Sub-tesla on-chip nanomagnetic metamaterial platform for angle-resolved photoemission spectroscopy

Abstract

Magnetically controlled states in quantum materials are central to their unique electronic and magnetic properties. However, direct momentum-resolved visualization of these states via angle-resolved photoemission spectroscopy (ARPES) has been hindered by the disruptive effect of magnetic fields on photoelectron trajectories. Here, we introduce an \textit{in-situ} method that is, in principle, capable of applying magnetic fields up to 1 T. This method uses substrates composed of nanomagnetic metamaterial arrays with alternating polarity. Such substrates can generate strong, homogeneous, and spatially confined fields applicable to samples with thicknesses up to the micron scale, enabling ARPES measurements under magnetic fields with minimal photoelectron trajectory distortion. We demonstrate this minimal distortion with ARPES data taken on monolayer graphene. Our method paves the way for probing magnetic field-dependent electronic structures and studying field-tunable quantum phases with state-of-the-art energy-momentum resolutions.

Figures (6)

• Figure 1: Examples of solid-state phenomena under magnetic field (see main text for details) and their corresponding energy scale. The blue and orange shaded areas indicate the accessible field strength and energy resolution of photoemission under magnetic field in previous approaches and the method proposed in this work, respectively.
• Figure 2: Calculated magnetic fields from different magnet configurations. (a) $z$-axis magnetic field ($B_z$) generated by cylindrical magnets with radii $R =$ 1 mm, 10 $\mu$m, 250 nm, and 70 nm, evaluated along the central axis of the cylinder. $z$ = 0 represents the top surface of the magnet. (b) Intensity plot of magnetic field distribution above one single-domain magnetic island (top), a nanomagnet array with all islands magnetized in the same direction (middle) and a nanomagnet array with alternating polarity (bottom) respectively. $R=70$ nm and an edge-to-edge gap of 25 nm are used. (c) Comparison of $B_z$ with respect to the distance from the top plane of the magnet between different scenarios shown in (b). (d) Comparison of $|B_z|$ distribution and histogram at 30 nm above the nanomagnet array between $R=70$ nm and $R=250$ nm.
• Figure 3: Simulated photoelectron trajectory and emission angle distribution maps under different magnetic fields. (a) A solenoid setup used in B-ARPES-Rice. (b) A single cylindrical magnet with radius $R = 1$ mm, showing representative positions at distance $d = 0$ (orange), 0.4 mm (purple), and 0.7 mm (red) from the center. Semi-transparent circles illustrate the broadening effect (see SI SI). (c) A nanomagnet array with alternating polarity, as proposed in this work. In all cases, the out-of-plane magnetic field is set to $|B_z|=30$ mT at $z$ = 30 nm. Grids in all panels represent the photoelectron emission angle distribution maps. Violet and green arrows correspond to the trajectories of the marked dots in the grids (see the main text for details).
• Figure 4: Design guidelines. (a) Island size required to achieve the desired $B_z$ field for different material magnetization strengths. (b) Maximum magnetization (left axis) and the corresponding effective current (right axis) for which the photoelectron deflection stays below certain thresholds---note that the total deflection does not depend on the island size (see SI SI).
• Figure 5: Experimental setup and stray field characterization. (a) Device schematic. (b) Optical image of the device. Green outlines indicate graphene boundaries on (red arrow) and off (white arrow) the magnetic pattern (light gray, top). The darker region corresponds to the hBN, and the white area to the gold contact pad. The inset (lower left) shows a magnified optical image of the graphene. (c) ARPES real-space scan overlaid with graphene boundaries, showing clear signals on/off the magnetic pattern and on the gold pad. (d) MFM image of the array of $R$ = 70 nm nanomagnets. Each island in the MFM image appears either black or white, indicating magnetic moments pointing upward and downward respectively. The inset shows a zoomed-in view of the MFM image. The scale bar (red) in the inset represents 0.5 $\mu$m. (e) $B_z$ map from scanning NV magnetometry. (f) Simulated $B_z$ map at 200 nm above the sample. (g) Simulated $B_z$ map at the graphene layer.