Spin excitations in cubic maghemite nanoparticles studied by time-of-flight neutron spectroscopy

We have determined the field dependence of collective magnetic excitations in iron oxide nanoparticles of cubic shape with 8.42(2) nm edge length and a narrow log normal size distribution of 8.2(2)% using time-of-flight neutron spectroscopy. The energy dependence of the uniform precession modes was investigated up to 5 T applied field and yields a Landé factor $g=2.05\left(2\right)$ as expected for maghemite ($\gamma$-Fe${}_2$O${}_3$) nanoparticles. A large effective anisotropy field of $B_{A,\mathrm{eff}}=0.45\left(16\right)$ T was determined, in excellent agreement with macroscopic measurements. This anisotropy is attributed to enhanced shape anisotropy in these monodisperse cubic nanoparticles. The combination of our results with macroscopic magnetization information provides a consistent view of the energy scales of superparamagnetic relaxation and collective magnetic excitations in magnetic nanoparticles.

Figure 1

Morphology of iron oxide nanocubes. (a) The SAXS and SANS by nanocubes dispersed in deuterated toluene were refined according to a spherical form factor model. Inset: TEM image (scale bar = 20 nm). (b) Scattering length density profiles for x rays (top) and neutrons (bottom); the relative contrasts are depicted as insets.

Figure 2

Magnetization and diffraction data. (a) Field dependent magnetization data. (b) Temperature dependent magnetization data. (c) Separation of nuclear and magnetic neutron scattering cross sections using neutron diffraction with polarization analysis. (d) Synchrotron XRPD by the nanoparticle powder. (e) TOF neutron diffraction and Le Bail refinement for two wavelength bands. Inset: profile of the (111) reflection after background subtraction.

Figure 3

Inelastic neutron scattering by iron oxide nanocubes. Scattering data measured in different applied magnetic fields in the vicinity of the (111) magnetic reflection is presented ($T=100$ K).

Figure 4

(a) Projections of the inelastic scattering data presented in Fig. 3 with refinement of the field dependent satellite reflections. (b) Field dependence of the determined satellite energy. Inset: data set after subtraction of the background scattering contribution and elastic line.

Figure 5

Schematic representation of superparamagnetic relaxation and collective magnetic excitation energies in nanoparticles. For the graph, uniaxial anisotropy according to the Stoner-Wohlfarth model and vanishing external magnetic field were assumed for simplicity. The excitation energy of the uniform precession states is presented in dependence of the angle $\theta$ between nanoparticle spin and local easy axis. The gray scale reflects the relative occupancy of energy levels at 100 K. The density of precession states and the populated states obtained by the Bose-factor weighting are given on the left.