Dipolar-coupled moment correlations in clusters of magnetic nanoparticles

Here, we resolve the nature of the moment coupling between 10-nm dimercaptosuccinic acid–coated magnetic nanoparticles. The individual iron oxide cores were composed of $>95\%$ maghemite and agglomerated to clusters. At room temperature the ensemble behaved as a superparamagnet according to Mössbauer and magnetization measurements, however, with clear signs of dipolar interactions. Analysis of temperature-dependent ac susceptibility data in the superparamagnetic regime indicates a tendency for dipolar-coupled anticorrelations of the core moments within the clusters. To resolve the directional correlations between the particle moments we performed polarized small-angle neutron scattering and determined the magnetic spin-flip cross section of the powder in low magnetic field at 300 K. We extract the underlying magnetic correlation function of the magnetization vector field by an indirect Fourier transform of the cross section. The correlation function suggests nonstochastic preferential alignment between neighboring moments despite thermal fluctuations, with anticorrelations clearly dominating for next-nearest moments. These tendencies are confirmed by Monte Carlo simulations of such core clusters.

Figure 1

(a) TEM image of the iron oxide cores. (b) Measured SAXS intensity $I\left(q\right)$ (radial average, $T=300\mathrm{K})$ of the dispersion and fit by IFT. Inset: Correlation function $C\left(r\right)r^2$ derived by the IFT of $I\left(q\right)$ and the expected profile of a homogeneous sphere calculated with Eq. (1) for $D=10\mathrm{nm}$ (grey area).

Figure 2

Neutron-diffraction pattern resolved by the Rietveld method. Residuals are represented by the blue line and the vertical tick marks indicate the positions of the nuclear (top) and magnetic (bottom) diffraction peaks. Inset: Ferrimagnetic structure of the iron oxide cores.

Figure 3

Mössbauer spectra and associated fits of the powder sample (a) and the frozen dispersion (b) at the indicated temperatures. (c) Comparison of the mean hyperfine field for the powder (black) and the frozen colloidal dispersion (red) for $T<40\mathrm{K}$. Both lines are linear fits. (d) RT Mössbauer spectrum of the particle powder.

Figure 4

(a) Normalized isothermal magnetization curves $M\left(H\right)/M_{\mathrm{S}}$ of the core clusters in powder form and colloidal dispersion measured at $T=300\mathrm{K}$. (b) In-phase $\left({\chi }^{\prime }\right)$ and out-of-phase $\left({\chi }^{″}\right)$ components of the $\mathrm{ACS}(T)$ measurements of the dispersion and the powder for frequencies $f=0.17–170\mathrm{Hz}$ (from top to bottom). Inset: Fit of the frequency dependency of the blocking temperatures $T_{\mathrm{B}}\left(f\right)$ to determine the characteristic attempt times ${\tau }_0$. (c) High-field $\left({\mu }_{0}H=1\mathrm{T}\right)$ magnetization vs temperature of the powder. The line corresponds to a modified Bloch-law in the temperature range 40–300 K. The slight upturn at low T (excluded from the fit) corresponds primarily to paramagnetic impurities in the sample cup and straw. (d) Inverse susceptibility $\left(1/\chi \right)$ vs temperature of the freeze dried powder, and the frozen dispersion (here using $f=0.17\mathrm{Hz})$. The solid lines corresponds to fits to a (Curie-Weiss) mean-field model [Eq. (2)]. The colloid thawed at around 260 K, as indicated by the kink in ${\chi }^{\prime }$ in panel (b), and thus the analysis was restricted to temperatures $T<260\mathrm{K}$.

Figure 5

SAXS intensity from Fig. 1 (colloidal dispersion) and the nuclear SANS intensity $I^{\mathrm{nuc}}\left(q\right)$ (powder; rescaled), derived from the non-spin-flip intensities of the POLARIS experiment. Additionally we show here the radial average of the spin-flip intensities $I^{\mathrm{sf}}\left(q\right)$ measured at 2 mT and 1 T [same as in inset of Fig. 6; in arbitrary units].

Figure 6

Results of the polarized SANS experiments of the powder at 300 K. (a) Spin flip intensity $I^{\mathrm{sf}}\left(\mathbf{q}\right)\left({\mu }_{0}H=2\mathrm{mT}\right)$ integrated over $\left|\mathbf{q}\right|=0.07–0.21{\mathrm{nm}}^{-1}$ as a function of $\mathrm{\Theta }$. Inset: Corresponding 2D scattering pattern $I^{\mathrm{sf}}\left(\mathbf{q}\right)$ (detector distance 13.4 m). NB indicates area of the primary neutron beam. (b) Azimuthal averages of $I^{\mathrm{sf}}\left(\mathbf{q}\right)\left({\mu }_{0}H=2\mathrm{mT}\right)$ in ${10}^{\circ }$ sectors around $\mathrm{\Theta }=0^{\circ },{45}^{\circ },{90}^{\circ }$ and the radial average, as well as the form factor $F\left(q\right)$ of a sphere [Eq. (A3)]. (c) The correlation function $C\left(r\right)r^2$ determined by an IFT of the radial average of $I^{\mathrm{sf}}\left(\mathbf{q}\right)$ measured at 2 mT, and the profile of a homogeneous sphere calculated with Eq. (1) for $D=10\mathrm{nm}$ (grey area). Inset: Comparison of the radial average $I^{\mathrm{sf}}\left(q\right)$ measured at 2 mT and 1 T, and fit of the measurement at 2 mT by IFT.

Figure 7

Monte Carlo simulations: (a) Averaged radial distribution function $g\left(r\right)$ (160 bins) of the ensemble of 320 clusters with 32 cores each. Inset: Snapshot of one simulated cluster. The volume of the spheres is directly proportional to the magnetic moment, and red-blue caps indicate the direction of the anisotropy axis. (b) Normalized polar plot of the magnetic pair correlations within the clusters without dipolar interactions and (c) with dipolar interactions.