- Email: [email protected]
Separation of the intrinsic and extrinsic mechanisms of the photo-induced anomalous Hall effect
Physica E 90 (2017) 55–60
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Separation of the intrinsic and extrinsic mechanisms of the photo-induced anomalous Hall effect
MARK
⁎
J.L. Yua,d, , Y.H. Chenb,c, S.Y. Chenga,d, X.L. Zenga, Y. Liub,c, Y.F. Laia, Q. Zhenga a College of Physics and Information Engineering, Institute of Micro/Nano Devices and Solar Cells, Fuzhou University, Fuzhou 350108, Fujian Province, China b Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, PR China c College of Materials, Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, PR China d Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering, Changzhou University, Changzhou 213164, Jiangsu, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Anomalous hall effect Intrinsic and extrinsic mechanisms Photocurrent spectra GaAs/AlGaAs quantum wells
The photocurrent spectra induced by the anomalous Hall effect (AHE) of the (001)-oriented GaAs/AlGaAs quantum wells (QWs) with well width of 3 and 7 nm have been investigated at room temperature. Ultra-thin InAs layers with a thickness of 1 monolayer have been inserted at GaAs/AlGaAs interfaces to tune the asymmetry of the QWs. It is demonstrated that the AHE current can be effectively tuned by the inserted ultrathin InAs layers and by the well width. A method has been proposed to separate the intrinsic and extrinsic mechanisms of the AHE, which can be also applied to spin Hall effect.
1. Introduction Spintronics has gained much attention due to its potential application in the field of information technology as well as the challenging fundamental physical questions that it poses [1–7]. The spin-orbit coupling (SOC) provides us a powerful way using electric field to generate and manipulate of spins of electrons [1]. SOC of semiconductor quantum wells (QWs) can be engineered by changing the structures of the QWs, for example, Rashba SOC can be tuned by varying the delta-doping position [8], and Dresselhaus SOC can be tailored by changing the well width of the QWs [9]. Circular photogalvanic effect (CPGE) offers us a method to investigate the SOC in lowdimensional semiconductor materials as well as to design new spintronics devices [10–12]. Besides CPGE, photo-induced anomalous Hall effect (AHE), which originates from inverse spin Hall effect (ISHE) [13], suggests another approach utilizing SOC to realize semiconductor spintronics [13–20], and it has been used to design spin-photovoltaic devices recently [21]. Similar to spin Hall effect, there are two mechanisms proposed theoretically for the AHE. The extrinsic mechanism is based on asymmetric Mott-skew or side-jump scattering from impurities in a spin-orbit coupled system [2,22], while the intrinsic mechanism is dependent only on the band structure of the materials, which arises from Rashba [3,23] or Dresselhaus SOC [24,25]. For a given system, both of the extrinsic and intrinsic
mechanism will contribute to the AHE, however, it is quite difficult to distinguish them [4,26]. Priyadarshi et al. distinguished the intrinsic and extrinsic contributions to the AHE in undoped GaAs QWs by subpicosecond time resolution technology [4]. In this paper, we propose another method combining CPGE and AHE to separate the intrinsic and extrinsic mechanisms of the AHE current. Besides, we also investigate the photocurrent spectra induced by the AHE of the (001)-oriented GaAs/AlGaAs multiple quantum wells (MQWs) with well width of 3 and 7 nm at room temperature. In order to enhance the asymmetry of the QWs, we insert InAs layers with a thickness of 1 monolayer (ML) at the interfaces of the QWs. We find that the AHE current can be effectively tuned by the inserted InAs layer and by the well widths of the QWs. 2. Sample and experiments The samples studied in this experiment are three undoped GaAs/Al Ga 0.7 As MQWs, named as sample A, B and C, respectively, grown on (001) SI-GaAs substrates by molecular beam epitaxy (MBE), which are the same with those used in Ref. [27]. There are 20 periods of GaAs/AlGaAs quantum wells with well width of 7 nm in sample A. Sample B has the same structure with that of sample A except that the well width is 3 nm. Sample C also contains 20 periods of 7 nm-GaAs/ AlGaAs QWs, and 1 monolaryer (ML)-thick InAs layer is inserted at the 0.3
⁎ Corresponding author at: College of Physics and Information Engineering, Institute of Micro/Nano Devices and Solar Cells, Fuzhou University, Fuzhou 350108, Fujian Province, China. E-mail addresses: [email protected] (J.L. Yu), [email protected] (Y.H. Chen).
http://dx.doi.org/10.1016/j.physe.2017.02.021 Received 20 December 2016; Received in revised form 24 January 2017; Accepted 6 February 2017 Available online 18 March 2017 1386-9477/ © 2017 Published by Elsevier B.V.
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 1. (a) Schematic diagram of the AHE experiments. (b) and (c) are gGeometries used to measure the CPGE current induced by Rashba (IR) and Dresselhaus (ID) SOC, respectively.
the geometries shown in Fig. 1 (b) and (c), respectively [28,29]. In Fig. 1, IR (ID) denotes the CPGE current induced by Rashba (Dresselhaus) SOC, and θ is the angle of incidence. In order to eliminate the influences of the anisotropic carrier mobility and carrier density in different samples, the photoconductive current I0 under DC bias are also measured.
interface of each GaAs/AlGaAs QWs, forming GaAs/InAs/Al 0.3 Ga 0.7 As structures. All of the samples are of high purity, which can be evident from the high resistance without lighting of the samples. The 2D densities of the photo-induced carriers in the three samples are about 109 cm−2 for the transition of 1H1E (the first valence subband of heavy holes to the first conduction subband of electrons) when they are excited by a laser with 60 mW at 840 nm. In the experiments, the samples are cleaved into squares of 4×4 mm2 along [110] and [110] directions. Two point contacts with a diameter of 0.5 mm and 3 mm apart, and two strip electrodes (0.5 mm×3 mm) with a distance of 3 mm, are made by indium deposition and annealed at about 420 ° in nitrogen atmosphere, as shown in Fig. 1(a). In the experiments, a mode-locked Ti-sapphire laser with a repetition rate of 80 MHz and with a full width at half maximum (FWHM) of 7 nm is used as the radiation source. Going through a polarizer and a photoelastic modulator (PEM), the light emitted from the laser become a circularly polarized light, whose polarization state is oscillating between right- (σ−) and left- (σ+) hand periodically. Then, the light with a light spot of 2.5 mm-diameter and with a power of 60 mW at 840 nm irradiates at the central line between two point contacts. It is worth noting that the contacts should not be illustrated by laser to avoid collecting the signal due to contacts (i.e., current induced by rectification at the contacts), and that the laser spot should have equal distances with the two point contacts in order to exclude the current due to the optically excited gradient of the carrier density (i.e., Dember effect). A longitudinal electric field is applied by the two strip electrodes, and the transverse photocurrent (i.e. AHE current, see Section 3) is collected by a lock-in amplifier in phase with the PEM through the two point contacts. The photoconductive current I0 with a DC bias of 1.5 V applied between two point contacts is obtained by collecting the photocurrent I0 at the same point contacts using a lock-in amplifier and a chopper. The spectra in the wavelength range of 750– 870 nm are measured. In order to obtain the ratio of Rashba and Dresselhaus SOC and thus to separate the intrinsic and extrinsic mechanism of AHE, CPGE measurements are also performed. The samples with 4×4 mm2 cleaved along [110] and [110] directions are prepared. Then, one pair of point contacts, with a distance of 3 mm, along [100] direction is prepared by indium deposition and annealed at about 420 °C in nitrogen atmosphere, as shown in Fig. 1 (b) and (c). In the CPGE measurement, a similar experimental setup with that used in AHE measurements is used except that the light irradiates obliquely on the sample with a angle of incidence ranges from −30 to 30° and that no electric field is applied on the sample. It should be noted that, (001)-grown zincblende structure-based QW belongs to point group C2v [11], in which the photocurrent can be only induced under oblique incidence of irradiation. The CPGE current is collected by the lock-in amplifier in phase with the PEM through the two electrodes. The CPGE current induced by Rashba and Dresselhaus SOC can be obtained by adopting
3. Results and discussions Fig. 2(a) shows the normalized transverse photocurrent spectra under different longitudinal electric fields (i.e., AHE current) in sample A. The solid symbols are the experimental data, and the solid lines are guides for eyes. The spectra are normalized by I0 / E0 corresponding to the transition of excitonic state 1H1E, where I0 is the photoconductive current detected at the point contacts when applying a DC-bias of 1.5 V between the point contacts, and E0 is the electric field between the two point contacts when applying a DC-bias of 1.5 V. It can be seen that the AHE current increases with the increasing of the longitudinal field, and the current flow reverses with the direction of the longitudinal field. Denoting I′AHE+ (I′AHE−) as the transverse current collected by the two point contacts at positive (negative) longitudinal field, one can obtain the AHE current accurately by (I ′AHE+ − I ′AHE− )/2 , as shown in Fig. 3. The solid symbols are the experimental data, and the solid lines are guides for eyes. One can see that, the energy positions of the excitonic state 1H1E and 1L1E can not be clearly distinguished in the AHE spectra due to the large FWHM of the Ti-sapphire laser. In order to find out the exact energy position of the excitonic transition 1H1E and 1L1E, we replace the Ti-sapphire laser with a 250 W tungsten lamp combined with a monochromator, which has a spectral resolution of 1 nm. The measurement results are shown in Fig. 2(b), from which the energy positions of the excitonic states 1H1E and 1L1E, indicated by solid and dashed arrows in Fig. 2(b) respectively, can be clearly located. The energy positions of the excitonic state 1H1E and 1L1E are also indicated by vertical dashed in Fig. 3. The generation of transverse photocurrent under longitudinal electric field is described as follows. Firstly, the spin polarized carriers are produced under the radiation of circularly polarized light, whose photon energy is equal to or larger than the excitonic states of the QWs, by two ways: (1) direct formation of free electrons and holes, and (2) creation of free carriers through excitons [19]. For the first case, under the irradiation of circularly polarized light, taking left-handed (σ+) circularly polarized light as an example, the electron in the valence band with spin angle momentum ms = −3/2 will jump to the conduction band with spin angle momentum ms = −1/2 , according to the optical selection rule. For the second case, excitons consisting of welldefined spins are created by circularly polarized light, and then the excitons are dissociated to produce free carriers by interaction with phonons, impurities and other excitons [19]. Then the spin polarized carriers will show lateral deflection due to spin Hall effect (SHE). To be 56
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 2. (a) Spectra of the normalized AHE current under different longitudinal electric fields detected in sample A. (b) Photoconductive current under a dc bias of 3 V measured by a spectrum system with a resolution of 1 nm in sample A, B and C. The solid and dashed arrows indicate the energy positions of the excitonic states 1H1E and 1L1E, respectively.
bands by the circularly polarized light with same helicity will jump to the opposite spin splitting branches in the conduction band, which will reverse the direction of the AHE current [19]. However, in our experiments, the AHE current of 1H1E and 1L1E show the same sign. Although the large FWHM of the laser (7 nm) will result in a little contribution of 1H1E when measuring the AHE current corresponding to the excitonic state 1L1E, this will not be the main reason, because the energy difference between 1H1E and 1L1E (about 10 nm for sample A (or C) and 15 nm for sample B) is larger than the FWHM of the laser and the similar phenomenon is also observed in InGaAs/ AlGaAs QWs measured by a spectrum system with a resolution of 1.5 nm [19]. The mixing or anticrossing of the light- and heavy-hole bands can also be excluded, since the band mixing effect at small k is so weak that it can be neglected [19]. We think that the phenomenon may be related to the contribution of holes to the AHE. The hole density is comparable to that of electron in the undoped QWs, which is different from the case in n-doped QWs that are dominated by electrons. So the contribution of holes to AHE current may not be neglected. Besides, it is theoretically found that the spin relaxation time of holes is of the same order of magnitude with that of electrons in quantum dots with large lateral dimensions [30]. This qualitative conclusions may be of some relevance also for QWs [31]. What is more, it was predicted that the AHE current in p-doped GaAs/AlGaAs QWs corresponding to 1H1E induced by intrinsic mechanism had the same sign with that of 1L1E [32]. Therefore, the contribution of holes to the AHE may be mainly responsible for the surprising phenomenon of same sign for 1H1E and 1L1E in AHE spectra. One can see from Fig. 3 that, there are also AHE current generated in the QWs when the photon energy is far away from the denoted energy positions of 1H1E and 1L1E (at 760 nm, for example), which may be attributed to the higher states of the QWs, such as the transition of 2H2E, 2L2E. In the following discussion, we only focus on the AHE current of 1H1E. By the normalization of I0 / E0 , we can eliminate the influences of the carrier mobility and the carrier density in different samples and thus enable a better comparison of the AHE conductivity in different samples. This is because the AHE current can be expressed as IAHE = σxyph SλE × e [14] and the photoconductive current I0 can be written as I0 = σ0 E0 S , where σxyph is the AHE conductivity, S is the crosssectional area of the AHE current or that of the photoconductive current, E is the longitudinal electric field applied along the two strips when measuring AHE current, e denotes the direction of light propagation, λ = ± 1 is the helicity of the light and σ0 is the photo-
Fig. 3. Spectra of the normalized AHE current detected in sample A, B and C under different longitudinal electric fields. The vertical dash lines indicate the energy positions of the excitonic states 1H1E and 1L1E. The solid lines are guides for eyes.
specific, according to SHE, electrons will show an anomalous velocity perpendicular to the electric field under the intrinsic or extrinsic mechanisms. The extrinsic mechanism is based on asymmetric Mottskew or side-jump scattering from impurities in a spin-orbit coupled system [2,22], while the intrinsic mechanism is dependent only on the band structure of the materials, which arises from Rashba [3,23] or Dresselhaus SOC [24,25]. Then the electrons with different spin directions will move to the opposite sides of the sample plane, leading to a spin current or spin accumulation in a direction transverse to the direction of the longitudinal field. If the carriers are spin polarized, the number of carriers moving along the left and right sides will be different, and a Hall-like current will present, which is named as AHE current. Generally, the AHE current corresponding to the transition of 1L1E is expected to flow at an opposite direction of 1H1E. This is because electrons excited from the heavy hole and light 57
Physica E 90 (2017) 55–60
J.L. Yu et al.
Since the AHE essentially stems from ISHE, they will have the same mechanisms, i.e., the extrinsic mechanism based on asymmetric impurities scattering and the intrinsic mechanism arised from Rashba or Dresselhaus SOC. It is expected that both of intrinsic and extrinsic mechanisms will contribute to the AHE for a given sample. Since sample A and B are grown under the same conditions by the same MBE system and they have the same structure except for the well width of the QW, the concentration of the impurities introduced by the residual doping are nearly equal in the two samples. However, sample C with InAs layers inserted at the interfaces of the QWs is grown at a different condition with that of sample A and B, which will result in different density of impurities in sample C. Therefore, we assume that the contribution made by the impurities to the AHE current for sample A and B is the same, and that the contribution made by the impurities to the AHE in sample A (or sample B) is different from that in sample C. For the intrinsic mechanism, it is reasonable to assume that its contribution to the AHE current is proportional to the strength of the Rashba or Dresselhaus SOC [33]. The relative ratio of Rashba or Dresselhaus SOC of the three samples can be obtained by CPGE measurements [27], i.e., we first measure the CPGE spectra induced by Rashba (named as IR) or Dresselhaus (named as ID) SOC and the photoconductive current I0 spectra under different angles of incidence; in order to eliminate the influence of absorbance and carrier mobility in different samples, we normalized the CPGE current by photoconductive current I0, as shown in Fig. 5(a)-(f); then we extract the normalized CPGE current IR / I0 (or ID / I0 ) corresponding to the transition of 1H1E at different angles of incidence, which are then fitted to the following equation [27].
Fig. 4. Dependence of the normalized AHE current on the longitudinal electric field corresponding to the transition of 1H1E for sample A, B and C, respectively. The solid lines are the linear fitting results.
conductivity. Therefore, we have
σxyph IAHE = E. I0 / E0 σ0
Iλ / I0 =
(1)
IAHE versus I0 / E0 σxyph / σ0 from
electric field E for a certain photon energy we can obtain the slope of the fitted curve. Fig. 4(a), (b) and (c) show the dependence of the AHE current corresponding to the transition of 1H1E on the longitudinal electric field for sample A, B and C, respectively. It can be seen that the intensity of the AHE current increases linearly with the applied longitudinal electric field. By linear fitting (solid lines), we can obtain the normalized AHE conductivity σxyph / σ0 for sample A, B and C are (3.1 ± 0.1) × 10−4 , (4.0 ± 0.1) × 10−4 , (8.6 ± 0.2) × 10−4 , respectively, as shown in Table 1. One can see that, the normalized AHE conductivity increases from sample A to C, which indicates that the AHE can be effectively tuned by changing the well width and by inserting an ultra-thin InAs layer at interfaces of the QWs. The photoinduced anomalous Hall conductivity corresponding to the excitonic state 1H1E of the three samples are all estimated to be in the order of 10−9Ω−1W −1, which agree well with that observed in InGaAs/AlGaAs QWs [19]. Table 1 Relative ratio of Rashba (αi /αA ) and Desselhaus coefficients ( βj /βA ) ( j = B, C ), the ratio of Rashba and Dresselhaus SOC (RD ratio, i.e., (α /β )i )(i = A, B, C ), the AHE conductivity ph ph /σ0 vs sample A σxy normalized by photoconductivity σ0 and the relative ratio of σxy corresponding to the transition of 1H1E for the three samples. Sample A
Sample B
Sample C
αj /αA
1.00 ± 0.08
0.89 ± 0.06
2.76 ± 0.45
βj /βA
1.00 ± 0.04
1.63 ± 0.47
1.09 ± 0.08
(α /β )i
0.78 ± 0.08 3.1 ± 0.1
0.48 ± 0.08 4.0 ± 0.1
1.98 ± 0.23 8.6 ± 0.2
1.00 ± 0.02
1.30 ± 0.50
2.78 ± 0.10
ph σxy σ0
(10−4)
⎛ σ ph ⎞ ⎛ σ ph ⎞ ⎜⎜ xy ⎟⎟ /⎜⎜ xy ⎟⎟ ⎝ σ 0 ⎠i ⎝ σ 0 ⎠A
n (cos θ +
n2 − sin2 θ )(n2 cos θ +
n2 − sin2 sin θ )
,
(2)
as shown in Fig. 5(g)-(i). Here θ is the angle of incidence, n is the refractive index of the GaAs material, and Aλ is a parameter related to the SOC of the QWs, i.e., when the current is induced by Rashba-type SOC (λ = R ), AR ∝ α , and when the current is induced by Dresselhaustype SOC (λ = D ), AD ∝ β . Here, α (β) is the Rashba (Dresselhaus) coefficient. Thus, by fitting the nomalized CPGE current at different angles using Eq. (2), the parameter AR (or AD ) in the normalized Rashba-type (or Dresselhaus-type) CPGE current are obtained, and the relative ratio of the Rashba (or Dresselhaus) SOC of the three samples can be obtained by the relative ratio of the corresponding AR (or AD ) parameters. Using this method, we obtain the relative ratio of the Rashba (or Dresselhaus) SOC of the three samples are αC / αA = 2.76 ± 0.45 αB / αA = 0.89 ± 0.06 , ( βB / βA = 1.63 ± 0.47, βC / βA = 1.09 ± 0.08), which are also shown in Table 1. Here αi and βi (i=A, B or C) are the Rashba and Dresselhaus coefficient for sample i (i=A, B or C), respectively. Taking the experimental error into account, we find that αA almost equals to αB, i.e., αA ≃ αB. The ratio of Rashba and Dresselhaus SOC (RD ratio) for 1H1E in the three samples are also determined by the relative ratio of the corresponding AR and AD parameters (i.e., α / β = AR / AD ), which are 0.78 ± 0.08, 0.48 ± 0.08 and 1.98 ± 0.23 for sample A, B and C, respectively. Using sample A as a reference sample, we get the relative ratios of the normalized AHE conductivity σxyph / σ0 vs that of sample A corresponding to the transition of 1H1E are 1.30 ± 0.50, and 2.78 ± 0.10 for sample B and C, respectively, as shown in Table 1. Thus, using sample A as a reference sample, we denote χSi , χRi , and χDi (i = A, B, C) as a relative ratio of AHE current in sample i contributed by the impurities scattering, Rashba and Dresselhaus SOC, respectively, to that of sample A, i.e., AHE AHE χSi = ISAHE / IAAHE , χRi = IRAHE , χDi = IDAHE . Here IAAHE denotes i i / IA i / IA AHE AHE AHE the AHE current in sample A. ISi , IRi and IDi represent the AHE current in sample i contributed by the impurities scattering, Rashba and Dresselhaus SOC, respectively. Then, we have
Thus, we can obtain the normalized AHE conductivity σxyph / σ0 from Fig. 3 by using Eq. (1), i.e., by linear fitting of the plot
Aλ sin θ cos2 θ
χSA + χRA + χDA = 1, 58
(3)
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 5. (a)-(f) CPGE spectra for sample A, B and C induced by Rashba- and Dresselhaus-type SOC normalized by the photoconductive current I0 at the angles of incidence from −30 to 30 degree with a step of 10 degree. All of the spectra are shifted vertically for clarity. The vertical dash lines indicate the energy position of the transition of 1H1E. The solid lines are guides for eyes. (g)-(i) Angular dependence of the normalized CPGE current for sample A, B and C induced by Rashba- and Dresselhaus-type SOC for the transition of 1H1E, respectively. The squares and circles are experiential results and the solid lines are the fitting results according to Eq. (2).
χSB + χRB + χDB = 1.30,
(4)
χSC + χRC + χDC = 2.78,
(5)
χRi β α χ = i , Di = i χRA αA χDA βA
(6)
χSB = χSA ,
χRA α = A = 0.78. χDA βA
Thus, we propose a method combining CPGE and AHE to separate the extrinsic and intrinsic mechanisms of the AHE, and this method is also applicable to determine the mechanism of SHE and ISHE, since they essentially originate from the same mechanisms. 4. Conclusion In conclusion, the photoinduced AHE spectra of GaAs/AlGaAs QWs with well width of 3 and 7 nm are investigated at room temperature. Ultra-thin InAs layers with a thickness of 1 ML have been inserted at the interfaces of GaAs/AlGaAs QWs to tune the asymmetry of the QWs. It is demonstrated that the AHE current shows strong dependence on the well width of the QWs, and its value is enhanced by the inserted InAs layer. Besides, we propose a method, which is also applicable to SHE or ISHE, to successfully separate the contribution of the intrinsic mechanism, i.e., the Rashba and Dresselhaus spin-orbit coupling, and the extrinsic mechanism, i.e., the scattering of impurities, to the AHE current for the transition of 1H1E.
(7)
By solving the above equations, we have χSA = χSB = 0.15, χRA = χRB = 0.37, χDA = 0.48, χDB = 0.78, χSC = 1.24 , χRC = 1.02 and χDC = 0.52 . It can be seen that the contributions made by the intrinsic mechanism to sample A, B and C are 85%, 88% and 55%, respectively, implying that the intrinsic mechanism plays a dominant role in all the three samples, which can be attributed to the fact that the samples are undoped and of high purity resulting in weak scattering of impurities [17]. The increase of the contribution by the intrinsic mechanism in sample B compared with that in sample A is due to the enhancement of Dresselhaus SOC induced by the reduced well width. The decrease of the intrinsic contribution in sample C may be attributed to the higher density of impurities in sample C introduced by the complicated growth process of sample C [27], which is also evident by the much weaker excitonic effect observed in the photoconductive current spectrum (shown in Fig. 1 in Ref. [27]) in sample C compared with that of sample A and B. Our observation is somewhat different from that reported in Ref. [4], which declared that the extrinsic mechanism make a major contribution to the AHE in undoped (001)-oriented GaAs QWs. This discrepancy may be owing to the following two reasons: (i) firstly, due to the different growth conditions between the samples that are used in our experiments and that are used in the Ref. [4], the impurities density in the samples may be different, which lead to different major mechanisms; (ii) secondly, the much smaller of the well width of the QWs in our samples may lead to larger SOC and thus enhance the contribution of the intrinsic mechanism.
Acknowledgement The work was supported by the National Natural Science Foundation of China (No. 61306120, No. 61674038, No. 61474114, No. 11574302), Natural Science Foundation of Fujian (Grant No. 2014J05073), National key Research and Development Program (2016YFB0402303) and Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (No. KF201405). References [1] Y. Kato, R.C. Myers, A.C. Gossard, D.D. Awschalom, Coherent spin manipulation without magnetic fields in strained semiconductors, Nature 427 (6969) (2004) 50–53.
59
Physica E 90 (2017) 55–60
J.L. Yu et al.
[18] C.M. Yin, N. Tang, S. Zhang, J.X. Duan, F.J. Xu, J. Song, F.H. Mei, X.Q. Wang, B. Shen, Y.H. Chen, J.L. Yu, H. Ma, Observation of the photoinduced anomalous Hall effect in GaN-based heterostructures, Appl. Phys. Lett. 98 (12) (2011) 122104. [19] J.L. Yu, Y.H. Chen, C.Y. Jiang, Y. Liu, H. Ma, L.P. Zhu, Observation of the photoinduced anomalous Hall effect spectra in insulating InGaAs/AlGaAs quantum wells at room temperature, Appl. Phys. Lett. 100 (2012) 142109. [20] J.L. Yu, Y.H. Chen, Y. Liu, C.Y. Jiang, H. Ma, L.P. Zhu, X.D. Qin, Intrinsic photoinduced anomalous Hall effect in insulating GaAs/AlGaAs quantum wells at room temperature, Appl. Phys. Lett. 102 (20) (2013) 202408. [21] J. Wunderlich, A.C. Irvine, J. Sinova, B.G. Park, L.P. Zarbo, X.L. Xu, B. Kaestner, V. Novak, T. Jungwirth, Spin-injection Hall effect in a planar photovoltaic cell, Nat. Phys. 5 (9) (2009) 675–681. [22] W.K. Tse, S.D. Sarma, Spin Hall effect in doped semiconductor structures, Phys. Rev. Lett. 96 (2006) 056601. [23] B.A. Bernevig, S.C. Zhang, Intrinsic spin Hall effect in the two-dimensional hole gas, Phys. Rev. Lett. 95 (2005) 016801. [24] B.A. Bernevig, S.C. Zhang, Spin splitting and spin current in strained bulk semiconductors, Phys. Rev. B 72 (2005) 115204. [25] V. Sih, R.C. Myers, Y.K. Kato, W.H. Lau, A.C. Gossard, D.D. Awschalom, Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases, Nat. Phys. 1 (1) (2005) 31–35. [26] C.G. Zeng, Y.G. Yao, Q. Niu, H.H. Weitering, Linear magnetization dependence of the intrinsic anomalous Hall effect, Phys. Rev. Lett. 96 (2006) 037204. [27] J.L. Yu, X.L. Zeng, S.Y. Cheng, Y.H. Chen, Y. Liu, Y.F. Lai, Q. Zheng, J. Ren, Tuning of Rashba/Dresselhaus spin splittings by inserting ultra-thin InAs layers at interfaces in insulating GaAs/AlGaAs quantum wells, Nanoscale Res. Lett. 11 (1) (2016) 477. [28] S.D. Ganichev, V.V. Bel'kov, L.E. Golub, E.L. Ivchenko, P. Schneider, S. Giglberger, J. Eroms, J. De Boeck, G. Borghs, W. Wegscheider, D. Weiss, W. Prettl, Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells, Phys. Rev. Lett. 92 (25) (2004) 256601. [29] S. Giglberger, L.E. Golub, V.V. Bel'kov, S.N. Danilov, D. Schuh, C. Gerl, F. Rohlfing, J. Stahl, W. Wegscheider, D. Weiss, W. Prettl, S.D. Ganichev, Rashba and Dresselhaus spin splittings in semiconductor quantum wells measured by spin photocurrents, Phys. Rev. B 75 (3) (2007) 035327. [30] D.V. Bulaev, D. Loss, Spin relaxation and decoherence of holes in quantum dots, Phys. Rev. Lett. 95 (7) (2005) 076805. [31] D.M. Gvozdic, U. Ekenberg, Superefficient electric-fieldcinduced spin-orbit splitting in strained p-type quantum wells, Europhys. Lett. 73 (6) (2006) 927. [32] X. Dai, F.C. Zhang, Light-induced Hall effect in semiconductors with spin-orbit coupling, Phys. Rev. B 76 (8) (2007) 085343. [33] K. Nomura, T. Jungwirth, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Edge-spin accumulation in semiconductor two-dimensional hole gases, Phys. Rev. B 72 (2005) 245330.
[2] Y.K. Kato, R.C. Myers, A.C. Gossard, D.D. Awschalom, Observation of the spin Hall effect in semiconductors, Science 306 (5703) (2004) 1910–1913. [3] J. Sinova, D. Culcer, Q. Niu, N.A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Universal intrinsic spin Hall effect, Phys. Rev. Lett. 92 (12) (2004) 126603. [4] S. Priyadarshi, K. Pierz, M. Bieler, Detection of the anomalous velocity with subpicosecond time resolution in semiconductor nanostructures, Phys. Rev. Lett. 115 (2015) 257401. [5] K.N. Okada, N. Ogawa, R. Yoshimi, A. Tsukazaki, K.S. Takahashi, M. Kawasaki, Y. Tokura, Enhanced photogalvanic current in topological insulators via fermi energy tuning, Phys. Rev. B 93 (2016) 081403. [6] R. Iguchi, K. Sato, D. Hirobe, S. Daimon, E. Saitoh, Effect of spin hall magnetoresistance on spin pumping measurements in insulating magnet/metal systems, Appl. Phys. Express 7 (1) (2014) 013003. [7] K. Kondou, H. Sukegawa, S. Kasai, S. Mitani, Y. Niimi, Y. Otani, Influence of inverse spin Hall effect in spin-torque ferromagnetic resonance measurements, Appl. Phys. Express 9 (2) (2016) 023002. [8] V. Lechner, L.E. Golub, P. Olbrich, S. Stachel, D. Schuh, W. Wegscheider, V.V. Bel'kov, S.D. Ganichev, Tuning of structure inversion asymmetry by the deltadoping position in (001)-grown GaAs quantum wells, Appl. Phys. Lett. 94 (24) (2009) 242109. [9] M.P. Walser, U. Siegenthaler, V. Lechner, D. Schuh, S.D. Ganichev, W. Wegscheider, G. Salis, Dependence of the Dresselhaus spin-orbit interaction on the quantum well width, Phys. Rev. B 86 (19) (2012) 195309. [10] C.M. Yin, H.T. Yuan, X.Q. Wang, S.T. Liu, S. Zhang, N. Tang, F.J. Xu, Z.Y. Chen, H. Shimotani, Y. Iwasa, Y.H. Chen, W.K. Ge, B. Shen, Tunable surface electron spin splitting with electric double-layer transistors based on InN, Nano Lett. 13 (5) (2013) 2024–2029. [11] S.D. Ganichev, W. Prettl, Spin photocurrents in quantum wells, J. Phys.-Condens. Matter 15 (20) (2003) R935–R983. [12] S.D. Ganichev, L.E. Golub, Interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy - a review, Phys. Status Solidi B-Basic Solid State Phys. 251 (9) (2014) 1801–1823. [13] L.P. Zhu, Y. Liu, C.Y. Jiang, J.L. Yu, H.S. Gao, H. Ma, X.Q. Qin, Y. Li, Q. Wu, Y.H. Chen, Spin depolarization under low electric fields at low temperatures in undoped InGaAs/AlGaAs multiple quantum well, Appl. Phys. Lett. 105 (15) (2014) 152103. [14] X. Dai, F.C. Zhang, Light-induced Hall effect in semiconductors with spin-orbit coupling, Phys. Rev. B 76 (2007) 085343. [15] M.I. Miah, Observation of the anomalous Hall effect in GaAs, J. Phys. D.-Appl. Phys. 40 (6) (2007) 1659–1663. [16] M.I. Miah, Electric field control photo-induced Hall currents in semiconductors, Mater. Chem. Phys. 111 (2–3) (2008) 249–253. [17] D.A. Vasyukov, A.S. Plaut, M. Henini, L.N. Pfeiffer, K.W. West, C.A. Nicoll, I. Farrer, D.A. Ritchie, Intrinsic photoinduced anomalous Hall effect, Phys. E-Low.Dimens. Syst. Nanostruct. 42 (4) (2010) 940–943.
60
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Separation of the intrinsic and extrinsic mechanisms of the photo-induced anomalous Hall effect
MARK
⁎
J.L. Yua,d, , Y.H. Chenb,c, S.Y. Chenga,d, X.L. Zenga, Y. Liub,c, Y.F. Laia, Q. Zhenga a College of Physics and Information Engineering, Institute of Micro/Nano Devices and Solar Cells, Fuzhou University, Fuzhou 350108, Fujian Province, China b Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, PR China c College of Materials, Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, PR China d Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering, Changzhou University, Changzhou 213164, Jiangsu, China
A R T I C L E I N F O
A BS T RAC T
Keywords: Anomalous hall effect Intrinsic and extrinsic mechanisms Photocurrent spectra GaAs/AlGaAs quantum wells
The photocurrent spectra induced by the anomalous Hall effect (AHE) of the (001)-oriented GaAs/AlGaAs quantum wells (QWs) with well width of 3 and 7 nm have been investigated at room temperature. Ultra-thin InAs layers with a thickness of 1 monolayer have been inserted at GaAs/AlGaAs interfaces to tune the asymmetry of the QWs. It is demonstrated that the AHE current can be effectively tuned by the inserted ultrathin InAs layers and by the well width. A method has been proposed to separate the intrinsic and extrinsic mechanisms of the AHE, which can be also applied to spin Hall effect.
1. Introduction Spintronics has gained much attention due to its potential application in the field of information technology as well as the challenging fundamental physical questions that it poses [1–7]. The spin-orbit coupling (SOC) provides us a powerful way using electric field to generate and manipulate of spins of electrons [1]. SOC of semiconductor quantum wells (QWs) can be engineered by changing the structures of the QWs, for example, Rashba SOC can be tuned by varying the delta-doping position [8], and Dresselhaus SOC can be tailored by changing the well width of the QWs [9]. Circular photogalvanic effect (CPGE) offers us a method to investigate the SOC in lowdimensional semiconductor materials as well as to design new spintronics devices [10–12]. Besides CPGE, photo-induced anomalous Hall effect (AHE), which originates from inverse spin Hall effect (ISHE) [13], suggests another approach utilizing SOC to realize semiconductor spintronics [13–20], and it has been used to design spin-photovoltaic devices recently [21]. Similar to spin Hall effect, there are two mechanisms proposed theoretically for the AHE. The extrinsic mechanism is based on asymmetric Mott-skew or side-jump scattering from impurities in a spin-orbit coupled system [2,22], while the intrinsic mechanism is dependent only on the band structure of the materials, which arises from Rashba [3,23] or Dresselhaus SOC [24,25]. For a given system, both of the extrinsic and intrinsic
mechanism will contribute to the AHE, however, it is quite difficult to distinguish them [4,26]. Priyadarshi et al. distinguished the intrinsic and extrinsic contributions to the AHE in undoped GaAs QWs by subpicosecond time resolution technology [4]. In this paper, we propose another method combining CPGE and AHE to separate the intrinsic and extrinsic mechanisms of the AHE current. Besides, we also investigate the photocurrent spectra induced by the AHE of the (001)-oriented GaAs/AlGaAs multiple quantum wells (MQWs) with well width of 3 and 7 nm at room temperature. In order to enhance the asymmetry of the QWs, we insert InAs layers with a thickness of 1 monolayer (ML) at the interfaces of the QWs. We find that the AHE current can be effectively tuned by the inserted InAs layer and by the well widths of the QWs. 2. Sample and experiments The samples studied in this experiment are three undoped GaAs/Al Ga 0.7 As MQWs, named as sample A, B and C, respectively, grown on (001) SI-GaAs substrates by molecular beam epitaxy (MBE), which are the same with those used in Ref. [27]. There are 20 periods of GaAs/AlGaAs quantum wells with well width of 7 nm in sample A. Sample B has the same structure with that of sample A except that the well width is 3 nm. Sample C also contains 20 periods of 7 nm-GaAs/ AlGaAs QWs, and 1 monolaryer (ML)-thick InAs layer is inserted at the 0.3
⁎ Corresponding author at: College of Physics and Information Engineering, Institute of Micro/Nano Devices and Solar Cells, Fuzhou University, Fuzhou 350108, Fujian Province, China. E-mail addresses: [email protected] (J.L. Yu), [email protected] (Y.H. Chen).
http://dx.doi.org/10.1016/j.physe.2017.02.021 Received 20 December 2016; Received in revised form 24 January 2017; Accepted 6 February 2017 Available online 18 March 2017 1386-9477/ © 2017 Published by Elsevier B.V.
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 1. (a) Schematic diagram of the AHE experiments. (b) and (c) are gGeometries used to measure the CPGE current induced by Rashba (IR) and Dresselhaus (ID) SOC, respectively.
the geometries shown in Fig. 1 (b) and (c), respectively [28,29]. In Fig. 1, IR (ID) denotes the CPGE current induced by Rashba (Dresselhaus) SOC, and θ is the angle of incidence. In order to eliminate the influences of the anisotropic carrier mobility and carrier density in different samples, the photoconductive current I0 under DC bias are also measured.
interface of each GaAs/AlGaAs QWs, forming GaAs/InAs/Al 0.3 Ga 0.7 As structures. All of the samples are of high purity, which can be evident from the high resistance without lighting of the samples. The 2D densities of the photo-induced carriers in the three samples are about 109 cm−2 for the transition of 1H1E (the first valence subband of heavy holes to the first conduction subband of electrons) when they are excited by a laser with 60 mW at 840 nm. In the experiments, the samples are cleaved into squares of 4×4 mm2 along [110] and [110] directions. Two point contacts with a diameter of 0.5 mm and 3 mm apart, and two strip electrodes (0.5 mm×3 mm) with a distance of 3 mm, are made by indium deposition and annealed at about 420 ° in nitrogen atmosphere, as shown in Fig. 1(a). In the experiments, a mode-locked Ti-sapphire laser with a repetition rate of 80 MHz and with a full width at half maximum (FWHM) of 7 nm is used as the radiation source. Going through a polarizer and a photoelastic modulator (PEM), the light emitted from the laser become a circularly polarized light, whose polarization state is oscillating between right- (σ−) and left- (σ+) hand periodically. Then, the light with a light spot of 2.5 mm-diameter and with a power of 60 mW at 840 nm irradiates at the central line between two point contacts. It is worth noting that the contacts should not be illustrated by laser to avoid collecting the signal due to contacts (i.e., current induced by rectification at the contacts), and that the laser spot should have equal distances with the two point contacts in order to exclude the current due to the optically excited gradient of the carrier density (i.e., Dember effect). A longitudinal electric field is applied by the two strip electrodes, and the transverse photocurrent (i.e. AHE current, see Section 3) is collected by a lock-in amplifier in phase with the PEM through the two point contacts. The photoconductive current I0 with a DC bias of 1.5 V applied between two point contacts is obtained by collecting the photocurrent I0 at the same point contacts using a lock-in amplifier and a chopper. The spectra in the wavelength range of 750– 870 nm are measured. In order to obtain the ratio of Rashba and Dresselhaus SOC and thus to separate the intrinsic and extrinsic mechanism of AHE, CPGE measurements are also performed. The samples with 4×4 mm2 cleaved along [110] and [110] directions are prepared. Then, one pair of point contacts, with a distance of 3 mm, along [100] direction is prepared by indium deposition and annealed at about 420 °C in nitrogen atmosphere, as shown in Fig. 1 (b) and (c). In the CPGE measurement, a similar experimental setup with that used in AHE measurements is used except that the light irradiates obliquely on the sample with a angle of incidence ranges from −30 to 30° and that no electric field is applied on the sample. It should be noted that, (001)-grown zincblende structure-based QW belongs to point group C2v [11], in which the photocurrent can be only induced under oblique incidence of irradiation. The CPGE current is collected by the lock-in amplifier in phase with the PEM through the two electrodes. The CPGE current induced by Rashba and Dresselhaus SOC can be obtained by adopting
3. Results and discussions Fig. 2(a) shows the normalized transverse photocurrent spectra under different longitudinal electric fields (i.e., AHE current) in sample A. The solid symbols are the experimental data, and the solid lines are guides for eyes. The spectra are normalized by I0 / E0 corresponding to the transition of excitonic state 1H1E, where I0 is the photoconductive current detected at the point contacts when applying a DC-bias of 1.5 V between the point contacts, and E0 is the electric field between the two point contacts when applying a DC-bias of 1.5 V. It can be seen that the AHE current increases with the increasing of the longitudinal field, and the current flow reverses with the direction of the longitudinal field. Denoting I′AHE+ (I′AHE−) as the transverse current collected by the two point contacts at positive (negative) longitudinal field, one can obtain the AHE current accurately by (I ′AHE+ − I ′AHE− )/2 , as shown in Fig. 3. The solid symbols are the experimental data, and the solid lines are guides for eyes. One can see that, the energy positions of the excitonic state 1H1E and 1L1E can not be clearly distinguished in the AHE spectra due to the large FWHM of the Ti-sapphire laser. In order to find out the exact energy position of the excitonic transition 1H1E and 1L1E, we replace the Ti-sapphire laser with a 250 W tungsten lamp combined with a monochromator, which has a spectral resolution of 1 nm. The measurement results are shown in Fig. 2(b), from which the energy positions of the excitonic states 1H1E and 1L1E, indicated by solid and dashed arrows in Fig. 2(b) respectively, can be clearly located. The energy positions of the excitonic state 1H1E and 1L1E are also indicated by vertical dashed in Fig. 3. The generation of transverse photocurrent under longitudinal electric field is described as follows. Firstly, the spin polarized carriers are produced under the radiation of circularly polarized light, whose photon energy is equal to or larger than the excitonic states of the QWs, by two ways: (1) direct formation of free electrons and holes, and (2) creation of free carriers through excitons [19]. For the first case, under the irradiation of circularly polarized light, taking left-handed (σ+) circularly polarized light as an example, the electron in the valence band with spin angle momentum ms = −3/2 will jump to the conduction band with spin angle momentum ms = −1/2 , according to the optical selection rule. For the second case, excitons consisting of welldefined spins are created by circularly polarized light, and then the excitons are dissociated to produce free carriers by interaction with phonons, impurities and other excitons [19]. Then the spin polarized carriers will show lateral deflection due to spin Hall effect (SHE). To be 56
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 2. (a) Spectra of the normalized AHE current under different longitudinal electric fields detected in sample A. (b) Photoconductive current under a dc bias of 3 V measured by a spectrum system with a resolution of 1 nm in sample A, B and C. The solid and dashed arrows indicate the energy positions of the excitonic states 1H1E and 1L1E, respectively.
bands by the circularly polarized light with same helicity will jump to the opposite spin splitting branches in the conduction band, which will reverse the direction of the AHE current [19]. However, in our experiments, the AHE current of 1H1E and 1L1E show the same sign. Although the large FWHM of the laser (7 nm) will result in a little contribution of 1H1E when measuring the AHE current corresponding to the excitonic state 1L1E, this will not be the main reason, because the energy difference between 1H1E and 1L1E (about 10 nm for sample A (or C) and 15 nm for sample B) is larger than the FWHM of the laser and the similar phenomenon is also observed in InGaAs/ AlGaAs QWs measured by a spectrum system with a resolution of 1.5 nm [19]. The mixing or anticrossing of the light- and heavy-hole bands can also be excluded, since the band mixing effect at small k is so weak that it can be neglected [19]. We think that the phenomenon may be related to the contribution of holes to the AHE. The hole density is comparable to that of electron in the undoped QWs, which is different from the case in n-doped QWs that are dominated by electrons. So the contribution of holes to AHE current may not be neglected. Besides, it is theoretically found that the spin relaxation time of holes is of the same order of magnitude with that of electrons in quantum dots with large lateral dimensions [30]. This qualitative conclusions may be of some relevance also for QWs [31]. What is more, it was predicted that the AHE current in p-doped GaAs/AlGaAs QWs corresponding to 1H1E induced by intrinsic mechanism had the same sign with that of 1L1E [32]. Therefore, the contribution of holes to the AHE may be mainly responsible for the surprising phenomenon of same sign for 1H1E and 1L1E in AHE spectra. One can see from Fig. 3 that, there are also AHE current generated in the QWs when the photon energy is far away from the denoted energy positions of 1H1E and 1L1E (at 760 nm, for example), which may be attributed to the higher states of the QWs, such as the transition of 2H2E, 2L2E. In the following discussion, we only focus on the AHE current of 1H1E. By the normalization of I0 / E0 , we can eliminate the influences of the carrier mobility and the carrier density in different samples and thus enable a better comparison of the AHE conductivity in different samples. This is because the AHE current can be expressed as IAHE = σxyph SλE × e [14] and the photoconductive current I0 can be written as I0 = σ0 E0 S , where σxyph is the AHE conductivity, S is the crosssectional area of the AHE current or that of the photoconductive current, E is the longitudinal electric field applied along the two strips when measuring AHE current, e denotes the direction of light propagation, λ = ± 1 is the helicity of the light and σ0 is the photo-
Fig. 3. Spectra of the normalized AHE current detected in sample A, B and C under different longitudinal electric fields. The vertical dash lines indicate the energy positions of the excitonic states 1H1E and 1L1E. The solid lines are guides for eyes.
specific, according to SHE, electrons will show an anomalous velocity perpendicular to the electric field under the intrinsic or extrinsic mechanisms. The extrinsic mechanism is based on asymmetric Mottskew or side-jump scattering from impurities in a spin-orbit coupled system [2,22], while the intrinsic mechanism is dependent only on the band structure of the materials, which arises from Rashba [3,23] or Dresselhaus SOC [24,25]. Then the electrons with different spin directions will move to the opposite sides of the sample plane, leading to a spin current or spin accumulation in a direction transverse to the direction of the longitudinal field. If the carriers are spin polarized, the number of carriers moving along the left and right sides will be different, and a Hall-like current will present, which is named as AHE current. Generally, the AHE current corresponding to the transition of 1L1E is expected to flow at an opposite direction of 1H1E. This is because electrons excited from the heavy hole and light 57
Physica E 90 (2017) 55–60
J.L. Yu et al.
Since the AHE essentially stems from ISHE, they will have the same mechanisms, i.e., the extrinsic mechanism based on asymmetric impurities scattering and the intrinsic mechanism arised from Rashba or Dresselhaus SOC. It is expected that both of intrinsic and extrinsic mechanisms will contribute to the AHE for a given sample. Since sample A and B are grown under the same conditions by the same MBE system and they have the same structure except for the well width of the QW, the concentration of the impurities introduced by the residual doping are nearly equal in the two samples. However, sample C with InAs layers inserted at the interfaces of the QWs is grown at a different condition with that of sample A and B, which will result in different density of impurities in sample C. Therefore, we assume that the contribution made by the impurities to the AHE current for sample A and B is the same, and that the contribution made by the impurities to the AHE in sample A (or sample B) is different from that in sample C. For the intrinsic mechanism, it is reasonable to assume that its contribution to the AHE current is proportional to the strength of the Rashba or Dresselhaus SOC [33]. The relative ratio of Rashba or Dresselhaus SOC of the three samples can be obtained by CPGE measurements [27], i.e., we first measure the CPGE spectra induced by Rashba (named as IR) or Dresselhaus (named as ID) SOC and the photoconductive current I0 spectra under different angles of incidence; in order to eliminate the influence of absorbance and carrier mobility in different samples, we normalized the CPGE current by photoconductive current I0, as shown in Fig. 5(a)-(f); then we extract the normalized CPGE current IR / I0 (or ID / I0 ) corresponding to the transition of 1H1E at different angles of incidence, which are then fitted to the following equation [27].
Fig. 4. Dependence of the normalized AHE current on the longitudinal electric field corresponding to the transition of 1H1E for sample A, B and C, respectively. The solid lines are the linear fitting results.
conductivity. Therefore, we have
σxyph IAHE = E. I0 / E0 σ0
Iλ / I0 =
(1)
IAHE versus I0 / E0 σxyph / σ0 from
electric field E for a certain photon energy we can obtain the slope of the fitted curve. Fig. 4(a), (b) and (c) show the dependence of the AHE current corresponding to the transition of 1H1E on the longitudinal electric field for sample A, B and C, respectively. It can be seen that the intensity of the AHE current increases linearly with the applied longitudinal electric field. By linear fitting (solid lines), we can obtain the normalized AHE conductivity σxyph / σ0 for sample A, B and C are (3.1 ± 0.1) × 10−4 , (4.0 ± 0.1) × 10−4 , (8.6 ± 0.2) × 10−4 , respectively, as shown in Table 1. One can see that, the normalized AHE conductivity increases from sample A to C, which indicates that the AHE can be effectively tuned by changing the well width and by inserting an ultra-thin InAs layer at interfaces of the QWs. The photoinduced anomalous Hall conductivity corresponding to the excitonic state 1H1E of the three samples are all estimated to be in the order of 10−9Ω−1W −1, which agree well with that observed in InGaAs/AlGaAs QWs [19]. Table 1 Relative ratio of Rashba (αi /αA ) and Desselhaus coefficients ( βj /βA ) ( j = B, C ), the ratio of Rashba and Dresselhaus SOC (RD ratio, i.e., (α /β )i )(i = A, B, C ), the AHE conductivity ph ph /σ0 vs sample A σxy normalized by photoconductivity σ0 and the relative ratio of σxy corresponding to the transition of 1H1E for the three samples. Sample A
Sample B
Sample C
αj /αA
1.00 ± 0.08
0.89 ± 0.06
2.76 ± 0.45
βj /βA
1.00 ± 0.04
1.63 ± 0.47
1.09 ± 0.08
(α /β )i
0.78 ± 0.08 3.1 ± 0.1
0.48 ± 0.08 4.0 ± 0.1
1.98 ± 0.23 8.6 ± 0.2
1.00 ± 0.02
1.30 ± 0.50
2.78 ± 0.10
ph σxy σ0
(10−4)
⎛ σ ph ⎞ ⎛ σ ph ⎞ ⎜⎜ xy ⎟⎟ /⎜⎜ xy ⎟⎟ ⎝ σ 0 ⎠i ⎝ σ 0 ⎠A
n (cos θ +
n2 − sin2 θ )(n2 cos θ +
n2 − sin2 sin θ )
,
(2)
as shown in Fig. 5(g)-(i). Here θ is the angle of incidence, n is the refractive index of the GaAs material, and Aλ is a parameter related to the SOC of the QWs, i.e., when the current is induced by Rashba-type SOC (λ = R ), AR ∝ α , and when the current is induced by Dresselhaustype SOC (λ = D ), AD ∝ β . Here, α (β) is the Rashba (Dresselhaus) coefficient. Thus, by fitting the nomalized CPGE current at different angles using Eq. (2), the parameter AR (or AD ) in the normalized Rashba-type (or Dresselhaus-type) CPGE current are obtained, and the relative ratio of the Rashba (or Dresselhaus) SOC of the three samples can be obtained by the relative ratio of the corresponding AR (or AD ) parameters. Using this method, we obtain the relative ratio of the Rashba (or Dresselhaus) SOC of the three samples are αC / αA = 2.76 ± 0.45 αB / αA = 0.89 ± 0.06 , ( βB / βA = 1.63 ± 0.47, βC / βA = 1.09 ± 0.08), which are also shown in Table 1. Here αi and βi (i=A, B or C) are the Rashba and Dresselhaus coefficient for sample i (i=A, B or C), respectively. Taking the experimental error into account, we find that αA almost equals to αB, i.e., αA ≃ αB. The ratio of Rashba and Dresselhaus SOC (RD ratio) for 1H1E in the three samples are also determined by the relative ratio of the corresponding AR and AD parameters (i.e., α / β = AR / AD ), which are 0.78 ± 0.08, 0.48 ± 0.08 and 1.98 ± 0.23 for sample A, B and C, respectively. Using sample A as a reference sample, we get the relative ratios of the normalized AHE conductivity σxyph / σ0 vs that of sample A corresponding to the transition of 1H1E are 1.30 ± 0.50, and 2.78 ± 0.10 for sample B and C, respectively, as shown in Table 1. Thus, using sample A as a reference sample, we denote χSi , χRi , and χDi (i = A, B, C) as a relative ratio of AHE current in sample i contributed by the impurities scattering, Rashba and Dresselhaus SOC, respectively, to that of sample A, i.e., AHE AHE χSi = ISAHE / IAAHE , χRi = IRAHE , χDi = IDAHE . Here IAAHE denotes i i / IA i / IA AHE AHE AHE the AHE current in sample A. ISi , IRi and IDi represent the AHE current in sample i contributed by the impurities scattering, Rashba and Dresselhaus SOC, respectively. Then, we have
Thus, we can obtain the normalized AHE conductivity σxyph / σ0 from Fig. 3 by using Eq. (1), i.e., by linear fitting of the plot
Aλ sin θ cos2 θ
χSA + χRA + χDA = 1, 58
(3)
Physica E 90 (2017) 55–60
J.L. Yu et al.
Fig. 5. (a)-(f) CPGE spectra for sample A, B and C induced by Rashba- and Dresselhaus-type SOC normalized by the photoconductive current I0 at the angles of incidence from −30 to 30 degree with a step of 10 degree. All of the spectra are shifted vertically for clarity. The vertical dash lines indicate the energy position of the transition of 1H1E. The solid lines are guides for eyes. (g)-(i) Angular dependence of the normalized CPGE current for sample A, B and C induced by Rashba- and Dresselhaus-type SOC for the transition of 1H1E, respectively. The squares and circles are experiential results and the solid lines are the fitting results according to Eq. (2).
χSB + χRB + χDB = 1.30,
(4)
χSC + χRC + χDC = 2.78,
(5)
χRi β α χ = i , Di = i χRA αA χDA βA
(6)
χSB = χSA ,
χRA α = A = 0.78. χDA βA
Thus, we propose a method combining CPGE and AHE to separate the extrinsic and intrinsic mechanisms of the AHE, and this method is also applicable to determine the mechanism of SHE and ISHE, since they essentially originate from the same mechanisms. 4. Conclusion In conclusion, the photoinduced AHE spectra of GaAs/AlGaAs QWs with well width of 3 and 7 nm are investigated at room temperature. Ultra-thin InAs layers with a thickness of 1 ML have been inserted at the interfaces of GaAs/AlGaAs QWs to tune the asymmetry of the QWs. It is demonstrated that the AHE current shows strong dependence on the well width of the QWs, and its value is enhanced by the inserted InAs layer. Besides, we propose a method, which is also applicable to SHE or ISHE, to successfully separate the contribution of the intrinsic mechanism, i.e., the Rashba and Dresselhaus spin-orbit coupling, and the extrinsic mechanism, i.e., the scattering of impurities, to the AHE current for the transition of 1H1E.
(7)
By solving the above equations, we have χSA = χSB = 0.15, χRA = χRB = 0.37, χDA = 0.48, χDB = 0.78, χSC = 1.24 , χRC = 1.02 and χDC = 0.52 . It can be seen that the contributions made by the intrinsic mechanism to sample A, B and C are 85%, 88% and 55%, respectively, implying that the intrinsic mechanism plays a dominant role in all the three samples, which can be attributed to the fact that the samples are undoped and of high purity resulting in weak scattering of impurities [17]. The increase of the contribution by the intrinsic mechanism in sample B compared with that in sample A is due to the enhancement of Dresselhaus SOC induced by the reduced well width. The decrease of the intrinsic contribution in sample C may be attributed to the higher density of impurities in sample C introduced by the complicated growth process of sample C [27], which is also evident by the much weaker excitonic effect observed in the photoconductive current spectrum (shown in Fig. 1 in Ref. [27]) in sample C compared with that of sample A and B. Our observation is somewhat different from that reported in Ref. [4], which declared that the extrinsic mechanism make a major contribution to the AHE in undoped (001)-oriented GaAs QWs. This discrepancy may be owing to the following two reasons: (i) firstly, due to the different growth conditions between the samples that are used in our experiments and that are used in the Ref. [4], the impurities density in the samples may be different, which lead to different major mechanisms; (ii) secondly, the much smaller of the well width of the QWs in our samples may lead to larger SOC and thus enhance the contribution of the intrinsic mechanism.
Acknowledgement The work was supported by the National Natural Science Foundation of China (No. 61306120, No. 61674038, No. 61474114, No. 11574302), Natural Science Foundation of Fujian (Grant No. 2014J05073), National key Research and Development Program (2016YFB0402303) and Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (No. KF201405). References [1] Y. Kato, R.C. Myers, A.C. Gossard, D.D. Awschalom, Coherent spin manipulation without magnetic fields in strained semiconductors, Nature 427 (6969) (2004) 50–53.
59
Physica E 90 (2017) 55–60
J.L. Yu et al.
[18] C.M. Yin, N. Tang, S. Zhang, J.X. Duan, F.J. Xu, J. Song, F.H. Mei, X.Q. Wang, B. Shen, Y.H. Chen, J.L. Yu, H. Ma, Observation of the photoinduced anomalous Hall effect in GaN-based heterostructures, Appl. Phys. Lett. 98 (12) (2011) 122104. [19] J.L. Yu, Y.H. Chen, C.Y. Jiang, Y. Liu, H. Ma, L.P. Zhu, Observation of the photoinduced anomalous Hall effect spectra in insulating InGaAs/AlGaAs quantum wells at room temperature, Appl. Phys. Lett. 100 (2012) 142109. [20] J.L. Yu, Y.H. Chen, Y. Liu, C.Y. Jiang, H. Ma, L.P. Zhu, X.D. Qin, Intrinsic photoinduced anomalous Hall effect in insulating GaAs/AlGaAs quantum wells at room temperature, Appl. Phys. Lett. 102 (20) (2013) 202408. [21] J. Wunderlich, A.C. Irvine, J. Sinova, B.G. Park, L.P. Zarbo, X.L. Xu, B. Kaestner, V. Novak, T. Jungwirth, Spin-injection Hall effect in a planar photovoltaic cell, Nat. Phys. 5 (9) (2009) 675–681. [22] W.K. Tse, S.D. Sarma, Spin Hall effect in doped semiconductor structures, Phys. Rev. Lett. 96 (2006) 056601. [23] B.A. Bernevig, S.C. Zhang, Intrinsic spin Hall effect in the two-dimensional hole gas, Phys. Rev. Lett. 95 (2005) 016801. [24] B.A. Bernevig, S.C. Zhang, Spin splitting and spin current in strained bulk semiconductors, Phys. Rev. B 72 (2005) 115204. [25] V. Sih, R.C. Myers, Y.K. Kato, W.H. Lau, A.C. Gossard, D.D. Awschalom, Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases, Nat. Phys. 1 (1) (2005) 31–35. [26] C.G. Zeng, Y.G. Yao, Q. Niu, H.H. Weitering, Linear magnetization dependence of the intrinsic anomalous Hall effect, Phys. Rev. Lett. 96 (2006) 037204. [27] J.L. Yu, X.L. Zeng, S.Y. Cheng, Y.H. Chen, Y. Liu, Y.F. Lai, Q. Zheng, J. Ren, Tuning of Rashba/Dresselhaus spin splittings by inserting ultra-thin InAs layers at interfaces in insulating GaAs/AlGaAs quantum wells, Nanoscale Res. Lett. 11 (1) (2016) 477. [28] S.D. Ganichev, V.V. Bel'kov, L.E. Golub, E.L. Ivchenko, P. Schneider, S. Giglberger, J. Eroms, J. De Boeck, G. Borghs, W. Wegscheider, D. Weiss, W. Prettl, Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells, Phys. Rev. Lett. 92 (25) (2004) 256601. [29] S. Giglberger, L.E. Golub, V.V. Bel'kov, S.N. Danilov, D. Schuh, C. Gerl, F. Rohlfing, J. Stahl, W. Wegscheider, D. Weiss, W. Prettl, S.D. Ganichev, Rashba and Dresselhaus spin splittings in semiconductor quantum wells measured by spin photocurrents, Phys. Rev. B 75 (3) (2007) 035327. [30] D.V. Bulaev, D. Loss, Spin relaxation and decoherence of holes in quantum dots, Phys. Rev. Lett. 95 (7) (2005) 076805. [31] D.M. Gvozdic, U. Ekenberg, Superefficient electric-fieldcinduced spin-orbit splitting in strained p-type quantum wells, Europhys. Lett. 73 (6) (2006) 927. [32] X. Dai, F.C. Zhang, Light-induced Hall effect in semiconductors with spin-orbit coupling, Phys. Rev. B 76 (8) (2007) 085343. [33] K. Nomura, T. Jungwirth, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Edge-spin accumulation in semiconductor two-dimensional hole gases, Phys. Rev. B 72 (2005) 245330.
[2] Y.K. Kato, R.C. Myers, A.C. Gossard, D.D. Awschalom, Observation of the spin Hall effect in semiconductors, Science 306 (5703) (2004) 1910–1913. [3] J. Sinova, D. Culcer, Q. Niu, N.A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Universal intrinsic spin Hall effect, Phys. Rev. Lett. 92 (12) (2004) 126603. [4] S. Priyadarshi, K. Pierz, M. Bieler, Detection of the anomalous velocity with subpicosecond time resolution in semiconductor nanostructures, Phys. Rev. Lett. 115 (2015) 257401. [5] K.N. Okada, N. Ogawa, R. Yoshimi, A. Tsukazaki, K.S. Takahashi, M. Kawasaki, Y. Tokura, Enhanced photogalvanic current in topological insulators via fermi energy tuning, Phys. Rev. B 93 (2016) 081403. [6] R. Iguchi, K. Sato, D. Hirobe, S. Daimon, E. Saitoh, Effect of spin hall magnetoresistance on spin pumping measurements in insulating magnet/metal systems, Appl. Phys. Express 7 (1) (2014) 013003. [7] K. Kondou, H. Sukegawa, S. Kasai, S. Mitani, Y. Niimi, Y. Otani, Influence of inverse spin Hall effect in spin-torque ferromagnetic resonance measurements, Appl. Phys. Express 9 (2) (2016) 023002. [8] V. Lechner, L.E. Golub, P. Olbrich, S. Stachel, D. Schuh, W. Wegscheider, V.V. Bel'kov, S.D. Ganichev, Tuning of structure inversion asymmetry by the deltadoping position in (001)-grown GaAs quantum wells, Appl. Phys. Lett. 94 (24) (2009) 242109. [9] M.P. Walser, U. Siegenthaler, V. Lechner, D. Schuh, S.D. Ganichev, W. Wegscheider, G. Salis, Dependence of the Dresselhaus spin-orbit interaction on the quantum well width, Phys. Rev. B 86 (19) (2012) 195309. [10] C.M. Yin, H.T. Yuan, X.Q. Wang, S.T. Liu, S. Zhang, N. Tang, F.J. Xu, Z.Y. Chen, H. Shimotani, Y. Iwasa, Y.H. Chen, W.K. Ge, B. Shen, Tunable surface electron spin splitting with electric double-layer transistors based on InN, Nano Lett. 13 (5) (2013) 2024–2029. [11] S.D. Ganichev, W. Prettl, Spin photocurrents in quantum wells, J. Phys.-Condens. Matter 15 (20) (2003) R935–R983. [12] S.D. Ganichev, L.E. Golub, Interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy - a review, Phys. Status Solidi B-Basic Solid State Phys. 251 (9) (2014) 1801–1823. [13] L.P. Zhu, Y. Liu, C.Y. Jiang, J.L. Yu, H.S. Gao, H. Ma, X.Q. Qin, Y. Li, Q. Wu, Y.H. Chen, Spin depolarization under low electric fields at low temperatures in undoped InGaAs/AlGaAs multiple quantum well, Appl. Phys. Lett. 105 (15) (2014) 152103. [14] X. Dai, F.C. Zhang, Light-induced Hall effect in semiconductors with spin-orbit coupling, Phys. Rev. B 76 (2007) 085343. [15] M.I. Miah, Observation of the anomalous Hall effect in GaAs, J. Phys. D.-Appl. Phys. 40 (6) (2007) 1659–1663. [16] M.I. Miah, Electric field control photo-induced Hall currents in semiconductors, Mater. Chem. Phys. 111 (2–3) (2008) 249–253. [17] D.A. Vasyukov, A.S. Plaut, M. Henini, L.N. Pfeiffer, K.W. West, C.A. Nicoll, I. Farrer, D.A. Ritchie, Intrinsic photoinduced anomalous Hall effect, Phys. E-Low.Dimens. Syst. Nanostruct. 42 (4) (2010) 940–943.
60