Vortex oscillations induced by spin-polarized current in a magnetic nanopillar: Analytical versus micromagnetic calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 14, 2009, Pages

  Khvalkovskiy, A V ^a,b   Grollier, J ^a   Dussaux, A ^a   Zvezdin, Konstantin A ^b,c   Cros, V ^a  

^a UNITÉ MIXTE DE PHYSIQUE CNRS THALES   (France)

^b Istituto PM Srl   (Italy)

^c PROKHOROV GENERAL PHYSICS INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 71249136821     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.140401     Document Type: Article

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20. The details of this calculation and verification will be given in a forthcoming publication. We note that for J≤ 107 A/ cm2 the contribution of WOe to the total density is relatively small (1-10%); however it can become predominant for larger J.
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23. The core of the approach of Ref. is the calculation of generalized forces acting on a soliton. This is the key difference to our approach, which is based on the calculation of the system energy dissipation. In terms of generality and validity these two approaches are equivalent.
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25. This fact, which makes vortex nanopillar STNOs very promising for applications, is explained by the general statement that the critical magnitude of excitation scales with the energy of the excited mode. For a vortex STNOs, this statement is illustrated by our expression [Eq.] and by earlier findings based on the Thiele approach (Ref.). A similar expression for uniform nanopillar STNOs is derived by A. N. Slavin and V. S. Tiberkevich, Phys. Rev. B 72, 094428 (2005). As the frequencies of the excitations differ by about an order of magnitude, the critical current densities also differ by approximately the same factor. 10.1103/PhysRevB.72.094428
26. From Eq. it follows a α exp (-α η′ ωt) at J=0. Therefore η and η′ are equivalent to each other; correspondingly, the simulations give a single value for η and η′.