Tunable correlation effects of magnetic impurities by cubic Rashba spin-orbit coupling

We theoretically study the influence of the $k$-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal $k$-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy; thus, the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this paper breaks the rotational symmetry, but the host material is still invariant under the operations ${\mathcal{R}}^{z}(\ensuremath{\pi}), {\mathcal{IR}}^{z}(\ensuremath{\pi}/2), {\mathcal{M}}_{xz}, {\mathcal{M}}_{yz}$, where ${\mathcal{R}}^{z}(\ensuremath{\theta})$ is the rotation of angle $\ensuremath{\theta}$ about the $z$ axis, $\mathcal{I}$ is the inversion operator, and ${\mathcal{M}}_{xz}$ (${\mathcal{M}}_{yz}$) is the mirror reflection about the $x\text{\ensuremath{-}}z$ ($y\text{\ensuremath{-}}z$) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three- or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a $2\ensuremath{\pi}$ rotation of $\mathbf{k}$, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal $k$-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.