arXiv subjects

D. A. Garanin

Publications and source records attributed to D. A. Garanin.

At least 91 records · Page 5Linked to original sources

arXiv2003

Quantum Nonlinear Switching Model

We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model \hat{H} = -H_z(t)S_z + V(\bf{S}) with H_z(\pm\infty) = \pm\infty and Ψ(-\infty)=|-S> we study the quantity P(t)=(1- _t/S)/2. The case V(\bf{S})=-H_x S_x corresponds to the standard Landau-Zener-Stueckelberg model of tunneling at avoided-level crossing for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and follows, e.g., from the classical Landau-Lifshitz equation. A term -DS_z^2 accounts for particles' interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in a good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0.

cond-mat.stat-mech↗

arXiv2003

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.

cond-mat.stat-mech↗

arXiv2002

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.

cond-mat.stat-mech↗

arXiv2002

Surface contribution to the anisotropy of magnetic nanoparticles

We calculate the contribution of the Neel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Neel surface anisotropy, scales with the particle volume and has cubic symmetry with preferred directions [+-1,+-1,+-1].

cond-mat.stat-mech↗

arXiv2002

Superradiance from crystals of molecular nanomagnets

We show that crystals of molecular nanomagnets can exhibit giant magnetic relaxation due to the Dicke superradiance of electromagnetic waves. Rigorous treatment of the superradiance induced by a field pulse is presented.

cond-mat.stat-mech↗

arXiv2002

Tunneling and EPR linewidths due to dislocations in Mn-12 acetate

We compute the width and shape of the EPR and tunneling resonances due to dislocations in Mn-12 acetate crystals. Uncorrelated dislocations produce the Gaussian shape of resonances while dislocations bound in pairs produce the Lorentzian shape. We stress that the uniaxial spin Hamiltonian together with crystal defects can explain the totality of experimental data on Mn-12.

cond-mat.stat-mech↗

arXiv2002

Quasiclassical Hamiltonians for large-spin systems

We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.

cond-mat.stat-mech↗

arXiv2002

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.

cond-mat.stat-mech↗

arXiv2001

Spin-wave theory for finite classical magnets and superparamagnetic relation

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H,T)=M(H,T)B_D[M(H,T)NH/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models [B_D(x) is the Langevin function, D is the number of spin components, N is the number of atoms in the particle]. It follows from general arguments and from our analytical results for the Heisenberg model at T << T_c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T > 1, as confirmed by our Monte Carlo calculations. At T <~ T_c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.stat-mech↗

arXiv2001

Boundary and finite-size effects in small magnetic systems

We study the effect of free boundaries in finite magnetic systems of cubic shape on the field and temperature dependence of the magnetization within the isotropic model of D-component spin vectors in the limit D \to \infty. This model is described by a closed system of equations and captures the Goldstone-mode effects such as global rotation of the magnetic moment and spin-wave fluctuations. We have obtained an exact relation between the intrinsic (short-range) magnetization M = M(H,T) of the system and the supermagnetization m = m(H,T) which is induced by the field. We have shown, analytically at low temperatures and fields and numerically in a wide range of these parameters, that boundary effects leading to the decrease of M with respect to the bulk value are stronger than the finite-size effects making a positive contribution to M. The inhomogeneities of the magnetization caused by the boundaries are long ranged and extend far into the depth of the system.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.stat-mech↗

arXiv2001

Spin tunneling via dislocations in Mn-12 acetate crystals

We show that dislocations should be the main source of spin tunneling in Mn-12 crystals. Long-range strains caused by dislocations produce broad distribution of relaxation times that has been seen in many experiments. When the external magnetic field is applied along the c-axis of the crystal, local rotations of the magnetic anisotropy axis due to dislocations result in the effective local transverse magnetic field that unfreezes odd tunneling resonances. Scaling law is derived that provides universal description of spin tunneling for all resonances.

cond-mat.stat-mech↗

arXiv2001

Effective classical Hamiltonians for spin systems: A closed form with quantum spin-wave effects

Thermodynamic properties of any quantum spin system can be described by the formally exact, although in general intractable, effective classical Hamilton function \cal H. Here we obtain an explicit form of \cal H which applies at T << J S^2, where J is the exchange and S in the spin value, and incorporates quantum effects at the level of the spin-wave theory (SWT). For a quantum Hamiltonian \hat H of Heisenberg form, \cal H is also Heisenberg but with a long-range effective exchange J_{ij}^{eff}, which is the price for including quantum effects. For three-dimensional magnets, classical SWT with \cal H yields the same results as quantum SWT for the original system, in the antiferromagnetic case with the 1/S correction to the ground-state energy.

cond-mat.stat-mech↗

arXiv2000

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)].

cond-mat.stat-mech↗

arXiv2000

Spin Tunneling in Mn-12 Cannot be Assisted by Phonons at Millikelvin Temperatures [Comment on PRL 83, 416 (1999) by Bellessa et al]

Recently, Bellessa et al in a Physical Review Letter entitled "Phonon-Assisted Tunneling in High-Spin Molecules: Experimental Evidence", reported observation of a peak in the imaginary part of the ac-susceptibility of Mn-12 molecular nanomagnet, that decreases strongly below 0.1 K down to 0.02 K. They explained this effect by a "phonon-induced tunneling process". The purpose of this Comment is to show that the explanation of Bellessa et al is logically inconsistent and physically impossible. All formulas in the Letter supporting that explanation are incorrect.

cond-mat.stat-mech↗

arXiv2000

Crystal Field -AS_z^2 Does Not Produce One-Phonon Transitions With Delta S_z=+-2 [Comment on EPL 46, 692 (1999) by Leuenberger and Loss]

Recently Leuenbeger and Loss suggested a theory of phonon-assisted relaxation in a molecular nanomagnet Mn-12 that "contrary to previous results is in reasonably good agreement ... with all experimental parameter values known so far". The purpose of this Comment is to show that the model of Leuenberger and Loss and its comparison with experiment are premised upon their incorrect use of the linear formula for the strain tensor. The spin-phonon coupling introduced by Leuenberger and Loss disappears if the nonlinear term in the strain tensor is taken into account.

cond-mat.stat-mech↗

arXiv2000

Thermally activated escape rates of uniaxial spin systems with transverse field

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.

cond-mat.stat-mech↗