Photon Energy Dependence of Kerr Rotation in Chalcogenide Superlattices
Takara Suzuki, Richarj Mondal, Yuta Saito, Paul Fons, Alexander V. Kolobov, Junji Tominaga, Hidemi Shigekawa, Muneaki Hase
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J u l Photon Energy Dependence of Kerr Rotation in Chalcogenide Superlattices
Takara Suzuki , Richarj Mondal , Yuta Saito , Paul Fons , Alexander V.Kolobov , , Junji Tominaga , Hidemi Shigekawa , and Muneaki Hase Department of Applied Physics, Faculty of Pure and Applied Sciences,University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology,Tsukuba Central 5, 1-1-1 Higashi, Tsukuba 305-8565, Japan and Department of Physical Electronics, Faculty of Physics,Herzen State Pedagogical University, St. Petersburg, 191186, Russia ∗ We report on pump-probe based helicity dependent time-resolved Kerr measurements of chalco-genide superlattices, consisting of alternately stacked GeTe and Sb Te layers under infrared ex-citation. The Kerr rotation signal consists of the specular Inverse Faraday effect (SIFE) and thespecular optical Kerr effect (SOKE), both of which are found to monotonically increase with de-creasing photon energy over a sub-eV energy range. Although the dependence of the SIFE can beattributed to a response function of direct third-order nonlinear susceptibility, the magnitude of theSOKE reflects cascading second-order nonlinear susceptibility resulting from electronic transitionsfrom bulk valence band to interface-originating Dirac states of the superlattice. PACS numbers:
I. INTRODUCTION
Structures fabricated from the alternate stacking ofGeTe and Sb Te layers, referred to as interfacial phasechange memory (iPCM) or chalcogenide superlattices(CSL), are known to form either Weyl or Dirac semimetalsystems, which have closely related topological insula-tor (TI) properties, depending on the thickness of theconstituent layers, and are believed to be excellent can-didates for power-saving nonvolatile memory applica-tions [1–4]. Ab initio band structure simulations ofCSL structures show a gapless band intersection, a so-called Dirac cone, is formed for the so-called invertedPetrov phase (Dirac semimetal phase) due to the hy-bridization of the electronic wave functions across theinterfaces between the GeTe and Sb Te layers [5]. Al-though recent angle-resolved photoemission spectroscopy(ARPES) study have examined the band structure of thechalcogenide alloy (Ge Sb Te ) [6], there has been nodirect experimental evidence for a Dirac-like electronicband structure in CSLs. To further examine the topolog-ical properties of CSLs and to further spintronics appli-cations, experimental investigation of the band structureof CSLs is required.TI-like characteristics can be discerned optically us-ing circularly polarized light due to the fact that theangular momentum of circularly polarized photons caninduce spin-selective excitations to/from topological sur-face states, which are a key signature of topological char-acter [7–10]. Under excitation by circularly polarizedlight, some solid materials show helicity dependent op-tical activity, such as polarization rotations and circulardichroism [11–14]. In this study, the authors focus on ∗ Electronic address: [email protected] nonlinear optical effects induced by femtosecond laser ir-radiation, these include the inverse Faraday effect (IFE)[15, 16] and the optical Kerr effect (OKE) [17], both ofwhich lead to polarization rotation. The former rotationoccurs due to magnetization induced by the circularlypolarized light irradiation while the latter is a result ofbirefringence through a third-order nonlinear optical pro-cess governed by the nonlinear susceptibility χ (3) .In a pump-probe experiment, the polarization rotationof the incident probe beam in a material is sensitive to thehelicity of excitation pulse. For instance, simple metals[18], magnetic materials [16] or chalcogenide compounds[19, 20] have shown specular IFE (SIFE) or specular OKE(SOKE). It is noteworthy that, in CSL, the SOKE signalbecomes larger than the SIFE even though the SIFE isusually larger in normal insulators such as chalcogenidealloys [20]. This is believed to arise from the large χ (2) ofthe topological Dirac state since third-order nonlinear op-tical processes are constituted from not only direct thirdorder processes but also cascading second-order nonlin-ear processes as expressed by χ (2) · χ (2) [19, 20]. In aprevious experiment by Mondal et al. , only near-infrared830 nm femtosecond laser pulses were used [20]. To ex-plore the relationship between the SOKE (SIFE) signaland the band structure of CSLs, pump-probe measure-ments over a wide wavelength (or photon energy) rangeare required. Here, we report on the photon energy de-pendence of the SIFE and SOKE signals in CSL by ob-serving the polarization rotation of the linearly polarizedprobe beam. In particular, 1200 ∼ II. EXPERIMENTAL
Reflection geometry pump-probe measurement werecarried out to obtain the transient Kerr rotation of thereflected probe pulse at room temperature [19]. The re-flected probe pulse was decomposed into two beams po-larized at +45 ◦ and − ◦ , respectively, by a Wollastonprism and detected by balanced Si-PIN photo-detectorsas illustrated in Fig. 1(a). The intensity difference of thetwo beams was defined as the Kerr rotation of the probepolarization: ∆ θ k . Femtosecond laser pulses (repetitionrate, 80 MHz; pulse width, 20 fs; and average power, 525mW) were generated by a mode locked Ti : sapphirelaser oscillator. Its output was amplified by a regener-ative amplifier system (RegA9040) to produce pulses of40 fs duration with an average power of 500 mW at a100 kHz repetition rate. Finally, the amplified pulseswere sent to an optical parametric amplifier (OPA9580)to generate IR pulses, whose wavelength was tuned from1200 to 1600 nm (1.03 – 0.775 eV). The 600 nm visiblephotons were also generated by doubling the 1200 nmphoton energy using second harmonic generation with a1 mm-thick β -barium borate (BBO) crystal. The pumpand probe wavelengths were identical in the present ex-periment. The output beam was split into an intensepump and weak probe beams. The pump and the probebeam were co-focused onto the sample to a spot size ofabout 70 µ m with an incident angle of about 15 ◦ and 10 ◦ with respect to the sample normal, respectively. A quar-ter wave plate (QWP) was inserted in the pump opticalpath to allow the pump helicity to be varied continuouslyfrom linear to circular, and data was recorded for every10-degree rotation of the QWP. Analyzing the optical re-sponse as a function of the pump helicity offers insightinto the role of topological Dirac state in the optical re-sponse. The Kerr rotation was recorded as a function oftime delay between the pump and probe over a range of20 ps by means of a horizontally shaking mirror with ascanning frequency of 10 Hz [23, 24]. The pump powerwas kept constant at 20 mW over the wavelength rangeused, which corresponds to a fluence of ≈
16 mJ/cm ,a value calculated using a focused beam diameter of ≈ µ m (measured using a knife-edge). An optical pen-etration depth of ≈
100 nm at 1550 nm was calculatedfrom the absorption coefficient [25], suggesting negligiblysmall inhomogeneous excitation effects along the sampledepth.The (GeTe) /Sb Te sample used was fabricated byradio-frequency magnetron sputtering at 230 ◦ C and wasdeposited onto a Si (100) substrate. For better z-axisorientation [26, 27], the Sb Te layers were grown firstto a thickness of 3 nm at room temperature and subse-quently GeTe (0.8 nm) and Sb Te (1.0 nm) layers werealternately deposited for 20 cycles ( ∼
36 nm) at elevatedtemperature. To prevent oxidization, a 20-nm-thick ZnS-SiO layer was deposited on top of the as-grown CSLwithout breaking the vacuum. D q k ( x - ) Time delay (ps) l = 1300 nm a = 70 deg. a = 130 deg. (a) (b)
FIG. 1: (a) Optical setup for transient Kerr rotation measure-ment is illustrated. (b) The time resolved Kerr rotation dataobtained at 1300 nm. Strong peak was observed at zero timedelay. Left ( α = 70 ◦ ) and right-handed elliptically polarizedlight excitation ( α = 130 ◦ ) results in different peak sign ( ± ). III. RESULTS AND DISCUSSION
Time resolved Kerr rotation signals (∆ θ k ) as a func-tion of the angle of the QWP ( α ) of 70 ◦ and 130 ◦ forthe excitation wavelength of 1300 nm (0.954 eV) are pre-sented in Fig.1(b). The transient peak at time delay zerohas the opposite sign and a different intensity level fromthe remainder of the spectra, depending on the pumphelicity. Both α = 70 ◦ and 130 ◦ correspond to an el-liptically polarized pump pulse and exhibit the largestpositive and negative transient, respectively. The peakintensity of ∆ θ k is plotted as a function of the QWP angle α in Fig.2 for different photon energies. The peak signalsfor the smaller photon energies shown in Fig.2 exhibit asignificantly asymmetric sin(2 α ) oscillation due to contri-butions from a smaller sin(4 α ) oscillation. The strongersin(2 α ) oscillation observed in the present study for theCSL samples compared to the previous report [20] may bea consequence of the two-orders larger pump fluence used,which is expected to induce stronger SIFE arising fromlarger third-order susceptibility contributions. All thedata were fit using Eq. (1) to extract the contributionsfrom the sin(2 α ) and sin(4 α ) components, correspondingto SIFE and SOKE signals, respectively [18, 28].∆ θ k ( α ) = C sin(2 α ) + L sin(4 α ) + D, (1) x - !" "" x - !" "" x - !" "" x - !" "" x - Data Fit D q k x - FIG. 2: QWP angle dependence of transient Kerr rotation.The peak intensity of the time resolved Kerr rotation is plot-ted for each photon energy. The closed circles represent theexperimental data and the solid lines correspond to the fitusing Eq. (1). where D is a polarization independent background. Thephoton energy dependences of the C (SIFE) and L (SOKE) terms are shown in Fig.3. As the photon energydecreased, the absolute values of C and L were found tosharply increase. The steeper increase in L over C maybe a consequence of TI properties [20]. To investigatethe sharp increases in the value of L and C shown in Fig.3, the effect of the photon energy dependent susceptibil-ity function on the SIFE and SOKE is examined, wheresecond- and third-order nonlinear susceptibilities are ex-pected to play major roles [19]. Based on the classicalDrude-Lorentz model and the quantum mechanical de- | C | ( x - ) Data
Fit by Eq.(2) | L | ( x - ) Data
Fit by Eq.(4)
Photon energy (eV) Photon energy (eV) (a) (b)
FIG. 3: Photon energy dependence of (a) C and (b) L . Theblack solid curves are fits based on Eqs. (2) and (4), respec-tively. The dashed line at 0.75 eV represents the upper boundphoton energy required for exciting electrons from BVB bandsto the Dirac bands. scription for the IFE [29, 30], the response function forthe induced magnetization (SIFE) for the off-resonantcase can be simply expressed by [31], χ (3) ( ω ; ω, ω, − ω ) ∝ ω ( ω − ω ) , (2)where ω is the resonant frequency of the system, whichmeans that even though the SIFE is enhanced by be-ing close to resonance, it does not vanish away from theresonance. Fig. 3(a) shows a fit of | C | using Eq. (2)with the fitting parameter of ¯ hω = 0.66 ± | C | )satisfactory. In contrast, for the SOKE case, it was as-sumed that the response function for L was dominatedby cascading χ (2) · χ (2) contributions [19]. In quantumtheory, the second-order nonlinear susceptibility for theoff-resonant case can be expressed by permutation of in-dexes as [31, 32]: χ (2) (0; ω, − ω ) = χ (2) ( − ω ; ω, ∝ ω − ω ) , (3)where χ (2) (0; ω, − ω ) represents optical rectificationand χ (2) ( − ω ; ω,
0) represents the electro-optic effect.Thus, SOKE signal generated via cascaded optical rec-tification and the electro-optic effect, χ (2) (0; ω, − ω ) · χ (2) ( − ω ; ω, χ (2) : χ (2) · χ (2) ∝ (cid:20) ω − ω ) (cid:21) . (4)The photon energy dependence of | L | in Fig. 3(b) waswell fit by Eq. (4) with ¯ hω = 0.62 ± FIG. 4: (a) The electronic band structure of the chalcogenide superlattice, (GeTe) /Sb Te inverted Petrov model, obtainedby ab initio calculations [34]. The solid arrows indicate the transition energies necessary to excite electrons from BVB states totopological Dirac states above the Dirac point (DP) at 0.75 eV and that to BCB states at 1.0 eV. The dashed arrow representsa possible transition from BVB to near the DP ( ≈ The good fit results seen in Fig. 3 using Eqs. (2) and(4) suggest that the increase in both C (SIFE) and L (SOKE) terms arises from possible resonant excitationat ≈ C and L values toward lowerphoton energies corresponds to the tail of the resonantexcitation from the BVB to around the Dirac point (DP)( ≈ L relative to C is expected to be a consequence of cascaded optical recti-fication and electro-optic effect, varying as ∼ ω − , wherespatial inversion symmetry at the interfaces is brokenby strain effects, leading a nonzero χ (2) [20]. Note thatthe Dirac states in a CSL are either topological interface states [22] or topological bulk states [5], as predicted by ab initio band structure simulations. Although furtherexperiments using yet lower photon energies are requiredto fully understand the enhancement of the Kerr rotationin the topological chalcogenide superlattice, our resultsoffer significant insight into the Dirac-cone oriented pho-ton energy dependence of spin excitation in modern twodimensional materials.In summary, we have investigated the photon energydependence of the Kerr rotation in a chalcogenide super-lattice using infrared (1200 ∼ α ) and sin(4 α ) components.Phenomenologically, the former contribution arises fromthe SIFE while the latter arises from SOKE. The photonenergy dependence of the relative contributions, labeled C and L respectively, shows a monotonic increase withdecreasing photon energy. The energy dependence of C can be attributed to the response function χ (3) , whilethat of L can be attributed to the photon energy depen-dence of χ (2) · χ (2) , where the response functions of χ (2) and χ (3) are derived from quantum theory. The sharp in-crease is attributed to resonant-like electronic excitationfrom BVB to Dirac states. Acknowledgments
This work was supported by CREST (Nos. JP-MJCR14F1 and JPMJCR1875), JST, Japan and theJapan Society for the Promotion of Science (Grants-in-Aid for Scientific Research: 17H06088). We acknowledge Ms. R. Kondou for sample preparation.
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