TmCu$_2$ - magnetoelastic effects and Neutron Spectra calculated with CF-phonon interaction

As an example for static and dynamic calculations including the crystal-field phonon interaction we present a ”simple” calculation on TmCu$_2$, all input files (calc.bat and logbook calc.pdf with all commands can be found in examples/tmcu2_cf_phonon. ”Simple” in this context means, that the input parameters are quite basic and not fine tuned to match the experiment. As input we used for this orthorhombic system the crystal structure (see TmCu2.cif), point charges $C_{Tm}=0.8\vert e\vert$ $C_{Cu}=-0.4\vert e\vert$ with a cutoff radius of 15 Å and a distance dependent Born von Karman longitudinal spring model as output by default from makenn -bvk.

Figure 21: Crystal field striction, i.e. the crystal field influence on the thermal expansion in TmCu$_2$. - calculation results

Figure 22: Crystal field striction, i.e. the crystal field influence on the thermal expansion in TmCu$_2$. - experimental results [40]

With mcphas -doeps the static thermodynamic properties have been calculated, in particular the strain tensor. The computed crystal field contribution to the thermal expansion (fig. 21) is in good agreement with the experimental data from powder X-ray diffraction (fig. 22).

Figure 23: Dispersive modes in TmCu$_2$ along (11L) at $T=20$ K, symbol size corresponds to the magnetic scattering cross section, red: calculation without crystal field phonon interaction, blue: calculation with crystal field phonon interaction.

By using mcdisp at the temperature of 20 K the magnetic and nuclear inelastic neutron scattering cross section can be calculated. We show in fig. 23 the magnetic scattering along the (11L) direction. Including the crystal field phonon interaction clearly leads to a dynamic Jahn-Teller effect: the flat modes split, shift and get dispersive and there is considerable magnetic intensity transfer to phonons. Thus the double peak feature in unpublished experimental data on powder can possibly be interpreted, see fig. 24

Figure 24: TmCu$_2$ neutron powder spectrum at $T=20$ K as measured on IN6 (Institute Laue Langevin) and SV22 (FZ-Juelich), M. Loewenhaupt, private communication.