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

Tunneling of a large spin via hyperfine interactions

We consider a large spin \bf S in the magnetic field parallel to the uniaxial crystal field, interacting with N >> 1 nuclear spins \bf I_i via Hamiltonian \cal H = -DS_z^2 - H_zS_z+ A{\bf S}\cdot \sum_{i=1}^N {\bf I}_i with A << D, at temperature T. Tunneling splittings and the selection rules for the resonant values of H_z are obtained perturbatively. The quantum coherence exists at T << ASI while at T >= ASI the coherence is destroyed and the relaxation of \bf S is described by a stretched dependence which can be close to log t under certain conditions. Relevance to Mn-12 acetate is discussed.Comment: 5 PR pages, 4 figures, submitted to PR

Inverse problem for the Landau-Zener effect

We consider the inverse Landau-Zener problem which consists in finding the energy-sweep functions W(t)=E1(t)-E2(t) resulting in the required time dependences of the level populations for a two-level system crossing the resonance one or more times during the sweep. We find sweep functions of particular forms that let manipulate the system in a required way, including complete switching from the state 1 to the state 2 and preparing the system at the exact ground and excited states at resonance.Comment: 7 EPL pages, 6 figure

Level splittings in exchange-biased spin tunneling

The level splittings in a dimer with the antiferromagnetic coupling between two single-molecule magnets are calculated perturbatively for arbitrary spin. It is found that the exchange interaction between two single-molecule magnets plays an important role in the level splitting. The results are discussed in comparison with the recent experiment.Comment: 12 pages, to be published in Phys. Rev.

Nonlinear response of single-molecule nanomagnets: equilibrium and dynamical

We present an experimental study of the {\em nonlinear} susceptibility of Mn$_{12}$ single-molecule magnets. We investigate both their thermal-equilibrium and dynamical nonlinear responses. The equilibrium results show the sensitivity of the nonlinear susceptibility to the magnetic anisotropy, which is nearly absent in the linear response for axes distributed at random. The nonlinear dynamic response of Mn$_{12}$ was recently found to be very large and displaying peaks reversed with respect to classical superparamagnets [F. Luis {\em et al.}, Phys. Rev. Lett. {\bf 92}, 107201 (2004)]. Here we corroborate the proposed explanation -- strong field dependence of the relaxation rate due to the detuning of tunnel energy levels. This is done by studying the orientational dependence of the nonlinear susceptibility, which permits to isolate the quantum detuning contribution. Besides, from the analysis of the longitudinal and transverse contributions we estimate a bound for the decoherence time due to the coupling to the phonon bath.Comment: 13 pages, 8 figures, resubmitted to Phys. Rev. B with minor change

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure

Mechanisms of decoherence in weakly anisotropic molecular magnets

Decoherence mechanisms in crystals of weakly anisotropic magnetic molecules, such as V15, are studied. We show that an important decohering factor is the rapid thermal fluctuation of dipolar interactions between magnetic molecules. A model is proposed to describe the influence of this source of decoherence. Based on the exact solution of this model, we show that at relatively high temperatures, about 0.5 K, the quantum coherence in a V15 molecule is not suppressed, and, in principle, can be detected experimentally. Therefore, these molecules may be suitable prototype systems for study of physical processes taking place in quantum computers.Comment: 4 pages RevTeX, 1 figure (PostScript

First- and Second-Order Transitions between Quantum and Classical Regimes for the Escape Rate of a Spin System

We have found a novel feature of the bistable large-spin model described by the Hamiltonian H = -DS_z^2 - H_xS_x.The crossover from thermal to quantum regime for the escape rate can be either first (H_x<SD/2) or second (SD/2<H_x<2SD) order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like Mn_12Ac.Comment: 4 pages, 4 figure

Resonant Magnetization Tunneling in Mn12 Acetate: The Absence of Inhomogeneous Hyperfine Broadening

We present the results of a detailed study of the thermally-assisted-resonant-tunneling relaxation rate of Mn12 acetate as a function of an external, longitudinal magnetic field and find that the data can be fit extremely well to a Lorentzian function. No hint of inhomogeneous broadening is found, even though some is expected from the Mn nuclear hyperfine interaction. This inconsistency implies that the tunneling mechanism cannot be described simply in terms of a random hyperfine field.Comment: Some minor revisions, title changed, updated figures, two added notes, one added reference. RevTeX, 4 pages, 3 postscript figures. Submitted to Rapid Communication