Reentrant paramagnetism induced by drastic reduction of magnetic couplings at surfaces of superparamagnetic nanoparticles

Superparamagnetism appears when the Néel-Brown relaxation time of magnetic nanoparticles is shorter than the measurement time. Recent experimental studies of different types of magnetic nanoparticles revealed the existence of another paramagnetic region below the standard blocking temperatures. Here we elucidate the microscopic origin of this reentrant paramagnetism using a phenomenological model, which exploits the effects of weaker magnetic coupling strengths at the surfaces of ultrasmall nanoparticles. Within this picture, we have calculated the total magnetization of various nanoparticle arrays upon both finite-field and zero-field cooling processes via detailed classical Monte Carlo simulations, and found that the appearance of the reentrant phenomena necessarily invokes a drastic reduction of the magnetic coupling strengths at the surfaces of the nanoparticles. Our predictions can be readily tested experimentally using a micro-SQUID, and is expected to be beneficial in further applications of superparamagnetic nanoparticles.

Figure 1

Schematic phase diagram of a magnetic nanoparticle. The reentrant paramagnetic phase emerges when the size of the nanoparticle is small enough.

Figure 2

Schematic view of the spin configurations of a magnetic nanoparticle at finite temperatures, highlighting the coexistence of a ferromagnetic core and a paramagnetic surface region.

Figure 3

Temperature dependence of the magnetization for ZFC and FC processes, where $J_S=1.0$ K. $T_B$ and $T_S$ in the ZFC curve indicate the blocking and saturation temperature, respectively. Inset: ZFC and FC curves of the magnetic nanoparticles with varying surface magnetic coupling strengths ranging from 1 to 5 K.

Figure 4

Hysteresis behaviors of the total magnetization as a function of the magnetic field at different temperatures.

Figure 5

Saturation behaviors of the total magnetization as a function of the magnetic field at different temperatures.

Figure 6

(a) Temperature dependence of the coercive field $H_C$. (b) Linear fitting of the coercive field $H_C$ as a function of $T^{1/2}$ between the temperature range of 9 K and 14 K.

Figure 7

Parameter space spanned by the surface magnetic coupling strength $J_S$ and magnetic nanoparticle radius $R$, in which the boundary separates the regions without (left) or with (right) the existence of the reentrant phenomena. The different curves correspond to different anisotropy parameters $K_{an}$.

Figure 8

Intensity of the reentrant magnetization as a function of the surface magnetic coupling strength $J_S$, plotted with $R=10a,d=3.1a$, and $h=0.05$ T.

Figure 9

Intensity of the reentrant magnetization as a function of the surface magnetic coupling strength and magnetic nanoparticle radius, plotted with different external magnetic fields: (a) 0.05 T and (b) 0.075 T.