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$_{80}$.
Highlights
A key parameter for the low-temperature magnetic coupling of in dinuclear lanthanide singlemolecule magnets (SMMs) is the barrier UFA resulting from the exchange and dipole interactions between the two 4f moments
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 Dy2ScN@C80 and Dy2TiC@C80
As a demonstration of the discriminative power of accurate angle determination, we show that the experimentally determined angles fit the Dy − X − Dy (X = N, C) bond angles from density functional theory (DFT) worse than the angles between the two quantization axes of the Dy magnetic moments from complete active space self-consistent-field (CASSCF) calculations
Summary
The Dy2ScN@C80 (Dy2TiC@C80) endofullerenes were produced using an arc-discharge synthesis using graphite rods packed with a mixture of Sc (Ti), Dy, and graphite powder under He atmosphere with small amounts of NH3 (CH4) [13,21]. The x-ray absorption measurements were carried out at the X-Treme beamline [25] of the Swiss Light Source. Absorption spectra were acquired by measuring the total electron yield (TEY) in the on-the-fly mode [26] while applying a magnetic field parallel to the x-ray beam. The SQUID measurements were performed using a Quantum Design MPMS3 Vibrating Sample Magnetometer (VSM). The endofullerenes were dissolved in toluene and spray-coated on an aluminum plate and drop cast into a polypropylene sample holder for the XMCD and SQUID measurements respectively
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