We examine static spin susceptibilities $chi_{alphabeta}({bf q})$ of spin components $S_{alpha}$ and $S_{beta}$ in the non-centrosymmetric tetragonal system. These show anomalous momentum dependences like $chi_{xx}({bf q})-chi_{yy}({bf q})sim q_x^2-q_y^2$ and $chi_{xy}({bf q})+chi_{yx}({bf q})sim q_x q_y$, which vanish in centrosymmetric systems. The magnitudes of the anomalous spin susceptibilities are enhanced by the on-site Coulomb interaction, especially, around an ordering wave vector. The significant and anomalous momentum dependences of these susceptibilities are explained by a group theoretical analysis. As the direct probe of the anomalous spin susceptibility, we propose a polarized neutron scattering experiment.
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