Kramers degeneracy and relaxation in vanadium, niobium and tantalum clusters

Abstract

In this work we use magnetic deflection of V, Nb, and Ta atomic clusters to measure their magnetic moments. While only a few of the clusters show weak magnetism, all odd-numbered clusters deflect due to the presence of a single unpaired electron. Surprisingly, for the majority of V and Nb clusters an atomic-like behavior is found, which is a direct indication of the absence of spin-lattice interaction. This is in agreement with Kramers degeneracy theorem for systems with a half-integer spin. This purely quantum phenomenon is surprisingly observed for large systems of more than 20 atoms, and also indicates various quantum relaxation processes, via Raman two-phonon and Orbach high-spin mechanisms. In heavier, Ta clusters, the relaxation is always present, probably due to larger masses and thus lower phonon energies, as well as increased spin-orbit coupling.

Probing the properties of size dependence and correlation for tantalum clusters: geometry, stability, vibrational spectra, magnetism, and electronic structure

“…An interesting atomic-like behavior, which is a direct indication of the absence of spin-lattice interaction, indicated various quantum relaxation processes for the tantalum clusters. 5 By comparing the experimental results with magnetic deection measurements, although they exhibited a similar oscillation trend and agreed well for larger Ta n (n ¼ 12-16) clusters, our calculated magnetic moments were generally higher. The measured value for those smaller tantalum clusters were between our calculated results based on the B3LYP/ LANL2DZ level and those previously reported by the GGA functional DFT method.…”

“…4 Gas-phase clusters represent an ideal model system to study quantum coherent phenomena at practically macroscopic scales. 5 Most recently, Kramers blocking of spin-lattice relaxation in clusters of vanadium-group elements have been studied, and this relaxation of the quantum phenomenon was clearly found to be more efficient for larger nuclear mass tantalum clusters. 5 Tantalum clusters and their oxide complexes have also gained attention for their enhanced oxygen reduction reaction as catalysts, [6][7][8] ferroelectric state, and spin uncoupling property related to their superconductivity characteristics.…”

“…5 Most recently, Kramers blocking of spin-lattice relaxation in clusters of vanadium-group elements have been studied, and this relaxation of the quantum phenomenon was clearly found to be more efficient for larger nuclear mass tantalum clusters. 5 Tantalum clusters and their oxide complexes have also gained attention for their enhanced oxygen reduction reaction as catalysts, [6][7][8] ferroelectric state, and spin uncoupling property related to their superconductivity characteristics. 9 Both experimental and theoretical studies have been carried out to investigate the characteristic parameters of neutral and charged tantalum clusters.…”

“…11 The magnetic moments were measured by a magnetic deection method and discussed by Kramers degeneracy theorem. 5 The gas-phase infrared (IR) spectra of tantalum cations and Ta n O 0,1,2 + (n ¼ 6-11) clusters were experimentally observed by Fielicke et al 12,13 The IR vibrational spectra of tantalum cation Ta n + clusters were simulated using density functional theory (DFT) by Du et al with comparison to the experimental ones, while a highstability icosahedral cluster (Ta 12 2+ ) with spherical aromaticity was also investigated. 14,15 The geometric and electronic structures of clusters can vary for different charge states, especially in terms of their vibrational pattern and structural ngerprint.…”

Strong permanent magnet gradient deflector for Stern–Gerlach-type experiments on molecular beams

“…The same scheme can be extended to experiments with various clusters of other types that are doped with a magnetic impurity. 14 Likewise, when certain clusters in a size sequence display negligible susceptibilities compared to their near neighbors 15,16 they may be used to track the undeflected beam even with the magnet in place. In other circumstances, the magnet can be moved out of the beam path by a precise mechanical translation stage.…”