Direct detection of photoinduced magnetic force at the nanoscale reveals magnetic nearfield of structured light

Abstract

We demonstrate experimentally the detection of magnetic force at optical frequencies, defined as the dipolar Lorentz force exerted on a photoinduced magnetic dipole excited by the magnetic component of light. Historically, this magnetic force has been considered elusive since, at optical frequencies, magnetic effects are usually overshadowed by the interaction of the electric component of light, making it difficult to recognize the direct magnetic force from the dominant electric forces. To overcome this challenge, we develop a photoinduced magnetic force characterization method that exploits a magnetic nanoprobe under structured light illumination. This approach enables the direct detection of the magnetic force, revealing the magnetic nearfield distribution at the nanoscale, while maximally suppressing its electric counterpart. The proposed method opens up new avenues for nanoscopy based on optical magnetic contrast, offering a research tool for all-optical spin control and optomagnetic manipulation of matter at the nanoscale.

Fig. 1.. The concept of photoinduced magnetic force detection.

Structured light with azimuthal symmetry and dominant axial magnetic field induces magnetic dipoles in two magnetic polarizable nanoparticles, and an exclusive magnetic dipolar force is created between them.

Fig. 2.. Schematic illustration of photoinduced magnetic force detection.

(A) Schematic of the PiFM instrument used in this work. (B) Zoom-in region of the Si truncated cone working as photoinduced magnetic nanoprobe and its image in the glass slip (or substrate). The rotating arrows represent the excited electric field under the magnetic resonance condition, and the bold blue arrows show the directions of probe and image magnetic dipoles m_tip and m_img, respectively. (C) Two photoinduced magnetic polarized nanoparticles exerting a magnetic force on each other.

Fig. 3.. Comparison of time-averaged optical forces exerted on the spherical Si probe.

These forces are in the system of two closely spaced probes shown in Fig. 2A, under APB illumination from the bottom. The abscissa represents the displacement of both spheres from the APB axis. The optical wavelength is 610 nm, corresponding to the magnetic Mie resonance. The curves represent results evaluated with the accurate total Lorentz force density in eq. S1 and the dipole approximation formulation in Eqs. 2 and 3. See also eq. S3. This result shows that ${\mathbf{F}}_{\text{tot},z}^{\text{Lorentz}}\approx {\mathrm{F}}_{\mathrm{m},z}^{\text{dipole}}$, for any displacement. See the Supplementary Materials for the incident beam and the geometrical parameters.

Fig. 4.. Simulation of the force profiles acquired by the on/off-state probes.

(A) Designed on-state (left) and off-state (right) Si truncated cones with height of 90 and 140 nm, respectively, when operating at 670 nm. The side tilt angle and bottom diameter for both structures are 20° and 150 nm, respectively. (B) Simulated magnetic force spectrum of the on-state probe (blue) and off-state probe (red), 5 nm above a glass substrate, under APB illumination. The on-state probe generates much larger magnetic force compared to off-state probe at 670 nm. (C and D) Simulated force profiles in the transverse (x-y) plane for the on-state probe and off-state probe, respectively, operating at 670 nm. The simulations have been performed with a focused APB of incident power of 150 μW with a minimum beam waist parameter w₀ = 0.7λ. The red dotted circle in (C) indicates the area of dominant magnetic force (contributing more than 90% to the total photoinduced force).

Fig. 5.. Experiment measurement of the force profiles with the corresponding probes.

(A to D) FIB images of the on-state Si truncated cone probe (A), off-state Si truncated cone probe (B), blunt Si probe (C), and sharp Si probe (D). (E to H) Corresponding measured force maps upon APB illumination from the bottom of the glass slip using the on-state Si truncated cone probe (E), off-state Si truncated cone probe (F), blunt Si probe (G), and sharp Si probe (H). The on-state probe (A) measures the solid-center circular spot (E) typical of the APB magnetic field. The red dotted circle in (E) indicates the area with dominant magnetic force (contributing more than 90% to the total photoinduced force).