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

TL;DR

This paper provides an analytical study of anisotropy effects in high-symmetry tetramer single molecule magnets, deriving energy spectra, thermodynamics, and spectroscopic properties, and predicts multiferroic behavior in certain symmetries.

Contribution

It offers exact analytical formulas for eigenstates and thermodynamics of anisotropic tetramers, and predicts multiferroic states in specific symmetries, advancing understanding of molecular magnetism.

Findings

Analytic expressions for eigenstate energies and thermodynamics.

First-order level-crossing inductions for various spins.

Prediction of multiferroic behavior in S4 and D2d symmetric tetramers.

Abstract

We study single-ion and exchange anisotropy effects in equal-spin $s_1$ tetramer single molecule magnets exhibiting $T_d$, $D_{4h}$, $D_{2d}$, $C_{4h}$, $C_{4v}$, or $S_4$ ionic point group symmetry. We first write the group-invariant quadratic single-ion and symmetric anisotropic exchange Hamiltonians in the appropriate local coordinates. We then rewrite these local Hamiltonians in the molecular or laboratory representation, along with the Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and three-center quartic Hamiltonians. Using our exact, compact forms for the single-ion spin matrix elements, we evaluate the eigenstate energies analytically to first order in the microscopic anisotropy interactions, corresponding to the strong exchange limit, and provide tables of simple formulas for the energies of the lowest four eigenstate manifolds of ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary $s_1$. For AFM tetramers, we illustrate the first-order level-crossing inductions for $s_1=1/2,1,3/2$, and obtain a preliminary estimate of the microscopic parameters in a Ni$_4$ from a fit to magnetization data. Accurate analytic expressions for the thermodynamics, electron paramagnetic resonance absorption and inelastic neutron scattering cross-section are given, allowing for a determination of three of the microscopic anisotropy interactions from the second excited state manifold of FM tetramers. We also predict that tetramers with symmetries $S_4$ and $D_{2d}$ should exhibit both DM interactions and multiferroic states, and illustrate our predictions for $s_1=1/2, 1$.