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arXiv:1510.03109 · Physical Review Letters

Observation of Tunneling-Assisted Highly Forbidden Single-Photon Transitions in a Ni4 Single-Molecule Magnet

Yiming Chen, M. D. Ashkezari, Charles Collett, Rafael A. Allão Cassaro, Filippo Troiani, Paul M. Lahti, Jonathan R. Friedman

Published Oct 27, 2016• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.117.187202

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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.
Quantum tunneling of the magnetization in a single molecule magnet has been studied in experiments that combine microwave spectroscopy with high sensitivity magnetic measurements. By monitoring spin-state populations in the presence of microwave radiation, the energy splittings between low lying superpositions of high-spin states of single molecule magnet Ni4 (S=4) have been measured. Absorption linewidths give an upper bound on the rate of decoherence. Pulsed microwave experiments provide a measure of energy relaxation time, which is found to increase with frequency.
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 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.
Motivated by the experimental observation of resonant tunneling in systems of half-integer spin, such as V15 and Mn4, we study the mechanism of the adiabatic change of the magnetization in systems with time-reversal symmetry. Although tunneling between the degenerate ground states is suppressed in a simple Kramers doublet, some types of perturbational interactions cause an avoided level crossing structure in the energy level structures when the system possesses additional degeneracy of the ground state. We show that a nonadiabatic transition governed by the Landau-Zener-Stückelberg mechanism occurs in many cases, and also find more general cases of adiabatic change of the magnetization in which LZS mechanism cannot be applied directly.
The implementation of quantum computation (QC) would revolutionize scientific fields ranging from encryption to quantum simulation. One intuitive candidate for the smallest unit of a quantum computer, a qubit, is electronic spin. A prominent proposal for QC relies on high-spin magnetic molecules, where multiple transitions between the many MS levels are employed as qubits. Yet, over a decade after the original notion, the exploitation of multiple transitions within a single manifold for QC remains unrealized in these high-spin species due to the challenge of accessing forbidden transitions. To create a proof-of-concept system, we synthesized the novel nuclear spin-free complex [Cr(C3S5)3](3-) with precisely tuned zero-field splitting parameters that create two spectroscopically addressable transitions, with one being a forbidden transition. Pulsed electron paramagnetic resonance (EPR) measurements enabled the investigation of the coherent lifetimes (T2) and quantum control (Rabi oscillations) for two transitions, one allowed and one forbidden, within the S = (3)/2 spin manifold. This investigation represents a step forward in the development of high-spin species as a pathway to scalable QC systems within magnetic molecules.
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.