Nanoscale magnetization and current imaging using scanning-probe magneto-thermal microscopy
Chi Zhang, Jason M. Bartell, Jonathan C. Karsch, Isaiah Gray, Gregory D. Fuchs
NNanoscale magnetization and current imaging usingscanning-probe magneto-thermal microscopy
Chi Zhang, Jason M. Bartell, Jonathan C. Karsch, Isaiah Gray, and Gregory D. Fuchs ∗ School of Applied and Engineering Physics,Cornell University, Ithaca, NY, United States.
Abstract
Magnetic microscopy that combines nanoscale spatial resolution with picosecond scale temporalresolution uniquely enables direct observation of the spatiotemporal magnetic phenomena that arerelevant to future high-speed, high-density magnetic storage and logic technologies. Magnetic mi-croscopes that combine these metrics has been limited to facility-level instruments. To address thisgap in lab-accessible spatiotemporal imaging, we develop a time-resolved near-field magnetic mi-croscope based on magneto-thermal interactions. We demonstrate both magnetization and currentdensity imaging modalities, each with spatial resolution that far surpasses the optical diffractionlimit. In addition, we study the near-field and time-resolved characteristics of our signal and findthat our instrument possesses a spatial resolution on the scale of 100 nm and a temporal resolu-tion below 100 ps. Our results demonstrate an accessible and comparatively low-cost approach tonanoscale spatiotemporal magnetic microscopy in a table-top form to aid the science and technologyof dynamic magnetic devices with complex spin textures. a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b dvanced magnetic microscopies are a key tool for advancing our understanding of novelmagnetic phenomena such as skyrmions, spinwaves, and domain walls [1–3]. Imaging thesephenomena increasingly requires 10-100 nanometer spatial resolution [1, 4–7] and 10-100picosecond temporal resolution [8, 9]. Simultaneously achieving both resolutions enablesstudy of both static and dynamic nanoscale magnetic textures that are interesting for high-performance technology, such as skyrmion dynamics and spin torque oscillators [10–12]. Un-fortunately, most magnetic microscopies offer either nanoscale spatial resolution or picosec-ond temporal resolution, but not both. The techniques with both of these characteristicsinclude x-ray based microscopes [13] which require a synchrotron facility, and time-resolvedelectron microscopes [14, 15] which are expensive and not widely available. No low-cost andwidely accessible tabletop techniques currently exist.To break free of the optical diffraction limit while retaining the stroboscopic imagingcapabilities offered by pulsed lasers, our approach is to use picosecond thermal pulses gener-ated by a near-field probe-sample interaction. Recently we have demonstrated time-resolvedmagneto-thermal microscopy, with picosecond temporal resolution and spatial resolutiondetermined by focused light [16–18]. In this technique, a focused light pulse generates amicroscale thermal gradient. Through the anomalous Nernst effect, the local magnetizationis transduced into a voltage. This approach has proven to be useful for imaging both localstatic and dynamic magnetization [16], as well as an applied current density [18]. It hasalso been applied to a wide range of materials beyond magnetic metals such as magneticinsulators [17] and antiferromagnets [16, 19–22] using the longitudinal spin Seebeck effect.The spatial resolution of time-resolved magneto-thermal microscopy can be further extendedto the nanoscale using a scanning probe for near-field excitation. We note a parallel work toours uses near-field magneto-thermal effects in a similar way with a continuous wave thermalgradient for detecting static magnetizations [22, 23].Here we demonstrate the spatiotemporal near-field magneto-thermal microscope for mag-netization and applied current density imaging. We confirm the near-field character of thesignal by its probe-sample distance dependence. By imaging current density around a nano-constriction that provides a well-controlled nanoscale feature, we demonstrate 100-nm-scalespatial resolution. We also verify the stroboscopic capabilities of the microscope by directlymeasuring a gigahertz frequency current density as a function of oscillation phase. Theseresults provide a table-top solution to nanoscale spatiotemporal magnetic microscopy aimed2t emerging complex nanoscale magnetic phenomena. RESULTSPrinciples of scanning magneto-thermal microscopy
Here, we introduce the operating principles of our scanning near-field magneto-thermalmicroscope. We organize them into three key elements: the magneto-thermal effect and itsextensions at the sample under local heating, the scanning probe that measures topography,and the near-field interaction between the illuminated tip and sample. We first discuss theprinciples of magneto-thermal microscopy (Fig. 1a) based on measuring thermally inducedelectric fields described by, E ANE ( x , t ) + E J ( x , t )= − N m ( x , t ) × ∇ T ( x , t ) + J ( x , t ) ∆ ρ ( ∆ T, x , t ) . (1)To experimentally access these effects, we apply a pulsed laser, either directly focused ornano-confined by the near-field tip, to create a transient local temperature increase, ∆ T , anda corresponding local gradient ∇ T . The local magnetization m subjected to ∇ T generatesan electric field E ANE through the anomalous Nernst effect (ANE) [24–26], with coefficient N [the first term of equation (1)]. Throughout this paper, we study in-plane magnetization,therefore the vertical thermal gradient from the laser dominates these signals. The deviceANE voltage produced from the local E ANE is proportional to the x projection of magne-tization of the sample within the thermally excited region (Fig. 1a). The second term ofequation (1) provides an extension of this technique to image current density. E J arisesfrom a current density J passing through the thermally excited sample volume with locallyincreased resistivity ∆ ρ . Ohm’s law requires an extra electric field E J = J ∆ ρ , which istime-dependent due to the picosecond transience of laser heating of thin metal films [18].These two signals combine to form a voltage pulse train that we amplify and demodulateby mixing it with an electrical reference pulse train [16, 18]. The voltage is then measuredby lock-in amplifiers. See Methods for more details on the electrical and optical circuits.For the scanning probe, we use a tuning fork-based atomic force microscope (AFM)in tapping mode. We use probe frequency feedback to maintain an average probe-sample3 ample V M ∆ E ANE FM T Sapphire sub. (a) (b) z y x FIG. 1. Experimental schematics. (a) Schematic of the scanning near-field magneto-thermal mi-croscope illustrating the configuration of the scan probe, the laser and the anomalous Nernst effect(ANE) in the ferromagnetic (FM) sample. (b) The near-field enhancement of the electric fieldgenerated by an optical pulse locally heats the sample in a region with size comparable to theradius of tip apex. The colors on the sample represent contours of temperature increase due tonear-field heating as discussed in Ref. [27]. separation. The probe is a gold-coated Si cantilever glued to a tuning fork. The tip radiusis 30 nm as received, which gets broader with scanning and reaches 50 nm or more bythe time we complete the alignment procedure and record data. The probe oscillates atthe tuning fork resonance frequency f = 32 kHz with a typical amplitude of 40 nm. Weilluminate the tip apex with laser pulses (p-polarized, angle of incidence 30 ○ , laser fluence1 mJ/cm with a 76 MHz repetition rate) from a Ti:sapphire laser (3-ps-wide, wavelength λ = 785 nm), focused using a microscope objective (numerical aperture NA = 0.42). Thenear-field interaction enhances the electric field in a region confined at the tip apex [28–31](Fig. 1b). This electric field heats the sample similarly to the focused laser, now as ananoscale heat source. The resultant heating profile is confined to an area comparable tothe tip radius, below 100 nm [27]. In the measurement, the light falls onto both the sampleand the tip. The focused light and the scanning probe near-field excitation both generatethermal profiles that induce “far-field” and “near-field” signals, respectively. We separatethese contributions using lock-in detection. To recover the far-field signal, we demodulateat the 2 kHz frequency of the laser chopper. To recover the near-field signal, we use the factthat near-field interactions drop off exponentially with increasing tip-sample distance on the4rder of the tip radius [29]. As the probe oscillates, this nonlinearity creates a modulation atthe probe frequency and harmonics (2 f , 3 f , etc. ). We throughout the paper demodulate thenear-field signal at the second harmonic of the probe frequency. Because some far-field lightcan be reflected or shadowed by tip probe motion, the first harmonic contains a mixture ofnear- and far-field signals. The far-field contributions are linear, however, and thus they arelargely suppressed in the 2 f demodulation channel [29, 32, 33]. Magnetic and current measurements with scanning near-field probe
In this section, we demonstrate that a scanning near-field magneto-thermal probe candetect local magnetization and current density. We study a 5 µ m x 12 µ m CoFeB (4nm)/Hf (2 nm)/Pt (4 nm) sample fabricated using photolithography [18]. A Pt capping layeras a thermal transduction layer improves uniform resolution when using different samplematerials underneath [27]. To align the tip and sample, we first scan the sample (on ascanning xy stage) using topography in standard AFM mode. Then, with the tip retracted,we align the laser to the same features on the sample using the far-field magneto-thermalsignal as in a conventional magneto-thermal microscope except here with a 30 ○ incidentangle. This process coarsely aligns the laser with the tip. We then approach the tip to thesurface and adjust the laser position to maximize the near-field signal.In Fig. 2a we show near-field imaging of a uniform magnetic state. We apply a satu-rating magnetic field perpendicular to the channel and measure near-field line scans acrossthe sample width as depicted in the schematic in Fig. 2b. The near-field signal changessign with magnetization direction, which demonstrates that we sense magnetic orientation.We note that the signal crosses zero and then decays at the sample edges rather than ap-proaching zero sharply. This is because there are some artifact signals getting into the 2 f demodulation channel. The amount of artifact varies from tip to tip, and could dependon tip sharpness and the slight misalignment between the laser and tip [see SupplementaryNote 2 for more discussions on artifacts]. In Fig. 2b, we apply DC current through thesample to measure near-field linecuts of current density. With the application of a 1.5 mAcurrent, in addition to some remnant magnetic signal [Equation (1)], the contribution fromcurrent density dominates the total signal. The near-field signal changes sign with currentpolarity, which confirms that the signal is sensitive to current density.5 N ea r- f i e l d s i gna l ( µ V ) Position ( µ m) Positive current Negative current -4-2024 N ea r- f i e l d s i gna l ( µ V ) Position ( µ m) Positive magnetic field Negative magnetic field -202 N ea r- f i e l d s i gna l ( µ V ) Position ( µ m) -4000400 F a r- f i e l d s i gna l ( µ V ) (a) (b) Laser
Probe
AFM topography
Far - field image Near - field image µ m (c) (d) (e) µV - nm µV - µV - Topography
Near
Far
FIG. 2. Line scans and magnetic multi-domain imaging. Near-field line scans across the samplewidth at opposite (a) magnetization orientations and (b) applied current polarity. (a) and (b)show forward and backward line traces indicated by the inset in (b). (c) Magnetic far-field imagesof a multi-domain state. With a scanning probe tip, (d) images and (e) representative linecuts oftopography, far-field and near-field images acquired simultaneously with the scanning probe.
Next, we demonstrate magnetic imaging of a multi-domain state. We demagnetize thesample using a series of minor loops with reducing field extent. First imaging without the tip,Fig. 2c shows a focused-light far-field image demodulated with respect to the optical chopper6hat shows magnetic domains in low resolution. In the dashed square region shown in Fig.2c, Fig. 2d,e show images and representative linecuts of tuning fork-AFM topography,the chopper referenced far-field signal, and the probe referenced near-field signal, acquiredsimultaneously with the scanning probe. We see that the near-field image agrees well withthe known far-field domain image, but has higher resolution. To estimate the characteristiclength of the near-field features, we fit a linecut across the domain wall to C ( + erf ( x − x √ δ )) ,with the full-width at half maximum (FWHM) of the curve given by 2 √ ln δ . The fit shownin Fig. 2e yields a width of 455 nm even at a 37 ○ angle with the domain wall direction, whichis below the optical diffraction limit of the set-up, approximately λ /(2 NA) = 1402 nm (NA= 0.28 used for Fig. 2c-e only). However, we expect the domain wall width of this materialto be wide due to its low anisotropy. The domain wall width δ = π √ AK u depends on theexchange stiffness A as compared to anisotropy K u , the in-plane uniaxial anisotropy in thisconfiguration. The in-plane uniaxial anisotropy of CoFeB is known to be weak or negligible[34–36]. Therefore, the feature size in this sample is likely limited by the actual domain wallwidth rather than the instrument resolution. We further characterize instrument resolutionin subsequent current imaging measurements.Here we discuss the sensitivity of the near-field scanning probe for magnetic and currentsignals. For magnetic signals, we use the standard deviation of the noise in the ANE voltage δ ANE , and our largest size V ANE,sat at saturated magnetization in the 5 µ m CoFeB. Themagnetization angle sensitivity is calculated using θ min = δ ANE V ANE,sat √ T C [16], where
T C is thelock-in time constant, and is estimated to be θ min = 4 . ○ /√ Hz for a 5 µ m-width sample. Thisis less sensitive than we have achieved with the conventional focused light magneto-thermalsetup, however, we note that the sensitivity is dependent on several factors including thesample impedance, the Nernst coefficient, and the sample width. The signal scales inverselywith the sample width due to the effective resistance shunting, and therefore the near-fieldscanning probe is most suitable for studying samples ≤ µ m wide. For current signalsensitivity, using the near-field signal at an applied current of 1.5 mA (Fig. 2b) and thestandard deviation of the noise, we estimate the current density sensitivity to be 3.57 × A/(m √ Hz) for a 5 µ m-width sample. The current density signal again scales inversely withthe sample width, and with better sensitivity in narrower-width devices. We note that weobtain better sensitivity to current density using the narrow channel sample discussed insubsequent current imaging measurements. 7 .60.40.20.0 ∆ f ( H z ) Tip-sample distance (nm) P r obe a m p li t ude ( V ) N ea r- f i e l d s i gna l ( µ V ) Magnetic + Current signal at -1mA Magnetic signal at 0mA
Probe frequency Probe amplitude (a) (b)
FIG. 3. Near-field characteristics. Tip-sample distance dependence of (a) near-field signals and(b) probe parameters (probe frequency and amplitude).
Near-field origin of the signal
Next we examine how the signal depends on tip-sample separation to study the origin ofour signals. Near-field interactions are only non-negligible when the tip is at short distancesfrom the sample, on the order of tip radius [29]. We measure both magnetic and currentsignals collected from the probe-demodulated lock-in as we bring the dynamically tapping tipclose to the sample. In our configuration, the laser is pre-aligned to the sample when the tipis approached, and the tip-sample displacement is controlled by retracting or approaching thetip. A near-field contribution drops off over nanoscale distances, while a far-field contributiondrops off with microscale displacements corresponding to the laser intensity distribution [32].We simultaneously measure the near-field signals as well as probe parameters for tip-heightcharacterization. Figure 3 shows that the near-field signals increase when the tip is in firstcontact with the sample, indicated by an initial increase of the frequency and decrease of theamplitude. The 100 nm short-range increase of the signal is consistent with the near-fieldinteraction [29]. In addition, Fig. 3a shows that the far-field artifact is largely suppressedwith demodulation of the signal at 2 f . 8 N ea r- f i e l d s i gna l ( µ V ) -1.0 0.0 1.0 Y position ( µ m) -150-100-500 F a r- f i e l d s i gna l ( µ V ) -1.0 0.0 1.0 Y position ( µ m) -10-50 10 (a) (b)(c) (d) J Neck Center of disk
FIG. 4. Current imaging and spatial resolution. (a) Topography and (b) current density imagesacquired by a near-field tip. The scale bar in (a) is 1 µ m. The inset of (a) is a wider field of view.Line cuts through two necks (as illustrated by the dashed line in the inset of (a)) of (c) far-fieldand (d) near-field signals for resolution comparison. (d) Inset: pure current density contributionobtained by computing the half difference of data acquired for positive and negative currents. Theline is a fit to the data with width δ = 74 nm. Details of the fit are given in the SupplementaryNote 1. Spatial resolution by current imaging
We further characterize the spatial resolution of the instrument by designing sampleswith sharp features suitable for benchmarking the spatial resolution. Here, we measurein current imaging mode, because current distributions can be designed and implementedthrough sample patterning. We use a new sample designed with narrow constrictions thatconfine the current density in a width comparable to the tip dimension. The sample is aNi Fe (5 nm)/Ru (2 nm) film, fabricated using e-beam lithography into a 2 µ m-diameter9isk with two 150 nm wide necks (Fig. 4a inset). Figure 4a,b show topography and near-field current density images taken with the near-field scanning probe, at an applied currentof -0.03 mA [see Supplementary Fig. 1c for data at opposite current]. The scan area onthe sample is 2 µ m x 2 µ m and we use a lock-in time constant of 200 ms. We see thatthe current density is indeed concentrated at the neck. By measuring line scans throughtwo necks (Fig. 4a inset), we compare signals between focused light far-field (Fig. 4c) andscanning probe near-field (Fig. 4d) microscopy. In Fig. 4c, we measure this sample in ourconventional magneto-thermal microscope [16–18] that uses directly focused light (angle ofincidence 90 ○ , numerical aperture of 0.9). By fitting the peak with a Gaussian function, theextracted FWHM resolution of 740 nm is consistent with the focused light setup resolution[16]. In Fig. 4d, the scanning near-field data has higher resolution than the far-field data.In addition, since the sample geometry is asymmetric around the neck, we expect the peakto be asymmetric, which is seen in the near-field signal.Now we estimate a spatial resolution from Fig. 4d. Based on a sharp feature in the linescan (the left side drop-off of the right side peak), the signal makes a full scale change involtage over ∼
100 nm, which qualitatively gives us a resolution on the level of 100 nm. Toquantitatively extract spatial resolution, we simulate the current density distribution aroundthe neck using COMSOL [see Supplementary Note 1 and Supplementary Fig. 1a], andconvolve it with a Gaussian point spread function, converted to voltage. We fit the simulatedresult to our data, with a Gaussian width δ as the fitting parameter. The representative fitgives δ = 74 nm (corresponding to a FWHM of 165 nm). This resolution is less than 1/4of our focused light magneto-thermal microscopy resolution with highest NA [16], which isconsistent with the sub-diffraction resolution of near-field microscopy. In our prior work inRef. [27], the spatial resolution for a near-field tip was simulated; for a tip radius of 45 nm(90 nm in diameter), the FWHM of the thermal gradient is 115 nm for magnetic imaging [27].Here, we note that the experimentally extracted value is for current imaging (determined bytemperature increase ∆ T ), not a magnetic measurement (determined by thermal gradient ∇ T ) [16, 18, 27]. A magnetic spatial resolution is likely higher than current [16], thereforebelow the extracted value. Based on the prior simulation in Ref. [27], we estimate the tipradius when we take the data to be 65 nm, which is consistent with the scanning electronmicroscope image of the tip taken after the measurements. We note that the resolution hereis only an upper bound and that it depends on the tip sharpness at the time of scanning.10 N ea r- f i e l d s i gna l ( µ V ) ϕ (degree) -101 N o r m a li z ed c u rr en t den s i t y f = 3.5 GHz -15-10-50510 N ea r- f i e l d s i gna l ( µ V ) -800 -400 0 400 800 Delay time (ps)
Positive current
Negative current -6-4-2024 N ea r- f i e l d s i gna l ( µ V ) -800 -400 0 400 800 Delay time (ps)
Positive field Negative field (a) (b) (c)
FIG. 5. Stroboscopic measurements of microwave current. Time-domain measurements of thenear-field voltage pulses produced by (a) current density (measured at the neck of the Ni Fe sample) and (b) magnetization (measured at the center of the CoFeB sample) as a function ofthe pulse delay τ between the voltage pulses generated at the sample and the 100 ps referencepulses. A pulse delay of zero corresponds to the two pulse trains entering the mixer at the sametime. The feature that follows the main peak is due to electrical reflections in the detection circuits[16, 17] (c) The normalized microwave current density at the neck of Ni Fe sample measuredas a function of ϕ stroboscopically probed by the thermal pulses. The red curve is a sinusoidalfit. The near-field signal is vertically offset to subtract the static magnetic signal contribution,obtained from the sinusoidal fitting. Temporal resolution and dynamics
With 3 ps laser pulses, the instrument temporal resolution to probe magnetization (cur-rent density) is determined by the temporal width of the generated thermal gradient ∇ T (temperature increase ∆ T ) [16]. In prior work using focused light magneto-thermal mi-croscopy, finite-element simulation showed that the thermal gradient pulse has a width of ∼
10 ps. An experimental observation of magnetization resonance up to 16.4 GHz verified anupper bound of temporal resolution at or below 30 ps [16]. For thermal gradients generatedby a near-field tip, the finite-element simulation gave a temporal width within 6 ps [27].Therefore, whether the excitation is from a far-field or near-field source, the picosecond-scale temporal resolution are expected to be similar. Here we experimentally examine thestroboscopic temporal properties of near-field magneto-thermal microscopy.Figure 5a,b show a measurement of the picosecond-scale voltage pulses that are directlycreated in response to a transient ∆ T or ∇ T in the presence of an applied current density ora static magnetization [16]. The short-lived thermal excitation of the sample is the origin of11he stroboscopic time dependence of magneto-thermal microscopy. We measure the pulsesby combining them in an electrical mixer with 100 ps electrical reference pulses that aresynchronized with the laser but have a controllable delay τ . The mixer output represents atime-domain heterodyning of the V ANE pulses, where we detect the component mixed downto DC but still containing the slower lock-in modulation [16, 18]. Figure 5a,b show themixed output voltage as a function of the delay τ , which can be understood as the temporalconvolution signal of the voltage pulses with the reference pulses [16]. In both plots, theconvolved signal widths are roughly 100 ps, similar to the reference pulse width. Therefore,the voltage pulses generated by the near-field thermal excitations must be shorter than 100ps, demonstrating a time-resolved nano-probe.In Fig. 5c, we also demonstrate a stroboscopic capability of the scanning probe to measurecurrent density with temporal resolution that significantly exceeds the oscillation period of a3.5 GHz current applied directly to our device. To make this measurement, we synchronizethe laser and microwave current by choosing a frequency at an integer multiple of the laserrepetition rate such that the thermal pulses constantly probe the current at the same phase, ϕ [16, 18]. Here, ϕ is a relative phase between the microwave current and the laser with a phaseoffset that depends on frequency and initial conditions. Time-resolved measurements ofcurrent imply that we can use our near-field microscope to make phase-sensitive observationsof microwave current within a nanoscopic volume. Fig. 5c shows normalized microwavecurrent density as a function of ϕ , showing the phase-sensitive response. As we rotate ϕ , weobserve the expected sinusoidal response in the near-field signal. DISCUSSION
In conclusion, we demonstrate scanning near-field magneto-thermal microscopy of mag-netization and current density using picosecond thermal pulses. This work represents an im-portant milestone for low-cost, table-top magnetic microscopy that unifies nanoscale spatialresolution with picosecond temporal resolution in the same instrument. Here we experimen-tally image magnetic domains with nanoscale resolution, and we verify the near-field originof both magnetic and current density contrast with a spatial resolution on the scale of 100nm. Additionally, we demonstrate picosecond-scale temporal resolution of current densityand magnetization, enabling a stroboscopic nanoscale probe of emerging magnetic devices in12hich we can directly probe both a stimulus and its response. For example, nanoscale phase-sensitive imaging could be useful for understanding mechanisms and phase-relationships inmutual synchronization locking of spin-orbit torque oscillators [12]. Meanwhile, the capabil-ity to image current from DC to microwave frequencies could clarify the origins of magneticresonances in spatially non-uniform spin-Hall nano-devices [37].We are optimistic that scanning probe magneto-thermal microscopy can be further de-veloped into a powerful tool to study the dynamics of nanoscale magnetic devices and spintextures. For example, the spatial and temporal resolution of our microscopy is compatiblewith measuring magnetic resonance from a single magnetic skyrmion, rather than from an en-semble [10]. Furthermore, magneto-thermal microscopy is compatible with a wide palette ofmagnetic materials beyond magnetic metals, including ferrimagnetic magnetic insulators [17]and antiferromagnetic insulators [19] (via the spin Seebeck effect), thus offering a versatileimaging tool. Scanning probe magneto-thermal microscopy is especially suitable for deviceswith sub-micron channel widths, and using materials that have strong magneto-thermal ef-fects. Indeed, improving the sensitivity of this instrument will be the most important stepforward in its future development. The magnetization sensitivity can be further improvedthrough optimization of the instrument ( e.g. detection electronics, impedance matching,probe amplitude optimization [29], tip sharpness) and through incorporation of near-fieldengineering (including a plasmonic coupling grating [32, 38–40]).
METHODSOptical excitation of near-field scanning tip
Figure 6a shows the optical path used to illuminate the probe tip in our scanning magneto-thermal microscope. A Ti:sapphire laser (Coherent MIRA 900) generates 3 ps pulses witha 76 MHz repetition rate and a 785 nm wavelength. The light first passes through a Fara-day isolator, a mechanical chopper (2 kHz), and a polarizer before being coupled into apolarization maintaining (PM) single mode (SM) fiber. The fiber carries the light into theenclosure of the scanning magneto-thermal microscope. The light that emerges from thefiber is collimated and sent through another polarizer and waveplate combination to ensurethat the light is p-polarized. We then focus the laser onto the scanning probe tip apex using13 ixer
LIA 1
LIA 2
Probe motion near - field Optical chopper far - field AWG
Synchronize to laser
Sample (a) (b)
FIG. 6. Optical setup and electrical circuits. (a) Schematic of the optical path used in the scanningmagneto-thermal microscopy. The outer solid boxed area outlines the enclosure. The inner dashedboxed area is the optical microscope used to image the tip and sample through the objective. Theobjective, beam splitter, half-waveplate, polarizer, and fiber collimator are mounted on a xyz -translation stage at an angle of 30 ○ to the sample surface. (b) Schematic of electric circuits fordetection in scanning magneto-thermal microscopy. a microscope objective with a 20 mm working distance and 0.42 NA. A beam expander andcamera are used to image the probe set-up to enable alignment of the laser, tip, and sample. Electrical detection
The electrical circuits are the same as those of the focused light magneto-thermal micro-scope [16, 18]. The voltage pulses generated at the sample are collected into a microwave14ransmission line and amplified by 40 dB with 3 GHz bandwidth. The amplified pulsesare then detected by mixing them in a DC-12 GHz mixer with 1.2 ns-duration electricalreference pulses, generated by an arbitrary waveform generator (AWG) that is referenced tothe laser repetition rate. (For data in Fig. 5a,b, different amplifiers with 15 GHz bandwidthand pulses of 100 ps width - the shortest reference pulses that can be produced by the AWG- are used for the temporal upper bound characterization.) This technique demodulates thepulsed signal at the laser repetition frequency. This approach is similar to the homodynedetection used in a lock-in amplifier (LIA), except instead of using a single frequency si-nusoidal reference signal, here we use a synchronous pulse train to demodulate the sum ofmultiple harmonics of laser repetition frequency, therefore recovering a larger demodulatedsignal. The voltage is sent to lock-in amplifiers which demodulate the signal at probe motionand chopper frequencies, respectively.
ACKNOWLEDGMENTS
We thank Dr. Long Ju, Dr. Samuel Berweger, and Harry Cheung for helpful discus-sions. Time-resolved and current imaging studies were supported by the DOE Office ofScience, Basic Energy Sciences (DE-SC0019997). Preliminary development and static mag-netic imaging was supported by the AFOSR (FA9550-14-1-0243). This work made use ofthe Cornell Center for Materials Research Shared Facilities which are supported throughthe NSF MRSEC program (DMR-1719875), and the Cornell NanoScale Facility, a memberof the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported bythe National Science Foundation (Grant NNCI-2025233).
AUTHOR CONTRIBUTIONS
G.D.F. and J.M.B. conceived the idea of the microscopy. J.M.B., J.C.K. and C.Z. built theapparatus. C.Z. and J.M.B. developed the instrument and acquired the data with assistancefrom I.G. C.Z. designed, fabricated the samples and performed numerical simulations. C.Z.and G.D.F. prepared the manuscript and all authors revised the manuscript.15 upplementary InformationNanoscale magnetization and current imaging usingscanning-probe magneto-thermal microscopy
SUPPLEMENTARY NOTE 1: CURRENT DENSITY DISTRIBUTION AND SPA-TIAL RESOLUTION EXTRACTIONA. Current density distribution
We simulate current density distribution around the neck (the tapered junction at thebase of the Ni Fe disk) for quantitatively extracting the resolution. The neck has a150 nm width, as shown in the atomic force microscopy (AFM) image in SupplementaryFigure 1(a) inset. We set the sample geometry in COMSOL closest to the real AFM profile[Supplementary Figure 1(a) inset]. We apply a current of 0.03 mA in the simulation, andSupplementary Figure 1(a) shows the image of the simulated y component of current density. B. Simulation equation for current density signal contribution
The current density signal contribution comes from the laser-induced local heating. Thelocal resistivity increase ∆ ρ from the local temperature increase ∆ T times the applied currentdensity J produces an additional voltage as described in the main text. To simulate thissignal, we consider the linear response regime of the resistivity dependence on temperature,such that ρ ( T ) = ρ ( + α ∆ T ) , i.e. ∆ ρ = ρ α ∆ T , where ρ is the resistivity at roomtemperature, ∆ ρ is the resistivity increase, and α is the temperature coefficient of resistivity.To derive the total voltage measured at the electrical contacts, we follow Ref. [16] anduse a simplified resistor model. We subdivide the sample into blocks labeled by k , withdimensions of dx , dy and dz . We consider the laser heating-induced additional voltage asour local voltage source. Therefore, ∆ V k ≈ i k ∆ R = J ∆ ρdy = J ρ α ∆ T dy , where ∆ V k ( i k ) islocal additional voltage (current) in block k , here y is the sample length direction, i.e. thedirection of the linecut in Figure 4(d), and x is the sample width direction. Using Kirchhoff’slaws, the global additional voltage at sample length ∆ V J calculated from the local voltage16 N ea r- f i e l d s i gna l ( µ V ) Y position ( µ m) -10010 N ea r- f i e l d s i gna l ( µ V ) -1.0 0.0 1.0 Y position ( µ m) +0.03 mA -0.03 mA (a)(c) (b)(d) (e) y yx Supplementary Figure 1. Current density distribution and spatial resolution extraction. (a) COM-SOL simulation on y component of current density. The coordinate system corresponds to thecurrent density image, not the inset. Inset: AFM image of the device. The scale bar is 1 µ m.(b) Example current density linecuts through two necks at both current polarities. (c) Currentdensity image acquired by a near-field tip at +0.03 mA (-0.03 mA is presented in the main text).Simulated curve fitted to the right side peak of half difference data, with a Gaussian width (d) δ = 74 nm and (e) δ = 88 nm. to take into account resistors in parallel is given by,∆ V J = ρ α ∫ J ( x, y ) ∆ T ( x, y tip − y ) w ( y ) dxdy (2)where we simulate the local current density J ( x, y ) using COMSOL, represent the laser-induced temperature profile ∆ T ( x, y tip − y ) as a Gaussian function at tip location ( , y tip ) ,and get the width w ( y ) from AFM topography profile which we also use in the COMSOLsimulation. We treat J and ∆ T as uniform in the z direction for simplicity. C. Quantitative extraction of spatial resolution from current imaging
To quantitatively extract the resolution for imaging current density, we numerically con-volve the current density from the COMSOL simulation with a Gaussian point spread func-tion of width δ , converted to voltage. We measure line scans across the top and bottomNi Fe necks at positive and negative currents [Supplementary Figure 1(b)], and take the17alf difference of the two to subtract out the magnetic contribution. We use the half dif-ference because our simulation is for the current density signal only. We note that theindividual linecuts are sharper than the half difference, and there could be some loss ofresolution due to any Y position shift between the two linecuts. We fit the simulated resultto the right side peak of the half difference data to extract δ . We notice that when theright side peak drops off to close to zero, there is an extra contribution that might be anartifact, and that leads to a broader slope. We fit to the data range indicated in orangepoints in Supplementary Figure 1(d), to balance the overall fit and the fit to the top of thepeak which is less sensitive to the artifact. In this case, we find a Gaussian width of δ = 74nm. We also show the fit to another parallel linecut that is 50 nm apart in x-direction, andwe find the δ = 88 nm [Supplementary Figure 1(e)]. D. Further discussions on spatiotemporal profiles of ∇ T and ∆ T Here, we provide further discussion about the spatiotemporal profiles of a temperaturegradient ∇ T and a temperature increase ∆ T , which have been simulated and studied in priorwork [16]. First, we explain the spatial resolution comparison between probing magnetizationand current density. When we measure in-plane magnetization, the spatial resolution islimited by the areal extent of the z-component of ∇ T , integrated over the time during which ∇ T z is nonzero. Even though ∆ T spreads laterally, ∇ T z does not spread much beyondthe excitation spot before it collapses to uniform temperature through the metal film [16].Therefore, the spatial resolution of the magnetic signal (limited by the excitation size) shouldbe higher than that of the current signal (limited by the lateral spreading of ∆ T ). Second,we discuss the complications of temporal response for current density measurements. Unlikethe temporal profile of ∇ T for magnetic signals, which is a sharp pulse with ∼
10 ps width,the temporal profile of ∆ T is highly asymmetric, with a sharp initial drop-off within 100ps, and then a slowly decaying tail extended to hundreds of picoseconds [16]. In a high-frequency microwave current measurement, the sharpest first 100 ps of ∆ T dominates thetemporal performance and gives the high-frequency responses [18], with the tail creating apartial cancellation in the signals. 18 a) (b) Supplementary Figure 2. Tip alignment and tip artifact. (a) Schematic representation of thealignment between the objective, scanning probe, and sample. The plane imaged by the microscopeobjective is tilted with respect to the sample. (b) Schematics of tip shadowing artifact.
SUPPLEMENTARY NOTE 2: TIP ALIGNMENT AND TIP ARTIFACT
An important step in operating the scanning probe magneto-thermal microscope is toalign the tip apex to the position in 3D space that corresponds to the point at the centerof the laser focus while the tip is engaged to the sample. The laser is oriented with itscentral axis at 30 ○ relative to the sample surface. The microscope objective is on a xyz stage controlled with piezo motors to adjust the laser position with <
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