Single-ion and exchange anisotropy in high-symmetry tetramer single molecule magnets

TL;DR

This paper develops a comprehensive theoretical framework for analyzing anisotropic interactions in high-symmetry tetramer single molecule magnets, providing exact eigenstates, level-crossing conditions, and methods to extract microscopic parameters from experimental data.

Contribution

It introduces a group-invariant Hamiltonian formulation and exact eigenstate evaluation for high-symmetry tetramers, including anisotropic exchange and single-ion effects, with analytical level-crossing and thermodynamic expressions.

Findings

Eigenstates evaluated to first order in interactions.

Analytical level-crossing inductions for various spins.

Procedures for extracting microscopic parameters from EPR.

Abstract

For equal-spin $s_1$ tetramer single molecule magnets with ionic point groups $g=T_d, D_{4h}, D_{2d}, C_{4h}, C_{4v}$, and $S_4$, we write the group-invariant single-ion, Dzaloshinskii-Moriya, and symmetric anisotropic near-neighbor and next-nearest-neighbor exchange Hamiltonians using the respective local axial and azimuthal vector groups. The anisotropic exchange renormalized near-neighbor and next-nearest-neighbor isotropic exchange interactions are $\tilde{J}_g$ and $\tilde{J}_g'$. Using our exact, compact forms for the single-ion matrix elements, we evaluate the eigenstates of the full Hamiltonian to first order in the various interactions. There are two types of ferromagnetic (FM) and antiferromagnetic (AFM) tetramers. In Type I, $\tilde{J}_g'-\tilde{J}_g>0$, the tetramers act as two dimers with the maximal pair quantum numbers $s_{13}=s_{24}=2s_1$ at low temperature. Type II tetramers with $\tilde{J}_g'-\tilde{J}_g<0$ are frustrated, with minimal values of the pair quantum numbers $s_{13}$ and $s_{24}$ at low temperature. For both Type I and Type II AFM tetramers, we evaluate the first-order level-crossing inductions analytically for arbitary $s_1$, and illustrate the results for $s_1=1/2, 1, 3/2$. Accurate Hartree expressions for the thermodynamics, electron paramagnetic resonance (EPR) absorption and inelastic neutron scattering cross-section are given. A procedure to extract the effective microscopic parameters for Types I and II tetramers using EPR is given.