Magnetoelastic coupling in URu2Si2 : Probing multipolar correlations in the hidden order state

Abstract

Time-reversal symmetry and magnetoelastic correlations are probed by means of high-resolution volume dilatometry in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ at cryogenic temperatures, and magnetic fields sufficient to suppress the hidden order state at ${H}_{\mathrm{HO}}(T=0.66\phantom{\rule{0.28em}{0ex}}\mathrm{K})\ensuremath{\simeq}35$ T. We report a significant magnetoelastic volume expansion at and above ${H}_{\mathrm{HO}}(T)$, and even above ${T}_{\mathrm{HO}}$, possibly a consequence of field-induced $f$-electron localization. We investigate in detail the magnetostriction and magnetization as the temperature is reduced across two decades in temperature from 30 K where the system is paramagnetic, to 0.5 K in the realm of the hidden order state. We find a dominant quadratic-in-field dependence $\mathrm{\ensuremath{\Delta}}L/L\ensuremath{\propto}{H}^{2}$, a result consistent with a state that is symmetric under time reversal. The data shows, however, an incipient yet unmistakable asymptotic approach to linear ($\mathrm{\ensuremath{\Delta}}L/L\ensuremath{\propto}1\ensuremath{-}H/{H}_{0}$) for $15\phantom{\rule{4.pt}{0ex}}\text{T}<H<{H}_{\mathrm{HO}}(0.66\phantom{\rule{4.pt}{0ex}}\text{K})\ensuremath{\sim}40$ T at the lowest temperatures. We discuss these results in the framework of a Ginzburg-Landau formalism that proposes a complex order parameter for the HO phase to model the $(H,T,p)$ phase diagram.