# 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.

## Key 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.