Microscopic Model for High-spin vs. Low-spin ground state in $[Ni_2{M(CN)_8]}$ ($M=Mo^V, W^V, Nb^{IV}$) magnetic clusters

TL;DR

This paper develops an exact microscopic model for Ni(II)-M magnetic clusters to explain the observed high-spin and low-spin ground states, revealing the importance of direct exchange, orbital splitting, and inter-orbital repulsions.

Contribution

It introduces a valence bond approach to exactly solve the model and maps out quantum phase diagrams showing spin state transitions based on key parameters.

Findings

Identifies parameters controlling high-spin and low-spin states.

Fits spin gap to an effective exchange constant within experimental range.

Discovers a parameter region with an intermediate spin ground state.

Abstract

Conventional superexchange rules predict ferromagnetic exchange interaction between Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that in some systems this superexchange is antiferromagnetic. To understand this feature, in this paper we develop a microscopic model for Ni(II)-M systems and solve it exactly using a valence bond approach. We identify the direct exchange coupling, the splitting of the magnetic orbitals and the inter-orbital electron repulsions, on the M site as the parameters which control the ground state spin of various clusters of the Ni(II)-M system. We present quantum phase diagrams which delineate the high-spin and low-spin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region in the parameter space where an intermediate spin state is the ground state. These results indicate that the spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian.