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arXiv:cond-mat/0609205

Quantum Dynamics of Molecular Nanomagnets in a Resonant Cavity and the Maser Effect

César Augusto Dartora, G. G. Cabrera

Published Sep 8, 2006• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0609205

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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.
Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
We report observation of coherent quantum oscillations in spin-10 Fe 8 molecular clusters. The powder of magnetically oriented Fe 8 crystallites was placed inside a resonator, in a dc magnetic field perpendicular to the magnetization axis. The field dependence of the ac-susceptibility was measured up to 5 T, at 680 MHz, down to 25 mK. Two peaks in the imaginary part of the susceptibility have been detected, whose positions coincide, without any fitting parameters, with the predicted two peaks corresponding to the quantum splitting of the ground state in the magnetic field parallel and perpendicular to the hard magnetization axis.
We introduce a modified version of the interaction picture applicable to situations in which the nonperturbed Hamiltonian is time-dependent but can be diagonalized by the same basis of states at all times. We probe the method using a simple model Hamiltonian to study the spin dynamics of molecular magnets with time-dependent fields. Fully quantum mechanical calculations show the superiority of our method compared to the usual time-dependent perturbation theory. Our approach takes into account time-dependent fields and converges rapidly to the exact solution.
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 analyze the interaction of a nanomagnet (ferromagnetic) with a single photonic mode of a cavity in a fully quantum-mechanical treatment and find that exceptionally large quantum-coherent magnet-photon coupling can be achieved. Coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of approximately 1 mm radius with a nanomagnet of approximately 100 nm radius and ferromagnetic resonance frequency of approximately 200 GHz. Eigenstates of the magnet-photon system correspond to entangled states of spin orientation and photon number, in which over 10{5} values of each quantum number are represented; conversely, initial (coherent) states of definite spin and photon number evolve dynamically to produce large oscillations in the microwave power (and nanomagnet spin orientation), and are characterized by exceptionally long dephasing times.