Features of SpinW

SpinW is a Matlab library that can define spin Hamiltonians including general quadratic exchange interactions, single ion anisotropy and external magnetic field, applying space group symmetries and solve the resulting equation of motion.

Summary

In short SpinW can solve the following spin Hamiltonian using classical and quasi classical numerical methods:

$$\mathcal{H} = \sum_{i,j} \textbf{S}_i J_{ij}\textbf{S}_j + \sum_{i,j}\textbf{S}_i A_i\textbf{S}_j + \textbf{B}\sum_i g_i\textbf{S}_i$$

where $\textbf{S}_i$ are spin vector operators, $J_{ij}$ are $[3\times 3]$ matrices describing pair coupling between spins, $A_{ij}$ are $[3\times 3]$ anisotropy matrices, $\textbf{B}$ is external magnetic field and $g_i$ is the g-tensor.

Crystal structures

• definition of crystal structure with arbitrary unit cell, using space group or symmetry operators
• definition of non-magnetic atoms and magnetic atoms with arbitrary moment size
• publication quality 3D plotting of crystal structures (atoms, labels, axes, surrounding polyhedron, anisotropy ellipsoids, DM vector, etc.)

Magnetic structures

• definition of magnetic structures using complex magnetization vectors
• representation of incommensurate structures using rotating frame coordinate system
• generation of magnetic structures on a magnetic supercell
• 3D visualization of magnetic structures

Magnetic interactions

• simple assignment of bonds based on length
• arbitrary quadratic exchange interactions are allowed (including DM, etc.)
• arbitrary single ion anisotropy tensor (easy-plane, easy-axis, etc.)
• Zeeman energy in homogeneous magnetic field including arbitrary g-tensor
• calculation of symmetry allowed elements of the above tensors based on the crystallographic space group

Optimization of magnetic structures

• minimization of the classical energy assuming single-k magnetic structure for fast and simple solution for ground state magnetic structure
• simulated annealing using the Metropolis algorithm on an arbitrary large magnetic supercell
• calculating properties in thermodynamical equilibrium (heat capacity, magnetic susceptibility, etc.)
• calculation of the magnetic structure factor
• simulation of magnetic neutron diffraction and diffuse scattering

Linear spin wave theory

• simulation of magnetic excitations in general commensurate and incommensurate magnetic structures using linear spin-wave theory
• calculation of spin wave dispersion, spin-spin correlation functions
• calculation of neutron scattering cross section for unpolarized neutrons including the magnetic form factor
• calculation of polarized neutron scattering cross sections
• possible to include different moment sizes for different magnetic atoms
• calculation of powder averaged spin wave spectrum

Plotting of spin wave spectrum

• plotting of dispersions and correlation functions
• calculation and plotting of the convoluted spectra for direct comparison with inelastic neutron scattering
• full integration into Horace for plotting and comparison with time of flight neutron data, see http://horace.isis.rl.ac.uk

Fitting spin wave spectra

• possible to fit any parameter in the Hamiltonian
• robust fitting, even when the number of simulated spin wave modes differs from the measured number of modes