Nuclear magnetic resonance studies of pseudospin fluctuations in URu${}_2$Si${}_2$

We report ${}^{29}$Si nuclear magnetic resonance measurements in single crystals and aligned powders of URu${}_2$Si${}_2$ in the hidden order and paramagnetic phases. The spin-lattice relaxation data reveal evidence of pseudospin fluctuations of U moments in the paramagnetic phase. We find evidence for partial suppression of the density of states below 30 K and analyze the data in terms of a two-component spin-fermion model. We propose that this behavior is a realization of a pseudogap between the hidden-order transition $T_{\mathrm{HO}}$ and 30 K. This behavior is then compared to other materials that demonstrate precursor fluctuations in a pseudogap regime above a ground state with long-range order.

Figure 1

(a) The ${}^{29}$Si spectrum at 18 K indicating the width of the NMR resonant frequency, centered at 99.695 MHz, and the frequencies around at which ${\left(T_{1}T\right)}^{-1}$ was measured. (b) ${\left(T_{1}T\right)}^{-1}$ as function of temperature for various values of frequency showing the consistency across the frequency range.

Figure 2

(a) Frequency-averaged ${\left(T_{1}T\right)}^{-1}$ versus $T$ for the aligned powder (open circles) and the single crystal (filled squares). Different fits to 2D AFM spin fluctuations as described in Eq. (3) using an LAD (red solid line) and LSQ (blue solid line) fit method, as well as a LAD fit to a Curie-Weiss law (green solid line). (b) The extracted joint density of states (JDOS) showing the pseudogap suppression below 30 K and the residual carrier density in the HO state; same color legend as in panel (a). The JDOS drops by roughly 25% in the pseudogap region between 30 K and 16 K and by another 70% below the HO state.

Figure 3

(a) ($T_{1}T$)/($T_{1}T$)${}_{\min }$ as function of $T/T_0$ for URu${}_2$Si${}_2$ and YBa${}_2$Cu${}_4$O${}_8$. The arrows indicate the onset of the pseudogap in both materials. (b) The scaling behavior of ($T_{1}T$)${}^{-1}$/($T_{1}T$)${}_0^{-1}$ as function of $T/T_0$ for URu${}_2$Si${}_2$ (black circles) as compared to other materials with AFM fluctuations.