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11. 7 eV above EF at r) are split by the SOC, for which we found that an additional intra-atomic noncollinear magnetism is introduced. For example, we observed an energy gap of 54 meV for the noncollinear magnetic state and 53 meV for the collinear state, between the M5 and M5* states (Fig. 12). Using only the eigenvector for either the Mg state or the M5. state, we calculated the magnetization density. Figures 13 (a) and (b) show the in-plane components for the M5 and M5. states, respectively, on the (001) plane $,a below the nucleus along [001].

Carbone, Nature 416,301 (2002). [45] N. M. Wallis, and W. Ho, Science 297,1853 (2002); and private communications. M. Pastor, J. Dorantes-DAvila, S. Pick, and H. DreyssB, Phys. Rev. Lett. 75,326 (1995). [47] B. Lazarovits, L. Szunyogh, and P. Weinberger, Phys. Rev. B 65, 104441 (2002). [48] M. J. Freeman, J. Magn. Magn. Mater. 38, 23 (1983); M. Weinert, W. J. Freeman, ICM2003 Proc. accepted. Q. Wu, Phys. Rev. B 67,020406(R) (2003). [50] P. Gambardella, S. Rusponi, M. Veronese, S. S. Dhesi, C. Grazioli, A.

As listed in Table IV, the calculated magnetostrictive coefficient agree with the experimental data available. Furthermore, the large values of Xoolindicatethat the contribution from itinerant electrons is comparable to that from the f-shell. Using a rigid band picture, we found that the difference in the magnetostrictive behavior of GdFe2 and GdCoa is mainly due to the change in band filling. 2) is predicted to be a strong magnetostrictive material with a positive sign for Xool (+450 x 4. 1. J.

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