Angular dependence of the tunnel magnetoresistance in transition-metal-based junctions

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 6, 2001, Pages

  Jaffres H ^a   Lacour, D ^a   Nguyen Van Dau, F ^a   Briatico, J ^a   Petroff, F ^a   Vaures A ^a  

^a INSTITUT D'OPTIQUE GRADUATE SCHOOL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

METAL;

ANISOTROPY; ARTICLE; GEOMETRY; MAGNETISM; MATHEMATICAL MODEL;

EID: 0035421547     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.064427     Document Type: Article

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35. This expression is rigorous at the order considered and can be derived by differentiating the energy derivative of the magnetization in the vicinity of the equilibrium state (formula presented) corresponding to (formula presented) and given by (formula presented). At the upper order, the angle modulation (formula presented) is calculated to be (formula presented), which does not introduce any relevant corrections.
36. Expressions of (formula presented) can be put into a general form as (formula presented) where (formula presented) is a small phase equaling (formula presented) (0) in the case of a linear response of the conductivity (resistance) vs (formula presented).
37. This integral is not straightforward to calculate. However, it approaches (formula presented) or (formula presented), which can be easily developed in order of h.