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Journal of Applied Physics

Quantum dynamical calculations in clusters of spin 1/2 particles: Resonant coherent quantum tunneling on the magnetization reversal

D. García-Pablos, N. Garcı́a, P. A. Serena, Hans A. De Raedt

Published Apr 15, 1996• 2 citations
Publisher

Abstract

We investigate the reversal of magnetization and the coherence of tunneling when an external magnetic field is rotated instantaneously in systems of a few (N) spin 1/2 particles described by an anisotropic Heisenberg Hamiltonian at T=0. The temporal evolution is calculated by a numerically exact solution of the time-dependent Schrödinger equation, and the mean value in time of each spin component is computed as a function of the magnetic field. The correlation function and the spectrum are analyzed in terms of the macroscopic quantum coherence. Our calculations demonstrate that this model for small (N<11) magnetic particles exhibit collective tunneling of the magnetization only for some specific resonant values of the applied magnetic field, at variance with the Stoner–Wohlfarth model.

DOI
10.1063/1.362103

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We investigate the reversal of magnetization and the coherence of tunneling when an external magnetic field is rotated instantaneously in systems of a few (N) spin 1/2 particles described by an anisotropic Heisenberg Hamiltonian at T=0. The temporal evolution is calculated by a numerically exact solution of the time-dependent Schrödinger equation, and the mean value in time of each spin component is computed as a function of the magnetic field. The correlation function and the spectrum are analyzed in terms of the macroscopic quantum coherence. Our calculations demonstrate that this model for small (N<11) magnetic particles exhibit collective tunneling of the magnetization only for some specific resonant values of the applied magnetic field, at variance with the Stoner–Wohlfarth model.
Quantum coherence in small single-domain ferromagnetic particles is studied using dynamical calculations of the reversal of a single quantum spin resulting from a rotation of an external magnetic field, for \ensuremath{\leqslant}S\ensuremath{\leqslant}75. The analysis of the time evolution of the spin, the temporal correlation, and the spectrum leads to the conclusion that, for small spin S\ensuremath{\leqslant}15, coherent tunneling back and forth between the easy directions occurs at some specific resonant fields only. Away from resonance, quantum coherence in the spin temporal evolution is absent. These results are in qualitative accordance with those obtained for a Heisenberg Hamiltonian with exact quantum calculations and are at variance with semiclassical approximations. However, as the spin becomes larger, the number of resonant fields increases, the resonances become very small, and coherence in time evolution is lost for any value of the magnetic field.
Quantum mechanical objects or nano-objects have been proposed as bits for information storage. While time-averaged properties of magnetic, quantum-mechanical particles have been extensively studied experimentally and theoretically, experimental investigations of the real time evolution of magnetization in the quantum regime were not possible until recent developments in pump–probe techniques. Here we investigate the quantum dynamics of effective spin systems by means of analytical and numerical treatments. Particular attention is paid to the quantum revival time and its relation to the magnetization tunneling. The quantum revival time has been initially defined as the recurrence time of a total wave-function. Here we show that the quantum revivals of wave-functions and expectation values in spin systems may be quite different which gives rise to a more sophisticated definition of the quantum revival within the realm of experimental research. Particularly, the revival times for integer spins coincide which is not the case for half-integer spins. Furthermore, the quantum revival is found to be shortest for integer ratios between the on-site anisotropy and an external magnetic field paving the way to novel methods of anisotropy measurements. We show that the quantum tunneling of magnetization at avoided level crossing is coherent to the quantum revival time of expectation values, leading to a connection between these two fundamental properties of quantum mechanical spins.
The two-dimensional Heisenberg antiferromagnet with an additional isotropic coupling to ``environmental'' spin degrees of freedom is studied by exact diagonalization of small clusters to examine the effect of decoherence from first principles. The dynamical correlation function for the staggered order parameter $c(\ensuremath{\omega})$ is calculated for two systems containing 101010 and 181818 electronic spins coupled to two environmental spins. The evolution of spectral weight in the main macroscopic quantum coherence resonance is followed as a function of environmental coupling and spin anisotropy and is discussed in connection with theoretical work on decoherence.
The precise definition and physical interpretation of a tunneling time is a fundamental problem in quantum mechanics. The lack of a well-defined time operator in quantum theory precludes the calculation of time in terms of an expectation value. Consequently, model calculations and simulation studies have been proposed and used to determine the time for a particle to traverse a quantum-mechanical barrier. The results offer both qualitatively and quantitatively, disparate predictions. One of the more commonly used approaches is the phase method, which we have applied to several one-dimensional model potentials to show that the tunneling time is characterized by the ratio of the typical decay length in the barrier to the incident velocity, τ∼(1/κ)/v0. We also show that the phase and the spin precession methods are equivalent when the magnetic field is applied throughout the space containing the particle wave function and the tunneling barrier. In principle, the spin precession method can be regarded as an operational definition of the tunneling time. It also has been shown that a tunneling time can be defined operationally for a time-dependent barrier, for which the model calculations predict a tunneling time given by the mean barrier width divided by the magnitude of the imaginary velocity of the particle in the barrier, τ∼d/‖v‖. This pseudokinematic result has been inferred by magnetic field dependent tunneling through heterostructures and computer simulation of wave packet tunneling through one-dimensional square barriers. Other tunneling time theories predict one or the other of the above mentioned characteristic times; several theories predict both. We interpret these different results for τ to mean that a tunneling time is not uniquely defined as a function of particle energy and the barrier shape unless the process in which the tunneling is involved is also specified. That is, the tunneling time is a meaningful and unique concept only for particular tunneling processes or definite operational procedures.
Discrete quantum phase space formalism is used to discuss some basic aspects of the spin tunneling occurring in Fe8 magnetic cluster by means of Wigner functions as well as Husimi distributions. Those functions were obtained for sharp angle states and symmetric combinations of the lowest energy doublet with the application of an external magnetic field. The time evolution of those functions carried out numerically allows one to extract valuable information about the dynamics of the states under consideration, in particular, the coherent oscillations associated with the spin tunneling. It is also shown that an entropy functional constructed out of the discrete Husimi distribution function allows to characterize the spin tunneling.
We investigate the macroscopic quantum spin coherence of a spinor condensate confined in an anisotropic potential. Under the single-mode approximation, we show that a spin-1 Rb condensate can be modeled as a biaxial quantum magnet. A direct consequence of the biaxial anisotropy is that the tunneling splitting oscillates as a function of the external magnetic field applied along the hard axis. We also propose an experimental scheme to detect the oscillatory behavior of the tunneling splitting by employing the Landau-Zener tunneling.