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The valence states and local structure of LiMn 2 O 4 have been investigated in comparison with those of ZnMn 2 O 4 and -MnO 2 by using x-ray-absorption spectroscopy on the Mn K edge, in order to study the Jahn-Teller ͑JT͒ transition in LiMn 2 O 4 at T a ϭ280 K. In the near-edge spectra, a systematic edge shift in accordance with the formal manganese valence was found, confirming the Mn 3ϩ /Mn 4ϩ mixed states in LiMn 2 O 4 . Extended x-ray-absorption fine structure reveals a structural disorder of MnO 6 octahedra in the cubic LiMn 2 O 4 above T a . The local structure is analyzed using a structural model in which LiMn 3ϩ Mn 4ϩ O 4 consists of isotropic Mn 4ϩ O 6 octahedra and anisotropic Mn 3ϩ O 6 octahedra distorted uniaxially by the JT effect. The magnitude of the local JT distortion, the ratio of the longer Mn-O distance to the shorter one, is found to be 1.17 at 300 K, which is as large as that of tetragonal ZnMn 2 O 4 ͑1.19͒. The local structure exhibits no change when the temperature is lowered below T a . These results imply that the low-temperature phase is induced by ordering the local JT distortion.

Shubnikov de Haas(SdH) oscillations have been measured for the semiconducting single domain SrTiO3 with Carrier concentration of 3.4×1018 cm-3 and 5.9×1018 cm-3. From the temperature dependence of the SdH amplitude, the cyclotron mass values are determined for the [001] and [110] magnetic field directions. We have found, from the angular dependence of the SdH oscillation, that there exist several branches of the frequencies among which the highest and lowest branches originate from the Fermi spheres at the Brillouin zone center, and the other ones from the extremal area which is interconnected through the magnetic breakdown tunneling paths. Energy band parameters based on the k p perturbation method are determined.

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