Atomic Force Manipulation of Single Magnetic Nanoparticles for Spin-Based Electronics

Magnetic nanoparticles (MNPs) are instrumental for fabrication of tailored nanomagnetic structures, especially where top-down lithographic patterning is not feasible. Here, we demonstrate precise and controllable manipulation of individual magnetite MNPs using the tip of an atomic force microscope. We verify our approach by placing a single MNP with a diameter of 50 nm on top of a 100 nm Hall bar fabricated in a quasi-two-dimensional electron gas (q2DEG) at the oxide interface between LaAlO3 and SrTiO3 (LAO/STO). A hysteresis loop due to the magnetic hysteresis properties of the magnetite MNPs was observed in the Hall resistance. Further, the effective coercivity of the Hall resistance hysteresis loop could be changed upon field cooling at different angles of the cooling field with respect to the measuring field. The effect is associated with the alignment of the MNP magnetic moment along the easy axis closest to the external field direction across the Verwey transition in magnetite. Our results can facilitate experimental realization of magnetic proximity devices using single MNPs and two-dimensional materials for spin-based nanoelectronics.


Dissection of MNP clusters
Due to the strong magnetic moment and the lack of coating, MNPs such as the C50s appear in clusters of sizes ranging from a few to dozens of particles. Fig.2 shows how such an agglomerate can be dissected using the tip of the AFM. This procedure does not yield only isolated particles but mostly smaller clusters of 2-4 particles which cannot be dissected further because the tip would just move the entire piece. We found it most effective to try to "slice" off protruding MNPs from chain-like agglomerates. With this technique we were able to extract 1-2 isolated MNPs from most clusters.

Estimations of the stray field from C50 MNPs
The MNP stray field can be estimated assuming it to be originating from a single dipole levitating above the surface at height of the MNPs radius d/2. This assumption holds true when evaluating the field outside of a uniformly magnetized sphere. The field of such a dipole is given by the following equation: 1 where A is the vector potential, r = r ′ − r mnp is the vector from MNP to a point in the q2DEG. r ′ is the vector to the point from the origin and r mnp is the position of the MNP, The thickness of the LAO layer of 4 nm and a q2DEG thickness of 10 nm is assumed.
The C50 MNP has diameter d = 50 nm and magnetic moment µ = 3 · 10 −17 Am 2 . The magnetic moment is directed inm = {sin Θ, 0, cos Θ} with Θ = 0 (perpendicular to the surface), For practical purposes the field is often averaged over the thickness of the q2DEG and then denoted ⟨B⟩.
where Q, k and ω 0 are quality factor, spring constant and resonance frequency of the tip respectively. The sign in the relations above implies that for an attractive interaction (positive force gradient), the shift in frequency or phase will be negative, which is associated with a dark contrast in the eventual image. When frequency is measured a feedback loop is applied that adjusts the frequency in order to keep the phase constant.
The MFM signal is simulated by assuming both tip and MNP to be single magnetic dipoles. In this approximation the force can be expressed analytically: The derivative of the force is calculated numerically with the central difference technique for a square grid of positions. The position of the tip is given by z 0 + δ above the surface, i.e. lift height plus effective distance to the MM of the tip (including e.g. tip dimensions, oscillations and coating.). The MNPs shape in x-direction, centered in the origin, is assumed to have the form h(x) = 2re −(|x|/(c+r)) 6 with particle radius r, convolution parameter c and analogously for the y−direction. The 3D shape of the particle is then h(x, y) = min h(x), h(y) .  Red arrows indicate magnetic moments orientation. Black solid and dashed lines indicate the particle shape and tip scan profile, respectively.