Questions about using spin-polarized and spin-orbit coupling calculations

Peter Blaha Tue, 24 Sep 2019 06:16:52 -0700

Answers inlined.

I have three questions concerning the inclusion of spin in a material in WIEN2k.

The three questions concern the two terms where a spin-dependent term appears in the Pauli Hamiltonian for magnetic systems, which are:

Question 1)

In the Pauli Hamiltonian a term appears which is a dot product of the spin-matrices of the system and an effective magnetic field.

The effective magnetic field is a summation of an external magnetic field and an exchange-correlation term. The exchange-correlation term B_xc, is expressed as a derivative of the density w.r.t. the magnetization (in the LDA framework) and that B_xc is parallel to the magnetization density vector. If I understand correctly then the material of interest is magnetic when B_xc is nonzero.

When doing a spin-polarized calculation, what happens then to the external magnetic field term? Is the external magnetic field term set to zero?

Usually, we do not apply an additional external field, but there is only an internal field (B_xc); i.e. the material is ferro-, ferri-,or antiferro-magnetic without an external field.

In special cases you want to look on the response of a material to an external field. This can be done using the FSM method for ferromagnets or applying an external field using the "orb" package.

Question 2)

The other term in the Pauli Hamiltonian is the spin-orbit coupling (SOC) term, which is proportional to (1/r x dV/dr ) (dV/dr = the derivative of the potential w.r.t. the radial coordinate).

When doing a calculation including SOC the script init_so asks for the magnetization direction (in hkl).

In a non-spin polarized calculation with SOC the magnetization direction has no meaning, is this correct?

Yes (at least for global/averaged quantities).

Question 3)

If the system of interest is a magnetic system then a spin-polarized calculation with SOC should give me 1) the strength of the magnetization along the chosen magnetization axis, and 2) the spin-up and spin-down density of states (DOS) along the chosen axis. But a spin-polarized calculation without SOC will not give me the spin-up and spin-down DOS. Is this correct?

No. Any spin-polarized calculation gives you a spin-up/dn DOS and you can also get the energy gain due to magnetization with respect to a non-spinpolarized calculation. However, without SO you do not get any information about the direction of the moment with respect to the lattice; i.e. "up" does NOT mean "001"-direction, and of course also no magnetic anisotropy (energy change when the magnetization direction changes, easy - hard axis). In addition, without SO you can get only spin-moments (dominating in 3d compounds), but for the orbital moments you need SO.

Reference: https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg19032.html