Kramers degeneracy and relaxation in vanadium, niobium and tantalum clusters

TL;DR

This study investigates magnetic properties and quantum relaxation phenomena in vanadium, niobium, and tantalum clusters, revealing quantum degeneracy effects and relaxation mechanisms in systems with more than 20 atoms.

Contribution

It provides experimental evidence of Kramers degeneracy and quantum relaxation processes in large atomic clusters, extending quantum phenomena understanding to bigger systems.

Findings

Odd clusters show unpaired electron magnetism.

V and Nb clusters exhibit atomic-like behavior, indicating absence of spin-lattice interaction.

Ta clusters show persistent relaxation likely due to phonon and spin-orbit effects.

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 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.