Quasi-local critical nature of cooperative paramagnetic fluctuations in CaRuO$_3$ metal

Ruthenate perovskites of the form ARuO$_3$, where A is alkaline earth metal, hold strong promises in developing new paradigm of the quantum magnetism. CaRuO$_3$ is of special interest among this group. The unusual combination of the absence of magnetic order and the anomalous non-Fermi liquid properties makes it an archetypal perovskite for the exploration of the quantum magnetism. Recently, we performed detailed electric, magnetic and neutron scattering measurements on high quality polycrystalline sample of CaRuO$_3$. The experimental results suggest that the underlying magnetism is depicted by the quantum mechanical fluctuations of Ru$^{4+}$- spins, confined to field-independent random domains that form a cooperative paramagnetic state at low temperature. The dynamic structure factor, which increases significantly below T $\sim$ 22 K, manifests a linear (E$\backslash$T) scaling, implying the Curie-Weiss type fluctuations with temperature as the most relevant parameter. Moreover, the linear dynamic scaling in conjunction with the divergence of the spin fluctuations mean relaxation time as T $\sim$ 0 K suggest the existence of a quasi-local critical behavior in the system.