Field Dependence of Magnetic Disorder in Nanoparticles

The performance characteristics of magnetic nanoparticles toward application, e.g., in medicine and imaging or as sensors, are directly determined by their magnetization relaxation and total magnetic moment. In the commonly assumed picture, nanoparticles have a constant overall magnetic moment originating from the magnetization of the single-domain particle core surrounded by a surface region hosting spin disorder. In contrast, this work demonstrates the significant increase of the magnetic moment of ferrite nanoparticles with an applied magnetic field. At low magnetic field, the homogeneously magnetized particle core initially coincides in size with the structurally coherent grain of 12.8(2) nm diameter, indicating a strong coupling between magnetic and structural disorder. Applied magnetic fields gradually polarize the uncorrelated, disordered surface spins, resulting in a magnetic volume more than 20% larger than the structurally coherent core. The intraparticle magnetic disorder energy increases sharply toward the defect-rich surface as established by the field dependence of the magnetization distribution. In consequence, these findings illustrate how the nanoparticle magnetization overcomes structural surface disorder. This new concept of intraparticle magnetization is deployable to other magnetic nanoparticle systems, where the in-depth knowledge of spin disorder and associated magnetic anisotropies are decisive for a rational nanomaterials design.

Popular Summary

Magnetic nanoparticles—a class of nanometer-scale beads that can be manipulated via magnetic fields—have diverse potential uses in a wide range of applications, such as medicine, data storage, and environmental cleanup. Their performance is determined by their magnetic moment (or their intrinsic magnetism) and their magnetization relaxation (how well they follow an external magnetic field). Typically, a magnetic nanoparticle is assumed to have a static, uniformly magnetized core surrounded by a structurally and magnetically disordered surface. Our work shows that an external magnetic field modifies the nanoparticle magnetization and that magnetic order can arise in the disordered region.

Using neutron scattering and exploiting the neutron polarization to resolve the nanoparticle magnetization, we find that the homogeneously magnetized core of ferrite nanoparticles coincides initially with the structurally ordered particle interior. As the external magnetic field is increased, the magnetic volume grows, eventually becoming 20% larger by volume than the coherent core. We attribute this growth to the gradual polarization of spins in the structurally disordered region toward the surface, and we use our findings to estimate the depth-resolved disorder distribution near the particle surface.

Our experimental results can serve as a benchmark for advanced computational modeling of nanoparticle spin structures. The experimental determination of the spin structure in individual magnetic nanoparticles and the quantitative characterization of magnetic disorder with nanoscale resolution provide a tool to control and gauge the magnetic properties of tailored magnetic nanoparticles.

Figure 1

Schematic of the structural and field-dependent magnetic NP morphology: The vertical cuts represent the structural morphology, consisting of a structurally coherent grain size (green) and structural disorder (blue) within the inorganic particle (gray). The horizontal cuts represent the magnetic morphology, consisting of a collinear magnetic core (red) and spin disorder (blue) within the inorganic particle surface layer (gray). The particle is surrounded by an oleic acid ligand layer (beige). Structural and magnetic particle sizes are equal in zero field (left), whereas the initially disordered surface spins are gradually polarized in the applied magnetic field such that the magnetic radius increases beyond the structurally disordered surface region (right).

Figure 2

(a) TEM bright field micrograph (scale bar, 50 nm) and (b) particle-size histogram based on the evaluation of 200 particles along with log-normal particle-size distribution obtained from TEM analysis (red surface) and SAXS refinement (line). (c) SAXS (red dots) and nuclear SANS (blue dots) data along with form factor fit (black lines) and (d) radial profiles of the nuclear (${\rho }_n$, gray) and magnetic scattering length densities (${\rho }_{\mathrm{mag}}$, red). Our model of the magnetic nanoparticle morphology consists of a coherently magnetized particle core with radius $r_{\mathrm{mag}}$ and a magnetically disordered surface shell with thickness $d_{\mathrm{dis}}$ within the inorganic NP with radius $r_{\mathrm{nuc}}$, stabilized by the oleic acid ligand shell with thickness $d_{\mathrm{surf}}$.

Figure 3

(a) Nuclear-magnetic scattering interference term $I^{+}-I^{-}$ (points) at various applied magnetic fields [same color code as in (b)] and corresponding fits (lines). Inset: Enlarged region of $Q=0.03–0.065{\AA }^{-1}$. (b) Field-dependent magnetic scattering length density ${\rho }_{\mathrm{mag}}$ profiles. (c) Field dependence of the derived magnetic radius $r_{\mathrm{mag}}$ and the disordered shell thickness $d_{\mathrm{dis}}$. The uncertainty intervals of nuclear ($r_{\mathrm{nuc}}$) and structurally coherent radius ($r_{\mathrm{XRD}}$) are indicated in gray and green, respectively.

Figure 4

Spin-resolved SANS (POLARIS) by cobalt ferrite nanoparticles: (a) non-spin-flip (NSF) ($I^{++},I^{--}$) and (b) averaged spin-flip (SF) $[(I^{+-}+I^{-+})/2]$ 2D scattering cross sections at an applied magnetic field of 1.2 T. (c)–(f) NSF and SF azimuthal scattering intensities, radially averaged in a $Q$ range of $0.006–0.016{\AA }^{-1}$, recorded at 0.3 and 1.2 T with corresponding fits (black line).

Figure 5

Macroscopic longitudinal magnetization ($⟨M_{\mathrm{VSM}}⟩$) measured at room temperature in comparison with the longitudinal particle core magnetization [$M_z(H)$] and the particle volume averaged magnetization ($⟨M⟩$), both derived from SANSPOL. Corresponding fits are shown as lines. Inset: Full data range for $⟨M_{\mathrm{VSM}}⟩$.

Figure 6

HRTEM micrographs of one representative NP with visible dislocation.

Figure 7

Dependence of (a) disorder energy $E_{\mathrm{dis}}$ as a function of the coherent magnetic particle radius (black line, spline fit of the data) and (b) the effective disorder energy density $K_{\mathrm{eff}}$ [black line, derivative of spline in (a)].

Figure 8

Rietveld refinement of PXRD pattern of cobalt ferrite NPs. The green and purple vertical lines correspond to the Bragg reflections of spinel cobalt ferrite [73] and of the sodium chloride structure [74], respectively.

Figure 9

Macroscopic magnetization measurement analyzed by numerical inversion. (a) VSM data (blue data) and reconstructed data by numerical inversion (black line). The red and orange contributions arise from the extracted large and small magnetic moment distributions, respectively, indicated in (b). $c$ denotes a scaling factor and $\mathrm{\Delta }\mu$ the binning width.

Figure 10

Room-temperature Mössbauer spectrum. Orange and green dashed lines correspond to the fitted doublet and broad sextet subspectra, respectively.

Figure 11

(a)–(c) EDX map of the distribution of Fe, O, and Co over a region containing 19–20 particles (scale bars of EDX maps, 10 nm) with (e) spectra reconstructed from the indicated area. (f) EDX line scan over an arbitrarily selected particle, displayed in (d).

Figure 12

(a) SANSPOL scattering cross sections $I^{+}$ and $I^{-}$ recorded at 1.2 T along with refinement (full lines). (b),(c) Corresponding 2D scattering patterns showing the $20°$ sectors around an angle of $\alpha =90°$ between the scattering vector $\mathbf{Q}$ and the applied magnetic field $\mathbf{H}$.

Figure 13

(a) Nuclear-magnetic scattering interference term $I^{+}-I^{-}$ (points) at various applied magnetic fields [same color code as in (b)] and corresponding fits (lines). Inset: Enlarged region of $Q=0.03–0.065{\AA }^{-1}$. (b) Field-dependent magnetic scattering length density ${\rho }_{\mathrm{mag}}$ profiles. (c) Macroscopic longitudinal magnetization $⟨M_{\mathrm{VSM}}⟩$ measured at room temperature in comparison with the particle volume averaged magnetization $⟨M⟩$ as derived from SANSPOL. Deviation in the intermediate field range is indicated (red box).

Figure 14

Fit of the SANSPOL cross term according to micromagnetic theory.