Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 2 / Section A(ii) / 13 / i / Solution

Only the magnetic-response physics is addressed here; biological and clinical application is user-deferred.

A single-domain particle has an approximately coherent magnetic dipole moment, but single-domain does not by itself imply rapid thermal reversal. If moments equilibrate within the measurement time, a dilute, noninteracting ensemble is superparamagnetic: its quasistatic magnetization is reversible, odd in field and approaches saturation with negligible remanence or magnetic coercivity.

For freely orientable classical moments,At small field, $\mathcal{L}(z)\simeq z/3$; at large field moments align. This Langevin form is an ideal limit, not a universal exact curve for anisotropic fixed-axis particles.

The missing timescale/magnetic anisotropy information must be stated: blocked single-domain particles can already show hysteresis. Also, a reversible quasistatic curve does not preclude a finite-frequency loss loop when relaxation lags an alternating field. The original curves illustrate an equilibrated dilute limit and possible blocked/interacting alternatives, not measured treatment performance.