mcdisp - the Calculation Program for Dispersive Excitations

ORLANDO: We have now learned how to do many static properties of solids, including magnetostriction and diffraction. Can we also do excitations ? I mean the dispersive excitations - we have so much data on inelastic neutron scattering, for example, which waits to be analysed ...

SIMPLICIUS: I have some expert in my institute who can deal with such data ...

ORLANDO: ... I know, I have already asked him for help, but it seems his interest is not in our particular compound.

SIMPLICIUS: Tell me what is interesting in your compound and I will talk to him.

EWALD: I think maybe here the program mcdisp might help to speed up a bit the process of finding a model. For a given field $\mathbf H$ and temperature $T$ the dynamics of the system can be calculated by the program mcdisp, for details on the theory see appendix M. mcdisp requires as input files the mcphas.j and single ion input files. In addition, the input file mcdisp.par and mcdisp.mf are needed (see description below).

mcdisp [options]

[file.mf]] calculates the dispersion of magnetic excitations needs as input file a file.mf (default mcdisp.mf) and mcdisp.par. Creates files ./results/mcdisp.qom and ./results/mcdisp.qei containing the dispersion of the magnetic excitations and the neutron scattering intensity.

Options are:

-max

restricts the single ion susceptibility used to maximum of the n lowest lying transitions, starting from the ground state (useful to save calculation time). – Note that by options -minE and -maxE also an energy interval may be given (minE,maxE): Single ion transitions with energies outside this energy interval are not considered.

option -d forces mcdisp to do calculation of intensities in dipole approximation only

-r

is used to calculate the energy dependence of the cross section via the direct evaluation of the dynamical susceptibility for a set of energy values (see appendix M). If option -r 0.032 is used, the energy dependence of the scattering cross section is calculated within limits [emin,emax] (given in file mcdisp.par). The number, 0.032 in our case, indicates the imaginary part of $\omega$ in units of meV (see equation (267) ). Setting it zero would lead to numerical divergencies, choosing it to large leads to large half widths of the calculated peaks. Output is stored in output file mcdisp.dsigma. Note: option -r will only work correctly if all the single ion modules which are used conform to the following convention: if $g_J\neq0$, then $\hat I_1=\hat J_x,\hat I_2=\hat J_y,\hat I_3=\hat J_z$, if $g_J=0$ then $\hat I_1=\hat S_x, \hat I_2=\hat L_x, \hat I_3=\hat S_y, \hat I_4=\hat L_y, \hat I_5=\hat S_z,\hat I_6=\hat L_z$ (here $\hat \mathbf S, \hat \mathbf L,\hat \mathbf J$ refer to the spin-, orbital- and total angular momentum, respectively in a coordinate system where $y\vert\vert b$, $z\vert\vert(a \times b)$ and $x$ perpendicular to $y$ and $z$).

-jqm

To create an output of the Fourier transform ${\mathcal J}({\mathbf Q})$

-jq

outputs largest eigenvalue of ${\mathcal J}({\mathbf Q})$ and corresponding eigenvector) or option

-jqe

(outputs all eigenvalues). If energies are given for hkls in mcdisp.par, output file mcdisp_scaled.jq contains scaled parameters such that energy of first hkl set corresponds to highest eigenvalue of ${\mathcal J}({\mathbf Q})$.

-cd

treat classical dipole interaction internally (for the the first three the interaction operators $I_1,I_2,I_3$, which must correspond to angular momentum $J$, such as in the so1ion module) and it is assumed that $(g_J.I_1,g_J.I_2,g_J.I_3)$ are the components of the magnetic moment ($g_J$ given in sipf file, thus setting it zero there will exclude the corresponding ion from the dipolar interaction calculation - this is the way for example to include phonon degrees of freedom in such a calculation), the classical dipole interaction is calculated using the series expansion for the classical dipolar expansion given by Bowden[30]. Using this option permits to avoid a large number of interaction constants in mcphas.j. If the dipolar interaction in equation (26) of[30] has to be evaluated for $\mathbf q=0$ or for a reciprocal lattice vector $\mathbf q=\mathbf q_L$, it is ambigous due to a factor $q_{\alpha}q_{\beta}/q^2$ which appears in the first term ”I” and in the second term ”II' in equation (26) of[30]. This ambigousity reflects the shape of the sample, compare the discussion on page 237 of [1]. In contrast to the static properties such as spin and mean fields and single ion excitation energies mcphasit (where $D^{eff}(q=0)$ is used) for the dispersion of excitations in mcdisp the Fourier transform of the classical dipolar interaction is calculated for q=0 using equation (5.5.6) in [1]. This corresponds to setting the zero by zero division in the first term ”I” and in the second term ”II” in equation (26) of[30] equal to the demagnetisation tensor, i.e. $q_{\alpha}q_{\beta}/q^2 \vert _{q\rightarrow 0} \sim \overline{n}_{\rm demag}$.

-v

option is to display more information.

-a

can be used to avoid overwriting output files in results, new results are appended.

-c

can be used to create a single ion transition file ./results/mcdisp.trs, which contains all single ion transitions used in the calculation. It also contains the neutron intensities of the non interacting subsystems. This file can be edited (uncommenting single ion transitions which should not by used by a # sign at the beginning of the line) and then the program can be restarted using the

-t

to read the single ion transition file ./results/mcdisp.trs and calculate energies and neutron intensities of dispersive modes.

-ninit n

to set the maximum number of low lying initial states, which will be considered in calculating a single ion susceptibility (not functional in all single ion modules).

-pinit p

to set the minimum thermal population of a initial state in order to be considered in the singleion ion susceptibility (not functional in all singleion ion modules).

-prefix 001

to allow for easy parallel processing: all output files results/mcdisp.* will then be created with prefix 001, i.e. results/001mcdisp.*. Moreover, in mcdisp.par it is then possible to enter variables like hklline= with prefix, in our case 001, i.e. 001hklline: this will trigger the program to read these variables only if started with the option -prefix 001. Another process maybe started with -prefix 002 and will read variables such as 002hklline and ignore 001hklline. Variables without prefixes will always be read and used, in conflicting cases the last appearance in file mcdisp.par will be taken (i.e. 001kf=1 ...kf=2 will set kf to 2, whereas kf=2 001kf=1 will set kf to 1 if mcdisp is started with prefix 001). After finishing the different processes, the results of the calculations stored e.g. in 001mcdisp.qei and 002mcdisp.qei may be merged by commands like appendfile mcdisp.qei 001mcdisp.qei 002mcdisp.qei.

-ignore_not_posdef_matrix_error

ignores error when energies get complex due to unphysical mf groundstate.

-x

to calculate resonant inelastic x-ray intensities (maximized with respect to azimuth) instead of neutron intensities.

-xa azstp

to calculate resonant inelastic x-ray intensities with complete azimuth dependence for each reflection in steps azstep (deg).

-xaf azimuth

to calculate resonant inelastic x-ray intensities for the given azimuth (deg).

-X[observable]

to calculate omega and Q dependent susceptibility tensor for an observable (e.g use -Xpel for RAMAN and inelastic X-ray scattering intensity on phonons).

mcdispit [options]

[file.mf]] same as mcdisp, but no graphic window