# #23 Considering Relativistic Effect in DFT: Spin-Orbit Coupling

Viewed : 1300 times,  2019-11-13 10:20:07

An electron has spin and magnetic moments and moves in the electric field induced by atomic nuclear. In the classic theory, an electron does not interact with its own magnetic field. However, according to the relativistic effect, an electron does weak interaction with its own magnetic field that induces its own orbital motion. This interaction is called Spin-Orbit Coupling (SOC). Sometimes, the bandgap open phenomenon splits the degenerate energy level because of this additional energy.

SOC is the relativistic effect, so it carries out a greater effect on the mass of the material and to elements with a big atomic number. [1],[2]

Apply SOC correction to the energy calculation to obtain a fine structure of the system. In this weekly tip, we will find out the change electronic structure with SOC correction using the band structure of GaAs.

##### 1. Apply SOC correction in Materials Square

Follow the descriptions below to apply SOC correction to your calculation in Materials Square.

First, you should select the “Spin-Orbit Coupling” correction option in “Scripting Option: Template.” Then, add “Noncollinear Calculation” and “Spin-Orbit Pseudopotential” keywords under &SYSTEM. Before starting a job, please check that both keywords were set as TRUE.

Next, you should set pseudopotential. Read this post for the description of pseudopotential:Weekly tip #19, , and refer to this documentation to learn how to add new pseudopotential:Add custom pseudopotential.

Pseudopotential can be divided into Non, Scalar, and Full, depending on the degree to which the relativistic effect is taken into account. When making the pseudopotential, the “Non” type pseudopotential does not consider the relativistic effect when making the pseudopotential, the “Scalar” type pseudopotential corrects only the kinetic energy, and the “Full” type pseudopotential considers a fully relativistic effect. Therefore, we should use the Full-Relativistic pseudopotential for SOC calculation.

Materials Square offers SSSP pseudopotential as default, but most of that is Scalar-Relativistic pseudopotential, so it cannot be used to calculate SOC. To perform SOC correction calculation, select the Full-Relativistic pseudopotential, which was added at the potential tab of the Quantum espresso module. In this example, we had downloaded that from PS Library.

##### 2. Spin-Orbit Coupling Calculation Results

We find out the effect of SOC correction using the band structure of GaAs, which is the representative semiconductor material and a great example of the spin-orbit, split-off bandgap.

The band structure of GaAs primitive cell is as follows.

👉 Check the result of Band structure

GaAs has a direct bandgap at the Gamma point. Magnify the band structure at the Γ point to see the bandgap in detail.

In the band structure from Scalar-Relativistic pseudopotential, the electron state around valence band edge is caused by p-like orbital (orbital angular momentum l=1), and the calculated bandgap E0 is 0.15 eV, and the experimental band gap of GaAs is 1.5 eV[4]. This bandgap underestimated is the general character of PBE functional, which was used in this example calculation. In this instance, we focus on band split, so we did not consider correction to the bandgap.

Every top valence band of Scalar-Relativistic band structure is degenerated at Γ point. However, the top valence bands split by the spin-orbit interaction when applying SOC correction. The split bands have the energy difference Δ0 because the two electronic states separated. Moreover, these split bands caused by the electron states correspond to the total angular momentum j = 3/2, j = 1/2.[2],[5]

Hence, there is a significant change in the band structure when considering spin-orbit coupling to calculation. In particular, the curvature or shape of band and bandgap is important to the semiconductor and can obtain spin relaxation, optical spin orientation, spin Hall effects, etc.,[6] which occur by the spin-orbit coupling, so it is essential to perform a simulation while considering the characteristic of a system. SOC makes the electron spin definable face what direction in real space.

We have confirmed that the spin-orbit coupling effect influences the electronic structure by comparing the results of spin-orbit coupling corrected and not corrected calculation for the GaAs, which is the representative semiconductor material.

We can obtain information about the orbital motion of an electron in a crystalline solid affected by the SOC. The band structure is especially important for semiconductors, so it is essential to consider special phenomenon like SOC when calculating the properties of a system.

Perform SOC calculation using Materials Square!

[1] Wu, T., Chen, X., Xie, H., Chen, Z., Zhang, L., Pan, Z., & Zhuang, W. (2019). Coupling of spin-orbit interaction with phonon anharmonicity leads to significant impact on thermoelectricity in SnSe. Nano Energy, 60, 673-679.
[2] Winkler, R., Papadakis, S., De Poortere, E., & Shayegan, M. (2003). Spin-Orbit Coupling in Two-Dimensional Electron and Hole Systems (Vol. 41, p. 211). Springer.
[3] Takeda, T. (1978). The scalar relativistic approximation. Zeitschrift für Physik B Condensed Matter, 32(1), 43-48.
[4] Wang, P. D., Holmes, S. N., Le, T., Stradling, R. A., Ferguson, I. T., & De Oliveira, A. G. (1992). Electrical and magneto-optical of MBE InAs on GaAs. Semiconductor science and technology, 7(6), 767.
[5] Surh, M. P., Li, M. F., & Louie, S. G. (1991). Spin-orbit splitting of GaAs and InSb bands near Γ. Physical Review B, 43(5), 4286.
[6] Gmitra, M., & Fabian, J. (2016). First-principles studies of orbital and spin-orbit properties of GaAs, GaSb, InAs, and InSb zinc-blende and wurtzite semiconductors. Physical Review B, 94(16), 165202.

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