Jahn-Teller induced multiple ferromagnetic exchange interactions in magnetic semiconductors

Ferromagnetic interactions among $3d$ impurities in compound semiconductors (II-VI, III-V, etc) are usually rationalized via ``double exchange'', ``$p$-$d$ exchange'', and ``superexchange'' type interactions, which ensue a description of the $3d$ impurity electronic configuration based on host symmetries. Obviously Jahn-Teller distortions break these symmetries and yield completely different, closed shell, electronic configurations for the impurities, which most theories~[1] simply describe as magnetically inactive. Nonetheless, such Jahn-Teller distorted $3d$ impurities e.g. in the AlN host exhibit strong short range ferromagnetic interactions. Superexchange models may offer some insight to ``closed shell'' magnetic interactions, not applicable to the present case, however. We investigate such peculiar magnetic interactions via density-functional calculations, and find that a Jahn-Teller distortion can trigger the formation of a 3d-3d chemical bond that stabilizes ferromagnetism via direct exchange~[2], and further facilitates a double exchange type interaction. This multiple exchange is what aligns parallel the spins of e.g. Cr impurities in AlN.\\[4pt] [1] A. Zunger, S. Lany, and H. Raebiger, Physics {\bf 3}, 53 (2010).\\[0pt] [2] H. Raebiger, S. Lany, and A. Zunger, PRL {\bf 99}, 167203 (2007).