= Solution
Along the \b[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 gives
$$
\boxed{M_{\parallel H}=M_s\frac{H}{H_k}\quad(|H|\leq H_k),\qquad H_k=\frac{2K_u}{\mu_0M_s},}
$$
followed 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.
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