Precise measurement of angles between two magnetic moments and their configurational stability in single-molecule magnets

TL;DR

This study precisely measures the angles between magnetic moments in dinuclear lanthanide single-molecule magnets, linking these angles to magnetic stability and coupling strength, and extends a pseudospin model to account for anisotropy axis variations.

Contribution

It introduces a method to determine the angle between magnetic moments from magnetization data and extends the pseudospin model to include anisotropy axis variations in SMMs.

Findings

Angles between magnetic moments are measured with better than 1° accuracy.

The measured angles agree with theoretical calculations of quantization axes.

Magnetization stability correlates with the orientation deviation of magnetic moments.

Abstract

A key parameter for the low-temperature magnetic coupling of in dinuclear lanthanide single-molecule magnets (SMMs) is the barrier $U_{FA}$ resulting from the exchange and dipole interactions between the two $4f$ moments. Here we extend the pseudospin model previously used to describe the ground state of dinuclear endofullerenes to account for variations in the orientation of the single-ion anisotropy axes and apply it to the two SMMs Dy$_2$ScN@C$_{80}$ and Dy$_2$TiC@C$_{80}$. While x-ray magnetic circular dichroism (XMCD) indicates the same $J_z=15/2$ Dy groundstate in both molecules, the Dy-Dy coupling strength and the stability of magnetization is distinct. We demonstrate that both the magnitude of the barrier $U_{FA}$ and the angle between the two $4f$ moments are determined directly from precise temperature-dependent magnetization data to an accuracy better than $1^{\circ}$. The experimentally found angles between the $4f$ moments are in excellent agreement with calculated angles between the quantisation axes of the two Dy ions. Theory indicates a larger deviation of the orientation of the Dy magnetic moments from the Dy bond axes to the central ion in Dy$_2$TiC@C$_{80}$. This may explain the lower stability of the magnetisation in Dy$_2$TiC@C$_{80}$, although it exhibits a $\sim 49\%$ stronger exchange coupling than in Dy$_2$ScN@C$_{80}$.