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SpinW is a MATLAB library that can plot and numerically simulate magnetic structures and excitations of given spin Hamiltonian using classical Monte Carlo simulation and linear spin wave theory.

The Projects


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

\[\mathcal{H}=\sum_{i,j}\mathbf{S}_iJ_{ij}\mathbf{S}_j + \sum_i \mathbf{S}_iA_i\mathbf{S}_i + \mathbf{B}\sum_i\mathbf{g}_i\mathbf{S}_i\]

where $S_i$ are spin vector operators, $J_{ij}$ are 3x3 matrices describing pair coupling between spins, $A_{ij}$ are 3x3 anisotropy matrices, $B$ is external magnetic field and $g_i$ is the g-tensor.

Crystal structures

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

Magnetic structures

  • definition of 1D, 2D and 3D magnetic structures
  • representation of incommensurate structures using rotating coordinate system or complex basis vectors
  • generation of magnetic structures on a magnetic supercell
  • plotting of magnetic structures

Magnetic interactions

  • simple assignment of magnetic interactions to neighbouring magnetic atoms based on distance
  • possible interactions: Heisenberg, Dzyaloshinskii-Moriya, anisotropic and general 3x3 exchange tensor
  • 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

Simulation of magnetic structures

  • classical energy minimization 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.)
  • magnetic structure factor calculation using FFT
  • simulation of magnetic neutron diffraction and diffuse scattering
  • 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

Our Partners

European Spallation Source
ISIS, Science & Technology Facilities Council
Paul Scherrer Institut
Helmholtz-Zentrum Berlin
Niels Bohr International Academy