Nature © Macmillan Publishers Ltd 19988 the fact that we have a quantized Hall resistance deep inside the insulator. Indeed, j 2 xx j xy 2 e 2 2h 2 e 2 2 h 12e 2 =hr xy r 2 xx r 2 xy simply from matrix inversion. As noted by Shahar et al. 10 , the semicircle relation follows directly as long as r xy h=e 2 . In addition, it is completely independent of the value of r xx . We emphasize that this relation holds for our entire range of T. Ando 21 ®rst calculated numerically the dependence of j xx on j xy and found a similar relation to the semicircle function. In the selfconsistent Born approximation and scaling theories, a behaviour of this kind is also expected 22 . A recent numerical study by R. N. Bhatt and S. Subramanian (personal communication), with symmetric and non-symmetric random potentials in a lowest-Landau-level model, con®rmed this result. For higher Landau levels, Wei et al. 23 and others 10 showed similar dependences. This is, however, the ®rst clear demonstration of this relation for n # 1 and j xx and j xy both smaller than e 2 /2h.The experiments presented covered a certain range of parameters, in particular in temperature and in disorder. Different behaviours occurring at even lower temperatures or higher mobilities are therefore possible and would be interesting to investigate in future. The existence of these insulators, however, can serve as guidelines for a complete understanding of two-dimensional systems in strong magnetic ®elds. M

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Intergrain tunneling magnetoresistance ͑TMR͒ subsisting up to room temperature has been observed for polycrystalline ceramics of Sr 2 FeReO 6 , which has ordered double perovskite structure with Curie temperature above 400 K. The first-principles band calculation predicts that Sr 2 FeReO 6 shows the half metallic ground state with the ferrimagnetic coupling of Fe and Re spins. The experimental results of electronic and magnetic properties are in accord with this picture. In fact, the magnitude of intergrain TMR with the magnetic field of 7 T at 4.2 and 300 K is as large as 21 and 7%, respectively, reflecting high spin polarization of carriers.

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Epitaxial thin films of Sr2FeMoO6, that are ordered double perovskite with half-metallic nature, have been successfully prepared on SrTiO3 (001) and (111) substrates by pulsed laser deposition in a narrow window of the temperature and oxygen pressure. From the surface morphology analysis for the atomic scale step-and-terrace structures, the film growth is concluded to take place with the chemical formula as the growth unit when the ordering direction is normal to the surface. The films showed metallic conduction with ferromagnetic transition temperature above 400 K and intergrain tunneling type magnetoresistance even at room temperature.