We study Gilbert damping in bulk metallic ferromagnets containing magnetic and nonmagnetic impurities in the presence of nonuniform magnetization precession. In this model, a microscopic expression for the Gilbert damping tensor is obtained using the linear response theory with respect to the interaction between magnetization and conduction electrons. We especially focus on a diagonal element of the tensor, which is a conventional Gilbert damping constant, and evaluate it numerically as a function of the wave vector q of magnetization precession. We show that the impurity scattering dominates Gilbert damping for 0 < jqj < k F" À k F# , while the Stoner excitation dominates for k F" À k F# < jqj < k F" þ k F# (k F is the Fermi wave number for spin electrons).

The phase of a TiO 2 layer formed on commercially pure Ti by two-step thermal oxidation using N 2 CO gas was investigated. The oxidation process comprised two steps: treatment in an N 2 (0.1, 1 and 5)%CO atmosphere and treatment in air. A Ti(C,N,O) phase was formed after the first-step treatment conducted at 8731123 K. In the second step, the oxidation of this phase at 573773 K resulted in the formation of an anatase phase, while its oxidation at 873 K resulted in the formation of a single rutile phase. An increase in the CO partial pressure in the first step lowered the temperature for anatase phase formation. Further, in the second step, a single-phase anatase layer was formed at temperatures of 623 and 673 K.

We study Gilbert damping in bulk metallic ferromagnets in the presence of nonmagnetic and magnetic impurities. A microscopic expression is obtained for the Gilbert damping parameter using linear response theory with respect to the interaction between magnetization and the conduction electrons in the ferromagnets. In an inhomogeneous precession system, a space-dependent damping torque term of the form ηM×∇r2M· is added to the space-independent term αM×M·. We show that the magnetic impurities contribute to both α and η, but the nonmagnetic impurities to only η in the absence of spin-orbit coupling.

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