Ultrafast supercontinuum fiber-laser based pump-probe scanning MOKE microscope for the investigation of electron spin dynamics in semiconductors at cryogenic temperatures with picosecond time and micrometer spatial resolution
T. Henn, T. Kiessling, W. Ossau, L. W. Molenkamp, K. Biermann, P. V. Santos
UUltrafast supercontinuum fiber-laser based pump-probe scanning MOKEmicroscope for the investigation of electron spin dynamics in semiconductorsat cryogenic temperatures with picosecond time and micrometer spatialresolution
T. Henn, T. Kießling, a) W. Ossau, L. W. Molenkamp, K. Biermann, and P. V. Santos Physikalisches Institut (EP3), Universit¨at W¨urzburg, 97074 W¨urzburg, Germany Paul-Drude-Institut f¨ur Festk¨orperelektronik, Hausvogteiplatz 5-7, 10117 Berlin,Germany (Dated: 14 October 2013)
We describe a two-color pump-probe scanning magneto-optical Kerr effect (MOKE) microscope which wehave developed to investigate electron spin phenomena in semiconductors at cryogenic temperatures withpicosecond time and micrometer spatial resolution. The key innovation of our microscope is the usage ofan ultrafast ‘white light’ supercontinuum fiber-laser source which provides access to the whole visible andnear-infrared spectral range. Our Kerr microscope allows for the independent selection of the excitation anddetection energy while avoiding the necessity to synchronize the pulse trains of two separate picosecond lasersystems. The ability to independently tune the pump and probe wavelength enables the investigation ofthe influence of excitation energy on the optically induced electron spin dynamics in semiconductors. Wedemonstrate picosecond real-space imaging of the diffusive expansion of optically excited electron spin packetsin a (110) GaAs quantum well sample to illustrate the capabilities of the instrument.PACS numbers: 85.75.-d, 72.25.Dc, 78.20.Ls, 75.40.Gb, 72.25.Fe, 72.25.-b
I. INTRODUCTION
The investigation of electron spin phenomena has de-veloped into an important field of solid state physicsin the recent past. Spin-sensitive magneto-optical spec-troscopy has emerged as a particularly successful tech-nique for the exploration of the electron spin dynam-ics in bulk and low-dimensional semiconductors. Tak-ing advantage of the spin selectivity of the optical in-terband transitions in zincblende-type semiconductors ,spin-polarized electrons are excited by above-barrier illu-mination of the sample with a circularly polarized pumplaser. In its simplest form, magneto-optical spectroscopyinfers the state of the electron spin system by using thedegree of circular polarization of the photoluminescenceas a tracer for the electron spin polarization. However,photoluminescence spectroscopy depends on the simulta-neous presence of both electrons and holes and is there-fore limited to time and length scales of the order of theminority carrier lifetime and the ambipolar charge diffu-sion length.A more sophisticated approach, pump-probe magneto-optical Kerr effect (MOKE) spectroscopy, eludes this lim-itation by deducing the electron spin polarization from ameasurement of the change of the major axis of opticalpolarization, the Kerr rotation, of a second probe laserwhich is reflected from the sample surface. Using fastpulsed laser sources and strong focussing optics, pump-probe MOKE microscopy allows for the investigation of a) E-mail: [email protected] the electron spin system with sub-picosecond time andmicrometer spatial resolution with ultra-high sensitivity.Pump-probe MOKE spectroscopy has been used exten-sively to study electron and hole spin transport and relax-ation processes in bulk semiconductors, quantum wells,and quantum dots. Notable applications of magneto-optical Kerr and Faraday microscopy include the observa-tion of electron spin lifetimes of the order of 100 ns (Ref.2) and spin drift over distances exceeding 100 µ m (Ref.3) in bulk n-GaAs, the study of the influence of electric,magnetic, and strain fields on optically excited electronspins, the optical investigation of electrical spin injectionin n-GaAs channels, the observation of the spin Hall ef-fect in bulk and low-dimensional semiconductors, andthe magneto-optical detection of single electron spins inquantum dots. In the traditional form of degenerate pump-probe spec-troscopy, the pulsed pump and probe lasers are obtainedfrom the same laser source, i.e. the excitation and detec-tion wavelengths are equal. In semiconductors, an appre-ciable Kerr rotation signal is only observed in the spectralvicinity of the excitonic optical resonances. The necessityto detect the small polarization signals therefore limitsthe excitation energies accessible by degenerate MOKEspectroscopy. However, a strong influence of the excita-tion energy on the electron spin dynamics due to pump-induced carrier heating and the resulting electron tem-perature gradients has been observed in the past bothfor bulk semiconductors and quantum wells.
Itis therefore desirable to independently control the pumpand probe wavelengths in MOKE spectroscopy experi-ments to enable the systematic investigation of the inter-relation between charge, spin and heat transport in the a r X i v : . [ phy s i c s . i n s - d e t ] O c t electron system of semiconductor heterostructures.In the past this ability has been achieved by elaboratesynchronization of the pulse trains of two independentTi:sapphire laser systems. Here we present a newapproach to time-resolved two-color pump-probe MOKEmicroscopy which is based on an ultrafast ‘white light’ su-percontinuum fiber-laser source. Such fiber-based super-continuum sources have become commercially availablein the recent past and are increasingly used in opticalspectroscopy experiments.The three main advantages of our instrument are (i)the ability to independently tune the excitation and de-tection energy while avoiding the necessity to synchronizetwo separate picosecond laser systems, (ii) access to thewhole visible and near-infrared spectral range for the in-vestigation of a wide range of different semiconductor ma-terial systems, and (iii) a significant reduction of the costinvolved in the development of a picosecond two-colorKerr microscope due to the utilization of a single, com-paratively inexpensive femtosecond fiber-laser source.We have developed the Kerr microscope to studylow-temperature electron spin transport by means oftime-resolved real-space imaging of the diffusion of op-tically excited electron spin packets in bulk semicon-ductors and quantum wells (QWs). Typical spin diffu-sion lengths in semiconductors are of the order of sev-eral micrometers.
In bulk n-GaAs long spin relax-ation times exceeding 100 ns are routinely observed.
However, spin relaxation in QWs is much faster and typ-ically happens on time scales of the order of hundredpicoseconds.
Time-resolved real-space imaging oflow-temperature electron spin diffusion processes there-fore requires an instrument which allows to investigateelectron spins with micrometer spatial and picosecondtime resolution at cryogenic temperatures. The pump-probe MOKE microscope presented here meets these re-quirements and is capable of measuring optically inducedelectron spin diffusion for sample temperatures between8 K-300 K with ≈ (cid:46) µ m spatial resolution.To illustrate the capabilities of the instrument, wedemonstrate picosecond real-space imaging of the diffu-sive expansion of an optically excited electron spin packetin a (110) GaAs quantum well sample. From the time-resolved measurement of the increase of the spin packetwidth we directly determine the spin diffusion coefficient D s as a function of excitation power and lattice temper-ature. II. KERR MICROSCOPY SETUP
In the following we provide a detailed description ofthe two-color pump-probe supercontinuum MOKE mi-croscope. A diagram of the experimental setup is shownin Fig. 1. To minimize disturbances by dynamic changesin the ambient environment we operate the Kerr micro-scope in a climate-controlled laboratory where we stabi-lize the temperature and relative humidity within ± ◦ C and below 35 %, respectively. The instrument is built onan optical table equipped with an active vibration iso-lation system. The detrimental effects of turbulent aircurrents on the polarization state of the pump and probelasers are reduced by enclosing the entire setup with alaminar flow box.Access to sample temperatures between 8 K and 300 Kis provided by an Oxford MicrostatHe model narrow tailliquid helium flow optical cryostat which enables the uti-lization of short focal length focussing optics. The cryo-stat is mounted on a 3-axis stage to allow for lateral scan-ning of the sample position and focussing of the pumpand probe beam.The sample is yieldably clamped to a copper holderwhich is mounted on the coldfinger of the cryostat. Careis taken to avoid a strain induced k -dependent splittingof the conduction band spin states which affects the elec-tron spin dynamics. A calibrated Cernox resonant tun-neling diode (RTD) temperature sensor is attached tothe backside of the copper holder for accurate measure-ments of the sample temperature. The cryostat is placedbetween the poles of an electromagnet which allows forthe application of external in-plane magnetic fields of upto 800 mT in Voigt geometry. A calibrated Hall sensor isused to monitor the external magnetic field at the sampleposition.The main optical components of the pump-probeMOKE microscope are the supercontinuum generation,the instrumentation for the independent spectral filteringof the pump and probe laser, the focussing and raster-scanning optics for the local optical electron spin exci-tation and detection and the manipulation of the probelaser position, and the balanced photoreceiver lock-in de-tection scheme for the measurement of the small spin-induced changes of the probe laser polarization. A de-tailed description of each component is given in the fol-lowing.
A. Supercontinuum generation
The generation of the ‘white light’ supercontinuumfrom which we derive the pump and probe laser beams isbased on nonlinear frequency conversion of a short near-infrared laser pulse in a tapered photonic fiber. For theoptical pumping of the fiber we use the output of a mode-locked PolarOnyx Uranus 1030 high power femtosecondlaser which provides pulses with a central wavelength of ≈ (cid:46)
300 fs.The pump pulse is coupled into the tapered fiber byan infinity corrected Olympus 10x plan achromat objec-tive (numerical aperture NA = 0 .
25) which is mountedon a 3-axis fiber launch system. A Faraday isolator isplaced in the pump beam path in front of the objec- prism linear polarizer pinhole lock-in amplifier delay line g r a t i ng c o m p r e ss o r fs fiber laser t ape r ed f i be r PEM piezo positioner 8K – 300K s a m p l e and R T D s en s o r i n c r o ys t a t ba l an c ed pho t od i ode s CMOS camera bandpass filter longpass filter Wollaston prism linear polarizer objective λ pump λ probe ω ref =50.1kHz compact spectrometer λ /2 plate electromagnet linear stage ! " " % & FIG. 1. Schematic of the two-color pump-probe MOKE microscope. The main optical components of the Kerr microscope arethe supercontinuum generation, the instrumentation for the independent spectral filtering of the pump and probe laser, thefocussing and raster-scanning optics for the local optical electron spin excitation and detection and the manipulation of theprobe laser position, and the balanced photoreceiver lock-in Kerr rotation detection scheme for the measurement of the smallspin-dependent changes of the probe laser polarization. tive to prevent unintentional back-reflection of the pumplight into the laser cavity. Owing to the high peak in-tensities achieved by the strong femtosecond pump laserin the thin tapered fiber, a variety of non-linear effectsincluding soliton fission, stimulated Raman and Brillouinscattering, four-wave-mixing, and self-phase modulationlead to a strong spectral broadening of the pump pulse. Depending on specific parameters such as fiber waist di-ameter, excitation pulse duration, pump wavelength, andpeak pulse power this spectral broadening results in thecreation of a smooth supercontinuum which can extendfrom ≈
400 nm − The configuration of the instrument described hereis optimized for the investigation of GaAs-based semi-conductor heterostructures. We therefore use a com-paratively thick fiber with a 4 µ m waist diameter whichleads to supercontinuum creation with appreciable spec-tral weight in the vicinity of the relevant ≈
800 nm spec-tral range. The maximum time-averaged power trans-mitted through the fiber is 880 mW. A typical spectrumof the output of the supercontinuum source is shown inFig. 2 (a) on a logarithmic scale. While the supercon-tinuum in the present configuration is limited to wave-lengths (cid:38)
550 nm, access to higher photon energies canbe obtained by using a thinner fiber.After exiting the fiber the supercontinuum light iscollimated by a second, infinity corrected, fiber launchmounted Olympus 4x plan achromat microscope objec-tive (NA = 0 . B. Spectral filtering of the pump and probe beam
The spectral position of the excitonic Kerr resonancedepends on the semiconductor material, the sample tem-perature, and in the case of low-dimensional systems onthe confinement energy. While it is usually sufficient tooperate the pump laser at fixed above-bandgap wave-lengths, MOKE microscopy requires a continuously tun-able probe laser to allow for a versatile investigation ofdifferent semiconductor heterostructures.To meet this requirement we have implemented aprism-based spectral filtering scheme for the probe laser.The probe beam is horizontally dispersed by a N-SF14glass prism. A high-dispersion glass type is used to en-hance the angular spread of the individual spectral com-ponents of the supercontinuum to achieve a high spectralresolution. To minimize reflection losses, the prism is op-erated under the condition of minimum deviation. The59.6 ◦ apex angle of the prism is designed such that theincident and exit angles are made Brewster’s angle forwavelengths between ≈ −
900 nm. The lossless trans-mitted horizontal polarization component of the initiallyunpolarized supercontinuum is subsequently used as thelinearly polarized probe laser beam as described below.The dispersed probe beam is focused by a f = 100 mmlens on a 50 µ m pinhole. In the focal plane the angulardispersion translates to a lateral displacement of the fo-cus position of different wavelength components of thesupercontinuum. The focussing lens is mounted on aPI miCos LS-65 linear stage which allows for horizontalscanning of the lens position with sub-micrometer reso-lution and uni-directional repeatability. Variation of thelens position allows for a selection of the desired wave-length component from the supercontinuum by the pin-hole. After passing the pinhole, the transmitted spectral
500 550 600 650 700 750 800 850
FWHM=3.9meV N o r m . i n t en s i t y Wavelength (nm)
600 700 800 900 1000 10 -3 -2 -1 N o r m . i n t en s i t y (a) Wavelength (nm)’white light’ supercontinuum 500 600 700 80002468 (b) F W H M ( m e V ) Wavelength (A)
FIG. 2. Spectra of the continuously tunable probe laserobtained by dispersive filtering of the white-light supercon-tinuum. Inset (a): Typical output spectrum of the pulsedfiber-laser source (4 µ m fiber waist diameter, 880 mW time-averaged total output power). Inset (b): Spectral width(FWHM) of the probe laser as a function of central laserwavelength λ probe . The red dashed line indicates the meanFWHM of 3.9 meV. component is collimated by a second f = 60 mm lens.By manipulating the position of the first lens while keep-ing the pinhole position fixed, the probe wavelength canbe tuned without changing the beam direction after thesecond lens.In Fig. 2 we exemplarily demonstrate the continuoustuning of the probe laser over a wide spectral range be-tween 520 nm and 820 nm by a systematic variation ofthe scanning lens position. For each lens position wemeasure the probe laser spectrum with a compact CCDspectrometer which can be introduced in the probe beampath after the filtering instrumentation.We determine the energy resolution of the prism filterby measuring the full-width at half maximum (FWHM)of the probe laser spectrum as a function of the cen-tral wavelength λ probe . In Fig. 2 (b) we show that nosystematic variation of the probe laser linewidth withincreasing λ probe is observed. The FWHM stays approx-imately constant over the whole examined wavelengthrange. The mean value of the FWHM is 3.9 meV and theFWHM never exceeds 5 meV. If necessary, the spectralresolution of the prism filter can be improved by using asmaller pinhole and a higher dispersion glass type; how-ever this leads to a reduction of the available probe laserpower.The pump laser wavelength is selected by passing thesupercontinuum through a standard optical bandpass fil-ter. A broad selection of high-quality dielectric bandpassfilters which cover the whole visible and near-infraredspectral range is commercially available. Depending onthe material system under investigation, filters with ap-propriate central wavelengths and passband widths can be introduced in the pump laser beam path. For themeasurements presented in this manuscript we employ adielectric bandpass with a central wavelength λ pump =780 nm and a spectral FWHM of 10 nm ( ≈
20 meV).A synchronized pair of conventional mechanical delaylines is placed in the pump beam path to introduce avariable time delay ∆ t between the pump and probepulses. The PI miCos LS-110 linear stages each havea travel range of 305 mm with 50 nm resolution and uni-directional repeatability. The present configuration pro-vides a maximum delay of 4 ns which can be extended bymulti-pass operation of the delay lines. C. Focussing and raster-scanning optics
The diffraction limit for the spatial resolution ∆ ofconventional far-field optical microscopy is determined bythe wavelength λ and the NA of the focussing objective: ∆ ≥
12 1 . λ NA (1)Achieving micrometer spatial resolution in the near-infrared and visible range therefore requires the use ofhigh NA focussing optics with short focal distances. Tominimize aberrations in the spatially resolved electronspin detection it is further desirable to utilize high-qualityroom-temperature microscope objectives which must beoperated outside the cryostat. Spatial constraints dic-tate to use short working distance optical cryostats andthe utilization of the same microscope objective for thefocusing of both the pump and probe laser beam.We use an infinity-corrected Mitutoyo 50x plan apoc-hromatic long working-distance microscope objective( f = 4 mm, NA = 0 .
42) to focus the pump and probebeam at normal incidence on the sample surface. To scanthe probe with respect to the fixed pump beam position,we introduce a pair of f = 4 mm aspheric lenses arrangedin confocal geometry in the probe beam path. The firstlens is mounted on a PI P-611.3 Nanocube 3-axis piezopositioner which offers 100 µ m travel range with nanome-ter resolution along each axis.Manipulation of the relative position of the asphericlens pair changes the angle of incidence on the micro-scope objective which translates to a change of the fo-cus position of the probe beam on the sample surface.Since the focal lengths of the microscope objective andthe aspheric lenses are equal, lateral scanning of thepiezo-mounted lens directly results in a translation of theprobe laser beam position at the sample surface by thesame distance. The Kerr microscope therefore offers a100 × µ m field of view.After reflection from the sample surface the pump andprobe lasers are collected by the same microscope ob-jective. Polarization retaining beamsplitters are used tosteer the pump and probe beams to the Kerr rotationdetection optics and to a CMOS camera which is placedin the focal plane of a f = 75 mm lens. The CMOS cam-era is used to monitor the focussing of both lasers andthe positioning of the probe beam. We additionally usethe CMOS camera for the determination of the spatialresolution of the MOKE microscope as described below. D. Optical spin excitation
We employ the standard optical orientation technique for the electron spin excitation by the pump laser. We usea Hinds Instruments PEM-100 photoelastic modulator (PEM) to periodically modulate the pump polarizationbetween σ + left and σ − right circular polarization ata frequency ( ω ref / π ) = 50 . ◦ to the horizontal by a high-quality Glan-Thompson polarizer. The fast axis of the PEM is orientedhorizontally and the retardation is set to λ/ S z oriented along the sample normal ˆ z .The benefit of the PEM modulation is twofold. First,the fast, sinusoidal change of the electron spin orientationprevents the unintentional polarization of nuclear spinsby transfer of angular momentum from the electron tothe lattice system. Second, the periodic modulation ofthe pump laser polarization enables lock-in detection ofthe small Kerr rotation signals.
E. Lock-in Kerr rotation detection
The spatially resolved electron spin detection by ourpump-probe Kerr microscope is based on the polarMOKE: In the presence of spin-polarized electrons, theprobe laser state is changed from the initially linear toelliptical polarization after reflection from the samplesurface. In polar geometry, the major axis of polar-ization is rotated by the Kerr angle θ . The ratio of themajor and minor axis of polarization is determined bythe tangent of the Kerr ellipticity φ . For the small polar-ization changes typically observed in pump-probe MOKEmicroscopy, the polar Kerr rotation depends linearly onthe electron spin polarization. Therefore a spatially re-solved measurement of the Kerr rotation θ ( r ) ∝ S z ( r )can be used to map the local electron spin polarization. The magnitude of Kerr rotations observed in pump-probe MOKE microscopy experiments is typically wellbelow 1 mrad. To facilitate the detection of the smallpolarization signals we employ a balanced photoreceiverlock-in detection scheme:
Before entering the focussing optics, the probe laser isset to vertical linear polarization by a Glan-Thompsonpolarizer. After reflection from the sample surface, theelliptical polarization state of the probe laser induced by the polar MOKE is described by the Jones vector: E out = (cid:18) cos( θ )cos( φ ) − i sin( θ )sin( φ )sin( θ )cos( φ ) + i cos( θ )sin( φ ) (cid:19) (2)After being collected by the microscope objective, themajor axis of polarization of the reflected probe beamis rotated by 45 ◦ by a Soleil-Babinet compensator. Thecompensator therefore is set to half-wave retardation andthe fast axis is tilted by 22.5 ◦ to the vertical.We use a Wollaston prism to split the probe laserinto two separate, linearly polarized beams carrying theˆ x (horizontal) and ˆ y (vertical) polarization componentswhich are focused on two separate photodiodes of a bal-anced photodetector. A high-transmission Semrock Ra-zorEdge ultra-steep longpass filter with an appropriatecut-off wavelength is placed in front of the Wollastonprism to prevent the collinear, modulated pump laserfrom entering the detector. The custom-built photode-tector used in our instrument is specifically optimizedfor raster-scanning microscopy to achieve highest possi-ble spatial homogeneity in the detection efficiency. Wetherefore employ large-area Hamamatsu Photonics pho-todiodes to compensate for the small lateral displacementof the probe beam focus position on the diode surfacecaused by the the raster-scanning of the probe beam po-sition on the sample.The two probe beam components evoke photocurrentswhich are proportional to the respective beam intensity I x,y ∝ | ( E out ) x,y | . A high-sensitivity transimpedanceamplifier is used to generate a voltage signal which isproportional to the photocurrent difference: V out ∝ ( I x − I y ) ∝ (cid:18) sin [2( θ − φ )] + sin [2( θ + φ )] (cid:19) (3)The periodic modulation of the optical spin excitationby the PEM leads to a sinusoidal time-dependence ofthe Kerr rotation and ellipticity, i.e. θ = θ K sin( ω ref t )and φ = φ K sin( ω ref t ). The photodetector output voltagecan be expanded in terms of odd harmonics of the PEMfrequency ω ref using the Jacobi-Anger identity as: V out ( t ) ∝ ∞ (cid:88) n =0 (cid:18) J n +1 [2( θ k − φ k )] + J n +1 [2( θ k + φ k )] (cid:19) × sin [(2 n + 1) ω ref t ] (4)where J k denotes the Bessel function of k th order.The voltage V out ( t ) is demodulated by a Stanford Re-search SR530 lock-in amplifier. The lock-in output volt-age V LI is proportional to the ω ref frequency componentof the input signal, i.e. the lock-in is only sensitive tothe n = 0 term of the series in Eq. (4). Further-more, since | θ K | (cid:28) | φ K | (cid:28)
1, the approximation J ( x ) ≈ x can be used. Therefore the lock-in outputvoltage is a direct measure of the local Kerr rotation, i.e. V LI ( r ) ∝ θ K ( r ).Finally, by repeatedly raster-scanning the probe withrespect to the pump spot position and measuring thelocal Kerr rotation θ K (∆ t, r ) as a function of the pump-probe delay ∆ t , full information on the spatio-temporaldynamics of the electron spin polarization S z (∆ t, r ) isobtained. This is the working principle of time-resolvedreal-space imaging of electron spins by pump-probe Kerrmicroscopy. III. INSTRUMENT CHARACTERIZATIONA. Spatial resolution
We determine the spatial resolution of the instrumentfrom CMOS camera images of the focused pump andprobe spots. The square pixel size of the camera is d CMOS = 5 . µ m. For the (75 mm / µ m onthe sample surface.From Eq. (1) the diffraction limit for the attain-able spatial resolution depends on the laser wavelength λ . In the present configuration the Kerr microscopeis optimized for the investigation of GaAs-based het-erostructures whose excitonic Kerr resonances are in the810 nm −
820 nm spectral range. We therefore character-ize the spatial resolution for an above-bandgap centralpump wavelength λ pump = 780 nm and a probe wave-length λ probe = 820 nm.In Figs. 3 (a,c) we show CMOS camera images ofthe focused pump and probe spots. Line cuts throughthe center of the radial symmetric intensity profiles areshown in Figs. 3 (b) for the pump and (d) for the probespot. The intensity profiles I ( r ) are well described by aGaussian I ( r ) = I × exp (cid:18) − r ∆ (cid:19) (5)where I is the maximum intensity and ∆ the (1 /e ) half-width of the spot. Gaussian fits of the spot intensityprofiles shown in Figs. 3 (b,d) yield ∆ Pump = 0 . µ mand ∆ Probe = 1 . µ m for the pump and probe beam. Theincreased probe spot width is mainly caused by the ad-ditional passage of the two aspheric lenses. We have ver-ified that the determination of spot widths from CMOScamera images yields identical results as the conventionalknife-edge scan technique. The net optical resolution∆ of the microscope is determined by the convolutionof both intensity profiles. From the convolution of theGaussian intensity profiles we obtain a spatial resolution∆ = (cid:113) ∆ + ∆ = 1 . µ m. B. Time resolution
Dispersion in the tapered fiber leads to a signifi-cant prolongation of the initial (cid:46)
300 fs infrared pumppulse. As a result, the total duration of the super-continuum pulse is of the order of 5 ps. However, asrevealed by cross-correlation frequency-resolved opticalgating (XFROG) characterization, the temporal widthof the arrival time distribution of individual spectral com-ponents of the supercontinuum with bandwidths compa-rable to our filtered pump and probe laser beams is typ-ically of the order of 500 fs (Refs. 22 and 33). Fromthis consideration we expect an overall time resolution of ≈ in situ , i.e. it does not require any modification of theexperimental setup or additional equipment, and consid-ers all optical components of the Kerr microscope in itsoperational configuration which could potentially impairthe time resolution of the instrument.In Fig. 3 (e) we show a typical time trace of theKerr rotation θ K (∆ t ) which we measure in a MBE-grown n-GaAs epilayer (room temperature electron den-sity n = 7 × cm − , 1 µ m layer thickness) for shortdelays between −
20 ps and 40 ps. The sample tempera-ture is T L = 8 K. For the detection of the Kerr rotationtransient the probe laser is tuned to the excitonic res-onance at λ probe = 820 nm. The pump wavelength is λ pump = 780 nm.Following the excitation at ∆ t = 0 ps we observe a verysteep rise of the Kerr rotation θ K (∆ t ). With increasing∆ t , the increase in the Kerr rotation signal graduallyslows down. We observe a (1 /e ) rise time t e = 4 ps forwhich θ K ( t e ) has reached 63 % of the maximum ampli-tude. The time t e can be used as a rather conservativeestimate for an upper limit for the time resolution of ourinstrument. However, we note that on the examined pi-cosecond timescale the negative-delay flank of the initialKerr rotation transient does not exhibit the Gaussian er-ror function type shape which is characteristic for a timeresolution limited observation of a transient optical non-linearity. This suggests an overall time resolution (cid:46) θ K (∆ t ) observed fordelays ∆ t (cid:38)
01 -20 -10 0 10 20 30 40
Data Fit I n t en s i t y (b) (1/e) width1.9(cid:181)m 3.4(cid:181)m (d) -6 -4 -2 0 2 4 6-6-4-2024 pump =780nm (a) X position ((cid:181)m) Y po s i t i on ( (cid:181) m ) pump -6 -4 -2 0 2 4 6 probe =820nm probe(c) X position ((cid:181)m) Data f =4ps (e) (d) K e rr r o t a t i on ( a r b un i t s ) Delay (ps) bulk n-GaAsn = 7x10 cm -3 T L = 8K FIG. 3. Characterization of the spatial and temporal resolution of the pump-probe MOKE microscope. (a,c) CMOS cameraimages of the focused pump and probe laser spots. (b,d) Normalized intensity profiles of the pump and probe laser obtainedfrom line cuts through the CMOS camera images. Red solid lines are Gaussian fits from which we determine the spatialresolution of the instrument. (e) Transient Kerr rotation θ K (∆ t ) in a n-GaAs epilayer at T L = 8 K. Red solid line is a fit to anexciton formation model from which we obtain an exciton formation time τ f ≈ exciton formation following the non-resonant optical elec-tron spin excitation. In bulk GaAs, the photo-inducedKerr rotation results from an energetic splitting ∆ E ofthe E excitonic resonances for σ ± light, the excitonicspin splitting. The size of the spin splitting deter-mines the magnitude of the Kerr rotation, i.e. θ K ∝ ∆ E .Since ∆ E is proportional to the exciton density n X , wecan obtain an estimate of the exciton formation time t f from the Kerr rotation transient θ K (∆ t ): Following Refs.35 and 36 we model the exciton formation for very shortdelays ∆ t > n X (∆ t ) ≈ n X, max [1 − exp( − ∆ t/t f )]. From thefit of θ K (∆ t ) ∝ n X (∆ t ) shown in Fig. 3 (e) we determinean exciton formation time t f = (4 . ± .
3) ps under ournon-resonant excitation conditions. This finite formationtime is causing the comparatively slow rise in the Kerr ro-tation transient which masks the instruments faster timeresolution.
IV. MEASUREMENTS AND DISCUSSION
To demonstrate the operation of our Kerr microscopewe present time-resolved real-space imaging measure-ments of the diffusion of optically excited electron spinpackets in a (110) GaAs QW. The exploration of thestrongly anisotropic electron spin relaxation rates in(110) QWs has received considerable attention in thepast.
In contrast, only a small amount of workhas been devoted to the experimental investigation ofelectron spin transport in such (110) QWs. Electronspin diffusion coefficients in (110) QWs have mainly beendetermined by transient spin grating measurements which have focused on elevated temperatures. As a firststep towards closing this gap we present low-temperature electron spin diffusion coefficients for a (110) GaAs QWsample which we determine directly from time-resolvedpump-probe MOKE microscopy.The sample has been grown by molecular beam epitaxy(MBE) on a semi-insulating (110)-oriented GaAs sub-strate. Growth was initiated by a 200 nm GaAs bufferlayer followed by 500 nm of Al . Ga . As and a se-ries of five identical 20 nm wide GaAs QWs which areembedded in 64 nm Al . Ga . As barriers. The sam-ple is capped by a 120 ˚A Al . Ga . As layer followedby a top 2 nm GaAs layer. Our standard continuous-wave Hanle-MOKE characterization and resonant spinamplification (RSA) measurements (not shown here)have revealed long out-of-plane spin lifetimes T zs (cid:38)
30 nsat low T L which suggests the presence of a low-densitytwo-dimensional electron gas (2DEG) in the QWs.For all measurements presented here, the central probelaser wavelength is tuned to the (1e-1hh) excitonic reso-nance at λ probe = 814 nm and the time-averaged probelaser power is P probe = 12 µ W. The pump central laserwavelength is λ pump = 780 nm and the pump power isvaried between P pump = 1 . µ W and 5 µ W as indicatedbelow.At low T L , the spin lifetime T zs is comparable to ourpulse-to-pulse interval t rep = 27 . B xy ≈ .Following pulsed local excitation by a Gaussian pumpspot, the time evolution of the lateral expansion of the -20 -10 0 10 20 Delay t (a)
Gaussian Data P pump =3(cid:181)W N o r m . K e rr r o t a t i on Radial distance ((cid:181)m) pump =3(cid:181)W Delay (ps) w s ( (cid:181) m ) =3.8(cid:181)m D s = (100–3) cm s -1
10 20 30 40 50100150200250 (c) pump power 5.0(cid:181)W 3.0(cid:181)W 1.5(cid:181)W D s ( c m s - ) T L (K)
10 20 30 40 10 s ( c m V - s - ) T L (K) s ~T -1L P pump =1.5(cid:181)W FIG. 4. (a) Time-evolution of an optically excited electronspin packet in the (110) QW sample at T L = 8 K. The dif-fusive spread of the spin packet is observed from the increasein the profile width for increasing delays (bottom to top; thedelay ∆ t is indicated above the respective curve). Markersare experimental data, red solid lines are Gaussian fits. (b)Linear increase of the squared (1/e) half width w s (∆ t ). For∆ t = 0 ps the spin packet width coincides with the optical res-olution ∆ = 3 . µ m indicated by the black dashed line. Thespin diffusion coefficient D s = (100 ±
3) cm s − is obtainedfrom the slope of a linear fit (red solid line). (c) Lattice tem-perature dependence of D s for different pump powers. Inset:Spin mobility µ s ( T L ) calculated via the Einstein relation from D s ( T L ) measured for the lowest pump power. electron spin packet in the (110) QW plane is: S z (∆ t, r ) = σ S z ,0 σ + 4 D s ∆ t exp (cid:18) − r w s − ∆ tT zs (cid:19) (6)with an initial (1 /e ) half width σ and amplitude S z ,0 .While spin relaxation leads to an decrease of the overallamplitude of the Gaussian spin packet, the squared (1 /e )half-width w s = σ + 4 D s ∆ t (7)only depends on the spin diffusivity D s (∆ t ) and increaseslinearly with time. To determine the electron spin diffu-sion coefficient of the (110) QWs we measure a series ofspin polarization profiles S z (∆ t, r ) for increasing delays∆ t and extract the spin packet width w s (∆ t ). From Eq.(7) we then directly obtain the spin diffusivity from theslope of a linear fit of the time-dependence of the spinpacket width. In Fig. 4 (a) we exemplarily show electron spin polar-ization profiles S z (∆ t, r ) which we measure at T L = 8 Kwith a pump power P pump = 3 µ W for delays up to814 ps together with Gaussian fits. The shape of the spinpacket remains Gaussian for all times and the diffusivespread of the spin packet with increasing ∆ t is clearlyobserved. The linear increase of the squared spin packetwidth w s (∆ t ) expected from Eq. (7) is confirmed in Fig.4 (b). From the slope of a linear fit (red solid line) we ob-tain a spin diffusion coefficient D s = (100 ±
3) cm s − .Following the above procedure, we measure the spindiffusivity D s for T L between 8 K and 40 K and pumppowers P pump = 1 . µ W, 3 µ W, and 5 µ W. Our resultsfor the dependence of D s on excitation density and latticetemperature are summarized in Fig. 4 (c).For all examined pump powers, we find that D s onlyvaries weakly with T L . We observe that reducing P pump from 5 µ W to 3 µ W results in a systematic decrease of thespin diffusion coefficient. However, an additional reduc-tion to a very low pump power of 1.5 µ W does not resultin a further significant decrease of D s . This suggests thatwe have reduced pump-induced disturbances sufficientlyto observe the intrinsic temperature dependence of thespin diffusivity. We therefore focus on D s ( T L ) obtainedfor the lowest pump power of 1.5 µ W for the followingdiscussion.Contrary to the case of bulk GaAs, we observe aconstant diffusivity D s ≈
100 cm s − which does notincrease with T L . A similar temperature-independentspin diffusion coefficient has also been observed previ-ously by transient spin-grating measurements in a (110)GaAs QW for elevated T L between 60 K and roomtemperature. Following Ref. 41 we use the Einsteinrelation to calculate the spin mobility µ s = ( e/k B T L ) D s of the non-degenerate (110) QW 2DEG. We then use thetemperature dependence µ s ( T L ) to infer the dominantscattering mechanism which limits the spin diffusivity.From the observed constant diffusivity D s and the Ein-stein relation, we expect a spin mobility µ s ∝ T − L , whichwe indeed observe, as shown in the inset of Fig. 4 (c).This temperature dependence of µ s is characteristic fora non-degenerate 2DEG for which the mobility is lim-ited by scattering with acoustic phonons for which theprobability increases ∝ ( k B T L ) (Ref. 41). V. SUMMARY
We have presented a supercontinuum fiber-laser pump-probe scanning MOKE microscope which enables the in-vestigation of spin relaxation and spin transport phenom-ena in semiconductor heterostructures with picosecondtime and micrometer spatial resolution at cryogenic tem-peratures. The pulsed supercontinuum laser source pro-vides access to the whole visible and near-infrared spec-tral range, therefore offering the possibility to investigatea wide range of different semiconductor material systems.By implementing two separate spectral filtering schemeswe have obtained the ability to independently select thepump and continuously tunable probe laser wavelength.We have demonstrated the capabilities of the Kerrmicroscope by providing an investigation of low-temperature electron spin propagation in (110) GaAsQWs. We have measured electron spin diffusion coeffi-cients of a low-density (110) QW 2DEG by time-resolvedreal-space imaging of the time-evolution of an opticallyexcited electron spin packet. From the temperature de-pendence of the spin mobility we have identified acousticphonon scattering as the dominant scattering mechanismwhich limits the low-temperature electron spin transportin the (110) QWs.We anticipate a broad variety of future applicationsfor the MOKE microscope presented here. The highspatial and temporal resolution of our instrument allowsfor the investigation of spin transport in both standardsemiconductor heterostructures and lithographically de-fined spin-transport devices. The ability to indepen-dently change the pump and probe energy further enablesus to control the electron temperature by variation of theexcitation excess energy. Our microscope thereby offersthe possibility to study the interplay of charge, spin andheat transport in semiconductors which is the subject ofthe emerging field of spin caloritronics . ACKNOWLEDGMENTS
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