Low-temperature magnetic order and spin dynamics in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$

Muon spin rotation and relaxation experiments have been carried out in single crystals of ${\mathrm{YbRh}}_2{\mathrm{Si}}_2,$ a compound that exhibits non-Fermi-liquid (NFL) behavior associated with a quantum critical point (QCP) at $T=0.\mathrm{}$ The zero-field muon relaxation rate is found to be independent of temperature down to 100 mK but to increase below $\sim 70\mathrm{mK},$ which suggests magnetic order at low temperatures. From the relation between the internal field at the ${\mu }^{+}$ stopping site and the hyperfine coupling constant the ordered ${\mathrm{Yb}}^{3+}$ moment is very small, $\sim 2\times {10}^{-3}{\mu }_B.$ Muon spin rotation linewidths in a transverse field of 6 kOe indicate a homogeneous susceptibility down to 2 K, which is an order of magnitude lower than the characteristic (Kondo) temperature $T_K\approx 25\mathrm{K}.$ This is evidence against the importance of disorder-driven NFL mechanisms in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2.$ In longitudinal magnetic fields the muon spin-lattice relaxation function $G\left(t\right)\mathrm{}$ is exponential, again indicative of a homogeneous system. The relaxation obeys the time-field scaling relation $G(t,H)=G(t/H),$ which suggests long-lived spin correlations at low temperatures. The ${\mathrm{Yb}}^{3+}$ spin dynamics derived from muon spin relaxation appear to be intimately related to critical magnetic fluctuations near the QCP.