Fig. 1-7 dHvA (de Haas-van Alphen) oscillation both in the superconducting mixed state and in the normal state of UPd2Al3 UPd2Al3 is in the superconducting mixed state if the magnetic field is below the upper critical field Hc2 (=39 kOe). However, it reverts to the normal state if the magnetic field is above Hc2. The oscillation in the region of the magnetic field below 31 kOe was first observed in the present experiment.

Fig. 1-8 Fourier spectrum of the dHvA oscillation in UPd2Al3 shown in Fig. 1-7 The alpha branch of the Fermi surface is observed both in the normal state and in the superconducting mixed state. The alpha branch in both states has the same dHvA frequency of 2.64 x 106 Oe, but its respective amplitude differs. The dHvA frequency gives information on the topology of the Fermi surface.

Fig. 1-9 Field dependence of the cyclotron effective mass and the Dingle temperature for the alpha branch of the Fermi surface in UPd2Al3 The Dingle temperature measures the degree of scattering of conduction electrons. In the superconducting mixed state with the magnetic field below the upper critical field Hc2 (=39 kOe), both the cyclotron effective mass and the Dingle temperature depend strongly on the magnetic field.

It is well known that the nature of metals is determined by their conduction electrons. The so-called Fermi Surface describes how the conduction electrons take the continuously distributed values in energy and momentum. When we apply the magnetic field to metals at extremely low temperatures, the energy of conduction electrons start to take discrete values, so that the quantum oscillation, called the de Haas-van Alphen (dHvA) effect occurs. By measuring the dHvA effect we can obtain information on the topology of the Fermi surface, the cyclotron effective mass of conduction electrons, and the scattering of conduction electrons (Fig. 1-9). We have measured the dHvA effect on a uranium compound UPd2Al3, which belongs to the heavy electron system. UPd2Al3 becomes superconducting at temperatures below 1.9 K. So far, however, the dHvA oscillation could not be observed in the superconducting state. It has been considered extremely difficult to observe the dHvA oscillation in the superconducting state, because the dHvA amplitude is suppressed by the superconducting energy gap appearing at the Fermi surface. In the present experiment, for the first time, we have succeeded in detecting the dHvA oscillation in the superconducting state of UPd2Al3 (Fig. 1-7, 1-8). The key to this breakthrough is in the growing of single crystals of high purity. When we apply the magnetic field to the sample in the superconducting state, the magnetic field enters into the sample as quantized flux lines: this is said to be in the superconducting mixed state. The present success has contributed to a deeper understanding of the quantum oscillation in the superconducting mixed state.

Reference Y. Haga et al., De Haas-Van Alphen Oscillation in Both the Normal and Superconducting Mixed States of UPd2Al3, J. Phys. Soc. Jpn., 68(2), 342 (1999).

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