Importance of the site-off-diagonal electron-phonon interaction on the self-trapped small magnetic polaron

Importance of the site-off-diagonal electron-phonon interaction, which has not usually been taken into account when comparing with another type of interaction decomposed from the electron-phonon interaction, i.e., the site-diagonal electron-phonon interaction, is emphasized on the self-trapped small magnetic polaron for antiferromagnetic semiconductors at $T=0\mathrm{}$ K. In the present work, the effect of the electron-phonon interaction on the magnetic polaron is studied for each type of the interaction, and the following results are obtained: A large magnetic polaron is stabilized by both types of interaction, and decomposition is not essential in this case. On the other hand, when the magnetic polaron becomes small, the decomposition becomes essential. In the case when the site-diagonal electron-phonon interaction is larger than a critical value, the small-magnetic-polaron state disappears and only the phonon-polaron state becomes stable. Contrary to this, in the case of the site-off-diagonal electron-phonon interaction, the small magnetic polaron coupled with the lattice distortion can be stable even in the large-value limit of the interaction.