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Physical Review A

Nonstationary behavior of a high-spin molecule in a bifrequency alternating current magnetic field

Iosif Davidovich Tokman, G. A. Vugalter

Published Jul 19, 2002• 18 citations
Publisher

Abstract

An interaction of a high-spin molecule with a bifrequency ac magnetic field, occurring at times much shorter than the molecule relaxation times, has been considered. The molecule is subjected to a dc magnetic field perpendicular to the easy anisotropy axis of the molecule. The bifrequency ac field is a superposition of two ac fields, one of which is perpendicular to the easy anisotropy axis and causes resonant transitions between the lower states of the fundamental and first excited doublets. The other ac field is parallel to the easy anisotropy axis and has a frequency much smaller than the frequency of the first ac field. It has been shown that, first, the molecule can absorb or emit energy, depending on the frequency of the low-frequency ac field, second, the bifrequency ac magnetic field induces tunneling of the molecule magnetization with the Rabi frequency. The conditions of observation of the effects predicted are discussed.

DOI
10.1103/physreva.66.013407

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An interaction of a high-spin molecule with a bifrequency ac magnetic field, occurring at times much shorter than the molecule relaxation times, has been considered. The molecule is subjected to a dc magnetic field perpendicular to the easy anisotropy axis of the molecule. The bifrequency ac field is a superposition of two ac fields, one of which is perpendicular to the easy anisotropy axis and causes resonant transitions between the lower states of the fundamental and first excited doublets. The other ac field is parallel to the easy anisotropy axis and has a frequency much smaller than the frequency of the first ac field. It has been shown that, first, the molecule can absorb or emit energy, depending on the frequency of the low-frequency ac field, second, the bifrequency ac magnetic field induces tunneling of the molecule magnetization with the Rabi frequency. The conditions of observation of the effects predicted are discussed.
We study the dynamics of molecular nanomagnets through a fully quantum mechanical model describing high-spin and high-anisotropy magnetic molecules subjected to a time-dependent magnetic field along the quantization axis, which continuously inverts the population of spin states. Crystals of molecular nanomagnets placed inside a resonant cavity interact with a quantized electromagnetic field. Relaxation of excited states takes place by means of spin-photon interaction, allowing stimulated emission of radiation and creating a maser effect.
The effect of the circularly polarized laser field on quantum spin systems in the steady-state regime, in which relaxation plays the central role, has been studied. The dynamical mean-field-like theory predicts several general results for the behavior of the time-average magnetization caused by the laser field. The induced magnetization oscillates with the frequency of the laser field (while Rabi-like oscillations, which modulate the latter in the dynamical regime, are damped by the relaxation in the steady-state regime). At high frequencies, that magnetization is determined by the value to which the relaxation process is directed. At low frequencies the slope of that magnetization as a function of the frequency is determined by the strength of the laser field. The anisotropy determines the resonance behavior of the time-averaged magnetization in both the ferromagnetic and antiferromagnetic cases with nonzero magnetic anisotropy. Nonlinear effects (in the magnitude of the laser field) have been considered. The effect of the laser field on quantum spin systems is maximal in resonance, where the time-averaged magnetization, caused by the laser field, is changed essentially. Out of resonance the changes in the magnetization are relatively small. The resonance effect is caused by the nonzero magnetic anisotropy. The resonance frequency is small (proportional to the anisotropy value) for spin systems with ferromagnetic interactions and enhanced by exchange interactions in the spin systems with antiferromagnetic couplings. We show that it is worthwhile to study the laser-field-induced magnetization of quantum spin systems caused by the high-frequency laser field in the steady-state regime in ``easy-axis'' antiferromagnetic spin systems (e.g., in Ising-like antiferromagnetic spin-chain materials). The effects of the Dzyaloshinskii-Moriya interaction and the spin-frustration couplings (in the case of the zigzag spin chain) have been analyzed.
It is shown that a linear polarized laser can cause magnetization of a spin system with magnetic anisotropy, the distinguished axis of which is perpendicular to the polarization of the laser field. In the dynamical regime the magnetization oscillates around the nonzero value determined by the parameters of the system. Oscillations have the frequency of the laser field, modulated by the lower Rabi-like frequencies. In the steady-state regime, for a large time scale greater than the characteristic relaxation time, the Rabi-like oscillations are damped, and the magnetization oscillates with the frequency of the laser field around the value which is determined by the relaxation rate also. Analytic results are presented for the spin-1/2 chain. The most direct manifestation of such a behavior can be observed in spin-1/2 Ising chain materials if the linear polarization of the laser field is chosen to be perpendicular to the Ising axis.
The response of the one-dimensional antiferromagnetic spin-1/2 chain to the ac staggered magnetic field is studied within the Hartree-Fock-like approximation. For a closed system that field produces oscillations of the magnetization with the frequency of the ac field, modulated by the large number of small Rabi frequencies. In the open system the Rabi oscillations decay due to relaxation processes. It is shown that those oscillations also contribute to the dynamics of the entanglement of the system. The calculated temperature and frequency dependence of the dynamical characteristics is strictly nonmonotonic, reflecting the complicated character of the common action of the homogeneous and staggered dc field.
We study the magnetic relaxation rate Γ of the single-molecule magnet Mn(12)-tBuAc as a function of the magnetic field component H(T) transverse to the molecule's easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that Γ increases abruptly at certain values of H(T). These increases are observed just beyond values of H(T) at which a geometric-phase interference effect suppresses tunneling between two excited energy levels. The effect is washed out by rotating H(T) away from the spin's hard axis, thereby suppressing the interference effect. Detailed numerical calculations of Γ using the known spin Hamiltonian accurately reproduce the observed behavior. These results are the first experimental evidence for geometric-phase interference in a single-molecule magnet with true fourfold symmetry.