0000000000285055
AUTHOR
Dmitry A. Garanin
Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model
We investigate the potential energy surface of a ${\ensuremath{\phi}}^{4}$ model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers ${\ensuremath{\alpha}}_{+},{\ensuremath{\alpha}}_{0},{\ensuremath{\alpha}}_{\ensuremath{-}}$ with ${\ensuremath{\alpha}}_{+}+{\ensuremath{\alpha}}_{0}+{\ensuremath{\alpha}}_{\ensuremath{-}}=1$, provided that the interaction strength $\ensuremath{\mu}$ is smaller than a critical value. The saddle index ${n}_{s}$ is equal to ${\ensuremath{\alpha}}_{0}$ and its distribution function has a maximum at ${n}_{s}^{\mathrm{max}}=1∕3$. The density $p(e)$ of stationary points with energy per particle $e$, as well as…
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.
Butterfly hysteresis curves generated by adiabatic Landau-Zener transitions
Butterfly hysteresis curves observed in dynamical magnetization measurements on systems of low-spin magnetic molecules such as ${\mathrm{V}}_{15}$ can be explained by the interplay of adiabatic Landau-Zener transitions and relaxation. We investigate the magnetization dynamics analytically in the basis of the adiabatic energy levels of the spin $1∕2$, to a qualitative accordance with experimental observations. In particular, reversible behavior is found near zero field, the corresponding susceptibility being bounded by the equilibrium and adiabatic susceptibilities.
Many-body Landau-Zener effect at fast sweep
The asymptotic staying probability P in the Landau-Zener effect with interaction is analytically investigated at fast sweep, epsilon = pi Delta^2/(2 hbar v) << 1. We have rigorously calculated the value of I_0 in the expansion P =~ 1 - epsilon + epsilon^2/2 + epsilon^2 I_0 for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction (DDI) generate huge values of I_0 because flip of one particle strongly influences many others. However, in the presence of strong static disorder making resonance for indiv…
Phonon superradiance and phonon laser effect in nanomagnets
We show that the theory of spin-phonon processes in paramagnetic solids must take into account the coherent generation of phonons by the magnetic centers. This effect should drastically enhance spin-phonon rates in nanoscale paramagnets and in crystals of molecular nanomagnets.
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.
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].
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 transition…
Thermal fluctuations and longitudinal relaxation of single-domain magnetic particles at elevated temperatures
We present numerical and analytical results for the swiching times of magnetic nanoparticles with uniaxial anisotropy at elevated temperatures, including the vicinity of T_c. The consideration is based in the Landau-Lifshitz-Bloch equation that includes the relaxation of the magnetization magnitude M. The resulting switching times are shorter than those following from the naive Landau-Lifshitz equation due to (i) additional barrier lowering because of the reduction of M at the barrier and (ii) critical divergence of the damping parameters.
Universal mechanism of spin relaxation in solids
We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.
Pulsed-field studies of the magnetization reversal in molecular nanomagnets
We report experimental studies of crystals of Mn12 molecular magnetic clusters in pulsed magnetic fields with sweep rates up to 4x10^3 T/s. The steps in the magnetization curve are observed at fields that are shifted with respect to the resonant field values. The shift systematically increases as the rate of the field sweep goes up. These data are consistent with the theory of the collective dipolar relaxation in molecular magnets.
Nonlinear response of superparamagnets with finite damping: an analytical approach
The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modelling of the experimental data and the determination of the damping coefficient in superparamagnets.
Field Dependence of the Electron Spin Relaxation in Quantum Dots
Interaction of the electron spin with local elastic twists due to transverse phonons has been studied. Universal dependence of the spin relaxation rate on the strength and direction of the magnetic field has been obtained in terms of the electron gyromagnetic tensor and macroscopic elastic constants of the solid. The theory contains no unknown parameters and it can be easily tested in experiment. At high magnetic field it provides parameter-free lower bound on the electron spin relaxation in quantum dots.
Interference effect in the Landau-Zener tunneling of the antiferromagnetically coupled dimer of single-molecule magnets
Two antiferromagnetically coupled tunneling systems is a minimal model exhibiting the effect of quantum-mechanical phase in the Landau-Zener effect. It is shown that the averaged staying probability oscillates vs resonance shift between the two particles, as well as vs sweeping rate. Such a resonance shift can be produced in Mn-4 dimers by the gradient of the magnetic field.
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 …
Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical and Dynamical Contributions
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of \alpha_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a…
Quantum dynamics of a nanomagnet in a rotating field
Quantum dynamics of a two-state spin system in a rotating magnetic field has been studied. Analytical and numerical results for the transition probability have been obtained along the lines of the Landau-Zener-Stueckelberg theory. The effect of various kinds of noise on the evolution of the system has been analyzed.