On the method of exchange bias measurement

Exchange bias is the observation of a hysteresis loop shift in ferromagnetic-antiferromagnetic compound structures [1]. Recently, such a shift was also observed in all ferromagnetic bilayer systems [2]. Conventionally, exchange bias fields are measured by determining the average coercive field of a hysteresis loop (two-point method). However, hysteresis loops in exchange biased systems can also change in shape and even exhibit asymmetrical reversal [3], which can affect the estimate of the exchange bias field significantly. A different method for measuring the exchange bias based on obtaining the ``center of mass'' for exchange biased hysteresis loops is proposed and analyzed in this work. The method is validated by numerical simulation, using a realistic model system composed of soft and hard ferromagnetic layers coupled antiferromagnetically. Our calculations allow us to determine the laterally averaged bias field $<$Hbias$>$ created by the hard layer grains. We find that $<$Hbias$>$ is in excellent quantitative agreement with the proposed ``center of mass'' measurement, but not with the conventional two-point method. [1] A. Berkowitz, K. Takano, J. Magn. Magn. Mater. 200,552 (1999) [2] A. Berger et. al., Appl. Phys. Lett. 85, 1571 (2004) [3] S. G. E. te Velthuis et. al., J. Appl. Phys. 87, 5046 (2001)