Particle moment canting in ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ nanoparticles

Polarization-analyzed small-angle neutron scattering methods are used to determine the spin morphology in high crystalline anisotropy, 11 nm diameter ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ nanoparticle assemblies with randomly oriented easy axes. In moderate to high magnetic fields, the nanoparticles adopt a uniformly canted structure, rather than forming domains, shells, or other arrangements. The observed canting angles agree quantitatively with those predicted from an energy model dominated by Zeeman and anisotropy competition, with implications for the technological use of such nanoparticles.

Figure 1

Hysteresis loops for ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ nanoparticle assemblies at 10, 100, 200, and 300 K. The 10 K hysteresis loop for bulk ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ is shown for comparison. Inset shows TEM image of as-grown particles.

Figure 2

(a) Experimental setup includes a polarizing supermirror and RF or conventional flipper to select the incident spin state and a ${}^3\mathrm{He}$ cell with in situ NMR flipper to select the scattered spin state. The scattering pattern is collected on a 2D detector. (b) Corrected 2D SANS images for 200 K, 1.4 T.

Figure 3

(a) Data for $N^2$ and $M_{\mathrm{PARL}}^2$ vs $Q$ and (b) $M_{\mathrm{PERP}}^2$ vs $Q$ for a variety of temperatures in 1.4 T, scaled to a $N^2$ Bragg peak height of 1000. Data for 10 K in a remanent field of $\approx 0.05$ T are also shown. Solid lines in (a) are for a close-packed array of fcc magnetic spheres with $\approx 13$% standard deviation in spacing distance whereas for (b) are for simple spheres of diameter 10.5 nm $\pm$ 0.4 nm. Error bars in the plot denote standard uncertainties.

Figure 4

(a) Modeling ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ with tilted angles for $T_d$ and $O_h$ sites referenced relative to an applied field H (green arrow). Angles are shown for the case of $O_h=T_d=\theta$; possible thermal excitations are indicated by dotted circular orbits. (b) Energy landscape for 10 K, 1.4 T showing minimum energy for no shell formation. (c) Energy savings per formula unit from canting in 1.4 T at 10 K (red), 100 K (orange), 200 K (blue), and 300 K (green). Minima are denoted by vertical lines.