Photon Energy Dependence of Kerr Rotation in Chalcogenide Superlattices

TL;DR

This study investigates how photon energy influences Kerr rotation in chalcogenide superlattices, revealing that nonlinear optical effects vary with photon energy and are linked to electronic transitions and interface states.

Contribution

It demonstrates the photon energy dependence of Kerr rotation signals and links the effects to specific electronic transitions and nonlinear susceptibilities in superlattices.

Findings

Kerr rotation signals increase as photon energy decreases.

SIFE response linked to third-order nonlinear susceptibility.

SOKE magnitude reflects cascading second-order nonlinear susceptibility.

Abstract

We report on pump-probe based helicity dependent time-resolved Kerr measurements of chalcogenide superlattices, consisting of alternately stacked GeTe and Sb$_{2}$Te$_{3}$ layers under infrared excitation. The Kerr rotation signal consists of the specular Inverse Faraday effect (SIFE) and the specular optical Kerr effect (SOKE), both of which are found to monotonically increase with decreasing photon energy over a sub-eV energy range. Although the dependence of the SIFE can be attributed to a response function of direct third-order nonlinear susceptibility, the magnitude of the SOKE reflects cascading second-order nonlinear susceptibility resulting from electronic transitions from bulk valence band to interface-originating Dirac states of the superlattice.

Equations

$$\Delta {\theta }_k(\alpha )=C\sin (2\alpha )+L\sin (4\alpha )+D,$$

$${\chi }^{(3)}(\omega ;\omega ,\omega ,-\omega )\propto \frac{1}{{\omega }^2(\omega -{\omega }_0)},$$

$${\chi }^{(2)}(0;\omega ,-\omega )={\chi }^{(2)}(-\omega ;\omega ,0)\propto \frac{1}{(\omega -{\omega }_0{)}^2},$$

$${\chi }^{(2)}\cdot {\chi }^{(2)}\propto {\left[\frac{1}{(\omega -{\omega }_0{)}^2}\right]}^2.$$

Full text

I Introduction

Structures fabricated from the alternate stacking of GeTe and Sb2Te3 layers, referred to as interfacial phase change memory (iPCM) or chalcogenide superlattices (CSL), are known to form either Weyl or Dirac semimetal systems, which have closely related topological insulator (TI) properties, depending on the thickness of the constituent layers, and are believed to be excellent candidates for power-saving nonvolatile memory applications simpson2011 ; lotnyk2017 ; kim2017 ; makino2014 . Ab initio band structure simulations of CSL structures show a gapless band intersection, a so-called Dirac cone, is formed for the so-called inverted Petrov phase (Dirac semimetal phase) due to the hybridization of the electronic wave functions across the interfaces between the GeTe and Sb2Te3 layers tominaga2014 . Although recent angle-resolved photoemission spectroscopy (ARPES) study have examined the band structure of the chalcogenide alloy (Ge2Sb2Te5) Kellner2018 , there has been no direct experimental evidence for a Dirac-like electronic band structure in CSLs. To further examine the topological properties of CSLs and to further spintronics applications, experimental investigation of the band structure of CSLs is required.

TI-like characteristics can be discerned optically using circularly polarized light due to the fact that the angular momentum of circularly polarized photons can induce spin-selective excitations to/from topological surface states, which are a key signature of topological character mclver2012 ; hsieh2011 ; boschinii2015 ; Takeno2018 . Under excitation by circularly polarized light, some solid materials show helicity dependent optical activity, such as polarization rotations and circular dichroism qiu2000 ; tse2010 ; wilks2004a ; wilks2003 . In this study, the authors focus on nonlinear optical effects induced by femtosecond laser irradiation, these include the inverse Faraday effect (IFE) ziel1965 ; kimel2005 and the optical Kerr effect (OKE) shen1984 , both of which lead to polarization rotation. The former rotation occurs due to magnetization induced by the circularly polarized light irradiation while the latter is a result of birefringence through a third-order nonlinear optical process governed by the nonlinear susceptibility $\chi^{(3)}$.

In a pump-probe experiment, the polarization rotation of the incident probe beam in a material is sensitive to the helicity of excitation pulse. For instance, simple metals wilks2004 , magnetic materials kimel2005 or chalcogenide compounds mondal2018 ; mondal2018a have shown specular IFE (SIFE) or specular OKE (SOKE). It is noteworthy that, in CSL, the SOKE signal becomes larger than the SIFE even though the SIFE is usually larger in normal insulators such as chalcogenide alloys mondal2018a . This is believed to arise from the large $\chi^{(2)}$ of the topological Dirac state since third-order nonlinear optical processes are constituted from not only direct third order processes but also cascading second-order nonlinear processes as expressed by $\chi^{(2)}\cdot\chi^{(2)}$ mondal2018 ; mondal2018a . In a previous experiment by Mondal et al., only near-infrared 830 nm femtosecond laser pulses were used mondal2018a . To explore the relationship between the SOKE (SIFE) signal and the band structure of CSLs, pump-probe measurements over a wide wavelength (or photon energy) range are required. Here, we report on the photon energy dependence of the SIFE and SOKE signals in CSL by observing the polarization rotation of the linearly polarized probe beam. In particular, 1200 $\sim$ 1600 nm IR pulses were used to investigate the TI band structure in detail. We found that both the SIFE and SOKE signals were strongly enhanced when the photon energy approached the energy required for direct excitation from core valence band states to topological Dirac states tominaga2014 ; mondal2018b ; Krizman2018 .

II Experimental

Reflection geometry pump-probe measurement were carried out to obtain the transient Kerr rotation of the reflected probe pulse at room temperature mondal2018 . The reflected probe pulse was decomposed into two beams polarized at $+45^{\circ}$ and $-45^{\circ}$, respectively, by a Wollaston prism and detected by balanced Si-PIN photo-detectors as illustrated in Fig. 1(a). The intensity difference of the two beams was defined as the Kerr rotation of the probe polarization: $\Delta\theta_{k}$. Femtosecond laser pulses (repetition rate, 80 MHz; pulse width, 20 fs; and average power, 525 mW) were generated by a mode locked Ti3+: sapphire laser oscillator. Its output was amplified by a regenerative amplifier system (RegA9040) to produce pulses of 40 fs duration with an average power of 500 mW at a 100 kHz repetition rate. Finally, the amplified pulses were sent to an optical parametric amplifier (OPA9580) to generate IR pulses, whose wavelength was tuned from 1200 to 1600 nm (1.03 – 0.775 eV). The 600 nm visible photons were also generated by doubling the 1200 nm photon energy using second harmonic generation with a 1 mm-thick $\beta$-barium borate (BBO) crystal. The pump and probe wavelengths were identical in the present experiment. The output beam was split into an intense pump and weak probe beams. The pump and the probe beam were co-focused onto the sample to a spot size of about 70 $\mu$m with an incident angle of about $15^{\circ}$ and $10^{\circ}$ with respect to the sample normal, respectively. A quarter wave plate (QWP) was inserted in the pump optical path to allow the pump helicity to be varied continuously from linear to circular, and data was recorded for every 10-degree rotation of the QWP. Analyzing the optical response as a function of the pump helicity offers insight into the role of topological Dirac state in the optical response. The Kerr rotation was recorded as a function of time delay between the pump and probe over a range of 20 ps by means of a horizontally shaking mirror with a scanning frequency of 10 Hz Hase2012 ; Hase2015 . The pump power was kept constant at 20 mW over the wavelength range used, which corresponds to a fluence of $\approx$ 16 mJ/cm2, a value calculated using a focused beam diameter of $\approx$ 70 $\mu$m (measured using a knife-edge). An optical penetration depth of $\approx$ 100 nm at 1550 nm was calculated from the absorption coefficient lee2005 , suggesting negligibly small inhomogeneous excitation effects along the sample depth.

The (GeTe)2/Sb2Te3 sample used was fabricated by radio-frequency magnetron sputtering at 230*∘C and was deposited onto a Si (100) substrate. For better z-axis orientation saito2015 ; saito2016 , the Sb2Te3* layers were grown first to a thickness of 3 nm at room temperature and subsequently GeTe (0.8 nm) and Sb2Te3 (1.0 nm) layers were alternately deposited for 20 cycles ($\sim$36 nm) at elevated temperature. To prevent oxidization, a 20-nm-thick ZnS-SiO2 layer was deposited on top of the as-grown CSL without breaking the vacuum.

III Results and discussion

Time resolved Kerr rotation signals ($\Delta\theta_{k}$) as a function of the angle of the QWP ($\alpha$) of 70*∘* and 130*∘* for the excitation wavelength of 1300 nm (0.954 eV) are presented in Fig.1(b). The transient peak at time delay zero has the opposite sign and a different intensity level from the remainder of the spectra, depending on the pump helicity. Both $\alpha$ = 70*∘* and 130*∘* correspond to an elliptically polarized pump pulse and exhibit the largest positive and negative transient, respectively. The peak intensity of $\Delta\theta_{k}$ is plotted as a function of the QWP angle $\alpha$ in Fig.2 for different photon energies. The peak signals for the smaller photon energies shown in Fig.2 exhibit a significantly asymmetric sin(2$\alpha$) oscillation due to contributions from a smaller sin(4$\alpha$) oscillation. The stronger sin(2$\alpha$) oscillation observed in the present study for the CSL samples compared to the previous report mondal2018a may be a consequence of the two-orders larger pump fluence used, which is expected to induce stronger SIFE arising from larger third-order susceptibility contributions. All the data were fit using Eq. (1) to extract the contributions from the sin(2$\alpha$) and sin(4$\alpha$) components, corresponding to SIFE and SOKE signals, respectively wilks2004 ; popov1996 .

[TABLE]

where $D$ is a polarization independent background. The photon energy dependences of the $C$ (SIFE) and $L$ (SOKE) terms are shown in Fig.3. As the photon energy decreased, the absolute values of $C$ and $L$ were found to sharply increase. The steeper increase in $L$ over $C$ may be a consequence of TI properties mondal2018a . To investigate the sharp increases in the value of $L$ and $C$ shown in Fig. 3, the effect of the photon energy dependent susceptibility function on the SIFE and SOKE is examined, where second- and third-order nonlinear susceptibilities are expected to play major roles mondal2018 . Based on the classical Drude-Lorentz model and the quantum mechanical description for the IFE battiato2014 ; berritta2016 , the response function for the induced magnetization (SIFE) for the off-resonant case can be simply expressed by robert2008 ,

[TABLE]

where $\omega_{0}$ is the resonant frequency of the system, which means that even though the SIFE is enhanced by being close to resonance, it does not vanish away from the resonance. Fig. 3(a) shows a fit of $|C|$ using Eq. (2) with the fitting parameter of $\hbar\omega_{0}$ = 0.66 $\pm$ 0.03 eV. Eq. (2) was found to fit the experimental data ($|C|$) satisfactory. In contrast, for the SOKE case, it was assumed that the response function for $L$ was dominated by cascading $\chi^{(2)}\cdot\chi^{(2)}$ contributions mondal2018 . In quantum theory, the second-order nonlinear susceptibility for the off-resonant case can be expressed by permutation of indexes as robert2008 ; Bosshard95 :

[TABLE]

where $\chi^{(2)}(0;\omega,-\omega)$ represents optical rectification and $\chi^{(2)}(-\omega;\omega,0)$ represents the electro-optic effect. Thus, SOKE signal generated via cascaded optical rectification and the electro-optic effect, $\chi^{(2)}(0;\omega,-\omega)\cdot\chi^{(2)}(-\omega;\omega,0)$, is simply proportional to the square of the $\chi^{(2)}$:

[TABLE]

The photon energy dependence of $|L|$ in Fig. 3(b) was well fit by Eq. (4) with $\hbar\omega_{0}$ = 0.62 $\pm$ 0.24 eV.

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 excitation at $\approx$0.60 – 0.66 eV. According to the simuilated electronic band structure, one can see that photon energies less than 0.75 eV will promote electrons from the bulk valence band (BVB) to near the top of the Dirac band (DB), while for larger photon energies than 0.75 eV (e.g., 1.0 eV) a direct optical transition will occur from underlying BVB to the bulk conduction band (BCB) across the DB (see Fig. 4). It has been reported that in a magnetic topological insulator, the photo-induced current becomes larger when electrons are excited to topological surface states and reaches a maximum when electrons are excited from one surface band to another ogawa2016 . We propose that the steep increase in both $C$ and $L$ values toward lower photon energies corresponds to the tail of the resonant excitation from the BVB to around the Dirac point (DP) ($\approx$0.65 eV), as indicated by the dashed arrow in Fig. 4(a) Krizman2018 . Importantly, the steeper increase in $L$ relative to $C$ is expected to be a consequence of cascaded optical rectification and electro-optic effect, varying as $\sim\omega^{-4}$, where spatial inversion symmetry at the interfaces is broken by strain effects, leading a nonzero $\chi^{(2)}$ mondal2018a . Note that the Dirac states in a CSL are either topological interface states Krizman2018 or topological bulk states tominaga2014 , as predicted by ab initio band structure simulations. Although further experiments using yet lower photon energies are required to fully understand the enhancement of the Kerr rotation in the topological chalcogenide superlattice, our results offer significant insight into the Dirac-cone oriented photon energy dependence of spin excitation in modern two dimensional materials.

In summary, we have investigated the photon energy dependence of the Kerr rotation in a chalcogenide superlattice using infrared (1200$\sim$1600 nm) femtosecond laser pulses. The measured pump helicity dependence yields a contribution from both sin(2$\alpha$) and sin(4$\alpha$) components. Phenomenologically, the former contribution arises from the SIFE while the latter arises from SOKE. The photon energy dependence of the relative contributions, labeled $C$ and $L$ respectively, shows a monotonic increase with decreasing photon energy. The energy dependence of $C$ can be attributed to the response function $\chi^{(3)}$, while that of $L$ can be attributed to the photon energy dependence of $\chi^{(2)}\cdot\chi^{(2)}$, where the response functions of $\chi^{(2)}$ and $\chi^{(3)}$ are derived from quantum theory. The sharp increase is attributed to resonant-like electronic excitation from BVB to Dirac states.

Acknowledgements.

This work was supported by CREST (Nos. JPMJCR14F1 and JPMJCR1875), JST, Japan and the Japan Society for the Promotion of Science (Grants-in-Aid for Scientific Research: 17H06088). We acknowledge Ms. R. Kondou for sample preparation.