Neutron scattering study of URu${}_{2-x}$Re${}_x$Si${}_2$ ($x=0.10$): Driving order towards quantum criticality

We report inelastic neutron scattering measurements in the hidden order state of URu${}_{2-x}$Re${}_x$Si${}_2$ with $x=0.10$. We observe that towards the ferromagnetic quantum critical point induced by the negative chemical pressure of Re doping, the gapped incommensurate fluctuations are robust and comparable in intensity to the parent material. As the Re doping moves the system toward the quantum critical point, the commensurate spin fluctuations related to hidden order weaken, display a shortened lifetime, and slow down. Halfway to the quantum critical point, the hidden order phase survives, albeit weakened, in contrast to its destruction by hydrostatic pressure and by positive chemical pressure from Rh doping.

Figure 1

Magnetic phase diagram of URu${}_{2-x}$Re${}_x$Si${}_2$ showing the antiferromagnetic (hidden order) and ferromagnetic phases. From Ref. 18; also see Refs. 19 and 20.

Figure 2

Inelastic scattering along the ($H$ 0 0) direction for an energy transfer of 2.9 meV at $T=2$ K (black squares) and $T=40$ K (red circles). At 40 K well above the hidden order transition at 17 K, there is partial suppression of the incommensurate fluctuations. In contrast, there is an almost complete suppression of the commensurate fluctuations associated with the hidden order. The lines are Gaussian fits at each of the three peak positions.

Figure 3

The temperature dependence of the commensurate (1 0 0) fluctuations in URu${}_{1.9}$Re${}_{0.1}$Si${}_2$ at 1.65 meV. A discontinuity in slope is observed at around the onset of the hidden order phase. The inset shows a closeup of the data below 30 K.

Figure 4

The fits to the incommensurate fluctuations (a) for URu${}_{1.9}$Re${}_{0.1}$Si${}_2$ at $T=2$ K and (b) for pure URu${}_2$Si${}_2$ at $T=3$ and 5 K (combined data). The blue line is the fit to Eq. (1) and the red line is a fit to a Lorentzian of energy $2\Delta$, amplitude $A$, and damping $2\gamma =\mathrm{FWHM}$, convoluted with the resolution function, as described in the text. For the Re doping, the nesting gap energy, $\Delta$, is reduced to 60$\%$ of its value in the pure system.

Figure 5

(a) The inelastic scattering at (1 0 0) in the URu${}_{1.9}$Re${}_{0.1}$Si${}_2$ sample, measured at $T=2$ K. (b) The (1 0 0) inelastic scattering in the pure URu${}_2$Si${}_2$ system, measured at $T=3$ and 5 K (combined data). Both were fit to a Gaussian for the elastic scattering, and a Lorentzian of energy ${\omega }_{{\vec{Q}}^{*}}=2\Delta$, amplitude $A$, and damping $2\gamma$ $=$ FWHM for the inelastic peak, convoluted with the resolution function. The commensurate fluctuations of the hidden order phase are damped in the presence of Re doping.

Figure 6

Locus of the half-widths in reduced wave vector $H$ of spin fluctuations around (1.4 0 0). These inverse dynamic correlation lengths are narrow in wave vector for low energies, but they broaden dramatically at higher energies. The black vertical line shows the centroid of the scattering arising from a column of itinerant excitations in the $E$-$\vec{Q}$ plane. The error bars for low-energy fits lie within the symbol size.