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arXiv · 1807.01967

RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems

Sonu Verma·Arijit Kundu·Tarun Kanti Ghosh
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Abstract

We consider Mn-doped bulk zinc-blende semiconductors described by the 4 $ \times$ 4 Luttinger Hamiltonian. In these semiconductors, Mn atom acts as an acceptor providing the system a mobile hole, and also acts like a magnetic impurity of spin $S=5/2$. We obtain exact analytical expressions of the hole mediated Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction between two Mn${}^{2+}$ ions. The RKKY interaction of the Luttinger system consists of collinear Heisenberg-like and Ising-like interactions. The characteristic beating patterns appear in the range functions of the RKKY interaction owing to the presence of multiple Fermi wave-vectors of the underlying $j=3/2$ states. As an application of the analytical form of the range function, from the finite temperature evaluation of the correlation functions, we calculate the contribution of RKKY interaction to the Curie-Weiss temperatures of a particular dilute magnetic semiconductor ZnMnTe where $4\times4$ Luttinger Hamiltonian is valid.

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Sonu Verma, Arijit Kundu, Tarun Kanti Ghosh. 2019-06-21. RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems. https://doi.org/10.1063/1.5097673

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