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Training of the exchange bias effect

Training of the exchange bias effect. Training effect:. reduction of the EB shift upon subsequent magnetization reversal of the FM layer. - origin of training effect. - simple expression for. NiO(001)/Fe(110)12nm/Ag3.4nm/Pt50nm. Co/CoO/Co 1-x Mg x O. empirical fit.

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Training of the exchange bias effect

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  1. Training of the exchange bias effect Training effect: reduction of the EB shift upon subsequent magnetization reversal of the FM layer - origin of training effect - simple expression for

  2. NiO(001)/Fe(110)12nm/Ag3.4nm/Pt50nm Co/CoO/Co1-xMgxO empirical fit J. Keller et al., PRB 66, 014431 (2002) Monte Carlo Simulations D. Paccard , C. Schlenker et al., Phys. Status Solidi 16, 301 (1966) U. Nowak et al., PRB 66, 014430 (2002) Examples: recent experiments and simulation A. Hochstrat, Ch. Binek and W. Kleemann, PRB 66, 092409 (2002)

  3. Meiklejon Bean FM interface magnetization: SFM AF interface magnetization: SAF const. -Simple expression - applicable for various systems Simple physical basis ? Phenomenological approach tFM coupling constant: J MFM:saturation magnetization of FM layer confirmation by SQUID measurements and MC simulations

  4. Change of AF spin configuration triggered by the FM loop through exchange interaction J SAF 2 n 4 5 3 6 7 Increases free energy by 1 - microscopic origin of n-dependence of SAF: deviation from the equilibrium value equilibrium AF interface magnetization under the assumption

  5. :phenomenological damping constant : measurement time of a single loop Relaxation towards equilibrium Lagrange formalism with potential F and strong dissipation (over-critical damping) Landau-Khalatnikov G.Vizdrik, S.Ducharme, V.M. Fridkin, G.Yudin, PRB 66 094113 (2003) Training not continuous process in time, but triggered by FM loop discretization of the LK- equation tn,n+1: time between loop #n and n+1 n : loop #

  6. where and Discretization: LK- differential equation  difference equation

  7. SAF 2 n 4 5 3 6 7 1 Minimization of free parameters: Physical reason : stable equilibriumat S=0 a<0 ruled out 1 a<0 0 S

  8. with where a>0 ruled out Non-exponential relaxation 2 0 Exponential relaxation negligible spin correlation non-exponential relaxation Exchange bias: AF spin correlation Simplified recursive sequence

  9. power law: recursive sequence: error <5% Correlation between: Substitution

  10. - Steep potential F large b deviations from equilibrium unfavorable small training effect, small - Training triggered via AF/FM coupling increases with increasing - damping relaxation rate large means strong decay of EB after a few cycles increases with increasing Physical interpretation:

  11. 1st& 9th hysteresis of NiO(001)/Fe 12nm Fe NiO Comparison with experimental results on NiO-Fe (001) compensated

  12. experimental data recursive sequence: start of the sequence power law: input from power law fit

  13. experimental data recursive sequence 0.015(mT)-2 e e 3.66mT min. and

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