Spin canting across core/shell Fe3O4/MnxFe3−xO4 nanoparticles

Magnetic nanoparticles (MNPs) have become increasingly important in biomedical applications like magnetic imaging and hyperthermia based cancer treatment. Understanding their magnetic spin configurations is important for optimizing these applications. The measured magnetization of MNPs can be significantly lower than bulk counterparts, often due to canted spins. This has previously been presumed to be a surface effect, where reduced exchange allows spins closest to the nanoparticle surface to deviate locally from collinear structures. We demonstrate that intraparticle effects can induce spin canting throughout a MNP via the Dzyaloshinskii-Moriya interaction (DMI). We study ~7.4 nm diameter, core/shell Fe3O4/MnxFe3−xO4 MNPs with a 0.5 nm Mn-ferrite shell. Mössbauer spectroscopy, x-ray absorption spectroscopy and x-ray magnetic circular dichroism are used to determine chemical structure of core and shell. Polarized small angle neutron scattering shows parallel and perpendicular magnetic correlations, suggesting multiparticle coherent spin canting in an applied field. Atomistic simulations reveal the underlying mechanism of the observed spin canting. These show that strong DMI can lead to magnetic frustration within the shell and cause canting of the net particle moment. These results illuminate how core/shell nanoparticle systems can be engineered for spin canting across the whole of the particle, rather than solely at the surface.

. Hyperfine parameters for the components of the Mössbauer spectrum measured at 10 K, where δ is the isomer shift, Bhf is the hyperfine field, Δ is the quadrupole splitting, and Γ is the line width.

Site  (mm/s) Bhf (T) Δ (mm/s) Γ (mm/s) Area (%)
I -Fe 3+ A 0.549 (5) 53.15(6) 0.026(9) 0.19(1) 26 (7) II -Fe 3+ B 0.492 (5) 51.78(7) 0.020(9) 0.22 (2) Figure S4. Field cooled (FC) and zero field cooled (ZFC) magnetization for (a) a dilute sample of the core/shell NPs. (b) Overlay of ZFC from both dilute and dense samples of nanoparticles. The blocking temperature of the particles in the dilute particles is lower than the dense samples, indicating that interparticle interactions have been reduced. The peak associated with blocking temperature is also much more distinct for dilute particles (fall off with increasing temperature is more abrupt) indicating that the dilute sample has reduced interparticle interactions. Here the applied field was 100 Oe.

M(a.u)
(a) (b) Data Note S5. Using the PASANS method, we obtained data for all four possible scattering cross-sections (↑↑, ↑↓, ↓↑, or ↓↓) corresponding to incident neutrons either spin up (↑) or spin down (↓) with the post-sample scattered neutrons, again either spin up (↑) or spin down (↓). For example, ↑↓, indicates the scattering from neutrons initially polarized spin up which then after scattering off the sample were found to polarized spin down; the scattering of this cross-section (↑↓) and the related one (↓↑) thus involve "spin-flipping" of the incident neutron relative to the scattered one.
These scattering cross-sections are proportional to the squared sum of the spatial nuclear N and magnetic M Fourier transforms 1 , 2 : where J is any Cartesian coordinate (X, Y, or Z), Q is the scattering vector, RK is the relative position of the Kth scatterer and N,M is the nuclear or magnetic scattering length density respectively. Note that the nuclear scattering is assumed isotropic in many cases, although in some systems, nuclear spins can be aligned. In contrast, the magnetic Fourier transform has directional components with selection rules governing the observed scattering; only the component of magnetic scattering perpendicular to Q can contribute.
While in general the complete angle-dependent polarization rules lead to complex expressions for the scattering cross-sections, these simplify in certain geometries and key angles. In the present case, we then extract the quantities N 2 , M 2 PAR and M 2 PERP in Fig. 6b from the underlying four cross-sections in the following way, taking sector averages of the data for the specified values of In the expression for N 2 , we note that the sample is isotropic in our case, given that the polycrystals of ordered nanoparticle assemblies do not have particular preferred directions. The expression for M 2 PERP is explicitly for a particular portion of the spin-flip data, while M 2 PAR equation is for the fraction that is coherent with the structural order.
Data Note S6. Details of atomistic simulations. The structure of the measured nanoparticles is complex and so we have adopted a simplified model based on a single crystal particle to capture the essential properties of the particles. We construct a single crystal of Magnetite with an inverse Spinel structure and lattice parameter 8.3941 Å, explicitly including the Oxygen sites due to their contribution to the DMI on octahedral Mn sites. A spherical particle is then cut from the crystal and different magnetic parameters are assigned based on the distance from the centre, defining a core region 5.6 nm in diameter and a shell of 0.7 nm thick. The magnetic properties of the system are described with a Heisenberg spin Hamiltonian of the form and are unit vectors describing the directions of spins on sites and , is the exchange tensor between sites and , is the spin moment at site and app is a vector describing the direction of the externally applied field. The exchange tensor describes isotropic, anisotropic and anti-symmetric (DMI) exchange interactions between two spin sites and and is given by The atomistic spin dynamics are computed numerically by solving the stochastic Landau-Lifshitz-Gilbert equation with Langevin dynamics 4 applied at the atomic level using the VAMPIRE software package 5 . The simulations were performed with critical Gilbert damping = 1to ensure a rapid convergence to an equilibrium spin state. Figure S7. Visualization of the simulated spin configuration of a decoupled superparamagnetic MnFe2O4 shell taking a slice through the y-z plane. The coloring of the atoms indicates the direction of magnetization on each site, with Oxygen sites shown as small dark spheres. The simulation temperature is set at 300K in a 1 T externally applied field along the [001] crystal direction. The shaded core region shows a nearly single domain state, while the shell shows much more disorder due to finite size effects. At high fields, the superparamagnetic shell is well aligned with the field direction leading to a Langevin-type saturation of the total magnetization Ms for the nanoparticle.