Similarity of the Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of ${\mathrm{URu}}_2{\mathrm{Si}}_2$

Shubnikov–de Haas measurements of high quality ${\mathrm{URu}}_2{\mathrm{Si}}_2$ single crystals reveal two previously unobserved Fermi surface branches in the so-called hidden order phase. Therefore, about 55% of the enhanced mass is now detected. Under pressure in the antiferromagnetic state, the Shubnikov–de Haas frequencies for magnetic fields applied along the crystalline $c$ axis show little change compared with the zero pressure data. This implies a similar Fermi surface in both the hidden order and antiferromagnetic states, which strongly suggests that the lattice doubling in the antiferromagnetic phase due to the ordering vector $Q_{\mathrm{AF}}=(001)$ already occurs in the hidden order. These measurements provide a good test for existing or future theories of the hidden order parameter.

Figure 1

(a) Magnetoresistance for several angles. (b) SdH oscillations in resistivity when the polynomial background is subtracted for two angles. (c) FFT spectra obtained for a field region of 5–8 T for the same angles.

Figure 2

(a) Angular dependence of the FFT frequencies obtained from SdH measurements in ${\mathrm{URu}}_2{\mathrm{Si}}_2$, reflecting the cross sectional areas of the different FS branches perpendicular to the magnetic field. The field range is 5–8 T as long as $H_{c2}$ is low enough, and then adapted to the available field range. (b) Angular dependence of the effective masses. Earlier results by Ohkuni et al. [25] are also plotted and are in excellent agreement.

Figure 3

(a) Pressure dependence of the magnetoresistance of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ for three pressures in the whole measured field range. (b) Low frequency oscillation appearing above the kink field $H_{\mathrm{kink}}$. (c) Schematic field dependence of a band in the HO and AF phases.

Figure 4

(a) FFT spectra of SdH measurements in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ for $H\parallel c$ at the lowest temperature of $T\approx 35\mathrm{mK}$ for $P=0.05\mathrm{GPa}$ and $T\approx 25\mathrm{mK}$ for $P=1.55\mathrm{GPa}$. (b) Pressure dependence of the FFT frequencies. The $\beta$ peak is split as explained in the text, indicated by the dashed lines. (c) Pressure dependence of the effective masses determined in a field range of 8–13 T.