Magnetic free energy at elevated temperatures and hysteresis of magnetic particles

We derive a free energy for weakly anisotropic ferromagnets which is valid in the whole temperature range 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.Comment: 16 pages, 4 figure

Finite-size versus Surface effects in nanoparticles

We study the finite-size and surface effects on the thermal and spatial behaviors of the magnetisation of a small magnetic particle. We consider two systems: 1) A box-shaped isotropic particle of simple cubic structure with either periodic or free boundary conditions. This case is treated analytically using the isotropic model of D-component spin vectors in the limit $D\to \infty$, including the magnetic field. 2) A more realistic particle ($\gamma$-Fe$_{2}$O$_{3}$) of ellipsoidal (or spherical) shape with open boundaries. The magnetic state in this particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions, and bulk and surface anisotropy. This case is dealt with by the classical Monte Carlo technique. It is shown that in both systems finite-size effects yield a positive contribution to the magnetisation while surface effects render a larger and negative contribution, leading to a net decrease of the magnetisation of the small particle with respect to the bulk system. In the system 2) the difference between the two contributions is enhanced by surface anisotropy. The latter also leads to non saturation of the magnetisation at low temperatures, showing that the magnetic order in the core of the particle is perturbed by the magnetic disorder on the surface. This is confirmed by the profile of the magnetisation.Comment: 6 pages of RevTex including 4 Figures, invited paper to 3rd EuroConference on Magnetic Properties of Fine Nanoparticles, Barcelona, October 9

Dipolar-controlled spin tunneling and relaxation in molecular magnets

Spin tunneling in molecular magnets controlled by dipole-dipole interactions (DDI) in the disordered state has been considered numerically on the basis of the microscopic model using the quantum mean-field approximation. In the actual case of a strong DDI spin coherence is completely lost and there is a slow relaxation of magnetization, described by t^{3/4} at short times. Fast precessing nuclear spins, included in the model microscopically, only moderately speed up the relaxation.Comment: 10 pages, 9 figures, to be published in EPJ

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-classical transition of the escape rate of uniaxial antiferromagnetic particles in an arbitrarily directed field

Quantum-classical escape rate transition has been studied for uniaxial antiferromagnetic particles with an arbitrarily directed magnetic field. In the case that the transverse and longitudinal fileds coexist, we calculate the phase boundary line between first- and second-order transitions, from which phase diagrams can be obtained. It is shown that the effects of the applied longitudinal magnetic field on quantum-classical transition vary greatly for different relative magnitudes of the non-compensation.Comment: to be appeared in Phys. Rev.

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

Tunneling with dissipation and decoherence for a large spin

We present rigorous solution of problems of tunneling with dissipation and decoherence for a spin of an atom or a molecule in an isotropic solid matrix. Our approach is based upon switching to a rotating coordinate system coupled to the local crystal field. We show that the spin of a molecule can be used in a qubit only if the molecule is strongly coupled with its atomic environment. This condition is a consequence of the conservation of the total angular momentum (spin + matrix), that has been largely ignored in previous studies of spin tunneling.Comment: 4 page

Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect

We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability P to remain in the initial state. The dimensionless quantity epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and monotonic, analytic sweep functions linearizable in the vicinity of the resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is the correction to the LSZ result due to the nonlinearity of the sweep. Further increase of the sweep rate with nonlinearity fixed brings the system into the nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1 depending on the type of sweep function. In case of slow sweep rates, i.e., epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t) the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta ^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there is only one singularity, that leads to the LZS result P=e^-epsilon with important corrections to the exponent due to nonlinearity. However, for, e.g., W(t) ~ t^3 there is a pair of singularities in the upper complex plane. Interference of their contributions leads to oscillations of the prefactor P_0 that depends on the sweep rate through epsilon and turns to zero at some epsilon. Measurements of the oscillation period and of the exponential factor would allow to determine Delta, independently.Comment: 11 PR pages, 12 figures. To be published in PR

Domain wall mobility in nanowires: transverse versus vortex walls

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.Comment: 5 pages, 6 figure

Quantum Step Heights in Hysteresis Loops of Molecular Magnets

We present an analytical theory on the heights of the quantum steps observed in the hysteresis loops of molecular magnets. By considering the dipolar interaction between molecular spins, our theory successfully yields the step heights measured in experiments, and reveals a scaling law for the dependence of the heights on the sweeping rates hidden in the experiment data on Fe$_8$ and Mn$_4$. With this theory, we show how to accurately determine the tunnel splitting of a single molecular spin from the step heights.Comment: 4 pages, 5 figure