Quantitative understanding of magnetic vortex oscillations driven by spin-polarized out-of-plane dc current: Analytical and micromagnetic numerical study

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 18, 2009, Pages

  Choi, Youn Seok ^a   Lee, Ki Suk ^a   Kim, Sang Koog ^a  

^a Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67449094444     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.184424     Document Type: Article

References (27)

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23. Similar to the derivation of the gyroscopic force and drag (damping) force under an assumption of a steady-state motion of the M configuration as in Ref., the force term FSTT driven by spin-polarized currents of Spol can be expressed as FSTT = [FSTT,x, FSTT,y] =- (aT /L) j0 Spol [V dV (m×m / x) z, V dV (m×m/y) z] where m=M/ Ms. By integrating numerically or analytically the above equation, we can formulate the FSTT term for a given M structure, i.e., for a vortex M structure with the "surface charge free" model (Ref.) as FSTT =δ Spol aT j0 (z ×X) with a proportional constant δ=2π, as reported in Ref. However, for the real vortex M structure obtained from micromagnetic simulations, we obtained a different value of δ=5.31, which is 25% smaller than the value of δ=2π for the analytical calculation mentioned above (Ref.). This discrepancy indicates that the real M configuration for the dynamic vortex motions driven by the STT term obtained from micromagnetic simulations differs from that of the "surface charge free" model. Consequently, the values of ωR and ωI obtained using Eqs. 3 3 slightly differ from those of the simulation results.
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25. K.-S. Lee and S.-K. Kim (private communication). The Zeeman energy term WOH of a displaced VC due to the OH contribution is expressed as WOH =- μ0 V dVM HOH, where M and HOH are the local magnetizations and the Oersted field distribution in the (x,y) plane, respectively. By adopting the "surface charge free" model (Ref.) and the Biot-Savart's formulation, we numerically calculated an analytical form of WOH = 1 2 c ip (45 68 RL Ms) j0 |X| 2 + WOH (0). Comparing this analytical form with WOH = 1 2 κOH |X| 2 + WOH (0), we obtain κOH =c ip ς j0 and its proportional constant, ς= 45 68 RL Ms in terms of R, L, and Ms.
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