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

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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Structural optimization is performed for LaMnO 3 with the first-principles pseudopotential method based on the local density approximation ͑LDA͒, the generalized gradient approximation, and the LDAϩU approximation. The Jahn-Teller distortion is reproduced even by LDA but the magnitude of the distortion for all three approximations is not quite large enough compared with the experimental value. The same analysis is performed also for the hypothetical ferromagnetic state. The Jahn-Teller distortion still exists but the magnitude is much reduced. The unit-cell shape becomes nearly cubic. These features are qualitatively consistent with the related experimental observations. If the crystal structure is optimized for each magnetic state, the present band calculation predicts the ferromagnetic state to be lower in energy than the A-type antiferromagnetic state, which is inconsistent with the experimental observation. The origin of the failure in the prediction of the ground state is discussed. ͓S0163-1829͑97͒05142-4͔

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