Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2017 / Paper 2 / Section A(ii) / 16 / ii

Along the easy axis, expect an approximately rectangular loop: after saturation the remanent magnetization is close to $\pm M_s$, and reversal occurs near $\pm H_c$ through nucleation and domain-wall motion. Permalloy is magnetically soft, so $H_c$ is ordinarily small, although defects and growth conditions set its actual value.

The axes are $M$ in $\mathrm{A}{\mathrm{m}}^{-1}$ and applied ${\mu }_{0}H$ in $\mathrm{mT}$. $M_s,H_c,H_k$ are symbolic because their measured values are not supplied. The $50\mathrm{mT}$ deposition field establishes an axis; it is not the measured coercive or anisotropy field.

Along the in-plane hard axis, the ideal uniform-magnetization model gives reversible rotation from the easy direction toward the applied field. With uniaxial anisotropy energy density $K_u{\sin }^2\theta$, minimization givesfollowed by saturation at $\pm M_s$. The right panel of the preceding figure therefore has a nearly linear central section, essentially zero remanence and ideally no hysteresis. Actual domains, misalignment and defects can produce rounding or a small loop. This is an in-plane hard axis; the much larger out-of-plane demagnetizing field is a different effect.