Noncollinear spin and spin orbital coupling

[jiejiang]

Dear ATK Forum,

I am interested in calculating transport with noncollinear spin and spin-orbital coupling.

I found the relevant tutorial, at
Introduction to noncollinear spin | QuantumATK R-2020.09 Documentation.

In this example, it sets up noncollinear calculation from collinear one.
The only difference is to change initial spin configuration from parallel (or anti-parallel)
to a rotated one.

My questions are

(1) after SCF, will the spin configuration go back to collinear case?
(2) there is one ground state only for carbon chain. The ground state is either collinear
spin or noncollinear. spin. Why can we have both collinear transport and noncollinear transport?
(3) without introducing spin-orbital coupling, we still can get noncollinear spin?
(4) is the spin orbital coupling (SOC) activated by just changing the exchange–correlation method
and pseudopotentials? Is there a paper about how does SOC implement in ATK?

Thanks,

Jie

[Jess Wellendorff]

Noncollinear (NC) spin means that the spin can point in any direction in space, not just "up" and "down". So the NC spin representation is a matrix with more entries that just 2. (1) if you do SCF with NC spin (e.g. NCGGA.PBE), the converged ground state will be in the noncollinear spin representation. (2) Noncollinear transport just means that you allow for ground-state spins pointing in any direction what calculating the transmission spectrum. (3) SOC requires NC representation, but you can do NC without the SOC. (4) yes, SOC is enabled by choosing the appripriate combination of basis set and pseudopotential (I recommend SG15 for this), e.g.

Code

#----------------------------------------
# Basis Set
#----------------------------------------
basis_set = [
    BasisGGAPseudoDojoSO.Carbon_Medium,
    ]

#----------------------------------------
# Exchange-Correlation
#----------------------------------------
exchange_correlation = SOGGA.PBE

[Jess Wellendorff]

Documentation:

• QuantumATK paper: https://iopscience.iop.org/article/10.1088/1361-648X/ab4007
• TechNote: https://docs.quantumatk.com/_downloads/TechNotes_Noncollinear.pdf

[jiejiang]

Dear Jess Wellendorff,

Thank you very much for your detailed and very clear explanation.
I got it.

Thanks again,

Jie