Thermodynamics and Magnetic Excitations in Quantum Spin Trimers: Applications for the Understanding of Molecular Magnets

Amelia Brumfield,Jason Haraldsen

doi:10.3390/cryst9020093

Abstract

Molecular magnets provide a playground of interesting phenomena and interactions that have direct applications for quantum computation and magnetic systems. A general understanding of the underlying geometries for molecular magnets therefore generates a consistent foundation for which further analysis and understanding can be established. Using a Heisenberg spin-spin exchange Hamiltonian, we investigate the evolution of magnetic excitations and thermodynamics of quantum spin isosceles trimers (two sides J and one side α J ) with increasing spin. For the thermodynamics, we produce exact general solutions for the energy eigenstates and spin decomposition, which can be used to determine the heat capacity and magnetic susceptibility quickly. We show how the thermodynamic properties change with α coupling parameters and how the underlying ground state governs the Schottky anomaly. Furthermore, we investigate the microscopic excitations by examining the inelastic neutron scattering excitations and structure factors. Here, we illustrate how the individual dimer subgeometry governs the ability for probing underlying excitations. Overall, we feel these calculations can help with the general analysis and characterization of molecular magnet systems.

Highlights

For over half a century, technology has been governed by the manipulation of the electron and its properties of charge and spin
We examine the effects of a variable dimer exchange embedded in a quantum spin trimer and verify that, regardless of spin and trimer geometry, the inelastic neutron scattering excitations for any trimer can be determined by the excitations of the individual bases
We have presented calculations of the thermodynamics, inelastic neutron scattering excitations, and structure factors for general isosceles trimers

Summary

Introduction

For over half a century, technology has been governed by the manipulation of the electron and its properties of charge and spin. It has been shown that the larger molecule-based magnets have excitations that are characterized by the smaller subgeometries of the system [35,36,37] This observation is important because it provides an opportunity to determine closed-form analytic solutions for systems that are typically solved numerically since most molecular magnetic systems are large clusters composed of high-spin atoms [30,32]. We examine the evolution of the thermodynamics as a function of spin and dimer exchange and show the quantum phase transition points in the heat capacity. These phase transitions allow for the possible tunability of quantum trimers with external fields (magnetic, strain, etc.)

The Heisenberg Trimer Model

Evolution of the Thermodynamic Properties

Inelastic Neutron Scattering Structure Factors

Conclusions