${\mathrm{Cr}}^{5+}$ in K${\mathrm{H}}_2$As${\mathrm{O}}_4$: A Halperin-Varma-Type Center

The electronic wave function of ${\mathrm{Cr}}^{5+}$ ($3d^1$) in K${\mathrm{H}}_2$As${\mathrm{O}}_4$ and K${\mathrm{H}}_2$P${\mathrm{O}}_4$ is identified as $d_{x^2-y^2}$. Its symmetry property in the hydrogen-bonded tetrahedron allows a rotational motion of $d_{x^2-y^2}\perp c$ which breaks the symmetry in the Halperin-Varma sense. We show that its local coupled relaxation time is one order of magnitude longer than the slow ferroelectric cluster dynamics which can be identified with the same center independently and that the motion perpendicular to the $c$ axis must be the cause.