Electronic transport and magnetic properties of Ge 1-x Mn x /Ge(100) films are investigated as a function of Mn dilution. Depending on x, characteristic temperatures separate different regimes in both properties. Resistivity exhibits an insulator-like behavior in the whole temperature range and, below about 80 K, two distinct activation energies are observed. At a higher temperature value, T R , resistivity experiences a sudden reduction. Hall coefficient shows a strong contribution from the anomalous Hall effect and, at T R , a sign inversion, from positive to negative, is recorded. The magnetic properties, inferred from magneto-optical Kerr effect, evidence a progressive decrease of the ferromagnetic long range order as the temperature is raised, with a Curie temperature T C not far from T R . The transport and magnetic results are qualitatively consistent with a percolation mechanism due to bound magnetic polarons in a GeMn diluted magnetic semiconductor, with localized holes [A. Kaminski and S. Das Sarma, Phys. Rev. B 68, 235210 (2003)].
We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.
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