Induced magnetization spiral in a nonmagnetic metal sandwiched between twoferromagnets

Calculation of the magnetic moment induced in a non-magnetic metal, sandwic hed between two ferromagnets with magnetizations at an arbitrary angle, is reported. It is found that the induced magnetization rotates along a comple x three-dimensional spiral and can undergo many complete 360 degrees rotati ons. A simple free-electron model is used to derive an analytic formula for the twist angle phi inside the spacer. This demonstrates that, contrary to the behavior of magnetization inside a domain wall in a ferromagnet, phi v aries non-uniformly inside the spacer and exhibits plateaus of almost const ant rotation separated by regions of sharp relations by large angles. The c alculation is extended to the case of a realistic Co/Cu/Co(0 0 1) trilayer described by s, p, d tight-binding bands fitted to an ab initio band struct ure. An analytic formula for the components of the induced moment (and henc e, for phi) is derived using the stationary phase approximation. Its validi ty is tested against a fully numerical calculation using the same band stru cture. The formula shows that the components of the induced magnetization e ach oscillate with a predominant short period determined. by the Cu Fermi s urface neck extrema. The twist angle again displays the same remarkable beh avior as in the free-electron model and depends in an intricate manner on g eometrical properties of the spacer Fermi surface as well as on the degree of confinement of carriers in the spacer quantum well. (C) 2000 Elsevier Sc ience B.V. All rights reserved.