Kagome – magnetic

The classical Heisenberg kagome antiferromagnet is a simple example of a magnetic system with a geometrically frustrated lattice. Using the forward Monte Carlo method, the Hamiltonian

\[E=-J\sum_{\langle i,j\rangle}\pmb{S}_i\cdot\pmb{S}_j\]

is used to describe the nearest neighbor antiferromagnetic interactions where the interaction strength is less than zero (\(J<0\)). The spin vectors \(\pmb{S}\) of the \(\mathrm{Ho^{3+}}\) ions are free to be oriented in any direction.

Example of kagome lattice with magnetic disorder

The spin-pair correlations of an \(8\times8\times8\) supercell are obtained from a forward Monte Carlo simulation. The first nearest neighbors are clearly antiferromagnetic while the second and third are ferromagnetic with the second being more strongly correlated than the third.

Spin-pair correlations

The diffuse scattering intensity is calculated over a range of -6 to 6 in each \(h\)-, \(k\)-, and \(l\)-direction with a bin size of 0.04 in each dimension. Averaging is done over 20 independent forward Monte Carlo simulations to improve the statistics.

Diffuse scattering intensity

RMC refinement

Setup, run, and analyze a refinement with magnetic disorder.

Crystal tab

Create a supercell for magnetic refinement.

• Click on Load CIF file, navigate to the tutorials/kagome/ directory, and locate the kagome.cif file.
• Change the refinement from Neutron nonmagnetic to Neutron magnetic.
• Create a supercell with size \(N_1=8\), \(N_2=8\), and \(N_3=8\).
• Change the atom to a \(\mathrm{Ho3+}\) ion.

Crystal tab

Intensity tab

Preprocess intensity obtained from forward Monte Carlo.

• Download the kagome-magnetic.nxs file.
• Click on Load NeXus file and locate the kagome-magnetic.nxs file.
• Under the Rebin tab, change the step size to 0.2 in each \(h\)-, \(k\)-, and \(l\)-direction.
• Under the Crop tab, change the \(h\)-, \(k\)-, and \(l\)-range from 0 to 6.

Intensity tab

Refinement tab

Perform the refinement.

• Change the number of RMC Cycles to 100.
• Change the filter size to 1.0 pixel in each \(h\)-, \(k\)-, and \(l\)-direction.
• Change the temperature prefactor to 1.00e+01 and decay constant to 1.00e-04.
• Click on run and save refinement file.

Refinement tab

Correlations tab

Calculate three-dimensional spin-pair correlations.

• Under the Three-dimensional tab, change Fraction to 0.1 and Tolerance to 1e-3.
• Click Calculate.
• Change Linear scaling to Logarithmic.

Correlations tab

Recalculation tab

Recalculate the intensity over the initial reciprocal space volume.

• In the table, change $h$, $k$ and $l$ filter size to 4.0.
• Change the Laue symmetry to cif which is inferred from the loaded kagome.cif file.
• Click Calculate.

Recalculation tab

• Navigate to File->Save to save all results into the refinement file.