatly influenced by the transverse
anisotropy constant as well as the transverse or longitudinal magnetic field.Comment: 5 pages + 3 figures, to be published in Phys. Rev.
Dislocation-induced spin tunneling in Mn-12 acetate
Comprehensive theory of quantum spin relaxation in Mn-12 acetate crystals is
developed, that takes into account imperfections of the crystal structure and
is based upon the generalization of the Landau-Zener effect for incoherent
tunneling from excited energy levels. It is shown that linear dislocations at
plausible concentrations provide the transverse anisotropy which is the main
source of tunneling in Mn-12. Local rotations of the easy axis due to
dislocations result in a transverse magnetic field generated by the field
applied along the c-axis of the crystal, which explains the presence of odd
tunneling resonances. Long-range deformations due to dislocations produce a
broad distribution of tunnel splittings. The theory predicts that at subkelvin
temperatures the relaxation curves for different tunneling resonances can be
scaled onto a single master curve. The magnetic relaxation in the thermally
activated regime follows the stretched-exponential law with the exponent
depending on the field, temperature, and concentration of defects.Comment: 17 pages, 14 figures, 1 table, submitted to PR
Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity
It is shown that crystals of molecular nanomagnets exhibit enhanced magnetic
relaxation when placed inside a resonant cavity. Strong dependence of the
magnetization curve on the geometry of the cavity has been observed, providing
evidence of the coherent microwave radiation by the crystals. A similar
dependence has been found for a crystal placed between Fabry-Perot
superconducting mirrors. These observations open the possibility of building a
nanomagnetic microwave laser pumped by the magnetic field
Quantum-Classical Phase Transition of Escape rate in Biaxial Spin Particles
The escape rates of the biaxial single domain spin particles with and without
an applied magnetic field are investigated. Using the strict potential field
description of spin systems developed by Ulyanov and Zaslavskii we obtain new
effective Hamiltonians which are considered to be in exact spin-coordinate
correspondence unlike the well studied effective Hamiltonians with the
approximate correspondence. The sharp first-order transition is found in both
cases. The phase diagram of the transitions depending on the anisotropy
constant and the external field is also given.Comment: 15 pages, 8 figure
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