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Physical review. B, Condensed matter

Dynamical calculations on the reversal of single quantum spins: Quantum coherence

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

Published Jan 1, 1997• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.55.937

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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.
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.
The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.
Within the framework of an idealized theoretical model, we study the effect of external static homogeneous exchange and magnetic field on the spin part of the singlet wave function of two electrons. We begin by revising the traditional (textbook) approach to the spin singlet. Basing our own approach solely on the property of invariance under rotations of the coordinate system and using the theory of spinor invariants, we derive a generalized representation of the spin singlet whose main feature is that the spins are in mutually time-reversed states. We show that exactly this feature predetermines the actual form of the Hamiltonian of interaction with the external field and stipulates time evolution of the singlet. Some applications of these results to the theory of superconductivity and spin chemistry are presented. In particular, it is shown that the case of ferromagnetic superconductors constitutes a good illustration of the validity of our quantum-mechanical consideration.
In the present thesis we perform a step towards understanding the effec- tiveness of Hamiltonian perturbation theory in quantum dynamics, which is made possible by the Hamiltonian framing of quantum mechanics. To such a purpose, we focus our attention on quantum spin chains, namely on the isotropic Heisenberg ferromagnet, which is well known to be equivalent, via the Jordan-Wigner transformation, to a system of interacting fermions, and is also known to be exactly integrable through the Bethe ansatz. The interaction term of the Hamiltonian, of order four in fermionic creation and annihilation operators, is treated as a perturbation in the regime of small excitations: small number of reversed spins or, equivalently, small number of fermions per site. The calculation of the first order normal form Hamiltonian amounts to erasing all the nonresonant interaction terms, and allows to draw interesting conclusions on the dynamics of the system, e.g. to determine ap- proximately conserved quantities. Moreover, we get a good correspondence between our perturbative energy spectrum and the exact one computed via the Bethe ansatz, the approximation being of course the more accurate the smaller is the number of fermions per site. The present method, here tested in an exactly solvable case, can be applied to any nonintegrable system of weakly interacting fermions (and/or bosons).
Abstract We examine the quantum dynamics of both a single spin- J particle and a pair of spin- J particles in the presence of static and rotating magnetic fields, which can be important for qudit-based quantum technologies. Notably, we find resonant, periodic oscillations between two maximally stretched states, irrespective of the value of J . Additionally, we observe periodic transitions between sublevels with magnetic quantum numbers of opposite signs. The dynamics also exhibit a periodic transfer of the spin to the maximally stretched state, starting from the ground state of the initial Hamiltonian. For a pair of spins, we derive various resonance conditions and further analyze the entanglement generated by dipole–dipole interactions. In the case of two spin-1/2 particles, the entanglement dynamics reveal resonances and kinks in the maximum entanglement, and their criteria can be obtained from the energy spectrum. Strikingly, we show that the kink can be exploited to engineer the entanglement dynamics. Finally, we briefly discuss the regime of weak dipolar interactions, which are relevant for dipolar Bose–Einstein condensates.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.