Training of the exchange bias effect Training 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

Examples: recent experiments and simulation Ni. O(001)/Fe(110)12 nm/Ag 3. 4 nm/Pt 50 nm Co/Co. O/Co 1 -x. Mgx. O empirical fit J. Keller et al. , PRB 66, 014431 (2002) A. Hochstrat, Ch. Binek and W. Kleemann, PRB 66, 092409 (2002) D. Paccard , C. Schlenker et al. , Phys. Status Solidi 16, 301 (1966) Monte Carlo Simulations U. Nowak et al. , PRB 66, 014430 (2002)

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

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

Relaxation towards equilibrium Landau-Khalatnikov Lagrange formalism with potential F and strong dissipation (over-critical damping) G. Vizdrik, S. Ducharme, V. M. Fridkin, G. Yudin, PRB 66 094113 (2003) : phenomenological damping constant 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 : measurement time of a single loop n : loop #

Discretization: LK- differential equation difference equation where and

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

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

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

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

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

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

experimental data recursive sequence min. 0. 015 (m. T)-2 e and e 3. 66 m. T