Wide-field magneto-optical microscope to access quantitative magnetization dynamicswith femtosecond temporal and sub-micrometer spatial resolution

F. Steinbach,1 D. Schick,1 C. von Korff Schmising,1, ∗ K. Yao,1 M. Borchert,1 W. D. Engel,1 and S. Eisebitt1, 2

1Max-Born-Institut fuer Nichtlineare Optik und Kurzzeitspektroskopie, Max-Born-Strasse 2A, 12489 Berlin, Germany2Institut fuer Optik und Atomare Physik, Technische Universitaet Berlin,

Strasse des 17. Juni 135, 10623 Berlin, Germany(Dated: November 2, 2021)

We introduce a wide-field magneto-optical microscope to probe magnetization dynamics withfemtosecond temporal and sub-micrometer spatial resolution. We carefully calibrate the non-lineardependency between the magnetization of the sample and the detected light intensity by determiningthe absolute values of the magneto-optical polarization rotation. With that, an analytical transferfunction is defined to directly map the recorded intensity to the corresponding magnetization, whichresults in significantly reduced acquisition times and relaxed computational requirements. The per-formance of the instrument is characterized by probing the magnetic all-optical switching dynamicsof GdFe in a pump-probe experiment. The high spatial resolution of the microscope allows foraccurately subdividing the laser-excited area into different fluence-regions in order to capture thestrongly non-linear magnetization dynamics as a function of the optical pump intensity in a singlemeasurement.

I. INTRODUCTION

More than two decades after the seminal work of Beau-repaire et al. demonstrating the sub-picosecond quench-ing of magnetization after optical excitation [1], the fieldof ultrafast magnetism has remained a topic of intenseresearch with frequent discoveries of new phenomena.Laser pulse excitation has been shown to enable novel andenergy-efficient pathways to manipulate magnetic order,ranging from ultrafast demagnetization, spin injectionacross interfaces [2–4], spatially controlled response inmicropatterned media [5–7], magnetization reversal viaall-optical switching (AOS) [8, 9] to the controlled nucle-ation of magnetic skyrmions [10, 11]. The latter examplesare processes that involve the transition to a state withan altered magnetic domain configuration, and, hence,require experimental techniques that give access to thelateral spatial dimension. Next to scanning techniquesutilizing a tightly focused laser beam [12, 13], wide-fieldmagneto-optical (MO) imaging based on the Kerr orFaraday Effect has become the most common approach toaccess spatial information with sub-micrometer to macro-scopic length scales [14]. Early applications, reachingnanosecond to picosecond temporal resolutions, studiedmagnetization dynamics in recording head writers [15]and domain wall oscillations of a patterned ferromag-netic film [16]. Recently, wide-field MO microscopy hasbeen increasingly used to investigate ultrafast magnetiza-tion dynamics and AOS [17–19] offering a time resolutiononly limited by the pulse duration of the femtosecond op-tical laser pulses [5, 9, 20–24]. However, retrieving quan-titative information from MO images, a prerequisite tostudy ultrafast magnetization dynamics, has only beenrarely reported in literature [13, 21], mostly because it

∗ korff@mbi-berlin.de

generally requires time-consuming polarization analysisand high performance computing. Finally, as optical ex-citation pulses typically exhibit a spatial intensity pro-file, a further advantage of MO imaging techniques is thepossibility to accurately map the intensity dependence oflaser-driven magnetization processes [21].

In this work, we describe a time-resolved, wide-fieldmicroscope setup exploiting the MO Faraday or KerrEffect. The setup is optimized to probe the ultrafastmagnetization dynamics of samples with perpendicu-lar magnetic anisotropy obtaining femtosecond tempo-ral and sub-micrometer spatial resolution. By acquiringmicroscope images as a function of the angular orien-tation of an optical analyzer, we extract absolute val-ues of spatially resolved polarization rotation angles,which are directly proportional to the sample’s magne-tization [13, 21]. By this, we derive a sample specificanalytical transfer function to obtain an explicit expres-sion for the dependence of the detected light intensityand the sample’s magnetization. Such a transfer functionhas to be calculated for each sample material for which adifferent magneto-optical response can be expected. Fortime-resolved measurements this formalism renders theanalyzer scans obsolete and effectively reduces the totalacquisition time without the need for extensive compu-tational requirements. We exploit the Gaussian intensitydistribution of the pump laser pulses to record a largerange of excitation fluences simultaneously, revealing ahighly non-linear relationship between the evolution ofthe magnetization and the excitation fluence. We bench-mark our experimental approach by probing the time-and fluence-dependent AOS in ferrimagnetic GdFe alloy.

II. EXPERIMENTAL SETUP

An overview of the wide-field, time-resolved MO mi-croscope in Faraday geometry is sketched in Fig. 1 (a).

arX

iv:2

107.

0737

5v2

[ph

ysic

s.op

tics]

1 N

ov 2

021

2

An Yb-based fiber laser (Amplitude Laser Group, Sat-suma HP) with a central wavelength of 1030 nm and avariable pulse length between 250 fs to 10 ps is used asthe light source. The laser pulses have a maximum pulseenergy of 20 µJ at a variable repetition rate between sin-gle shot and 500 kHz, set by an acousto-optical modula-tor. We implement a pump-probe geometry by splittingthe laser pulses into two replicas with an intensity ratioof 30/70 (transmission/reflection). A mechanical delaystage (Newport, FMS300cc) controls the arrival time ofthe probe versus the pump pulses, allowing for delaysbetween −10 ps and 1.7 ns with a bi-directional repeata-bility of about 10 fs. The beampath of the pump pulsesis kept fixed in order to avoid any pointing instabilities,as their footprint on the sample is much smaller com-pared to the probe pulses. The latter are guided via themechanical delay stage and are actively stabilized to min-imize spatial fluctuations of the illumination. The probepulses are frequency doubled to a wavelength of 515 nmin a barium borate (BBO) crystal and focused onto thesample to homogeneously illuminate the field of view ofapproximately 200 µm. The pump pulses are focused bya separate lens onto the sample and a bandpass filter(Thorlabs, FESH0750) prevents them from entering thecamera. A dichroic mirror in front of the sample withhigh reflectivity for 515 nm and high transmissivity for1030 nm ensures full collinearity of the pump and probepulses. Both optical paths are equipped with attenua-tors consisting of a motorized half-waveplate and a fixedGlan-Thompson polarizer with an extinction > 105. Themotor rotary stages (Newport, CONEX-AG-PR100P) al-low for a minimum angular step size of 1 m° with a bi-directional repeatability of 3 m°. Rotating the waveplateallows for accurately setting the pulse energy between0.002 µJ to 0.7 µJ for the probe beam and between 0.01 µJto 4 µJ for the pump beam. The attenuator is calibratedwith a commercial powermeter (Thorlabs, S120C).

In Faraday geometry the polarization images of thesamples are projected by an objective lens (ZeissEC Epiplan-NEOFLUAR 50X, NA 0.8) and a tube lensonto a CMOS camera (Hamamatsu C13440-20CU). Thedichroic, complex index of refraction of the magneticsamples causes changes of the polarization state of theprobe light, both, in ellipticity and orientation. The ro-tation of the plane of polarization is quantified by theso-called Faraday angle θF and is directly proportional tothe magnetization of the sample. An MO image emergesin a crossed-polarizer geometry, where a motorized an-alyzer optic (Thorlabs, LPVISA100) with an extinctionof > 107 behind the sample is set close to 90◦ with re-spect to the direction of the incoming light polarization.The camera then only detects light with an altered po-larization state due to transmission through magneticallyordered regions of the sample.

The magnetic state of the samples can be controlled byan external electromagnet with a maximum out-of-planefield strength of 300 mT at the sample position. In ad-dition to hysteresis loops, the external magnetic field is

applied during pump-probe measurements to re-saturatethe samples and to enable field-dependent studies. Thelater point is of importance for deterministic AOS exper-iments, where every odd pump pulse initiates AOS andevery even pump pulse resets the sample to its initialmagnetic state without requiring an external magneticfield. To record the transient magnetization dynamicsa mechanical chopper is synchronized to block the evenprobe pulses, allowing to follow the dynamics induced byodd pump pulses only at half the available laser repeti-tion rate [25].

The setup can be easily adapted to change between atransmission (Faraday) and reflection (Kerr) geometry,e.g. for the investigation of optically opaque samples.In reflection geometry, the pump pulse is focused by theimaging microscope objective, while the light path of theprobe pulse is aligned according to a Kohler illuminationleading to a uniform light distribution on the sample. Acontinuous-flow cryostat is available to control the sampletemperature between 10 K to 450 K. For temperature-dependent measurements, we account for the finite sizeof the evacuated cryostat by using a long-working dis-tance objective (Edmund Optics, 50X EO Long WorkingDistance) providing a spatial resolution of approximately1 µm. We use the open-source software Sardana [26] tocontrol the fully automatized setup, which can operatein a unsupervised mode by running through user-definedmacro files. This allows for systematic measurements,automatically scanning different parameters like temper-ature, fluence, or the external magnetic field.

We demonstrate the performance of the setup by inves-tigating a magnetic Gd24Fe76(20 nm) alloy sandwichedbetween two Ta(5 nm) layers, grown onto a glass sub-strate by DC magnetron sputtering. Its magnetization isperpendicular to the sample plane with a coercive field of15 mT. The sample exhibits AOS which is evidenced bythe two magneto-optical images shown in Fig. 1 (b) and(c), which are recorded before and after single pulse exci-tation in thermal equilibrium. The magnetic contrast forthe saturation magnetization M+ is given by green andthe area with reversed magnetization M− due to AOSis encoded by a blue color. We confirm a spatial reso-lution of below 1 µm, by evaluating the lineout betweenthe two oppositely magnetized domains and defining theresolution as the width between 90% and 10% of the totalintensity contrast.

A. Faraday Rotation Analysis

We apply the Jones calculus to establish the relation-ship between the detected light intensity on the cameraand the Faraday angle, θF. The probe pulse is described

as the electric field vector ~Ein =(Ex

Ey

), where Ex and

Ey are the complex horizontal (x) and vertical (y) com-ponents of the field. The polarization-dependent opticalelements are described by matrices and consist of the

3

beamsplitter

delay stage

magnetdichroic mirror

lens 1

attenuator

fiber laser

camera

filteranalyzer

objectivesample

lens 2attenuator

chopperBBO

tube lens

(a)

(b) (c)

τ

inte

nsi

ty (

arb

. u.)

0

1

FIG. 1. (a) Wide-field magneto-optical microscope setup. Afemtosecond fiber laser is used as a light source for the micro-scope. For time-resolved measurements, a pump/probe con-figuration is used. The pump pulses excite the sample at thefundamental laser wavelength of 1030 nm, while the magneticstate of the sample is probed with the second harmonic at awavelength of 515 nm. (b) Intensity image of a saturated sam-ple corresponding to the out-of-plane magnetization directionM+. (c) Intensity image of the sample after excitation with asingle pump pulse. The dark color corresponds to a reversedmagnetization direction, M−. Both images were recorded inthermal equilibrium long after optical excitation. The scalebar in both images corresponds to 15 µm.

horizontally aligned polarizer P and the magnetic sam-ple S as well as components that contribute to parasiticFaraday rotations F, and finally the analyzer A, alignedat an angle α with respect to incoming polarization di-rection, c.f. Eq. 1. After transmission through the sam-ple, the probe light polarization exhibits a magnetization-dependent Faraday rotation, θF, and change of ellipticity,η. The parasitic Faraday angle, φ, depends on the exter-nal magnetic fields, Bext, and is mainly caused by theglass lenses inside the objective [27].

P =

[1 00 0

]S =

[cos θF + iη sin θF − sin θF + iη cos θFsin θF − iη cos θF cos θF + iη sin θF

]F =

[cosφ − sinφsinφ cosφ

]A =

[sin2 α sinα cosα

sinα cosα cos2 α

](1)

In front of the camera the electric field vector is given

by ~Eout = AFSP ~Ein. The intensity, I, detected by thecamera is then calculated by [21]

I = | ~Eout|2 = I0[(

1− η2)

sin2 (α+ θF + φ) + η2]

≈ I ′0 (α+ θF + φ)2

+ Iε (2)

where I0 is the incoming intensity and Iε is an elliptic-ity depended offset. The final step of Eq. 2 correspondsto a small-angle approximation. Evidently, the detectedintensity depends non-linearly on the Faraday angle andtherefore on the magnetization of the sample.

We determine the absolute Faraday rotation of thesample by scanning the analyzer angle, α, for oppositeout-of-plane magnetization directions, M±, as well as fora demagnetized state M = 0, i.e. for an average over amagnetic multi-domain pattern, as shown in Fig. 2 (a).We fit the data with the quadratic function accordingto Eq. 2. The different positions of the minima of theparabolas for measurements with opposite magnetizationdirections, M±, are marked with dotted vertical lines anddetermine the maximum, sample specific Faraday rota-tion, ±θsample = ±0.45◦. The Faraday rotation of thedemagnetized state (orange line) is zero and located be-tween the response of M− and M+ (blue and green lines,respectively). The intensity offset is caused by the el-lipticity, η, of the sample, which also depends on themagnetization. Importantly, in this plot parasitic Fara-day rotations, φ, only lead to a constant offset on theα axis, independent of the magnetic state of the sampleand do not influence θsample. Subtraction of the parasiticFaraday rotation ensures that we find the analyzer angleα = 0 as the minimum of Eq. 2 for the demagnetizedstate. These measurements allow us to determine theintensity contrast according to

C(α) =I(M+, α)− I(M−, α)

I(M+, α) + I(M−, α)(3)

For the GdFe alloy sample the maximum contrast is at± 0.9◦ and is determined by the values of θsample, theincoming intensity I0, and the offset Iε, see Fig. 2 (b). Wenote that the highest signal to noise ratios are achievedfor the analyzer angles which maximize C.

B. Magnetization Normalization

To normalize the Faraday rotation to a correspondingmagnetization two additional analyzer scans are needed.One scan is performed with a saturated sample for onemagnetization direction, M+/−, set by an external mag-netic field, B+/−. Another analyzer scan is performedwith a blank substrate applying the same external mag-netic field as used in the previous measurement, B+/−,to extract the parasitic Faraday rotation φ. This yieldsthe absolute value of θsample. Note, that for measure-ments without external magnetic field only the saturatedα-scan is necessary as φ equals zero.

4

3 2 1 0 1 2 3analyzer angle (°)

0.0

0.2

0.4

0.6

0.8in

tens

ity (a

rb. u

.)(a)

M + demag. M

3 2 1 0 1 2 3analyzer angle (°)

0.6

0.4

0.2

0.0

0.2

0.4

0.6

inte

nsity

con

trast

C

(b)

data pointsfit

FIG. 2. (a) Scan of the analyzer angle, α, for three differentmagnetic states, M+ saturation (blue), M− saturation (green)and M0 (orange), i.e. a fully demagnetized state where thesample’s magnetization projection averaging to zero in theout-of-plane direction. The shift of the parabolic fit func-tions is caused by the Faraday rotation of the different mag-netic states of the sample. The vertical dotted lines markthe Faraday rotation of the sample, ±θsample = ±0.45◦ (b)Intensity contrast for different analyzer angles with maximaat α = ±0.9◦. The contrast is calculated according to Eq. 3using the data points and the fits shown in panel (a).

The Faraday angles, ±θsample, correspond to the sat-uration magnetizations M± such that we can calculatethe transient magnetization normalized between -1 and1 according to

M(t) =θF(t) + θsample

θsample− 1 (4)

Therefore, the measurements not only yield absolutevalues of the Faraday rotation, but also allow to followrelative changes of the magnetization.

III. ALL-OPTICAL MAGNETIC SWITCHING

We perform time-resolved experiments to measure themagnetization dynamics of the GdFe alloy after optical

excitation. To this end, we record analyzer scans for eachtime delay and extract the associated Faraday rotations.In Fig. 3 (a), we show two MO images for selected timedelays at t =1 ps and t =1700 ps. The background of theimages are corrected by subtraction of an image recordedbefore time delay zero at t = −2 ps. At a time delayof 1 ps a circular area with a diameter of approximately30 µm is fully demagnetized. The edges of the field ofview correspond to very weakly excited areas and, hence,have almost remained in the initial magnetization state,M+. After 1700 ps only a small switched spot (M−) witha diameter of approximately 15 µm remains, while theexternal magnetic field has almost completely reset themagnetization of the surrounding areas.

1 ps 1700 ps

1000 100 101 102 103

delay (ps)

1.0

0.5

0.0

0.5

1.0

norm

. mag

netiz

atio

n M

(t)(b)

fitdata

1

0

1

norm

. mag

. M(t)

(a)

FIG. 3. (a) Magnetization of the GdFe sample at differentdelays after optical excitation. The small black circle in firstimage (1 ps) marks the integration area with a size of about0.2 µm2 for the time-resolved transient shown in panel (b).The scale bar corresponds to 25 µm.(b) Transient magneti-zation of the sample after laser excitation for a fluence of4.9 mJ cm−2 extracted by integrating the central area shownin the left panel of (a). Note that the time axis is linear be-tween −2 ps and 3.5 ps and logarithmic for later times up to1.7 ns. The transition is marked by the dashed vertical line.

Integration over a circular area positioned at the centerof the excitation with a diameter of 0.5 µm (black circlein Fig. 3 (a)) yields the magnetization dynamics for themaximal excitation fluence Fmax = (4 ln 2 · ε)/(π · δ2) =4.9 mJ cm−2, where ε is the pulse energy and δ corre-

5

sponds to FWHM of the laser spot. The correspond-ing values of the magnetization as a function of time areshown in Fig. 3 (b). For this measurement, we recordedMO images for 12 distinct analyzer angles, α, with anexposure time of 100 ms at each of the 113 time delaypoints. Taking into account additional time required tomove the different motors and read out the CCD images,this measurement took approximately 16 minutes. Themagnetization dynamics is fitted with a bi-exponentialfunction and convolved by a Gaussian function to ac-count for the time resolution of our experiment [28]. Thetime resolution is determined independently by a crosscorrelation of the pump and probe pulses, which for pulsedurations of 250 fs, amounts to approximately 350 fs.The magnetization of the GdFe alloy decreases veryquickly after excitation and reverses its sign in less thantwo picoseconds. Then the magnetization reaches aswitched state of 0.8 ·M− after approximately 400 ps.

1000 100 101 102 103

delay (ps)

1.0

0.5

0.0

0.5

1.0

1.5

2.0

norm

. int

ensit

y (a

rb. u

.)

(a)

: 0.6°: 1.2°

ref.

: -1.8°: -0.6°

0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25norm. intensity (arb. u.)

0.6

0.4

0.2

0.0

0.2

0.4

0.6

norm

. far

aday

ang

le

(°)

(I)

(b)

: 1.2°: 0.6°: 0.0°

: -0.6°: -1.8°

FIG. 4. (a) Normalized intensities as a function of time de-lay measured for different fixed analyzer angles α. The verydifferent response highlights the non-linear relation betweenintensity and Faraday rotation. (b) Normalized Faraday an-gle as a function of the time-dependent intensity. For a suffi-ciently large Faraday angle e.g. α = −1.8°, a unique transferfunction θ(I) = 0.8(I + 0.02)2 + 1 can be defined (red line).

To further demonstrate the importance to measurenormalized Faraday angles in order to extract quanti-

tative magnetization dynamics from MO images, we plottransients for different fixed analyzer angles in Fig. 4 (a).The region of interest is identical to our previous analysisand corresponds to the circular area with a diameter of0.5 µm as shown in the left MO image of Fig. 3 (a). Wenormalize the intensities by assuming that the intensitybefore time delay zero is equal to one and after a delayof 400 ps equal to −0.8, in accordance with the magne-tization dynamics shown in Fig. 3 (b). This assumptionwould be correct if quantitative magnetization dynamicscould be extracted for arbitrary analyzer angles providedthey lead to a finite intensity contrast. As a reference, weadditionally plot the transient magnetization as shown inFig. 3 (b) as a solid blue line. Obviously, the intensitytransients for different analyzer angles are very different,illustrating the strongly nonlinear relationship betweendetected intensity and magnetization. For example, forthe negative analyzer angle, α = −0.6◦, the normal-ized intensity values almost completely reverse their signwithin 2 ps, while for the positive angle, α = 0.6◦, the de-tected intensity crosses zero only after 100 ps. Interpret-ing the dynamical pathway of the magnetization betweenthe two stable magnetic states, M±, is clearly not pos-sible without prior polarization analysis of the sample.This is an important message and should be consideredwhen referring to published work on transient Faradayor Kerr microscopy [5, 9, 20, 22–24, 29]. Furthermore,not only the apparent dynamics are different, but alsothe noise. This is expected when recalling how the inten-sity contrast, C, varies for different angles α as shown inFig. 2 (b). In Fig. 4 (b), we plot the Faraday angle forfive different values of the analyzer angle, α, as a functionof the normalized time-dependent intensities after opticalexcitation. For small analyzer angles the Faraday anglepasses through the minimum as the sample is reversingits magnetization and the measured intensities do not al-low to differentiate between M+ and M−. However, fora sufficiently large analyzer angle, α = −1.8°, every in-tensity can be assigned to a unique Faraday angle. Thisallows the definition of a transfer function θ(I) (red linein Fig. 4 b) and establishes an analytical relationship be-tween measured intensity and Faraday angle. Note thatsetting the analyzer angle to α ≈ ±0.6°, i.e. close to themaximum contrast, C (cf. Fig. 2 (b)), no unique trans-fer function can be defined. We like to point out thatthe sample specific Faraday-intensity relationship can notonly be retrieved in time-resolved measurements, but inprinciple in any experiment where the variation of an ex-ternal parameter allows to continuously change the mag-netization of a sample, i.e. by temperature-dependentmeasurements.The determination of a unique transfer function impliesthat further measurements for this sample do not requireanalyzer scans at each time delay to extract the correctmagnetization dynamics.

6

IV. FLUENCE DEPENDENCE

The possibility to locally analyse the magnetic statewithin microscope images allows us to measure the flu-ence dependence of the magnetization dynamics withina single acquisition. As the spatial intensity distribu-tion of our laser pulse exhibits a Gaussian shape witha FWHM δ, the fluence F (R) with radius R fromthe center of the beam varies according to F (R) =Fmax exp (−8 ln 2 ·R2/δ2). For the following experiment,the pump pulse was focused to 100 µm × 100 µm FWHM,while the sample was probed with a beam of 330 µm ×400 µm FWHM. The FWHM were accurately determinedwith a beam profiler (Dataray, WinCamD-THz). For amaximum fluence Fmax of 4.9 mJ cm−2, we show the vari-ation of the fluence as a function of spatial position, R,in Fig. 5 (a). In the same figure, we additionally plot thecorresponding upper bound with which we can resolvedifferent excitation fluences experimentally (orange line).Assuming a spatial resolution of <1 µm, we determine amaximum value of <0.07 mJ cm−2, spatially coincidingwith the largest slope of the fluence distribution. Wedemonstrate the strongly nonlinear fluence dependence ofAOS, by further investigating the magnetization dynam-ics of the GdFe sample. In Fig. 5 (b), we show the MOimages calculated via the previously determined transferfunction, θ(I), for two selected time delays. In the mid-dle of the excitation distribution the fluence is the highestand decreases with increasing radius, R. We perform anazimuthal integration over pixels with the same fluenceusing the Phython package PyFAI, correcting for smalldeviations from a perfect radially symmetric excitationprofile [30]. Two exemplary integration pathways corre-sponding to 4.7 mJ cm−2 and 3.6 mJ cm−2 are drawn inthe left panel of Fig. 5 (b). We like to point out, thatfor inhomogeneous pump beam profiles or for excitationpatterns that exhibit a tailored structure, the intensitydistribution can also be directly recorded by the CCDcamera of our imaging system. This allows to assign ev-ery pixel of the MO images a measured value of the pumpintensity.

In Fig. 6 (a) the transients for different fluences areshown. It is noteworthy that very small differences influence lead to significant quantitative and even qual-itative changes of the magnetization dynamics. Com-paring the dynamics at a radius of 11 µm (4.8 mJ cm−2)with dynamics at 21 µm (4.4 mJ cm−2) shows a tremen-dously different dynamics although the difference of thetwo radii is only about 10 % of the FWHM of the pumppulse. This is an important observation, as for the morecommon approach of magneto-optical Kerr/Faraday Ef-fect pump-probe experiments, using focused laser beams,the response within the probe spot is integrated, poten-tially bluring the differences between a fluence-dependentresponse. For integrating MOKE experiments, our mea-surements show that it is crucial to ensure a sufficientlylarge ratio of the FWHM of pump and probe pulses inorder avoid integration over distinct dynamics. For the

1 ps 1700 ps

0 50 100 150 200position (µm)

0

1

2

3

4

5

fluen

ce (m

J/cm

2 )

(a)

1

0

1

norm

. mag

. M(t)

(b)

0.00

0.02

0.04

0.06

0.08

flue

nce

(mJ/c

m2 )

FIG. 5. (a) Variation of the fluence (black line) and of thefluence resolution (orange line) as a function of spatial po-sition, R. (b) Normalized magnetization maps for differentdelays after excitation with a peak fluence of 4.9 mJ cm−2.Pixels on the circular segments (black lines shown in imagefor t = 1 ps) correspond to positions that are excited bythe same fluence. The inner ring corresponds to a fluence of4.7 mJ cm−2, the outer ring to 3.6 mJ cm−2. The scale barcorresponds to 25 µm.

investigated GdFe sample, the ratio should remain wellbelow 1/10. To present the complete information con-tained in the series of time resolved MO images, we plota 2D map of the fitted transient magnetization both asa function of fluence and time delay in Fig. 6 (b). Threedifferent fluence regions can be differentiated. Below4.2 mJ cm−2 the sample only demagnetizes transientlyand relaxes back to its original magnetization direction.Between 4.2 mJ cm−2 and 4.5 mJ cm−2 the sample com-pletely switches its magnetization, ending up in a mag-netically reversed state. For a fluence in excess of thisvalue, the sample completely demagnetizes, but then re-saturates to its initial state. Evidently, only for a rela-tively small fluence range the sample switches its magne-tization completely.The ability to generate such a fluence map showsthe strength of a spatially resolving microscopic ap-proach compared to a common used, spatially integratingMOKE/Faraday setup. As the entire fluence range is en-coded in a single MO image, the fluence dependence onultrafast magnetization dynamics can be carried out withhigh fidelity. With a known transfer function, θ(I), thefluence- and time-dependent magnetization map shownin Fig 6 (b) required an acquisition time of only 3 min-utes.

7

100 0 100 101 102 103

delay (ps)

1.5

1.0

0.5

0.0

0.5

1.0no

rm. m

agne

tisat

ion

M(t)

(a)

4.8 mJ/cm2

4.5 mJ/cm24.4 mJ/cm2

3.0 mJ/cm2

1000 100 101 102 103

delay (ps)

1

2

3

4

fluen

ce (m

J/cm

2 )

(b)

-1.0

-0.5

0.0

0.5

1.0

norm

. mag

n. M

(t)

FIG. 6. (a) Magnetic transients for different fluences whichwere extracted for different radii of the recorded images. Thered dotted line marks a switching of 70 %. (b) Fluence-delay-magnetization map for Gd24Fe76 sample. The map is a resultof bi-exponential fits. The 2D map very clearly depicts thestrongly nonlinear fluences dependence of AOS.

V. CONCLUSIONS

We demonstrated a wide-field magneto-optical micro-scope setup to measure the magnetization via Faradayrotation with a femtosecond temporal and sub 1 µm spa-tial resolution. By performing analyzer angle scans foreach time delay, it is possible to extract the absolute valueof the transient Faraday rotation for different regions ofinterests in the MO images. For an adequately chosen an-alyzer angle, we demonstrate that one can define a samplespecific, analytic transfer function to calculate Faradayrotations from measured intensities, greatly reducing ex-perimental acquisition times and computational require-ments. We emphasize that a polarization analysis is anecessary requirement to extract quantitative statementsabout demagnetization and all-optical switching timesfrom MO images. Furthermore, we underlined the advan-tages of wide-field polarization microscopy allowing si-multaneous measurements of different excitation fluenceswith a resolution of <0.07 mJ cm−2. In future, we fore-see further applications of our setup for the investigationof magnetization dynamics in chemically and magneti-cally inhomogeneous samples, for micropatterned mag-netic systems or for studies employing a structured illu-mination.

VI. ACKNOWLEDGEMENT

We gratefully acknowledge financial support by theDFG through TRR227, project A02.

VII. DATA AVAILABILITY

The data that support the findings ofthis study are openly available in Zenodo athttp://doi.org/10.5281/zenodo.5152989.

VIII. REFERENCES

[1] E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot,Ultrafast spin dynamics in ferromagnetic nickel, Phys.Rev. Lett. 76, 4250 (1996).

[2] D. Rudolf, C. La-O-Vorakiat, M. Battiato, R. Adam,J. M. Shaw, E. Turgut, P. Maldonado, S. Mathias,P. Grychtol, H. T. Nembach, T. J. Silva, M. Aeschli-mann, H. C. Kapteyn, M. M. Murnane, C. M. Schneider,and P. M. Oppeneer, Ultrafast magnetization enhance-ment in metallic multilayers driven by superdiffusive spincurrent, Nat. Commun. 3, 1037 (2012).

[3] A. Melnikov, I. Razdolski, T. O. Wehling, E. T.Papaioannou, V. Roddatis, P. Fumagalli, O. Akt-sipetrov, A. I. Lichtenstein, and U. Bovensiepen, Ultra-

fast transport of laser-excited spin-polarized carriers inAu/Fe/MgO(001), Phys. Rev. Lett. 107, 1 (2011).

[4] T. Kampfrath, M. Battiato, P. Maldonado, G. Eil-ers, J. Notzold, S. Mahrlein, V. Zbarsky, F. Freimuth,Y. Mokrousov, S. Blugel, M. Wolf, I. Radu, P. M. Oppe-neer, and M. Munzenberg, Terahertz spin current pulsescontrolled by magnetic heterostructures, Nat. Nanotech-nol. 8, 256 (2013).

[5] M. Savoini, R. Medapalli, B. Koene, A. R. Khorsand,L. Le Guyader, L. Duo, M. Finazzi, A. Tsukamoto,A. Itoh, F. Nolting, A. Kirilyuk, A. V. Kimel, and T. Ras-ing, Highly efficient all-optical switching of magnetizationin GdFeCo microstructures by interference-enhanced ab-

8

sorption of light, Phys. Rev. B 86, 1 (2012).[6] C. von Korff Schmising, B. Pfau, M. Schneider, C. M.

Gunther, M. Giovannella, J. Perron, B. Vodungbo,L. Muller, F. Capotondi, E. Pedersoli, N. Mahne,J. Luning, and S. Eisebitt, Imaging ultrafast demagne-tization dynamics after a spatially localized optical exci-tation, Phys. Rev. Lett. 112, 217203 (2014).

[7] L. Le Guyader, M. Savoini, S. El Moussaoui, M. Buzzi,A. Tsukamoto, A. Itoh, A. Kirilyuk, T. Rasing, A. V.Kimel, and F. Nolting, Nanoscale sub-100 picosecond all-optical magnetization switching in GdFeCo microstruc-tures, Nat. Commun. 6, 1 (2015).

[8] C. D. Stanciu, A. Tsukamoto, A. V. Kimel, F. Hansteen,A. Kirilyuk, A. Itoh, and T. Rasing, Subpicosecondmagnetization reversal across ferrimagnetic compensa-tion points, Phys. Rev. Lett. 99, 217204 (2007).

[9] K. Vahaplar, A. M. Kalashnikova, A. V. Kimel,D. Hinzke, U. Nowak, R. Chantrell, A. Tsukamoto,A. Itoh, A. Kirilyuk, and T. Rasing, Ultrafast path foroptical magnetization reversal via a strongly nonequilib-rium state, Phys. Rev. Lett. 103, 66 (2009).

[10] M. Finazzi, M. Savoini, A. R. Khorsand, A. Tsukamoto,A. Itoh, L. Duo, A. Kirilyuk, T. Rasing, and M. Ezawa,Laser-induced magnetic nanostructures with tunabletopological properties, Phys. Rev. Lett. 110, 1 (2013).

[11] F. Buttner, B. Pfau, M. Bottcher, M. Schneider,G. Mercurio, C. M. Gunther, P. Hessing, C. Klose,A. Wittmann, K. Gerlinger, L. M. Kern, C. Struber,C. von Korff Schmising, J. Fuchs, D. Engel, A. Churikova,S. Huang, D. Suzuki, I. Lemesh, M. Huang, L. Caretta,D. Weder, J. H. Gaida, M. Moller, T. R. Harvey, S. Za-yko, K. Bagschik, R. Carley, L. Mercadier, J. Schlappa,A. Yaroslavtsev, L. Le Guyarder, N. Gerasimova,A. Scherz, C. Deiter, R. Gort, D. Hickin, J. Zhu, M. Tur-cato, D. Lomidze, F. Erdinger, A. Castoldi, S. Maffes-santi, M. Porro, A. Samartsev, J. Sinova, C. Ropers, J. H.Mentink, B. Dupe, G. S. Beach, and S. Eisebitt, Obser-vation of fluctuation-mediated picosecond nucleation ofa topological phase, Nat. Mater. 20, 30 (2021).

[12] M. R. Freeman and J. F. Smyth, Picosecond time-resolved magnetization dynamics of thin-film heads, J.Appl. Phys. 79, 5898 (1996).

[13] A. Laraoui, J. Venuat, V. Halte, M. Albrecht, E. Beaure-paire, and J. Y. Bigot, Study of individual ferromagneticdisks with femtosecond optical pulses, J. Appl. Phys.101, 1 (2007).

[14] J. McCord, Progress in magnetic domain observation byadvanced magneto-optical microscopy, J. Phys. D. Appl.Phys. 48, 333001 (2015).

[15] D. Chumakov, J. McCord, R. Schafer, L. Schultz,H. Vinzelberg, R. Kaltofen, and I. Monch, Nanosecondtime-scale switching of permalloy thin film elements stud-ied by wide-field time-resolved Kerr microscopy, Phys.Rev. B 71, 014410 (2005).

[16] B. Mozooni, T. von Hofe, and J. McCord, Picosecondwide-field magneto-optical imaging of magnetization dy-namics of amorphous film elements, Phys. Rev. B 90,054410 (2014).

[17] M. Beens, M. L. M. Lalieu, A. J. M. Deenen, R. A.Duine, and B. Koopmans, Comparing all-optical switch-ing in synthetic-ferrimagnetic multilayers and alloys,Phys. Rev. B 100, 220409 (2019).

[18] A. Ceballos, A. Pattabi, A. El-Ghazaly, S. Ruta, C. P.Simon, R. F. Evans, T. Ostler, R. W. Chantrell,E. Kennedy, M. Scott, J. Bokor, and F. Hellman,Role of element-specific damping in ultrafast, helicity-independent, all-optical switching dynamics in amor-phous (Gd,Tb)Co thin films, Phys. Rev. B 103, 24438(2021).

[19] C. Banerjee, K. Rode, G. Atcheson, S. Lenne, P. Sta-menov, J. M. D. Coey, and J. Besbas, Ultra-fast doublepulse all-optical re-switching of a ferrimagnet, Phys. Rev.Lett. 126, 177202 (2020).

[20] K. Vahaplar, A. M. Kalashnikova, A. V. Kimel, S. Ger-lach, D. Hinzke, U. Nowak, R. Chantrell, A. Tsukamoto,A. Itoh, A. Kirilyuk, and T. Rasing, All-optical magne-tization reversal by circularly polarized laser pulses: Ex-periment and multiscale modeling, Phys. Rev. B 85, 1(2012).

[21] Y. Hashimoto, A. R. Khorsand, M. Savoini, B. Koene,D. Bossini, A. Tsukamoto, A. Itoh, Y. Ohtsuka,K. Aoshima, A. V. Kimel, A. Kirilyuk, and T. Ras-ing, Ultrafast time-resolved magneto-optical imaging ofall-optical switching in GdFeCo with femtosecond time-resolution and a µm spatial-resolution, Rev. Sci. Instrum.85, 063702 (2014).

[22] Y. Tsema, G. Kichin, O. Hellwig, V. Mehta, A. V. Kimel,A. Kirilyuk, and T. Rasing, Helicity and field dependentmagnetization dynamics of ferromagnetic Co/Pt multi-layers, Appl. Phys. Lett. 109, 072405 (2016).

[23] A. Stupakiewicz, K. Szerenos, D. Afanasiev, A. Kir-ilyuk, and A. V. Kimel, Ultrafast nonthermal photo-magnetic recording in a transparent medium, Nature542, 71 (2017).

[24] S. Wang, C. Wei, Y. Feng, H. Cao, W. Li, Y. Cao, B.-O. Guan, A. Tsukamoto, A. Kirilyuk, A. V. Kimel, andX. Li, Dual-shot dynamics and ultimate frequency of all-optical magnetic recording on GdFeCo, Light Sci. Appl.10, 8 (2021).

[25] D. Schick, F. Steinbach, T. Noll, C. Struber, D. Engel,C. von Korff Schmising, B. Pfau, and S. Eisebitt, High-speed spatial encoding of modulated pump–probe signalswith slow area detectors, Meas. Sci. Technol. 32, 025901(2020).

[26] https://sardana-controls.org/.[27] T. Ishibashi, Z. Kuang, Y. Konishi, K. Akahane, X. Zhao,

T. Hasegawa, and K. Sato, Novel magneto-optical micro-scope using optical modulation technique, Trans. Magn.Soc. Jpn. 4, 278 (2004).

[28] I. Radu, C. Stamm, A. Eschenlohr, F. Radu, R. Abrudan,K. Vahaplar, T. Kachel, N. Pontius, R. Mitzner, K. Holl-dack, A. Fohlisch, T. A. Ostler, J. H. Mentink, R. F. L.Evans, R. W. Chantrell, A. Tsukamoto, A. Itoh, A. Kir-ilyuk, A. V. Kimel, and T. Rasing, Ultrafast and dis-tinct spin dynamics in magnetic alloys, SPIN 05, 1550004(2015).

[29] M. Elazar, M. Sahaf, L. Szapiro, D. Cheskis, and S. Bar-Ad, Single-pulse magneto-optic microscopy: a new toolfor studying optically induced magnetization reversals,Opt. Lett. 33, 2734 (2008).

[30] J. Kieffer and D. Karkoulis, PyFAI, a versatile library forazimuthal regrouping, J. Phys. Conf. Ser. 425, 202012(2013).