Progam Workflow

Technically the Hamiltonian (106) is of the general form for McPhase [35], with single ion and interaction terms. The corresponding mean field procedure can be done by an internal single ion module ”epsilon”, which represents not an ion, but the strain. Given $\langle u_{j}^{\alpha} \rangle$ and $\langle O_{\gamma}(\vec J_i) \rangle$ and appropriate interaction constants to the ”epsilon” from (95) and (103), respectively, the right side in (108) can be evaluated in each mean field loop in module ”epsilon” function Icalc. Then elastic constants in (108) can be used to calculate a new strain $\bar \epsilon$, a six component vector. Via the aforementioned appropriate interaction constants (from (96) and (104)) the strain will produce mean fields on lattice displacements and magnetic charge density (crystal field) and so on ... The free energy returned by the module ”epsilon” should correspond to the elastic energy per unit cell given by equation (94).

For the dynamics the ”epsilon” module should not yield any single ion excitations. The excitations can be calculated without taking into account the term $H_{mix}$, because this is linear in the displacement operators and in the harmonic approximation the spectrum of the harmonic Einstein oscillator will not change with such an internal force. The strain has only to be taken into account as a linear modification of the crystal field parameters in the first term of equation (103). This is done automatically by creating the file mcdisp.mf with the ”epsilon” module.

Elastic constants and mixing term parameters $G_{mix}$ should be created with the option -bvk of the program makenn and stored in the file mcphas.j. Using makenn with the option -cfph will create the magnetoelastic parameters $G_{\rm cfph}$ and $\Gamma_{\rm cfph}$.

If the program mcphas is started with option -doeps and it finds elastic constants in the input file mcphas.j, it will use these and determine selfconsistently the strain $\epsilon$ by solving equations (108). Elastic energy and strain tensor are stored in results/mcphas.fum.

In this way it should be possible to model Jahn Teller transitions, phase diagrams, magnetostriction, thermal expansion (magnetic part) and dynamics consistently based only on point charges and Born von Karman springs.

The length change $\Delta L/L$ of a sample in a dilatometer experiment can be calculated from the strain tensor components using ¹⁵

$$\frac{\Delta L}{L}=\sum_{\alpha\beta} \epsilon_{\alpha\beta} \hat L_{\alpha} \hat L_{\beta}$$ (104)

where $\hat \mathbf L$ denotes the unit vector in the direction of measurement.

Utopia: in a further step stress tensor components could be envisaged to act similar as an external magnetic field in McPhase, these will only act on the ”espilon” module and on no other module. The equations given above have to be adapted accordingly and then it should be possible to calculate in addition to magnetic phase diagrams also stress dependence of Jahn Teller transitions and excitations.