Shifted loops and coercivity from field-imprinted high-energy barriers in ferritin and ferrihydrite nanoparticles

We show that the coercive field in ferritin and ferrihydrite depends on the maximum magnetic field in a hysteresis loop and that coercivity and loop shifts depend both on the maximum and cooling fields. In the case of ferritin, we show that the time dependence of the magnetization also depends on the maximum and previous cooling fields. This behavior is associated to changes in the intraparticle energy barriers imprinted by these fields. Accordingly, the dependence of the coercive and loop-shift fields with the maximum field in ferritin and ferrihydrite can be described within the frame of a uniform-rotation model considering a dependence of the energy barrier with the maximum and the cooling fields.

Figure 1

Detail of magnetization loops for ferritin obtained at 3.2 K (4.2 K in the case of $H_{\text{max}}=30\times {10}^4$ Oe) after ZFC (a) and FC with $H_{\text{cool}}=2\times {10}^4$ Oe (b) measured for different $H_{\text{max}}$. $H_0^{-}$ and $H_0^{+}$ correspond to the field values at which magnetization crosses zero in the decreasing and increasing field branches of the hysteresis loop, respectively.

Figure 2

Fields at which magnetization crosses zero ($H_0^{-}$ and $H_0^{+}$) for different cooling fields $H_{\text{cool}}$ as a function of the maximum field $H_{\text{max}}$, for ferritin (a) and ferrihydrite nanoparticles (b). Lines represent fit to Eq. (10).

Figure 3

Dependence of the fields at which magnetization crosses zero ($H_0^{-}$ and $H_0^{+}$) (a), $H_C$ and $H_S$ (b) on the cooling field $H_{\text{cool}}$ for a maximum field $H_{\text{max}}=30\times {10}^4$ Oe, for ferritin. The ZFC values are shown in open symbols (which in the case of $H_0^{-}$ and $H_0^{+}$ corresponds to the same value). Lines connecting the FC values are eye guides.

Figure 4

(a) Magnetization measured at $H_{\text{max}}$ ($-H_{\text{max}}$) before removing the field down to 50 ($-50$) Oe ($M@H_{\text{max}}$) obtained after ZFC and FC with $H_{\text{cool}}=0.5\times {10}^4$ Oe, and difference between $M@H_{\text{max}}$ after FC and ZFC $\Delta M@H_{\text{max}}$; (b) first value of the remanent magnetization measured at 50 ($-50$) Oe [$M\left(t_0\right)$] obtained after ZFC and FC with $H_{\text{cool}}=0.5\times {10}^4$ Oe and difference between the FC and ZFC values; (c) magnetic viscosity $S$ measured at 50 ($-50$) Oe after a previous $H_{\text{max}}$ ($-H_{\text{max}}$). Measurements were performed in ferritin.

Figure 5

Dependence of the (a) coercive field $H_C$ and (b) loop shift $H_S$ on the maximum field $H_{\text{max}}$ in ferritin, for different cooling fields $H_{\text{cool}}$. Lines in panels (a) and (b) represent fits to Eqs. (11) and (12), respectively. Inset shows zoom over the low $H_{\text{max}}$ region.