Dynamic magnetic hysteresis in uniaxial superparamagnetic nanoparticles in superimposed ac and dc magnetic fields of arbitrary amplitude is considered using Brown’s model of coherent rotation of the magnetization. The dependence of the area of the dynamic hysteresis loop on the temperature, frequency, and ac and dc bias fields is analyzed. In particular, the dynamic hysteresis loop of a single-domain ferromagnetic particle is substantially altered by applying a relatively weak dc field. Furthermore, it is shown that at intermediate to low ac field amplitudes, the dc bias field permits tuning of the magnetic power absorption of the particles, while for strong ac field amplitudes the effect becomes entirely analogous to that produced by the exchange biased anisotropy. Simple analytical formulas are provided in the linear response regime for the steady-state magnetization and loop area, exhibiting perfect agreement with the numerical solution of Brown’s Fokker–Planck equation. Comparison with previous results is also given.

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The nonlinear ac susceptibility and dynamic magnetic hysteresis (DMH) of a single domain ferromagnetic particle with biaxial anisotropy subjected to both external ac and dc fields of arbitrary strength and orientation are treated via Brown's continuous diffusions model [W. F. Brown, Jr., Phys. Rev. 130, 1677 (1963)] of magnetization orientations. The DMH loops and nonlinear ac susceptibility strongly depend on the dc and ac field strengths, the polar angle between the easy axis of the particle, the external field vectors, temperature, and damping. In contrast to uniaxial particles, the nonlinear ac stationary response and DMH strongly depend on the azimuthal direction of the ac field and the biaxiality parameter Δ.