Simulation of magnetoelastic response of iron nanowire loop

We analyzed the magnetoelastic responses of one-dimensional iron nanowire loop systems with quantum statistical mechanics, treating the particles in the systems as identical bosons with an arbitrary integer spin. Under the assumptions adopted, we demonstrated that the Hamiltonian of the system can be separated into two parts, corresponding to two Ising subsystems, describing the particle spin and the particle displacement, respectively. Because the energy of the particle motion at atomic scale is quantized, there should be more the strict constraint on the particle displacement Ising subsystem. Making use of the existing results for Ising system, the partition function of the system was derived into two parts, corresponding respectively to the two Ising subsystems. Then the Gibbs distribution was obtained by statistical mechanics, and the description for the magnetoelastic response was derived. The magnetoelastic responses were predicted with the developed approach, and the comparison with the results calculated with VASP demonstrates the validity of the developed approach.