Magnetic Force Microscope (MFM)

1. Theory

• Definition: A magnetic force microscope is a dynamic AFM with a magnetically coated tip that maps the stray-field force gradient above a sample at a set lift height (Park; Babcock).
• Interaction: The force on the tip is $\vec{F}={\mu }_0({\vec{m}}_{tip}\cdot \nabla )\vec{H}$, and the measured quantity is its vertical gradient, which follows the second derivative of the stray field (Schneiderbauer and Giessibl; Babcock).
• Detection: The gradient shifts the cantilever resonance, read as frequency shift (FM) or phase shift (AM) (Schneiderbauer and Giessibl; Park; Kazakova et al.).
• Separation from topography: A two-pass lift mode records topography first and then retraces it at constant height so long-range magnetic forces dominate (Park; Babcock).

2. Working Principle

• Probe: A silicon cantilever sputter-coated with a ferromagnet such as Co-Cr, magnetized along the tip axis (Babcock; Parker et al.).
• First pass: Non-contact or tapping topography (Park).
• Second pass: The tip follows the stored profile at a lift height of about 10 to 200 $\mathrm{nm}$ while the phase or frequency shift is recorded (Park; Babcock; Parker et al.).
• Optimization: Lower lift and smaller tip radius improve resolution; amplitude and lift are tuned to avoid crosstalk and tip-sample contact (Parker et al.; Park).

3. Applications

• Data storage: Imaging bits, track widths and recording heads, and local coercivity on a 100 $\mathrm{nm}$ scale (Babcock; Schneiderbauer and Giessibl).
• Spintronic and nanomagnetic devices: Artificial spin-ice arrays (Parker et al.) and domain walls in racetrack memory (Kazakova et al.).
• Materials: Ferrite distribution in duplex steel, ferrimagnetic GdFe and shape-memory Ni-Mn-Ga (Park; Parker et al.).

Magnetic Tip-Sample Interaction

Name	Formula	Related Formulae	Variables/Constants
Force on a magnetic tip	${\vec{F}}_{mag}={\mu }_0\left({\vec{m}}_{tip}\cdot \nabla \right){\vec{H}}_{sample}$	$F_z={\mu }_0{m}_z\frac{\partial H_z}{\partial z}$	${\vec{F}}_{mag}:magnetostaticforce$ ${\vec{m}}_{tip}:tipmoment$ ${\vec{H}}_{sample}:strayfield$ $\begin{array}{r}{\mu }_0:vacuumpermeability;Schneiderbauerand\\ Giessibl:vectorform;Babcock:vertical\\ componentforatipwithfixedvertical\\ momentm=m_z;Parkeretal.:Co-Crprobe\\ withnominal1\times 10^{-13}emumomentand400\mathrm{Oe}\\ coercivity\end{array}$ $\begin{array}{r}(computed:1\times 10^{-13}emuis1\times 10^{-16}A/{\mathrm{m}}^2;\\ assumed:0.1Tfielddecayingover100\mathrm{nm},\\ gradient1\times 10^{6}T/m;computed:F_z=100\mathrm{pN})\end{array}$
Force gradient	$k_{ts}=-\frac{\partial F_z}{\partial z}=-{\mu }_0{m}_z\frac{{\partial }^2{H}_z}{\partial z^2}$	$k_{eff}=k+k_{ts}$	$k_{ts}:tip-sampleforcegradient$ $k_{eff}:effectivespringconstant$ $\begin{array}{r}k:cantileverspringconstant;\\ SchneiderbauerandGiessibl:k_{t}s\\ definition;Babcock:resonancesensitive\\ tothesecondderivativeofthestray\\ fieldandtheeffectivespringconstant\\ alteredbysamplefields;Parkeretal.:\\ signalproportionaltomagnitudeandsign\\ oftheverticalforcegradient\end{array}$ $\begin{array}{r}(computed:withtheassumedfieldand100\\ \mathrm{nm}decay,k_{ts}=1\times 10^{-3}N/m)\end{array}$
Static deflection estimate	$\delta z=\frac{F_z}{k}$	$\frac{\delta z_{res}}{\delta z_{static}}\sim Q(\text{resonant enhancement})$	$\begin{array}{r}\delta z:staticdeflection;Babcock:about1\\ \mathrm{nm}non-resonantdeflectionfor1\mu \mathrm{m}\\ featuresand100\mathrm{Oe}magnetization,\\ resonantdetectionpreferred;Kazakovaet\\ al.:thephasesignalscalesas(Q/k)\sigma ,so\\ resonantdetectiongainsroughlyQ(my\\ reading)\end{array}$ $\begin{array}{r}(assumed:k=2.8N/m;computed:100\mathrm{pN}\\ deflectstheleverby0.036\mathrm{nm})\end{array}$

Detection and Lift Mode

Name	Formula	Related Formulae	Variables/Constants
Frequency shift (FM detection)	$\Delta f=\frac{f_0}{2k}⟨k_{ts}⟩$	${⟨k_{ts}⟩}_{min}=\frac{2k}{f_0}\delta \left(\Delta f\right)$	$\Delta f:frequencyshift$ $\begin{array}{r}{f}_0:freeresonance,\delta (\Delta f):frequency\\ noise;SchneiderbauerandGiessibl:qPlus\\ withk=1800N/m,f_{0}about31\mathrm{kHz},Qabout\\ 2000,A=100\mathrm{nm},B=120\mathrm{Hz},1.14\mathrm{mHz}\\ noise,minimum1.32\times 10^{-4}N/magainst\\ 4.87\times 10^{-7}N/mforacommercialMFM\\ cantilever;Babcock:0.1\mathrm{Hz}detectableon\\ a50\mathrm{kHz}resonance\end{array}$ $\begin{array}{r}(computed:1800N/mat31\mathrm{kHz}with1.14\\ \mathrm{mHz}gives1.32\times 10^{-4}N/m,matchingthe\\ source;assumedk=2.8N/m:0.1\mathrm{Hz}at50\\ \mathrm{kHz}is1.1\times 10^{-5}N/m)\end{array}$
Phase shift (AM detection)	$\Delta \varphi \approx -\frac{Q}{k}\frac{\partial F_z}{\partial z}$	$\Delta \varphi \approx \frac{Q}{k}{k}_{ts}$	$\Delta \varphi :phaseshiftinradians$ $\begin{array}{r}Q:qualityfactor;Kazakovaetal.,Eq.7:\\ \Delta \varphi \approx (Q/k)\sigma ,signsetbythephase\\ convention;ParkandBabcock:phaseor\\ amplitudeshiftsmappedastheMFMsignal\end{array}$ $\begin{array}{r}(assumed:Q=200,k=2.8N/m;computed:\\ k_{ts}=1\times 10^{-4}N/mgives7.1\times 10^{-3}\mathrm{rad},0.41\\ degrees)\end{array}$
Two-pass lift mode	$z_2\left(x,y\right)=z_1\left(x,y\right)+h_{lift}$	$h_{lift}:>30\mathrm{nm}(\text{AM}),<10\mathrm{nm}(\text{FM})$	$z_1:topographyfromthefirstpass$ $\begin{array}{r}{h}_{lift}:liftheight;Park:firstpass\\ non-contacttopography,secondpassat\\ user-definedliftfollowingtheprofile,\\ AMabove30\mathrm{nm}andFMtypicallybelow10\\ \mathrm{nm};Babcock:LiftModetypically20to200\\ \mathrm{nm};Parkeretal.:10\mathrm{nm}routinely,15\mathrm{nm}\\ onNi-Mn-Ga,startat25\mathrm{nm}andworkdown\end{array}$ $\begin{array}{r}(computed:a100\mathrm{nm}decaylengthmeans\\ each10\mathrm{nm}ofliftreducesthefieldby\\ about10percent)\end{array}$

Resolution and Practical Limits

Name	Formula	Related Formulae	Variables/Constants
Lateral resolution	$d_{MFM}\text{improves as}{h}_{lift}\text{decreases}$	$V_{mag}\uparrow :\text{sensitivity}\uparrow ,\text{resolution}\downarrow$	$d_{MFM}:resolvablemagneticfeaturesize$ $\begin{array}{r}{r}_{tip}:magnetictipradius;Babcock:\\ routinelybetterthan50\mathrm{nm},bitsassmall\\ as120\mathrm{nm};Parkeretal.:resolution\\ increaseswithdecreasinglift,tipradius\\ about35\mathrm{nm},200\mathrm{nm}domainsand250by\\ under100\mathrm{nm}barsresolved;Park:FM-MFM\\ higherresolutionthanAM;Kazakovaet\\ al.:activemagneticvolume{V}_{mag}raises\\ sensitivityandlowersresolution,and\\ largerseparationenlargestheinteraction\\ volume\end{array}$ $\begin{array}{r}(computed:Parke{r}^{\prime }s35\mathrm{nm}tipradiusis70\\ \mathrm{nm}across,belowthe100\mathrm{nm}barwidth\\ resolved)\end{array}$
Areal bit density	$D=\frac{1}{w_{bit}{l}_{bit}}$	$1{\text{in}}^2=6.4516\times 10^{-4}{\mathrm{m}}^2$	$D:bitsperunitarea$ $\begin{array}{r}{w}_{bit},l_{bit}:bitwidthandlength;\\ SchneiderbauerandGiessibl:41GBMaxtor\\ disk,about2Gbitpersquareinch(1.9\\ deduced),bitsabout200by600\mathrm{nm},decay\\ about100\mathrm{nm};Babcock:densitiesabove5\\ Gbitpersquareinchdemonstrated(seethe\\ Q/A)\end{array}$ $\begin{array}{r}(computed:200by600\mathrm{nm}gives5.4Gbit\\ persquareinch)\end{array}$
Tip perturbation of soft samples	$H_{tip}<H_{c,sample}(\text{non-perturbing})$	$H_{sample}<H_{c,tip}(\text{tip not switched})$	$H_{tip}:strayfieldofthetip$ $\begin{array}{r}{H}_c:coercivefield;Babcock:domainsin\\ softmaterialsperturbedbythetipfield;\\ Parkeretal.:400\mathrm{Oe}nominaltip\\ coercivity;Kazakovaetal.:high-moment\\ probesperturblow-coercivitydisks,\\ low-momenthigh-coercivityprobesreduce\\ switching;conditions(myreading)\end{array}$ $\begin{array}{r}(computed:400\mathrm{Oe}correspondsto{\mu }_{0}H=40\\ mT)\end{array}$

Important Questions

Ques: What force does an MFM tip feel and what is actually measured?

A magnetostatic force from the stray field, but the image shows its vertical gradient. Schneiderbauer and Giessibl write $\vec{F}={\mu }_0({\vec{m}}_{tip}\cdot \nabla )\vec{H}$, and Babcock models the tip as a fixed vertical dipole, so $F_z={\mu }_0{m}_z\partial H_z/\partial z$. Resonant detection responds to the gradient, which follows the second derivative of the field (Babcock). Parker’s Co-Cr tip has a nominal moment of $1\times 10^{-13}$ emu, $1\times 10^{-16}$ $A/{\mathrm{m}}^2$ (computed). For an assumed 0.1 T field decaying over 100 $\mathrm{nm}$, the force is about 100 $\mathrm{pN}$ and the gradient about $1\times 10^{-3}$ $N/m$ (assumed; computed). On a 2.8 $N/m$ lever, 100 $\mathrm{pN}$ deflects it only 0.036 $\mathrm{nm}$ (computed), which is why Babcock prefers resonant detection. Reference: M. Schneiderbauer and F. J. Giessibl, ‘qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution’, arXiv:1104.0528 (2011) (fetch-tool summary); K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); A. C. Parker, O. O. Maryon, M. T. Kaffash, M. B. Jungfleisch and P. H. Davis, ‘Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains’, J. Vis. Exp. 185, e64180 (2022) (fetch-tool summary).

Ques: How small a force gradient can MFM detect?

Down to about $1\times 10^{-7}$ to $1\times 10^{-4}$ $N/m$, depending on the sensor. From $\Delta f=f_0⟨k_{ts}⟩/(2k)$, Schneiderbauer and Giessibl obtain 1.14 $\mathrm{mHz}$ frequency noise for a qPlus sensor with k = 1800 $N/m$ at 31 $\mathrm{kHz}$, giving $1.32\times 10^{-4}$ $N/m$, a value the formula reproduces (computed). For a commercial MFM cantilever they give $4.87\times 10^{-7}$ $N/m$, 271 times smaller (computed), because the soft lever converts a given gradient into a much larger frequency shift. Babcock states that 0.1 $\mathrm{Hz}$ is detectable on a 50 $\mathrm{kHz}$ resonance, $1.1\times 10^{-5}$ $N/m$ for an assumed 2.8 $N/m$ lever (computed). The stiff qPlus sensor trades sensitivity for stable small-amplitude operation without the jump to contact of soft levers (Giessibl). Reference: M. Schneiderbauer and F. J. Giessibl, ‘qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution’, arXiv:1104.0528 (2011) (fetch-tool summary); K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); F. J. Giessibl, ‘Advances in atomic force microscopy’, arXiv:cond-mat/0305119 (Rev. Mod. Phys. 75, 949, 2003): soft cantilevers jump to contact, stiff sensors allow small amplitudes (fetch-tool summary).

Ques: Should the lift height be above 30 nm or as low as 10 nm?

The sources differ. Park recommends more than 30 $\mathrm{nm}$ in amplitude-modulation MFM to minimize crosstalk from surface features and below 10 $\mathrm{nm}$ only in frequency-modulation MFM, whereas Parker et al. report routinely reaching 10 $\mathrm{nm}$ on artificial spin-ice samples and 15 $\mathrm{nm}$ on Ni-Mn-Ga, starting at 25 $\mathrm{nm}$ and stepping down. Babcock gives 20 to 200 $\mathrm{nm}$ as typical. For general AM work the 30 $\mathrm{nm}$ guidance is more likely safe, while 10 $\mathrm{nm}$ is achievable on flat, well-characterized samples with careful amplitude tuning (my reading). With a 100 $\mathrm{nm}$ field decay length, each 10 $\mathrm{nm}$ reduction raises the signal by about 10 per cent and sharpens features (computed; Schneiderbauer and Giessibl). Reference: Park Systems, ‘Magnetic Force Microscopy (MFM)’, AFM modes page (fetch-tool summary); A. C. Parker, O. O. Maryon, M. T. Kaffash, M. B. Jungfleisch and P. H. Davis, ‘Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains’, J. Vis. Exp. 185, e64180 (2022) (fetch-tool summary); K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); M. Schneiderbauer and F. J. Giessibl, ‘qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution’, arXiv:1104.0528 (2011) (fetch-tool summary).

Ques: How do phase and frequency detection compare?

Both read the same gradient; FM is more direct and usually more sensitive. In AM detection the drive frequency is fixed and the phase shifts by about $\Delta \varphi \approx (Q/k)k_{ts}$ (Kazakova et al., Eq. 7); with assumed Q = 200 and k = 2.8 $N/m$, a gradient of $1\times 10^{-4}$ $N/m$ gives $7.1\times 10^{-3}$ $\mathrm{rad}$, 0.41 degrees (computed). In FM detection a phase-locked loop tracks the resonance and outputs $\Delta f=f_0{k}_{ts}/(2k)$ (Schneiderbauer and Giessibl). Park states that FM-MFM offers improved sensitivity and higher resolution, permitting lift heights below 10 $\mathrm{nm}$. Babcock notes that amplitude, phase and frequency shifts can all be mapped. Kazakova et al. describe schemes that feed back on dissipation while the frequency shift carries the conservative interaction. Reference: Park Systems, ‘Magnetic Force Microscopy (MFM)’, AFM modes page (fetch-tool summary); M. Schneiderbauer and F. J. Giessibl, ‘qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution’, arXiv:1104.0528 (2011) (fetch-tool summary); K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); O. Kazakova et al., ‘Frontiers of magnetic force microscopy’, J. Appl. Phys. 125, 060901 (2019), Royal Holloway preprint: phase shift Delta phi = pi/2 - arctan(k/(Q sigma)) approx (Q/k) sigma (Eq. 7), Delta omega approx -omega0 sigma/(2k) (Eq. 10), active magnetic volume proportional to sensitivity and inversely to resolution, larger separation increases interaction volume and lowers signal, high-moment probes perturb low-coercivity disks, low-moment high-coercivity probes reduce switching, difference images with oppositely magnetized probes, dissipation feedback separating conservative frequency shift, racetrack memory (fetch-tool summary).

Ques: What lateral resolution does MFM reach?

Typically tens of nanometres, limited by lift height and tip size. Babcock states resolution is routinely better than 50 $\mathrm{nm}$ and shows bits as small as 120 $\mathrm{nm}$. Parker et al. resolved 200 $\mathrm{nm}$ domains in Ni-Mn-Ga and bar magnets about 250 $\mathrm{nm}$ long and under 100 $\mathrm{nm}$ wide with a tip of about 35 $\mathrm{nm}$ radius, and state that resolution improves as lift height decreases. Kazakova et al. add that a larger active magnetic volume raises sensitivity but lowers resolution, so tip size is a trade-off. Park attributes higher resolution to FM operation at low lift. At larger separation the interaction volume grows and the signal falls (Kazakova et al.), so fine patterns need low lift. Reference: K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); A. C. Parker, O. O. Maryon, M. T. Kaffash, M. B. Jungfleisch and P. H. Davis, ‘Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains’, J. Vis. Exp. 185, e64180 (2022) (fetch-tool summary); Park Systems, ‘Magnetic Force Microscopy (MFM)’, AFM modes page (fetch-tool summary); O. Kazakova et al., ‘Frontiers of magnetic force microscopy’, J. Appl. Phys. 125, 060901 (2019), Royal Holloway preprint: phase shift Delta phi = pi/2 - arctan(k/(Q sigma)) approx (Q/k) sigma (Eq. 7), Delta omega approx -omega0 sigma/(2k) (Eq. 10), active magnetic volume proportional to sensitivity and inversely to resolution, larger separation increases interaction volume and lowers signal, high-moment probes perturb low-coercivity disks, low-moment high-coercivity probes reduce switching, difference images with oppositely magnetized probes, dissipation feedback separating conservative frequency shift, racetrack memory (fetch-tool summary).

Ques: Does a 200 by 600 nm bit match the stated 2 Gbit per square inch?

Not exactly. Schneiderbauer and Giessibl image a 41 GB Maxtor disk with a stated density of about 2 Gbit per square inch, 1.9 deduced from their data, and an approximate bit size of 200 by 600 $\mathrm{nm}$. A 200 by 600 $\mathrm{nm}$ cell gives 5.4 Gbit per square inch (computed), almost three times higher. The stated density is more likely correct, because it is deduced from the measured track and bit pitch and fits drives of that capacity; the bit dimensions probably describe the magnetized region without guard bands and track spacing (my reading). Babcock, writing earlier, reports densities above 5 Gbit per square inch and 120 $\mathrm{nm}$ bits in test media, so MFM resolves either scale comfortably. Reference: M. Schneiderbauer and F. J. Giessibl, ‘qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution’, arXiv:1104.0528 (2011) (fetch-tool summary); K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places).

Ques: Can the MFM tip disturb the sample it images?

Yes, in soft magnetic materials. Babcock warns that domains in magnetically soft materials can be perturbed by the tip stray field. Kazakova et al. show a high-moment probe perturbing a low-coercivity nickel disk, and use low-moment, high-coercivity probes to reduce tip switching. Parker’s Co-Cr probes have a nominal coercivity of 400 $\mathrm{Oe}$, a field of 40 mT (computed), adequate for most thin-film domains. Remedies include low-moment tips and difference images taken with oppositely magnetized probes (Kazakova et al.). Babcock also notes that topography can contaminate magnetic data, the reason for lift mode, and that noncontact methods risk destructive tip crashes. Parker et al. report that drive amplitude settings need care: they give about 500 $\mathrm{mV}$ for 50 $\mathrm{nm}$ oscillation in the text but 250 $\mathrm{mV}$ in a figure caption. Reference: K. Babcock, ‘Magnetic force microscopy: High-resolution imaging for data storage’, Digital Instruments, Data Storage (1994) (fetch-tool summary; OCR-garbled in places); A. C. Parker, O. O. Maryon, M. T. Kaffash, M. B. Jungfleisch and P. H. Davis, ‘Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains’, J. Vis. Exp. 185, e64180 (2022) (fetch-tool summary); O. Kazakova et al., ‘Frontiers of magnetic force microscopy’, J. Appl. Phys. 125, 060901 (2019), Royal Holloway preprint: phase shift Delta phi = pi/2 - arctan(k/(Q sigma)) approx (Q/k) sigma (Eq. 7), Delta omega approx -omega0 sigma/(2k) (Eq. 10), active magnetic volume proportional to sensitivity and inversely to resolution, larger separation increases interaction volume and lowers signal, high-moment probes perturb low-coercivity disks, low-moment high-coercivity probes reduce switching, difference images with oppositely magnetized probes, dissipation feedback separating conservative frequency shift, racetrack memory (fetch-tool summary).

References

1. M. Schneiderbauer and F. J. Giessibl, “qPlus Magnetic Force Microscopy in Frequency-Modulation Mode with milli-Hertz Resolution,” arXiv:1104.0528, 2011. Available: https://arxiv.org/pdf/1104.0528
2. K. Babcock, “Magnetic force microscopy: High-resolution imaging for data storage,” Digital Instruments, reprinted from Data Storage, PennWell, 1994. Available: https://ftp.mirrorservice.org/sites/www.bitsavers.org/pdf/santaClaraUniversity/IIST/Babcock_-_Magnetic_Force_Microscopy_1994.pdf
3. A. C. Parker, O. O. Maryon, M. T. Kaffash, M. B. Jungfleisch and P. H. Davis, “Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains,” Journal of Visualized Experiments, no. 185, e64180, 2022. Available: https://par.nsf.gov/servlets/purl/10396717
4. O. Kazakova, R. Puttock, C. Barton, H. Corte-Leon, M. Jaafar, V. Neu and A. Asenjo, “Frontiers of magnetic force microscopy,” Journal of Applied Physics, vol. 125, 060901, 2019; preprint. Available: https://pure.royalholloway.ac.uk/files/33330230/Frontiers_of_MFM_PrePrint.pdf
5. F. J. Giessibl, “Advances in atomic force microscopy,” Reviews of Modern Physics, vol. 75, pp. 949-983, 2003; arXiv:cond-mat/0305119. Available: https://arxiv.org/pdf/cond-mat/0305119v1
6. Park Systems, “Magnetic Force Microscopy (MFM),” AFM modes page. Available: https://www.parksystems.com/en/products/research-afm/AFM-modes/Special-Modes/magnetic-force-microscopy—mfm-

Related pages in this vault: Atomic Force Microscope (AFM), Kelvin Probe Force Microscope (KPFM), Magnetic Materials and Magnetic Circuits, Magnetoresistive Random Access Memory (Toggle and STT-MRAM), Piezoresponse Force Microscope (PFM), Scanning Microwave Impedance Microscope (sMIM), Scanning Spreading Resistance Microscope (SSRM), Toggle Magnetic Random Access Memory (Toggle MRAM), Spin-Orbit Torque Magnetic Random Access Memory (SOT-MRAM), Spin-Transfer Torque Magnetic Random Access Memory (STT-MRAM), Voltage-Controlled Magnetic Anisotropy MRAM (VCMA-MRAM).