MnO – magnetic

This example is courtesy of Joseph A. M. Paddison, Matthias J. Gutmann, J. Ross Stewart, Matthew G. Tucker, Martin T. Dove, David A. Keen, and Andrew L. Goodwin Phys. Rev. B 97, 014429

Getting started on analysis.sns.gov

1. Open a terminal (Ctrl+Alt+T)
2. Create a directory on your Desktop mkdir ~/Desktop/Workshop/
3. Copy over CIF and data files cp /SNS/software/scd/examples/MnO.* ~/Desktop/Workshop/
4. Launch rmc-discord /SNS/software/scd/rmc-discord.sh

RMC refinement

There are four main steps to performing a reverse Monte Carlo refinement:

1. Define a supercell
2. Load and preprocess a diffuse scattering intensity dataset
3. Setup and perform a refinement
4. Calculate and visualize the correlations

Crystal tab

To define a supercell, it is first necessary to construct a unit cell from the average structure.

1. Begin by loading a crystallographic information file (CIF) or magnetic CIF file
   • The button is located on the upper left corner of window Load CIF.
   • Choose MnO.cif.
   • The parameters are extracted from the CIF file and populated into two tables.
   • The left hand table displays all atoms in the unit supercell.
   • The right hand table gives the basic atom site information.
     • Modifying the atom site information on the right automatically updates the unit cell table on the right.
2. Modify (if necessary) the atom site table
   • Begin by choosing between Neutron and X-ray refinement in the upper right combo box.
   • By selecting refinement type first, the relevant parameters are available to edit including nuclei and ions.
     • For magnetic refinement, Neutron must be selected to access magnetic information.
   • To display, different parameters, choose from Site parameters, Structural parameters, and if available Magnetic parameters.
     • In Site parameters, along with the atom (isotope for neutron, ion for X-ray), its occupancy and fractional coordinates \(u\), \(v\), \(w\) can be modified. An atom may also be de-activated or activated for refinement.
     • In Structural parameters, the anisotropic displacement parameters \(U_{ij}\) may be modified. The equivalent isotropic parameter \(U_\text{iso}\) and its principal components will be updated (\(U_1\), \(U_2\), \(U_3\)). If available, Magnetic parameters allows the magnetic ion to be chosen along with the magnetic moment component along the crystal axes. If a valid .mcif is used, the magnetic symmetry will be accounted for. The \(g\)-factor can also be specified.
   • Select Magnetic parameters, choose \(\mathrm{Mn2+}\) ions and deactivate site 2 since oxygen is nonmagnetic.
   • Create a supercell with size \(N_1=8\), \(N_2=8\), and \(N_3=8\) by entering the number of cells along each crystal axes.
3. Optionally save the CIF file of the supercell and visualize it in external program VESTA

Crystal tab

Hints

• The size of the supercell defines the maximum resolution of the refined reciprocal space pattern.
  • A larger supercell is needed to refine finer reciprocal space features.
    • Along each dimension \(i\), the resolution in reciprocal lattice units is \(1/N_i\).
  • Start with a small number (e.g. \(4\times4\times4\)) and increase as needed.
    • Too large of a supercell uses more memory and takes longer to refine.
    • Too small of a supercell may not resolve the diffuse scattering features.

Intensity tab

Once a supercell is defined, the experimental data can be loaded and preprocessed for refinement

1. Load a HDF5 (H5) with the diffuse scattering data
   • The button is located on the upper left corner of window Load NeXus file.
   • Choose MnO.h5.
   • The loaded data are displayed as three separate reciprocal space slices: \((0kl)\), \((h0l)\), and \((hk0)\).
   • The table displays the binning information along each reciprocal space dimension.
   • The tabs give basic options for rebinning, cropping, and punching out Bragg peaks.
2. View the data
   • In the upper left corner of the plots, select between the Intensity and Error.
   • In the lower right corner of the plots, choose between Linear and Logarithmic scaling.
   • Change the Min and Max limits of the colorbar.
   • Change the index of the slices displayed for \(h\), \(k\), and \(l\).
3. Rebin and crop the data (if necessary)
   • The table can be directly modified updating the size, min, and max values.
   • The Rebin tab gives binning options that bins the data into equal sizes.
   • The Centered at integer check boxes give only the options where the binning is centered over each integer \(h\), \(k\), and \(l\). - The Crop table allows the \(h\)-, \(k\)-, and \(l\)-range to be specified.
   • The Reset button resets the binning and cropping to the original values of the loaded data. - Rebin the data to \(0.12\times0.12\times0.12\) and crop to -3 to 3 along each dimension.
4. The Bragg peaks are already removed

Crystal tab

Hints

• View the data in logarithmic scale to better observe the diffuse scattering.
• Select a region of interest that covers at least the primitive features of the observed diffuse scattering.

Refinement tab

Setup and run a refinement.

1. Choose the refinement type by selecting the Magnetic, Occupational, or Displacive check box
   • Under each corresponding tab is a set of options relevant to that disorder type.
   • Choose Magnetic and leave the check box marked for Fixed moment
2. Set the refinement temperature prefactor and decay constant
   • The temperature Prefactor is the initial temperature.
   • Start at 1e+4.
   • The decay Constant is the rate at which the temperature decreases with each move as a Newtonian cooling function. - Start at 1e-3.
3. Choose between a single run or Batch job by specifying the number of runs
   • More runs can be averaged together to improve statistics.
4. Choose the Gaussian filter size for each \(h\), \(k\), and \(l\) size in number of pixels
   • Using Gaussian filtering reduces the noise at the expense of increasing the time of the refinement.
   • Choose 1.0x1.0x1.0 to start.
5. Start the refinement by clicking Run
   • The refinement may be stopped by clicking Stop.
   • Once stopped, the refinement may be continued or Reset for a new refinement.
   • View the intensity plot type to compare the Calculated and Experiment datasets.
   • Change the slice, scaling, and colorbar limits.
   • View different refinement static plots.

Crystal tab

Hints

• One cycle is defined as the number of moves equal to the number of atoms in the supercell.
  • Typically 100 cycles is sufficient to obtain a good refinement.
• Start off with only a few cycles (e.g. 10) to check the temperature prefactor and decay constant.
  • At the beginning, the temperature needs to be high enough such that most bad moves are accepted and very few are rejected.
  • The decay rate should be cool the system gradually such that more and more bad moves are rejected, and by the end, nearly any bad moves are accepted.
  • Cooling too quickly can quench the system into a metastable state.
  • Increasing the number of cycles by 10 typically requires decreasing the decay rate by a factor of 10 to keep a similar cooling schedule.
• Increasing the number of batch jobs improves the statistics of the correlations and the recalculated diffuse scattering pattern.

Correlations tab

After completing a refinement, the pair correlations can be calculated.

1. There are two tabs for calculating correlations: Spherical average and Three-dimensional
   • In each, the Fraction determines the largest separation vector that can be constructed multiplying this value by the longest separation vector possible in the supercell.
   • In each, the Tolerance corresponds to the maximum number of decimal places for distinguishing unique pairs.
   • Specifying 1e-2, for example, means that distances 0.333 and 0.334 are equivalent distances since they round to 0.33 using two decimal places. - The Average check box averages common separation vectors with different atom-pair types.
   • By unclicking Average, it is possible to only plot certain atom-pair types by utilizing the check boxes in the table. - The correlations may be saved as either a CSV file or VTK file which can be opened in external programs like ParaView for visualization.
2. Calculate the one-dimensional and three-dimensional correlations
   • In the upper right of each tab are the different correlation options: Magnetic, Occupancy, and Displacement
   • Select Magnetic type to and click Calculate to obtain the correlations.
   • Increase the Fraction to 0.5. - In the upper left of each tab is the option to plot the Correlations or Collinearity (if Magnetic or Displacement). - In the bottom left is the option to plot in Linear or Logarithmic scale.
3. The additional options for Three-dimensional correlations include choosing an \(hkl\) slice
   • Use integer \(h\), \(k\), and \(l\) to specify the Miller plane.
   • Choose a distance \(d\) from the origin where \((hkl)\cdot[uvw]=d\).

Crystal tab

Hints

• Start with a small Fraction (e.g. 0.125) and gradually increase it by small increments up to 1.0 to extend the cutoff distance of pair correlation calculation.
  • Specifying too large a fraction will take more time and consume more memory than may be available.
• Increase the Tolerance (e.g. 1e-4 to 1e-3) if more unique pairs by separation vector are identified than actually exist.
  • Unique pairs are identified by common atom pair type and separation distance(s).

Recalculation tab

Crystal tab

Hints

• Although it is possible to recalculate the full volume of reciprocal space, it requires more time than simply calculating a slice.
  • If specifying a slice, make one of the sizes of \(h\), \(k\), and \(l\) equal to 1 and set the minimum value for the slice.
• Applying Laue symmetry to the data can improve the recalculated pattern.
  • At most, the diffuse scattering will have at most the Laue symmetry of the crystal.
  • The nature of the short range ordering can have lower symmetry than that of the average structure.