NMR investigation of antiferromagnetism and coherence in ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$

We report ${}^{31}\mathrm{P}$ and ${}^{29}\mathrm{Si}$ NMR in single crystals of ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$ for $x=0.09$ and $x=0.33$. The spectra in the $x=0.33$ sample are consistent with a homogenous commensurate antiferromagnetic phase below $T_N\sim 37$ K. The Knight shift exhibits an anomaly at the coherence temperature $T^{*}$ that is slightly enhanced with P doping. Spin-lattice-relaxation rate data indicate that the density of states is suppressed for $x=0.09$ below 30 K, similar to the undoped compound, but there is no evidence of long-range order at this concentration. Our results suggest that Si substitution provides chemical pressure and electronic tuning mediated by filling of the $s/p$ shells with minimal electronic inhomogeneity.

Figure 1

${}^{31}\mathrm{P}$ NMR spectra of ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x, x=0.09$ and 0.33. The spectra have not been corrected for temperature or $T_2$. The dashed line is a model of incommensurate AFM as discussed in the text, and the solid lines are Gaussian fits.

Figure 2

The internal field at the P in ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$ with $x=0.33$ ($•$, blue) and at the Si site in the pure compound ($⧫$, gray) in the large-moment antiferromagnetic phase. Data for the latter are reproduced from Ref. [12].

Figure 3

P and Si Knight shifts in ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$ for $x=0$, 0.09, and 0.33. Data for the pure compound are reproduced from Ref. [23], but have been scaled by 0.8475 to agree with the results in the single crystal [24].

Figure 4

Knight shift vs the magnetic susceptibility in ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$ with $x=0$, 0.09, and 0.33. Solid lines are fits to the high temperature data as described in the text.

Figure 5

$K_{\text{HF}}$ vs temperature in ${\mathrm{URu}}_2{\mathrm{Si}}_{2-x}{\mathrm{P}}_x$. The solid lines are fits to Eq. (1), and the dashed vertical lines indicate $T_{\text{HO}}$ for $x=0$, and $T_N$ for $x=0.33$.

Figure 6

${\left(T_{1}T\right)}^{-1}$ vs temperature for the Si at $x=0$, and the P at $x=0.09$ and 0.33. The data for $x=0$ are reproduced from Ref. [23], and have been scaled by ${{(}^{31}\gamma {/}^{29}\gamma )}^2$ for comparison. The solid line is a fit to the $x=0.33$ data as described in the text.