Impact of core-shell dipolar interaction on magnetic phases of spherical core-shell nanoparticles

We show that confinement in small volumes affects the interplay of exchange and dipolar interactions and the magnetic phases of hard and soft spherical core-shell nanoparticles. Large variations in the magnetization of thin shells may occur due to the core dipolar field gradient within the shell. The reversal field is tunable by the trends imposed by the dipolar and core-shell interface exchange energies. We show, for instance, that the reversal field of a ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(30 nm)@${\mathrm{MnFe}}_2{\mathrm{O}}_4$(6 nm) particle ranges from 15.5 kOe for antiferromagnetic coupling down to 2.5 kOe for ferromagnetic coupling.

Figure 1

Hysteresis curve of a ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(22 $\mathrm{nm})@{\mathrm{CoFe}}_2$(2 nm) nanoparticle and of the ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(22 nm) core (in the bottom inset). The top inset shows the ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core dipolar field on the ${\mathrm{CoFe}}_2$ shell, and the color bar indicates the dipolar field strength.

Figure 2

Hysteresis curves of 30-nm-diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core nanoparticles with 6-nm-thick (left) ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ and (right) ${\mathrm{CoFe}}_2$ shells for strong interface exchange energy.

Figure 3

Magnetic pattern (top panels) and dipolar field maps of 30-nm-diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core nanoparticles with 6-nm-thick (a) and (b) ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ and (c) and (d) ${\mathrm{CoFe}}_2$ shells at selected points of the hysteresis curves shown in Fig. 2. The color bar indicates the dipolar field strength (in kOe) and applies to both the shell dipolar field in the core and the core dipolar field in the shell.

Figure 4

Hysteresis curves of 30-nm-diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core nanoparticles with 6-nm-thick (a) ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ and (b) ${\mathrm{CoFe}}_2$ shells and the inverted hysteresis of the (c) ${\mathrm{MnFe}}_2$ and (d) ${\mathrm{CoFe}}_2$ shells in the absence of interface exchange energy $\left(A^{*}=0\right)$.

Figure 5

(a) Average of the 30-nm-diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core dipolar at the $\theta \cong \pi /2$ belt at the 6-nm-thick ${\mathrm{CoFe}}_2$ shell. (b) Average of the dipolar field of the 6-nm-thick ${\mathrm{CoFe}}_2$ shell on the 30-nm-diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ core. The close-ups (i) and (ii) show the shell magnetic pattern and the dipolar field produced in the core for selected points of the hysteresis shown in Fig. 4. The color bar gives the intensity of the dipolar field (in kOe).

Figure 6

Reversal field of ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(30 nm) @${\mathrm{MnFe}}_2{\mathrm{O}}_4$(6 nm) (curve with solid circles) and ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(30 nm) @${\mathrm{CoFe}}_2$(6 nm) (curve with open circles) nanoparticles. The inset shows the reversal field of ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(30 nm)@${\mathrm{MnFe}}_2{\mathrm{O}}_4(\delta$ nm) and ${\mathrm{CoFe}}_2{\mathrm{O}}_4$(30 nm)@${\mathrm{CoFe}}_2(\delta$ nm) for $A^{*}=0.8$ and $\delta =2$, 4, 6, and 8 nm, corresponding to a shell volume fraction ranging from $30\%$ to $73\%$