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Magnetic force microscopy (MFM), a scanning probe microscopy (SPM) derivative of atomic force microscopy (AFM), enables imaging of the relatively weak but long-range magnetic forces experienced by a magnetized probe tip as it travels above a sample surface1,2,3,4,5. AFM is a non-destructive characterization technique that employs a nanometer-scale tip at the end of a pliable cantilever to map surface topography6 as well as measure material (e.g., mechanical, electrical, and magnetic) properties7,8,9 with nanoscale resolution. Deflection of the cantilever due to tip-sample interactions of interest is measured via reflection of a laser off the back of the cantilever and into a position-sensitive photodiode10. High-resolution imaging of a material's local magnetic properties via MFM provides the unique opportunity to characterize the magnetic field strength and orientation in novel materials, structures, and devices at the nanoscale4,5,11,12,13,14,15,16,17. To perform MFM, an AFM probe whose tip has been magnetized vertically (i.e., perpendicular to the probe cantilever and sample surface) is mechanically oscillated at its natural resonance frequency at a fixed height above the sample surface. Resultant changes in oscillation amplitude (less sensitive, and hence less common), frequency, or phase (described here) are then monitored to measure magnetic field strength qualitatively. More specifically, frequency modulation MFM produces a map of shifts in the oscillation frequency or phase, proportional to the magnitude and sign of the magnetic force gradient experienced by the probe. In order to maintain a constant height above the sample during MFM measurements, a dual-pass mode of operation is typically employed. The sample topography is first mapped via standard AFM techniques, followed by interleaved MFM imaging of each sequential scan line at a user-determined lift height (tens to hundreds of nm) off the sample surface. Employing such an interleaved dual-pass acquisition mode enables separation of the short-range tip-sample van der Waals interactions used to map the topography from the relatively longer-range magnetic forces experienced during the interleaved lift mode pass. However, MFM spatial resolution increases with decreasing lift height18, so there is an inherent tension between increasing MFM resolution and avoiding topographical artifacts due to van der Waals forces. Likewise, MFM sensitivity is proportional to the oscillation amplitude during the lift mode pass, but the maximum allowable oscillation amplitude is limited by the lift height and rapid changes in sample topography (i.e., high aspect ratio features).
Recent studies have highlighted the wealth of opportunities associated with the application of nanomagnetism and nanomagnonics, developed via artificial spin-ice (ASI) structures and magnonic crystals, as functioning devices for logic, computation, encryption, and data storage19,20,21,22. Composed of nanomagnets arranged in distinct extended lattice formations, artificial spin ices exhibit emergent magnetic dipoles or monopoles that can be controlled via an external stimulus19,20,23,24,25. In general, ASIs favor a moment configuration that minimizes the energy (e.g., in a two-dimensional (2D) square ASI, two moments point in and two point out of every vertex), with the low energy microstates following rules analogous to crystalline spin-ice materials21,26,27,28. Similarly, a recent MFM-enabled study demonstrated a three-dimensional (3D) ASI lattice system constructed from rare-earth spins situated on corner-sharing tetrahedra, where two spins point toward the center of the tetrahedra and two spins point out, resulting in two equal and opposite magnetic dipoles and hence a net zero magnetic charge at the tetrahedra centers23. Depending upon the alignment of an applied magnetic field relative to the sample surface, significant differences in the magnetic ordering and correlation length were observed. The alignment and control of ASI dipoles thus warrant further investigation. Methods for measuring ASI magnetic field distributions have included using a magneto-optical noise spectrometer29 or X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM)25; however to achieve spatial resolutions equal to or greater than that of MFM with XMCD-PEEM, extremely short wavelengths (i.e., high energy X-rays) are required. MFM offers a much simpler characterization technique that does not require exposure of samples to potentially damaging high energy X-rays. Additionally, MFM has been used to not only characterize ASI microstates21,23,27, but also for topological defect driven magnetic writing using high magnetic moment tips30. Accordingly, MFM can play a vital role in furthering ASI research and development, specifically through its ability to correlate sample topography with magnetic field strength and orientation, thereby revealing the magnetic dipoles associated with specific topographic features (i.e., ASI lattice elements).
High-resolution MFM likewise provides significant insight into the relationship between the structure of ferromagnetic shape memory alloys and their nanoscale magnetomechanical properties14,17,31,32,33. Ferromagnetic shape memory alloys, commonly referred to as magnetic shape memory alloys (MSMAs), exhibit large (up to 12%) magnetic field induced strains, carried through twin boundary motion29,33,34,35. MFM techniques have been used to investigate the complex relationships between twinning during deformation and martensitic transformation, indentation, micro-pillar deformation, and nanoscale magnetic responses of MSMAs15,16,17,36. Of particular note, MFM has been combined with nanoindentation to create and read a four-state nanoscale magnetomechanical memory17. Similarly, next-generation magnetic recording technologies are being pursued via heat-assisted magnetic recording (HAMR), achieving linear densities of 1975 kBPI and track densities of 510 kTPI37. The increased areal density required to enable greater, more compact data storage has resulted in a significant reduction in the defined track pitch of HAMR technologies, accentuating the need for high-resolution MFM imaging.
In addition to ASIs and MSMAs, MFM has been successfully used to characterize various magnetic nanoparticles, nanoarrays, and other types of magnetic samples3,38,39. However, ultimate MFM resolution and sensitivity are limited both by things beyond the user's control (e.g., AFM detection electronics, MFM probe technology, underlying physics, etc.) and by choice of imaging parameters and environment. Meanwhile, feature sizes in magnetic devices continue to decrease40,41, creating smaller magnetic domains, thus making MFM imaging increasingly more challenging. Additionally, the magnetic dipoles of interest are not always oriented out-of-plane, parallel to the magnetization vector of the probe. High-resolution imaging of the stray fields emanating from the ends of in-plane or nearly in-plane oriented dipoles, as is the case in the ASI structures shown here, requires greater sensitivity. Achieving high-resolution MFM images, especially of such in-plane magnetized samples composed of nanoscale magnetic domains, thus depends on appropriate choice of MFM probe (e.g., thickness, coercivity, and moment of the magnetic coating, which can at times be at odds with improving sensitivity or lateral resolution18 or preservation of the sample's magnetic alignment30), imaging parameters (e.g., lift height and oscillation amplitude, as mentioned above, as well as minimizing tip coating wear during topography line imaging), and sample quality (e.g., surface roughness and contamination, including polishing debris or surface water due to ambient humidity). In particular, the presence of water adsorbed on the sample surface due to ambient humidity can introduce strong tip-sample van der Waals forces that can significantly interfere with measuring magnetic forces and limit the minimum achievable lift height for MFM measurements. MFM operation within an inert atmosphere glovebox eliminates nearly all surface contaminants, allowing for lower lift heights and higher resolution coupled with greater sensitivity. Accordingly, in the sample examples shown here, an AFM system housed in a custom inert atmosphere glovebox filled with argon (Ar) containing <0.1 ppm oxygen (O2) and water (H2O) has been employed to enable extremely low lift heights (down to 10 nm). This subsequently enables exquisitely high-resolution MFM imaging capable of resolving alternating magnetic domains <200 nm wide within a larger crystallographic twin and magnetic dipoles (nanoscale bar magnets) <100 nm wide and ~250 nm long.
This article explains how to acquire high-resolution, high-sensitivity MFM images by combining the use of an inert atmosphere glovebox with careful sample preparation and optimal choice of imaging parameters. The described methods are especially valuable for imaging in-plane oriented dipoles, which are traditionally difficult to observe, and therefore exemplary high-resolution MFM images are presented of both Ni-Mn-Ga MSMA crystals exhibiting distinct nanoscale magnetic domains within crystallographic twins and across twin boundaries, as well as nanomagnetic ASI arrays fabricated with an in-plane magnetic dipole orientation. Researchers in a wide variety of fields desiring high-resolution MFM imaging can significantly benefit from employing the protocol outlined here, as well as the discussion of potential challenges such as topographical artifacts.