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Register a new userDirect Spectroscopic Observation of Berry Phase Interference in the Ni$_4$ Single-Molecule Magnet
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Added by
Jonathan R. Friedman
Publication date
2020
fields
Physics
and research's language is
English
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Berry phase effects in spin systems lead to the suppression of tunneling effects when different tunneling paths interfere destructively. Such effects have been seen in several single-molecule magnets (SMMs) through measurements of magnetization dynamics, where the experimental signal may arise from the contributions of numerous energy levels. Here we present experimental measurements of Berry phase interference effects that are determined through electron-spin resonance on a four-fold symmetric SMM. Specifically, we measure transitions between tunnel-split excited states in the Ni$_4$ SMM in the presence of a transverse field in the hard plane of the crystalline sample. By using a home-built rotation apparatus, the direction of the sample can be changed textit{in situ} so that that the field direction can be swept through the entire hard plane of the sample. When the field is in certain directions in the plane, we observe a splitting of the transition, a hallmark of Berry phase interference. The experimental results are well reproduced by theoretical predictions, and fitting of the data provides information about the effects of dipolar interactions and sample misalignment.
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A Mn4 single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (HT) dependence of the magnetization tunneling probability when a longitudinal field (HL) is present, contrary to symmetric patterns observed for HL=0. Reversal of HL results in a reflection of the transverse-field asymmetry about HT=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.
Magnetization measurements of a molecular clusters Mn12 with a spin ground state of S = 10 show resonance tunneling at avoided energy level crossings. The observed oscillations of the tunnel probability as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum phase interference of two tunnel paths of opposite windings. Mn12 is therefore the second molecular clusters presenting quantum phase interference.
We present a method for precisely measuring the tunnel splitting in single-molecule magnets using electron-spin resonance, and use these measurements to precisely and independently determine the underlying transverse anisotropy parameter, given a certain class of transitions. By diluting samples of the SMM Ni$_4$ via co-crystallization in a diamagnetic isostructural analogue we obtain markedly narrower resonance peaks than are observed in undiluted samples. Using custom loop-gap resonators we measure the transitions at several frequencies, allowing a precise determination of the tunnel splitting. Because the transition under investigation occurs at zero field, and arises due to a first-order perturbation from the transverse anisotropy, we can determine the magnitude of this anisotropy independent of any other Hamiltonian parameters. This method can be applied to other SMMs with tunnel splittings arising from first-order transverse anisotropy perturbations.
Here we respond briefly to a comment on our work in arXiv:cond-mat/0405501.
We study the magnetic relaxation rate Gamma of the single-molecule magnet Mn_{12}-tBuAc as a function of magnetic field component H_T transverse to the molecules easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that Gamma 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 spins hard axis, thereby suppressing the interference effect. Detailed numerical calculations of Gamma 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 four-fold symmetry.
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