Running McPhase and McDisp

The programs mcphas and mcdisp are run completely the same way as usual, only the output files contain also information about the (thermal) expectation values of

dependent on temperature and magnetic field. Using the module so1ion the notation $<\hat J_a>$ , $<\hat J_b>$ , $<\hat J_c>$ , $<\hat J_d>$ , $<\hat J_e>$ , etc. correspond to

, $<O_{22}(s)>$ , $<O_{21}(s)>$ , $<O_{20}>$ , $<O_{21}>$ , $<O_{22}>$ , $<O_{33}(s)>$ , ... respectively. Note that by the higher order interactions not only the static properties are changed, but also the dispersion of the magnetic excitations is influenced.

The directory examples/gdru2si2 contains an example of a simulation of biquadratic (i.e. isotropic quadrupolar) interactions leading to an improved description of magnetic susceptibility.

For DyCu

the conversion of the magnetic axis due to quadrupolar exchange has been calculated according to the model [8]. The calculated quadrupolar phase diagram is shown in figure 15.

**Figure 15:** DyCu: calculated quadrupolar phased diagram. When applying a large magnetic field parallel to the axis of the orthorhombic crystal, the system undergoes a structural transformation associated with a reorientation of the structural unit cell. This effect can be modelled by a large quadrupolar interaction.[plot created with program *phased*]
$\includegraphics[angle=-90, width=0.5\textwidth]{figsrc/dyphased.eps}$

When large quadrupolar interactions are present, the excitation spectrum is changed and quadrupolar modes (orbitons) with a finite dispersion are expected. These modes correspond to an cooperative oscillation of the quadrupolar moments such as shown in figure 16. The program mcdisp is able to calculate this dispersion and the corresponding neutron scattering cross section as shown in figure 17 for the case of PrCu

**Figure 16:** Orbital excitations viewed as correlated changes in 4f-charge densities.
$\includegraphics[angle=0, width=0.6\textwidth]{figsrc/orbiton.eps}$

**Figure 17:** PrCu: calculated dispersion of quadrupolar excitations in a field of 5 Tesla parallel to the axis of this orthorhombic system. [plot created with program *displaycontour*]
$\includegraphics[angle=0, width=0.5\textwidth]{figsrc/prcu2_0k0_5T.eps}$