Domain cooperation in ferromagnetic hysteresis

We present precise experimental data suggesting that domains cooperate in f erromagnetic hysteresis. This model has potential applications in magnetost rictive transducers, transformer design, magnetoelastic effects and hystere sis in general. For an annealed 3% nickel steel alloy, we measured magnetic induction from the demagnetized state to near saturation, the reversal to near saturation and return branches from both these curves. Modeling variab les include the coercive field, saturation magnetization, initial susceptib ility and the hysteresis effective field. Magnetization is scaled to its sa turation value and magnetic field to its coercive value in the direction of field change, and susceptibility is scaled to its reversible function. Sca led differential susceptibility increases from its reversible value exponen tially with magnetization change from any reversal and decreases exponentia lly with decreasing slope to its reversible value at saturation. We define the slope of this exponential to be a hysteresis constant divided by the sc aled effective field, and this dimensionless field is the square root of 2 for hysteresis loops of polycrystalline domains with fully nucleated walls. Rayleigh's hysteresis constant, valid for heavily worked steels over a sma ll region, transforms to our cooperative hysteresis constant at larger fiel ds. For the saturate curve, the scaled effective field reaches a minimum le ss than 1 near the coercive field as domain interactions increase through w all nucleation and their local fields. Variation in the effective field cau ses hysteresis loops to creep upon cycling.