[Wien] Spin-polarization and spin-orbit coupling

[Peter Blaha]

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.


> 
> Cheers,
> 
> Luigi Maduro
> 
> PhD candidate
> Kavli Institute of Nanoscience
> 
> Department of Quantum Nanoscience
> 
> Faculty of Applied Sciences
> 
> Delft University of Technology
> 
> 
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-- 

                                       P.Blaha
--------------------------------------------------------------------------
Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
WWW:   http://www.imc.tuwien.ac.at/TC_Blaha
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