Gapped excitations in the high-pressure antiferromagnetic phase of ${\text{URu}}_2{\text{Si}}_2$

We report a neutron scattering study of the magnetic excitation spectrum in each of the three temperature and pressure driven phases of ${\mathrm{URu}}_2{\mathrm{Si}}_2$. We find qualitatively similar excitations throughout the $\left(H0L\right)$ scattering plane in the hidden-order and large-moment phases, with no changes in the $\hslash \omega$ widths of the excitations at the $\mathrm{\Sigma }=(1.407,0,0)$ and $Z=(1,0,0)$ points, within our experimental resolution. There is, however, an increase in the gap at the $\mathrm{\Sigma }$ point from 4.2(2) meV to 5.5(3) meV, consistent with other indicators of enhanced antiferromagnetism under pressure.

Figure 1

The scattering intensity as a function of energy and scattering vector along various high-symmetry directions in the ($H0L$) plane in the three phases studied: (a) At ambient pressure and 25 K, in the paramagnetic (PM) phase. For ease of viewing, the data have been scaled up by a factor of 2. The phonon at $(2,0,0)$ is visible, as are magnetic excitations at the $\mathrm{\Sigma }$ point. (b) Data collected at ambient pressure and 2 K, in the HO phase. (c) Data collected at 1.02 GPa and 4 K, in the AF phase. The scattering here looks qualitatively similar to the HO phase, albeit with a larger gap at the $\mathrm{\Sigma }$ point. The reduced statistical quality results from the reduced neutron transmission through the pressure cell and the subtraction of a strong background signal from the pressure cell and the solid helium pressure transmitting medium.

Figure 2

Constant-energy slices in the ($H0L$) plane in each of the three phases of ${\mathrm{URu}}_2{\mathrm{Si}}_2$. Energies shown are 2 meV, 5 meV, 8 meV, and 11 meV (clockwise from top left). The range of integration of energies for the slices was $\pm 0.5$ meV and the bin size was 0.013 ${\AA }^{-2}$. The data in the PM phase [panel (a)] have been scaled up by a factor of 2, as in Fig. 1. The lower left of the figure shows the Brillouin zone of ${\mathrm{URu}}_2{\mathrm{Si}}_2$, with the arrows indicating the directions shown in Fig. 1.

Figure 3

The energy dependence of the scattering intensity for crystal momentum $Z$ (filled circles) and $\mathrm{\Sigma }$ (open circles) in each phase. The error bars represent 1 standard deviation, $\sigma$. The lines are fits as described in the text, with the horizontal dashed lines showing the fitted background. (a) In the PM phase, a weak and broad spectrum of scattering is seen at $Z$, with a more pronounced but also broad peak at $\mathrm{\Sigma }$. (b) In the HO phase, the scattering is more intense at both wave vectors and intensity at $\mathrm{\Sigma }$ has shifted to higher energy. (c) In the AF phase, both peaks are still present; the peak at $(1.4,0,0)$ has shifted to slightly higher energies. Note that the fitted background lies below the axis here, due to the subtraction described in the text. Inset: The scattering along $\left(10L\right)$ in the AF phase. When normalized, the peak intensity at $(1,0,0)$ corresponds to a sample-averaged staggered moment of 0.36(9) ${\mu }_B$.