All AFM/MFM imaging was performed in the Boise State University Surface Science Laboratory (SSL). The glovebox AFM system used in this work was purchased under National Science Foundation Major Research Instrumentation (NSF MRI) Grant Number 1727026, which also provided partial support for PHD, ACP, and OOM. Partial support for OOM was further provided by NSF CAREER Grant Number 1945650. Research at the University of Delaware, including fabrication and electron microscopy characterization of artificial spin-ice structures, was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0020308. The authors thank Drs. Medha Veligatla and Peter M&#252;llner for helpful discussions and preparation of the Ni-Mn-Ga samples shown here, as well as Dr. Corey Efaw and Lance Patten for their contributions to the MFM standard operating procedure including in the Supplementary File 1.

NOTE: In addition to the protocol below, a detailed step-by-step MFM standard operating procedure (SOP) specific to the instrument used here and geared towards general MFM imaging is included as Supplementary File 1. To supplement the video portion of this manuscript, the SOP includes images of the probe holder, tip magnetizer and magnetization procedure, software settings, etc.
1. MFM probe preparation and installation
<ol>
	<li>Open the AFM control software and select the MFM workspace (see Table of Materials).</li>
	<li>Mount an AFM probe with a magnetic coating (e.g., Co-Cr, see Table of Materials) on an appropriate probe holder (see Table of Materials), magnetize the probe, and install the probe holder on the AFM head. 
	NOTE: MFM probes require a magnetic coating; the probes used in this study utilized a cobalt-chromium (Co-Cr) alloy coating with a nominal coercivity of 400 Oe and a magnetic moment of 1 x 10-13 EMU, resulting in an ~35 nm radius of curvature for the coated n-doped silicon probe. Probes with a smaller radius of curvature or lower or higher magnetic moment or coercivity are available, depending upon sample and imaging needs (e.g., a low moment probe may be needed when imaging a low coercivity sample to avoid inadvertently flipping the magnetization direction of the sample with the probe, or conversely a high moment probe may be used to write a magnetic pattern18). See the Table of Materials for an extensive, but non-exhaustive, list of MFM probe options, keeping in mind that a thinner magnetic coating will yield a sharper MFM tip (and hence potentially improved spatial resolution) but at the likely cost of decreased sensitivity due to a lower magnetic moment.
	<ol>
		<li>Carefully place the probe holder on a mounting block (see Supplementary Figure S1), then load the probe onto the probe holder, align, and secure in place with a spring-loaded clip (see Supplementary Figure S2). Ensure the probe is parallel to all edges and not touching the back of the holder&#39;s channel by inspecting it under an optical microscope. Gently manipulate the probe as necessary with a pair of tweezers. 
		NOTE: Electrostatic discharge (ESD) can damage the metallic coating on the MFM probe and/or sensitive AFM electronics, so be careful to discharge any static buildup prior to handling and consider wearing anti-ESD gloves and/or using a grounding wrist strap or mat depending on the environmental conditions (e.g., relative humidity).</li>
		<li>Magnetize the probe vertically (i.e., perpendicular to the probe cantilever) using a strong permanent magnet (see Table of Materials) for a few (~2-5) seconds so that the magnetic dipole orientation of the probe tip will be perpendicular to the sample. 
		NOTE: For reference, the probe magnetizer used here (see Table of Materials and Supplementary Figure S3) has a coercivity of ~2000 Oe and is designed so that the case fits over the probe holder, with the magnet oriented such that its magnetic moment is aligned parallel to the probe tip and perpendicular to the cantilever.</li>
		<li>Carefully remove the AFM head. Install the probe and probe holder by aligning the holes on the probe holder with the contact pins on the head. Reinstall the head on the AFM and secure in place. Again, be careful as ESD can damage the probe or sensitive AFM electronics.</li>
	</ol>
	</li>
	<li>Align the laser onto the center of the MFM probe cantilever and into the position-sensitive detector (PSD).
	<ol>
		<li>For optimal sensitivity, align the laser on the back of the cantilever to the location corresponding to the tip setback from the distal end of the cantilever.</li>
		<li>Maximize the sum signal on the PSD while minimizing the left/right and up/down deflections to center the reflected laser beam on the detector. Set the laser X and Y deflection signals as close to zero as possible to obtain maximum detectable deflection range for producing an output voltage proportional to the cantilever deflection.</li>
	</ol>
	</li>
</ol>
2. Sample preparation and installation
<ol>
	<li>Place the sample over the AFM chuck vacuum port. Avoid using a magnetic sample holder, as this could affect the sample and/or interfere with the MFM measurement. Turn on the chuck vacuum to secure the sample to the AFM stage.
	<ol>
		<li>Secure the sample well for imaging to avoid introduction of noise due to nanoscale sample vibrations. If an airtight seal cannot be formed between the base of the sample and the AFM stage vacuum port, affix the sample to a metal puck (see Table of Materials) or glass microscope slide using an appropriate bonding adhesive.</li>
		<li>Ensure that the sample is as smooth as possible, ideally with nanometer scale surface roughness and free of debris (e.g., residual polishing compound in the case of a metal alloy sample such as single crystal Ni-Mn-Ga), to enable low lift heights leading to high resolution and sensitivity of MFM imaging (see Discussion).</li>
	</ol>
	</li>
</ol>
3. Initial setup and sample approach
<ol>
	<li>Returning to the AFM control software (MFM workspace), align the crosshairs within the optical microscope view to be positioned over the back of the MFM probe cantilever where the tip is located, using the known tip setback based on the selected probe.</li>
	<li>Position the AFM stage and sample so that the region of interest (ROI) is directly beneath the AFM tip. Lower the AFM head until the sample surface comes into focus in the optical view. Be careful not to crash the probe into the sample surface, as this could result in probe and/or sample damage. 
	&#8203;NOTE: The AFM control software used here provides two focusing options: Sample (default) and Tip Reflection. The default option employs a 1 mm focal length, meaning the AFM cantilever will be ~1 mm above the surface when the surface appears in focus in the optical view. Tip Reflection mode uses a 2 mm focal length, so the surface will appear in focus when the AFM cantilever is ~2 mm above the surface, while the tip reflection will appear in focus when the cantilever is ~1 mm above the surface (in the case of a reflective sample surface). The suggested method for approaching the surface is to begin in Tip Reflection mode and approach at full speed (100%) until the sample surface comes into focus, then switch to Sample (default) and approach at medium speed (20%) until the surface again comes into focus.</li>
</ol>
4. Topography imaging (main line)
NOTE: The protocol described below assumes the use of intermittent contact (tapping) mode for topography imaging.
<ol>
	<li>Perform a cantilever tune by choosing start and end frequencies that will sweep the dither piezo drive frequency across a region chosen to span the expected resonance frequency of the selected probe (e.g., 50-100 kHz for a probe with nominal f0 = 75 kHz).</li>
	<li>Depending on the particular AFM system and software employed (see Table of Materials), utilize a single-click auto tune feature to automate the steps below based on the known nominal values for the chosen probe type. 
	NOTE: Tuning the cantilever involves identifying its natural resonance frequency and adjusting the drive amplitude (at or near that frequency) so the cantilever oscillates at an appropriate target amplitude (in nanometers).
	<ol>
		<li>Choose a drive frequency for the main line cantilever tune that is offset to slightly lower frequency than the resonance peak (~5% decrease in amplitude from the peak) to compensate for shifts in the resonance frequency due to changing tip-sample interactions during tip-sample approach.</li>
		<li>Choose a drive amplitude that results in a target amplitude corresponding to ~50 nm cantilever oscillation (~500 mV amplitude on the PSD for the AFM system and MFM probe employed here, see Table of Materials) as a good starting point. 
		NOTE: To convert the measured photodiode deflection signal (in mV or V) into an oscillation amplitude (in nm) requires knowledge of the nominal or measured probe deflection sensitivity.</li>
		<li>Choose an amplitude setpoint corresponding to ~0.8x of the free space target amplitude (i.e., ~40 nm for a free space amplitude of 50 nm) as a good starting point for topography imaging. 
		NOTE: A higher amplitude setpoint will result in a gentler engage but will increase the likelihood of a false engage (i.e., the instrument/software mistakenly thinking the probe is engaged on the surface due to a slight decrease in oscillation amplitude arising from random fluctuations/transient forces acting on the cantilever). Conversely, a lower amplitude setpoint decreases the probability of a false engage, but at the expense of potentially increased tip wear or sample damage upon engaging.</li>
	</ol>
	</li>
	<li>Engage on the sample surface and set the desired scan size depending upon the sample and features of interest (typically somewhere between &#60;1 &#181;m to tens of &#181;m in X and Y).</li>
	<li>Increase the amplitude setpoint in increments of 1-2 nm until the tip just loses contact with the sample surface, as seen by the trace and retrace lines failing to track each other in the height sensor channel. Then, decrease the amplitude setpoint by ~2-4 nm so the tip is just in contact with the sample surface. 
	&#8203;NOTE: The above will help to minimize the tip-sample interaction force, thereby preserving the sample, lengthening the probe tip life, and improving MFM performance by minimizing tip wear, in particular premature loss of the magnetic coating, as well as the possibility of introducing tip artifacts into the topography and/or magnetic phase images.</li>
	<li>Optimize the proportional (P) and integral (I) gains by adjusting them so they are high enough to force the feedback system to track the sample surface topography while minimizing noise. To do this, increase the gains until noise just begins to appear in the error channel, then back off slightly. The system is typically more sensitive to the I gain than the P gain.</li>
</ol>
5. MFM imaging (interleaved lift mode pass)
<ol>
	<li>Once the AFM topography imaging parameters have been optimized, withdraw a short distance (&#8805;200 nm) from the surface and return to the probe tuning menu. Perform a second cantilever tune to be used to acquire the interleaved lift mode MFM line, making sure to unlink the results of this tune from the previous main line parameters.
	<ol>
		<li>In contrast to the 5% peak offset employed for the main (topography) line tune in Step 4.2.1, for the interleaved lift mode (MFM) tune, set the peak offset to 0% (i.e., drive the probe at its natural free space resonance frequency during the interleaved MFM pass, since the probe will be oscillating outside the region where strongly attractive or repulsive van der Waals electrostatic forces are felt). Choose start and end frequencies that will sweep the drive frequency across a region spanning the resonance frequency of the probe, similar to step 4.1.</li>
		<li>Adjust the interleaved lift mode target (or drive) amplitude to be slightly less than the main line target (or drive) amplitude chosen in step 4.2.2 (e.g., ~45 nm target amplitude for the interleaved lift mode MFM pass if using a 50 nm target amplitude for the topography main line). This will enable high sensitivity MFM imaging without striking the surface (i.e., generating topographical artifacts or phase spikes) when utilizing low lift heights for optimal lateral resolution.</li>
	</ol>
	</li>
	<li>Leave the cantilever tune window, reengage on the surface, and optimize the MFM imaging parameters.
	<ol>
		<li>Set the initial lift scan (interleaved MFM pass) height to 25 nm, then gradually decrease in increments of ~2-5 nm. Once the probe begins to just strike the surface, sharp spikes will appear in the MFM phase channel; immediately increase the scan height by ~2-5 nm to preserve the probe tip and prevent introduction of topographical artifacts.</li>
		<li>Increase the&#160;interleave drive amplitude in small increments corresponding to ~2-5 nm in interleave&#160;oscillation amplitude until the interleave drive amplitude exceeds the mainline drive amplitude, or the probe begins to contact the surface as evidenced by spikes in the MFM phase channel. Then, decrease the interleave&#160;drive amplitude slightly (corresponding to ~1-2 nm increments) so that no spikes are seen in the MFM phase channel.</li>
		<li>Continue iteratively optimizing the lift scan height and interleave&#160;drive amplitude by adjusting in progressively smaller increments until a high-resolution MFM image free of topographical artifacts is obtained.
		<ol>
			<li>Because the tip-sample van der Waals interactions responsible for topography artifacts drop off much more rapidly with distance than the desired long-range magnetic forces, to evaluate the origin of features in the MFM magnetic phase image, investigate the lift height dependence of these features. Topography artifacts will tend to disappear (appear) abruptly with small increases (decreases) in lift height, whereas true magnetic phase responses will change gradually (e.g., resolution and signal to noise will improve with decreasing lift height).</li>
			<li>Likewise, if changes are observed in the magnetic moment alignment of low coercivity samples upon repeated scanning, this may be indicative of tip-induced switching that will necessitate the use of a low moment probe (see Table of Materials) and potentially higher lift heights as well.</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>

The authors have nothing to disclose.

High-resolution MFM imaging requires that a corresponding high-resolution, high-fidelity topography scan first be acquired for each line. This topography scan is typically obtained through intermittent contact or tapping mode AFM, which employs an amplitude modulation feedback system to image sample topography47. The fidelity of the topography scan can be optimized by adjusting the amplitude set point of the cantilever and feedback gains as described in the Protocol. The amplitude setpoint is crit...

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&#39;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&#39;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&#39;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 &#60;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 &#60;200 nm wide within a larger crystallographic twin and magnetic dipoles (nanoscale bar magnets) &#60;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.

<table><tbody><tr><td>Atomic force microscope</td><td>Bruker</td><td>Dimension Icon</td><td>Uses Nanoscope control software</td></tr><tr><td>Glovebox, inert atmosphere</td><td>MBraun</td><td>LabMaster Pro MB200B + MB20G gas purification unit</td><td>Custom design (leaktight electrical feedthroughs, vibration isolation, acoustical noise and air current minimization, etc.) and depth for use with Bruker Dimension Icon AFM, 3 gloves, argon atmosphere</td></tr><tr><td>MFM probe</td><td>Bruker</td><td>MESP</td><td>&lt;em&gt;k&lt;/em&gt; = 3 N/m, &lt;em&gt;f&lt;sub&gt;0&lt;/sub&gt;&lt;/em&gt; = 75 kHz, &lt;em&gt;r&lt;/em&gt; = 35 nm, 400 Oe coercivity, 1 x 10&lt;sup&gt;-13&lt;/sup&gt; EMU moment. An improved version with tighter specifications, the MESP-V2, is now available. We have also used Bruker&#039;s MESP-RC (2x higher resonance frequency than the standard MESP, &lt;em&gt;f&lt;sub&gt;0&lt;/sub&gt;&lt;/em&gt; = 150 kHz, with a marginally stiffer nominal spring constant of 5 N/m) and other MESP variants designed for low (0.3 x 10&lt;sup&gt;-13&lt;/sup&gt; EMU) or high (3 x 10&lt;sup&gt;-13&lt;/sup&gt; EMU) moment (i.e., MESP-LM or MESP-HM, respectively) or coercivity. A variety pack of 10 probes containing 4x regular MESP, 3x MESP-LM, and 3x MESP-HM variants is available from Bruker as MESPSP. Other vendors also manufacture MFM probes with specifications similar to the MESP (e.g., PPP-MFMR from Nanosensors, also available in a variety of variants, including -LC for low coercivity, -LM for low moment, and SSS for &quot;super sharp&quot; decreased tip radius; MAGT from AppNano, available in low moment [-LM] and high moment [-HM] variants). Similarly, Team Nanotec offers a line of high resolution MFM probes (HR-MFM) with several options in terms of cantilever spring constant and magnetic coating thickness.</td></tr><tr><td>MFM test sample</td><td>Bruker</td><td>MFMSAMPLE</td><td>Section of magnetic recording tape mounted on a 12 mm diameter steel puck; useful for troubleshooting and ensuring the MFM probe is magnetized and functioning properly</td></tr><tr><td>Nanscope Analysis</td><td>Bruker</td><td>Version 2.0</td><td>Free AFM image processing and analysis software package, but proprietary, designed for, and limited to Bruker AFMs; similar functionality is available from free, platform-independent AFM image processing and analysis software packages such as Gwyddion, WSxM, and others</td></tr><tr><td>Probe holder</td><td>Bruker</td><td>DAFMCH or DCHNM</td><td>Specific to the particular AFM used; DAFMCH is the standard contact and tapping mode probe holder, suitable for most MFM applications, while DCHNM is a special nonmagnet version for particularly sensitive MFM imaging</td></tr><tr><td>Probe magnetizer</td><td>Bruker</td><td>DMFM-START</td><td>MFM &quot;starter kit&quot; designed specifically for the Dimension Icon AFM; includes 1 box of 10 MESP probes (see above), a probe magnetizer (vertically aligned, ~2,000 Oe magnet in a mount designed to accommodate the DAFMCH or DCHNM probe holder, above), and a magnetic tape sample (MFMSAMPLE, above)</td></tr><tr><td>Sample Puck</td><td>Ted Pella</td><td>16218</td><td>Product number is for 15 mm diameter stainless steel sample puck. Also available in 6 mm, 10 mm, 12 mm, and 20 mm diameters at https://www.tedpella.com/AFM_html/AFM.aspx#anchor842459</td></tr><tr><td>Scanning electron microscope (SEM)</td><td>Zeiss Merlin</td><td>Gemini II</td><td>SEM parameters: 5 keV accelaration voltage, 30 pA electron current, 5 mm working distance. Due to nm scale ASI lattice features, the aperture and stigmation alignment were adjusted before acquisition to produce high quality images.</td></tr></tbody></table>

optimizing magnetic force microscopy resolution and sensitivity to visualize nanoscale magnetic domains

Magnetic force microscopy (MFM) enables mapping local magnetic fields across a sample surface with nanoscale resolution. To perform MFM, an atomic force microscopy (AFM) probe whose tip has been magnetized vertically (i.e., perpendicular to the probe cantilever) is oscillated at a fixed height above the sample surface. The resultant shifts in the oscillation phase or frequency, which are proportional to the magnitude and sign of the vertical magnetic force gradient at each pixel location, are then tracked and mapped. Although the spatial resolution and sensitivity of the technique increases with decreasing lift height above the surface, this seemingly straightforward path to improved MFM images is complicated by considerations such as minimizing topographical artifacts due to shorter range van der Waals forces, increasing the oscillation amplitude to further improve sensitivity, and the presence of surface contaminants (in particular water due to humidity under ambient conditions). In addition, due to the orientation of the probe's magnetic dipole moment, MFM is intrinsically more sensitive to samples with an out-of-plane magnetization vector. Here, high-resolution topographical and magnetic phase images of single and bicomponent nanomagnet artificial spin-ice (ASI) arrays obtained in an inert (argon) atmosphere glovebox with &lt;0.1 ppm O2 and H2O are reported. Optimization of lift height and drive amplitude for high resolution and sensitivity while simultaneously avoiding the introduction of topographical artifacts is discussed, and detection of the stray magnetic fields emanating from either end of the nanoscale bar magnets (~250 nm long and &lt;100 nm wide) aligned in the plane of the ASI sample surface is shown. Likewise, using the example of a Ni-Mn-Ga magnetic shape memory alloy (MSMA), MFM is demonstrated in an inert atmosphere with magnetic phase sensitivity capable of resolving a series of adjacent magnetic domains each ~200 nm wide.

Artificial spin-ice (ASI) lattices 
Artificial spin ices are lithographically defined two-dimensional networks of interacting nanomagnets. They exhibit frustration by design (i.e., the existence of many local minima in the energy landscape)21,42,43. High-resolution MFM imaging to elucidate the magnetic configurations and interactions between the array components offers the unique opportunity to better under...

Watch this Scientific Journal Video about Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains at JoVE.com

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Magnetic force microscopy (MFM) employs a vertically magnetized atomic force microscopy probe to measure sample topography and local magnetic field strength with nanoscale resolution. Optimizing MFM spatial resolution and sensitivity requires balancing decreasing lift height against increasing drive (oscillation) amplitude, and benefits from operating in an inert atmosphere glovebox.

Magnetic force microscopy (MFM) enables mapping local magnetic fields across a sample surface with nanoscale resolution. To perform MFM, an atomic force ...

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2.6K Views.  Boise State University. Magnetic Force Microscopy, of MFM, maakt gebruik van een verticaal gemagnetiseerde atomaire krachtmicroscopiesonde om monstertopografie en lokale magnetische veldsterkte met nanoschaalresolutie te meten. Door de afnemende hefhoogte in evenwicht te brengen met de toenemende amplitude van de aandrijving of oscillatie, kunnen de ruimtelijke resolutie en gevoeligheid van MFM worden geoptimaliseerd. Spin-wave computing-toepassingen van kunstmatig spinijs vertrouwen op kennis van de magnetisatietex...

Video: Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. It consists of two magnetic measurement heads on both sides of the sample mounted on the legs of a u-shaped support. The sample is locally exposed to a magnetic excitation field consisting of two distinct frequencies, a stronger component at about 77 kHz and a weaker field at 61 Hz. The nonlinear magnetization characteristics of superparamagnetic particles give rise to the generation of intermodulation products. A selected sum-frequency component of the high and low frequency magnetic field incident on the magnetically nonlinear particles is recorded by a demodulation electronics. In contrast to a conventional MPI scanner, p-FMMD does not require the application of a strong magnetic field to the whole sample because mixing of the two frequencies occurs locally. Thus, the lateral dimensions of the sample are just limited by the scanning range and the supports. However, the sample height determines the spatial resolution. In the current setup it is limited to 2 mm. As examples, we present two 20 mm &#215; 25 mm p-FMMD images acquired from samples with 1 &#181;m diameter maghemite particles in silanol matrix and with 50 nm magnetite particles in aminosilane matrix. The results show that the novel MPI scanner can be applied for analysis of thin biological samples and for medical diagnostic purposes.

A scanner for imaging magnetic particles in planar samples was developed using the planar frequency mixing magnetic detection technique. The magnetic intermodulation product response from the nonlinear nonhysteretic magnetization of the particles is recorded upon a two-frequency excitation. It can be used to take 2D images of thin biological samples.

The setup of a planar Frequency Mixing Magnetic Detection (p-FMMD) scanner for performing Magnetic Particles Imaging (MPI) of flat samples is presented. ...

Fabrication of Magnetic Nanostructures on Silicon Nitride Membranes for Magnetic Vortex Studies Using Transmission Microscopy Techniques

Electron and x-ray magnetic microscopies allow for high-resolution magnetic imaging down to tens of nanometers. However, the samples need to be prepared on transparent membranes which are very fragile and difficult to manipulate. We present processes for the fabrication of samples with magnetic micro- and nanostructures with spin configurations forming magnetic vortices suitable for Lorentz transmission electron microscopy and magnetic transmission x-ray microscopy studies. The samples are prepared on silicon nitride membranes and the fabrication consists of a spin coating, UV and electron-beam lithography, the chemical development of the resist, and the evaporation of the magnetic material followed by a lift-off process forming the final magnetic structures. The samples for the Lorentz transmission electron microscopy consist of magnetic nanodiscs prepared in a single lithography step. The samples for the magnetic x-ray transmission microscopy are used for time-resolved magnetization dynamic experiments, and magnetic nanodiscs are placed on a waveguide which is used for the generation of repeatable magnetic field pulses by passing an electric current through the waveguide. The waveguide is created in an extra lithography step.

A protocol for the fabrication of magnetic micro- and nanostructures with spin configurations forming magnetic vortices suitable for transmission electron microscopy (TEM) and magnetic transmission x-ray microscopy (MTXM) studies is presented.

Electron and x-ray magnetic microscopies allow for high-resolution magnetic imaging down to tens of nanometers. However, the samples need to be prepared ...

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

The quest to understand correlated electronic systems has pushed the frontiers of experimental measurements toward the development of new experimental techniques and methodologies. Here we use a novel home-built uniaxial-strain device integrated into our variable temperature scanning tunneling microscope that enables us to controllably manipulate in-plane uniaxial strain in samples and probe their electronic response at the atomic scale. Using scanning tunneling microscopy (STM) with spin-polarization techniques, we visualize antiferromagnetic (AFM) domains and their atomic structure in Fe1+yTe samples, the parent compound of iron-based superconductors, and demonstrate how these domains respond to applied uniaxial strain. We observe the bidirectional AFM domains in the unstrained sample, with an average domain size of ~50-150 nm, to transition into a single unidirectional domain under applied uniaxial strain. The findings presented here open a new direction to utilize a valuable tuning parameter in STM, as well as other spectroscopic techniques, both for tuning the electronic properties as for inducing symmetry breaking in quantum material systems.

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Using uniaxial strain combined with spin-polarized scanning tunneling microscopy, we visualize and manipulate the antiferromagnetic domain structure of Fe1+yTe, the parent compound of iron-based superconductors.

The quest to understand correlated electronic systems has pushed the frontiers of experimental measurements toward the development of new experimental ...

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Photonic band structure enables understanding how confined electromagnetic modes propagate within a photonic crystal. In photonic crystals that incorporate magnetic elements, such confined and resonant optical modes are accompanied by enhanced and modified magneto-optical activity. We describe a measurement procedure to extract the magneto-optical band structure by Fourier space microscopy.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by ...

Magnetic Field Mapping using Off-Axis Electron Holography in the Transmission Electron Microscope

Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by overlapping two parts of an electron wave, one of which has passed through a region of interest on a specimen and the other is a reference wave. The resulting off-axis electron hologram can be analyzed digitally to recover the phase difference between the two parts of the electron wave, which can then be interpreted to provide quantitative information about local variations in electrostatic potential and magnetic induction within and around the specimen. Off-axis electron holograms can be recorded while a specimen is subjected to external stimuli such as elevated or reduced temperature, voltage, or light. The protocol that is presented here describes the practical steps that are required to record, analyze, and interpret off-axis electron holograms, with a primary focus on the measurement of magnetic fields within and around nanoscale materials and devices. Presented here are the steps involved in the recording, analysis, and processing of off-axis electron holograms, as well as the reconstruction and interpretation of phase images and visualization of the results. Also discussed are the need for optimization of the specimen geometry, the electron optical configuration of the microscope, and the electron hologram acquisition parameters, as well as the need for the use of information from multiple holograms to extract the desired magnetic contributions from the recorded signal. The steps are illustrated through a study of specimens of B20-type FeGe, which contain magnetic skyrmions and were prepared with focused ion beams (FIBs). Prospects for the future development of the technique are discussed.

Guidelines are presented for recording and interpreting off-axis electron holograms to provide quantitative images of magnetic fields in nanoscale materials and devices in the transmission electron microscope.

Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by ...

Magnetic Tweezers in a Microplate Format

Mechanobiology describes how the physical forces and mechanical properties of biological material contribute to physiology and disease. Typically, these approaches are limited single-molecule methods, which restricts their availability. To address this need, a microplate assay was developed that enables mechanical manipulation while performing standard biochemical assays. This is achieved using magnets incorporated into a microplate lid to create multiple magnetic tweezers. In this format, force is exerted across biomolecules connected to paramagnetic beads, equivalent to a typical magnetic tweezer. The study demonstrates the application of this tool with FRET-based assays to monitor protein conformations. However, this approach is widely applicable to different biological systems ranging from measuring enzymatic activity through to the activation of signaling pathways in live cells.

Here, we describe the use of a novel microplate assay to enable mechanical manipulation of biomolecules while performing ensemble biochemical assays. This is achieved using a microplate lid modified with magnets to create multiple static magnetic tweezers across the microplate.

Mechanobiology describes how the physical forces and mechanical properties of biological material contribute to physiology and disease. Typically, these ...

Biochemistry

High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

Single-molecule magnetic tweezers (MTs) have served as powerful tools to forcefully interrogate biomolecules, such as nucleic acids and proteins, and are therefore poised to be useful in the field of mechanobiology. Since the method commonly relies on image-based tracking of magnetic beads, the speed limit in recording and analyzing images, as well as the thermal fluctuations of the beads, has long hampered its application in observing small and fast structural changes in target molecules. This article describes detailed methods for the construction and operation of a high-resolution MT setup that can resolve nanoscale, millisecond dynamics of biomolecules and their complexes. As application examples, experiments with DNA hairpins and SNARE complexes (membrane-fusion machinery) are demonstrated, focusing on how their transient states and transitions can be detected in the presence of piconewton-scale forces. We expect that high-speed MTs will continue to enable high-precision nanomechanical measurements on molecules that sense, transmit, and generate forces in cells, and thereby deepen our molecular-level understanding of mechanobiology.

Here, we describe a high-speed magnetic tweezer setup that performs nanomechanical measurements on force-sensitive biomolecules at the maximum rate of 1.2 kHz. We introduce its application to DNA hairpins and SNARE complexes as model systems, but it will be also applicable to other molecules involved in mechanobiological events.

Single-molecule magnetic tweezers (MTs) have served as powerful tools to forcefully interrogate biomolecules, such as nucleic acids and proteins, and are ...

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

This paper elaborates the sample preparation protocols required to obtain optimal domain patterns using the Bitter method, focusing on the extra steps compared to standard metallographic sample preparation procedures. The paper proposes a novel bespoke rig for dynamic domain imaging with in situ BH (magnetic hysteresis) measurements and elaborates the protocols for the sensor preparation and the use of the rig to ensure accurate BH measurement. The protocols for static and ordinary dynamic domain imaging (without in situ BH measurements) are also presented. The reported method takes advantage of the convenience and high sensitivity of the traditional Bitter method and enables in situ BH measurement without interrupting or interfering with the domain wall movement processes. This facilitates establishing a direct and quantitative link between the domain wall movement processes&#8211;microstructural feature interactions in ferritic steels with their BH loops. This method is anticipated to become a useful tool for the fundamental study of microstructure&#8211;magnetic property relationships in steels and to help interpret the electromagnetic sensor signals for non-destructive evaluation of steel microstructures.

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

This paper elaborates the sample and sensor preparation procedures and the protocols for using the test rig particularly for dynamic domain imaging with in situ BH measurements in order to achieve optimal domain pattern quality and accurate BH measurements.

This paper elaborates the sample preparation protocols required to obtain optimal domain patterns using the Bitter method, focusing on the extra steps ...

Bioengineering

Fabrication of Magnetic Platforms for Micron-Scale Organization of Interconnected Neurons

The ability to direct neurons into organized neural networks has great implications for regenerative medicine, tissue engineering, and bio-interfacing. Many studies have aimed at directing neurons using chemical and topographical cues. However, reports of organizational control on a micron-scale over large areas are scarce. Here, an effective method has been described for placing neurons in preset sites and guiding neuronal outgrowth with micron-scale resolution, using magnetic platforms embedded with micro-patterned, magnetic elements. It has been demonstrated that loading neurons with magnetic nanoparticles (MNPs) converts them into sensitive magnetic units that can be influenced by magnetic gradients. Following this approach, a unique magnetic platform has been fabricated on which PC12 cells, a common neuron-like model, were plated and loaded with superparamagnetic nanoparticles. Thin films of ferromagnetic (FM) multilayers with stable perpendicular magnetization were deposited to provide effective attraction forces toward the magnetic patterns. These MNP-loaded PC12 cells, plated and differentiated atop the magnetic platforms, were preferentially attached to the magnetic patterns, and the neurite outgrowth was well aligned with the pattern shape, forming oriented networks. Quantitative characterization methods of the magnetic properties, cellular MNP uptake, cell viability, and statistical analysis of the results are presented. This approach enables the control of neural network formation and improves neuron-to-electrode interface through the manipulation of magnetic forces, which can be an effective tool for in vitro studies of networks and may offer novel therapeutic biointerfacing directions.

This work presents a bottom-up approach to the engineering of local magnetic forces for control of neuronal organization. Neuron-like cells loaded with magnetic nanoparticles (MNPs) are plated atop and controlled by a micro-patterned platform with perpendicular magnetization. Also described are magnetic characterization, MNP cellular uptake, cell viability, and statistical analysis.

The ability to direct neurons into organized neural networks has great implications for regenerative medicine, tissue engineering, and bio-interfacing. ...

Combining 3D Magnetic Force Actuator and Multi-Functional Fluorescence Imaging to Study Nucleus Mechanobiology

A fundamental question in mechanobiology is how living cells sense extracellular mechanical stimuli in the context of cell physiology and pathology. The cellular mechano-sensation of extracellular mechanical stimuli is believed to be through the membrane receptors, the associated protein complex, and the cytoskeleton. Recent advances in mechanobiology demonstrate that the cell nucleus in cytoplasm itself can independently sense mechanical stimuli simultaneously. However, a mechanistic understanding of how the cell nucleus senses, transduces, and responds to mechanical stimuli is lacking, mainly because of the technical challenges in accessing and quantifying the nucleus mechanics by conventional tools. This paper describes the design, fabrication, and implementation of a new magnetic force actuator that applies precise and non-invasive 3D mechanical stimuli to directly deform the cell nucleus. Using CRISPR/Cas9-engineered cells, this study demonstrates that this tool, combined with high-resolution confocal fluorescent imaging, enables the revelation of the real-time dynamics of a mechano-sensitive yes-associated protein (YAP) in single cells as a function of nucleus deformation. This simple method has the potential to bridge the current technology gap in the mechanobiology community and provide answers to the knowledge gap that exists in the relation between nucleus mechanotransduction and cell function.

This study presents a new protocol to directly apply mechanical force on the cell nucleus through magnetic microbeads delivered into the cytoplasm and to conduct simultaneous live-cell fluorescent imaging.

A fundamental question in mechanobiology is how living cells sense extracellular mechanical stimuli in the context of cell physiology and pathology. The ...

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

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