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arXiv:1210.6105 · Physical Review Letters

Geometric-Phase Interference in a Mn12 Single-Molecule Magnet with Fourfold Rotational Symmetry

Spencer Adams, Eduardo H. da Silva Neto, S. Datta, J. F. Ware, Christos Lampropoulos, George Christou, Yuri Myasoedov, Eli Zeldov, Jonathan R. Friedman

Published Feb 20, 2013• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.110.087205

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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.
Abstract Preservation of quantum coherence can be achieved by harnessing a system’s topology—encoding information in global geometric properties of quantum states insensitive to local perturbations. The robustness arises as certain geometric properties depend only on the trajectory of a quantum operation and the curvature in the controlled-parameter space, rather than on details of the system’s dynamics, thereby offering a topology-based framework for fault-tolerant quantum computation. To probe a system’s topology, geometric phase interference (Berry phase) has been studied in various optical systems and condensed matter physics, including molecular magnets (MMs). However, its direct detection in 4f-based MMs—prospective qudit (multi-level qubits) platforms—has remained elusive due to large tunnel gaps and environmental coupling. Here, we report a magneto-spectroscopic approach: the μSQUID-EPR technique, to directly resolve tunnel splittings in the 160 Gd-based MM [ 160 GdPc₂]⁻ (Pc = phthalocyanine). By irradiating single crystals with microwaves under transverse magnetic fields, we map the spin manifold and report the first direct observation of pronounced oscillations in the tunnel splitting—a signature of quantum phase interference. These oscillations reveal topological quenching of tunnelling and highlight the role of fourth-order transverse anisotropy in shaping the spin orientation space. Our findings uncover a nontrivial topological structure in 4f-MMs, opening possibilities towards holonomic quantum computation.
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.
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An antiferromagnetically exchange-coupled dimer of single molecule magnets which possesses a large spin tunneling has been investigated. For this system, the ground and first excited states are entangled states, and the Hamiltonian is effectively similar to that of a two-state system at 2sth order in perturbation theory; thus this system can be mapped to an entangled pseudospin 1/2 particles. We study the effects of interaction and rotation of this system about its staggered easy-axis direction. The corresponding Hamiltonian of a rotated two-state entangled spin system is derived with its exact low-energy eigenstates and eigenvalues. We briefly discuss the effect of a dissipative environment on this rotated two-state system.
A new approach to the magnetic hysteresis loop and magnetization relaxation of molecule magnet, Mn12, is presented. The method, so called "quasi-thermal equilibrium (QTE) + erase phase (EP)" (QTE + EP), leads the dissipation in state evolution. The method gives an method to approach an irreversible quantum dynamic tunnelling and time evolution of system and straightly leads the hysteresis loops. The QTE can work well for the double-well system and is able to be extended to the multi-wells quantum system. The EP is based on the physics of random interaction with the environment that results the phase de-coherence or say "re-initial" of the phase of quantum state during the time evolution. The stairs in the magnetic loops of Mn12 we have obtained quantitatively show the quantum resonant tunnelling. The relaxation of magnetization from initial lowest state is calculated for different temperatures and well shows the exponential behavior. The theoretical results well agree with the experiments.
Forbidden transitions between energy levels typically involve violation of selection rules imposed by symmetry and/or conservation laws. A nanomagnet tunneling between up and down states violates angular momentum conservation because of broken rotational symmetry. Here we report observations of highly forbidden transitions between spin states in a Ni_{4} single-molecule magnet in which a single photon can induce the spin to change by several times ℏ, nearly reversing the direction of the spin. These observations are understood as tunneling-assisted transitions that lift the standard Δm=±1 selection rule for single-photon transitions. These transitions are observed at low applied fields, where tunneling is dominated by the molecule's intrinsic anisotropy and the field acts as a perturbation. Such transitions can be exploited to create macroscopic superposition states that are not typically accessible through single-photon Δm=±1 transitions.