Steady state in noncollinear magnetic multilayers

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 18, 2004, Pages 1-6

  Zhang, Jianwei ^a   Levy, Peter M ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; CONSTANTS AND COEFFICIENTS; ELECTROCHEMISTRY; ENTROPY; MAGNETISM; MATHEMATICAL ANALYSIS; STEADY STATE;

EID: 12144266933     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.184442     Document Type: Article

References (36)

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32. n. When we include the angular dependence coming from multiple reflections they enter in the demominator of the transmission amplitudes (see Ref. 6), and complicate its angular dependence. However for the 3d transition-metal normal metal interfaces we consider, e.g., Co/Cu, the dominant transmission is carried by the majority band and the reflection in this channel is small; therefore the correction due to multiple reflections is quite small.
33. Peter Zahn and Ingrid Mertig (private communication).
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35. S. Urazhdin, R. Loloee, and W. P. Pratt Jr., cond-mat/0403441 (unpublished); see their Eq. (1) and Ref. 15. Also see S. Urazhdin et al., cond-mat/0409085 (unpublished).
36. If one injects the transverse components of the spin current at a point the ensuing radial currents move outward and do not interfere. However in a multilayered structure they are injected across a plane, i.e., the interface; so that waves emanating from different points across the surface take different times to arrive at a point away from the interface. This was first presented by Albert Pert at the International Symposium on Metallic Multilayers (MML'01) 24-29 June 2001, Aachen, Germany; see also M. D. Stiles and A. Zangwill, Phys. Rev. B 66, 014407 (2002) for an excellent discussion of how oscillating but nondecaying functions can interfere to produce a seemingly exponential decay.