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

NiO(001)/Fe(110)12nm/Ag3.4nm/Pt50nm Examples: recent experiments and simulation A. Hochstrat, Ch. Binek and W. Kleemann, U. Nowak et al., PRB 66, (2002) Monte Carlo Simulations Co/CoO/Co 1-x Mg x O J. Keller et al., PRB 66, (2002) empirical fit D. Paccard, C. Schlenker et al., Phys. Status Solidi 16, 301 (1966) PRB 66, (2002)

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

- microscopic origin of n-dependence of S AF : Change of AF spin configuration triggered by the FM loop through exchange interaction J equilibrium AF interface magnetization deviation from the equilibrium value under the assumption n S AF Increases free energy by

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

Discretization: LK- differential equation  difference equation where and

Minimization of free parameters: n S AF Physical reason : 1 a<0 ruled out stable equilibrium at  S=0 0 SS a<0

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

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

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

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

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

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