Phonon Hamiltonian - bertdupe/Matjes GitHub Wiki

This page includes all the interactions which can be used when evaluating the magnetic Hamiltonian:

Most interactions are inserted though a keyword, which is followed by a set of lines which include the different entries for that particular interaction. No empty lines or comment lines shall appear between the lines which would be treated as signature of the end of entries, however comments at the end of each line are possible. Each interaction keyword shall only appear once.

Force constant

The force constants can be switched on through the keyword phonon_harmonic. This interaction the atom types of the connected atoms, the distance between them, and the real value.

For example,

phonon_harmonic
1 1 1  1.0d-3
1 2 2  0.1d-3

defines a force constant of magnitude 1.0meV between all atoms of atom-type 1 which have the minimal (1), distance between themselves and an interaction between the second neighbors of atom-types 1 and 2 with magnitude 0.1meV.

Force tensor

You have the possibility to input the full Force tensor. The format is shown below. The force tensor have to be written in line (should not matter because force tensors are symmetric). You need to tell the code along which direction the force tensor should be applied. The tensor will then be rotated for each of the bounds.

force_tensor
1 1 1 Fxx Fxy Fxz Fyx Fyy Fyz Fzx Fzy Fzz Rx Ry Rz

This input means that you have a non-zero force tensor between atom 1 and atom 1 for the first nearest neighbor along the direction Rx Ry Rz. The force tensor is then applied with the sign of 'c_phtensor' which is by default -1. It can be changed in the input

Acoustic sum rule

The acoustic sum rule (ASR) is taken into account automatically. It enforces that the energy stays 0 for a uniform atomic displacement. The ASR can be disabled with ' cancel_ASR .T.'

Dipolar interaction

The dipolar interaction can be calculated using either the conventional Hamiltonian setup or the more efficient discrete fourier-transformation implementation which requires FFTW3 (CPP_FFTW3). It is highly advised to use the fft implementation which will be much faster even for medium-sized computational grids. In case of periodic boundary conditions the number of considered periodic cells has to be specified through mag_dip_period_cut, in case of open boundaries the respective value is ignored. In the ferroelectric case, the surface charges can be considered. So far no conditions on the charges are implemented - like in the magnetic case.

The inputs are:

ph_dip_use T
ph_dip_fft T
ph_dip_period_cut 30 30  1

, where ph_dip_use signifies that the DDI interaction is calculated. The FFTW implementation is used when ph_dip_fft is True (default), otherwise the slower/dense implementation in the normal space is used.

ph_dip_fft F naturally results in very dense Hamiltonians, which should only be used for testing purposes in small systems, where, due to the dense nature, is advantageous to use the dense Hamiltonian implementation CPP_DENSE.

Stark energy

The Stark energy will automatically be taken into account if the external electric field E_ext is non-zero. It couples the electric field and the phonons that carrie a non-zero Born effective charge. Alternatively, it can be manually switched on through the logical keyword enable_stark T which might be necessary in case of time-dependent external magnetic field changes.

Rank 4 phonon interaction (4-phonon interaction)

The 4-phonon interaction has the same symmetry as the 4-spin interaction. It can be considered in case of a lattice where the nearest patches of 4 atom sites of a given atom-type have equal edge sizes (ie. square and hexagonal lattices). It is switched on through:

U_Phonon_r4
1 1.0d-3

where, the first integer defines the atom-type and the second term defines the magnitude.

Biquadratic phonons

This interaction has the same symmetry as the Biquadratic magnetic exchange. The input of the rank 4 phonon is equivalent to the Heisenberg exchange with for example:

U_biq
1 1 1 0.2d-3

, which creates an interaction of the first neighbors of atom-type 1 of magnitude 0.2meV.