  We show that there are diversified Ruderman-Kittel-Kasuya-Yosida (RKKY)
interactions between magnetic impurities, mediated by itinerant electrons, in a
centrosymmetric crystal respecting a nonsymmorphic space group. We take the
$P4/nmm$ space group as an example. We demonstrate that the different type of
interactions, including the Heisenberg-type, the Dzyaloshinskii-Moriya
(DM)-type, the Ising-type and the anisotropic interactions, can appear in
accordance with the positions of the impurities in the real space. Their
strengths strongly depend on the location of the itinerant electrons in the
reciprocal space. The diversity stems from the position-dependent site groups
and the momentum-dependent electronic structures guaranteed by the
nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic
symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals
can be promising platforms to design magnetic interactions.

Mesoscale and Nanoscale Physics