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arXiv:cond-mat/0302015 · Physical Review B

Coherence window in the dynamics of quantum nanomagnets

Philip C. E. Stamp, I. S. Tupitsyn

Published Jan 8, 2004• 54 citations
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Abstract

Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow-field region in which both phonon- and nuclear-spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the Fe-8 nanomolecule, for Ni particles, and for Ho ions in ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.$ The reduction in the decoherence, compared to low field rates, can exceed six orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.

DOI
10.1103/physrevb.69.014401

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Decoherence in many solid-state systems is anomalously high, frustrating efforts to make solid-state qubits. We show that in nanomagnetic insulators in large transverse fields, there can be a fairly narrow-field region in which both phonon- and nuclear-spin-mediated decoherence are drastically reduced. As examples we calculate decoherence rates for the Fe-8 nanomolecule, for Ni particles, and for Ho ions in LiHoxY1\ensuremath−xF4.{\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.LiHox​Y1\ensuremath−x​F4​. The reduction in the decoherence, compared to low field rates, can exceed six orders of magnitude. The results also give limitations on the observability of macroscopic coherence effects in magnetic systems.
We consider here the problem of a "central spin", with spin quantum number S≫1S \gg 1S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes magnetic grains or magnetic macromolecules (ferromagnetically or antiferromagnetically ordered) interacting with nuclear spins and with any surrounding paramagnetic electronic spins. It has also been used to describe Si:PSi:PSi:P near the metal-insulator transition, and quantum spin glasses. In this paper we consider the possible coherent motion of the central spin. We reduce the model to an effective low-energy Hamiltonian, and then calculate the correlation function using instanton methods. The general solution is given for the unbiased case, for all relevant values of the couplings. Under certain conditions, nuclear spin diffusion also plays a role. The results are then used to calculate the spectral absorption for 2 experimental systems, viz., TbFe3TbFe_3TbFe3​ grains, and ferritin molecules. Our results have general implications for the observation of mesoscopic and macroscopic quantum coherence, and for the foundations of quantum mechanics. They show that a spin environment usually has a very destructive effect on coherence, which cannot be understood using the conventional "oscillator bath" models of quantum environments.
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Due to the quantum evolution of molecular magnetic moments, the magnetic state of nanomagnets can suffer spontaneous changes. This process can be completely quenched by environment-induced decoherence. However, we show that for typical small supported atomic objects, the substrate-induced decoherence does change the magnetic-moment evolution but does not quell it. To be specific and to compare with experiment, we analyze the spontaneous switching between two equivalent magnetization states of atomic structures formed by Fe on Cu2N/Cu (1 0 0), measured by Loth et al (2012 Science 335 196-9). Due to the substrate-induced decoherence, the Rabi oscillations proper to quantum tunneling between magnetic states are replaced by an irreversible decay of long characteristic times leading to the observed stochastic magnetization switching. We show that the corresponding switching rates are small, rapidly decreasing with system's size, with a 1/T thermal behavior and in good agreement with experiments. Quantum tunneling is recovered as the switching mechanism at extremely low temperatures below the μK range for a six-Fe-atom system and exponentially lower for larger atomic systems. The unexpected conclusion of this work is that experiments could detect the switching of these supported atomic systems because their magnetization evolution is somewhere between complete decoherence-induced stability and unobservably fast quantum-tunneling switching.
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We systematically investigate the universal spin decoherence dynamics of a localized electron in an arbitrary nuclear spin bath, which can even be far away from equilibrium due to the weak nuclear-lattice interaction. We show that the electron spin relaxation dynamics (as well as spin pure dephasing and Hahn echo decay) can always have a universal behavior as long as the initial state is composed of a sufficiently large amount of spin eigenstates. For a given system, the pattern of the universal dynamics depends on the complicated initial condition only via a single parameter, which measures the amount of phase coherence between different spin eigenstates in the initial state. Our results apply even when the number of the involved nuclei is not large and, therefore, provide a solid foundation in the comparison of the theoretical/numerical results to the experimental measurement. As an example, we also show the numerical results for systems of noninteracting spin bath in a zero magnetic field regime and discuss the features of universal decoherent dynamics.