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2009 METALS, SUPERCONDUCTORS...Fermi surface study in the hidden order state of URu 2 Si 2The heavy fermion superconductor URu 2 Si 2 has attractedmuch attention for the past two decades because of the socalledhidden order (HO) phase below T 0 = 17.5K, wherea tiny magnetic moment of 0.03µ B with the wave vectorQ 0 = (1,0,0) appears. The associated entropy at T 0 is,however, too large. That is why many theoretical modelshave been proposed, such as, spin- and/or charge-densitywave, higher orbital ordering, helicity order, etc. Furthermoreit was recently reported that a new phase transition ora crossover appears at H ∗ = 23T below 2K [Shishido et al.Phys. Rev. Lett. 102, 156403 (2009)]. Above H ∗ , a newdHvA frequency with relatively light effective mass was detectedin a high quality sample. Nevertheless, there are stillundetected Fermi surfaces, considering the large specificheat coefficients and carrier numbers. It is important to determinethe electronic states from the microscopic point ofviews. One of the most powerful experimental probe is thede Haas-van Alphen (dHvA) or Shubnikov-de Haas (SdH)effects. Recently, we succeeded in growing high qualityURu 2 Si 2 single crystals (RRR > 200) in order to performthe SdH experiments. Here we report the recent results ofSdH experiments using high quality single crystals at highfields up to 34T and at low temperatures down to 30mK.Figure 84(a) shows the magnetoresistance for the currentalong [100] at various field directions in URu 2 Si 2 . Thelarge magnetoresistance and clear SdH oscillation indicatethe high quality of our sample. The kink is clearly detectedfor H ‖ [001] at H ∗ = 24T, which shifts to the higher fieldwith increasing the field angle from [001] to [100]. Theangular dependence of H ∗ is shown in Fig. 84(b). H ∗ approximatelyfollows the 1/cosθ-dependence. We show infigure 85 the typical SdH oscillation for H ‖ [001] and forthe field tilted 52deg from [001] to [100]. As clearly seenin figure 85, the SdH amplitude abruptly increases aboveH ∗ for H ‖ [001], while the SdH amplitude at field angle52deg smoothly increases, following the Lifshitz-Kosevichformula. Below H ∗ , the fast Fourier transform (FFT) analysisshows three kinds of SdH branches, namely α, β andγ. The cyclotron effective masses for H ‖ [001] below H ∗are 12m 0 and 18m 0 for branch α and β, respectively. Althoughthe number of wave is not enough to analyze thedata, the SdH frequency for branches α and β shows nochange above H ∗ , however, the cyclotron mass for branchβ seems to decrease above H ∗ . These results clearly indicatethat the electronic state is changed above H ∗ in the HOstate. Further experiments, such as thermoelectric power,are required to confirm this point.Figure 84: (a)Magnetoresistance at various field directions from[001] to [100] at 30mK in URu 2 Si 2 . (b)Angular dependence ofH ∗ , which is defined as a kink of magnetoresistance. The solidline corresponds to the 1/cosθ dependence.Figure 85: Typical Shubnikov-de Haas oscillations for the fieldalong [001] and for the field tilted 52deg from [001] to [100].I. SheikinD. Aoki, E. Hassinger, V. Taufour, J. Flouquet (CEA-Grenoble),63