First-Principles Approach to Noncollinear Magnetism: Towards Spin Dynamics

A description of noncollinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within the optimized effective potential (OEP) framework. With the example of a magnetically frustrated Cr monolayer it is shown that the resulting magnetization density exhibits much more noncollinear structure than standard calculations. Furthermore, a time-dependent generalization of the noncollinear OEP method is well suited for an ab initio description of spin dynamics. We also show that the magnetic moments of solids Fe, Co, and Ni are well reproduced.

Figure 1

Fully noncollinear magnetization density and $\mathbf{B}$ field obtained using the LSDA and exchange-only EXX functionals for an unsupported Cr monolayer in Néel state. Arrows indicate the direction, and information about the magnitude (in atomic units) is given in the color bar.

Figure 2

$\mathbf{m}(\mathbf{r})\times {\mathbf{B}}_{\mathrm{x}}(\mathbf{r})$ for an unsupported Cr monolayer, in the same plane as Fig. 1, obtained using the EXX functional. Arrows indicate the direction, and information about the magnitude (in atomic units) is given in the color bar.