Observation of the photoinduced anomalous Hall effect in GaN-based

APPLIED PHYSICS LETTERS 98, 122104 共2011兲

Observation of the photoinduced anomalous Hall effect in GaN-based heterostructures C. M. Yin,1 N. Tang,1,a兲 S. Zhang,1 J. X. Duan,1 F. J. Xu,1 J. Song,1 F. H. Mei,1 X. Q. Wang,1 B. Shen,1,b兲 Y. H. Chen,2 J. L. Yu,2 and H. Ma2 1

State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, People’s Republic of China 2 Laboratory of Semiconductor Materials Science, Institute of Semiconductors, CAS, Beijing 100083, People’s Republic of China

共Received 29 January 2011; accepted 4 March 2011; published online 21 March 2011兲 The photocurrent has been measured in Al0.25Ga0.75N / GaN heterostructures at room temperature, and the photoinduced anomalous Hall effect 共AHE兲 was observed. The AHE current changes linearly with the varied longitudinal electric fields. Due to the strong Rashba spin–orbit coupling of the two-dimensional electron gas in Al0.25Ga0.75N / GaN heterostructures, the intrinsic anomalous Hall mechanism is supposed to contribute to the photoinduced AHE. The photoinduced AHE measurement proposed in this study could be used to other spin related measurements at room temperature. © 2011 American Institute of Physics. 关doi:10.1063/1.3569948兴 The spin Hall effect 共SHE兲 and the anomalous Hall effect 共AHE兲 have drawn much attention in the research of semiconductor spintronics,1,2 due to the universal value of the intrinsic spin Hall conductivity,3,4 and the probable application to spintronic devices.5 Recently, a SHE transistor combining the spin transistor and the SHE provides an experimental tool for exploring spin Hall and spin precession phenomena in an electrically tunable semiconductor layer.6 Moreover, the AHE in spin polarized systems can detect magnetization and magnetic domain dynamics.7 Both the SHE and the AHE originate from a variety of mechanisms, including the extrinsic mechanisms of asymmetric Mottskew and side-jump scatterings from impurities in a spin– orbit coupled system, and the intrinsic mechanism due to the Rashba spin–orbit coupling 共SOC兲, which is inherent to the band structure.1 The SHE was observed in semiconductor films, including GaAs and InGaAs, with scanning Kerr rotation measurements at 30 K,8 and then a direct electric measurement of the SHE was reported in a diffusive metallic conductor 共aluminum兲 at 4.2 K.9 Moreover, former observations of the SHE were mostly performed in bulk films at low temperatures.1 Miah reported the photoinduced AHE detected at room temperature in GaAs films but there were large uncertainties for the experimental points arising from the rather poor signalto-noise ratio.7 As we know, the Rashba SOC is usually very weak in bulk semiconductor films, and thus the SHE and the AHE might be observed at room temperature in semiconductor heterostructures where the Rashba SOC is much stronger. In this letter, the photoinduced AHE has been measured at room temperature in Al0.25Ga0.75N / GaN heterostructures, where the Rashba SOC of the two-dimensional electron gas 共2DEG兲 is very strong.10 It is found that the AHE current changes linearly with the varied longitudinal electric fields, and the anomalous Hall conductivity of the 2DEG is determined to be ␴AH = 9.0⫻ 10−10 ⍀−1. a兲

Electronic mail: [email protected]. b兲 Electronic mail: [email protected]. 0003-6951/2011/98共12兲/122104/3/$30.00

Al0.25Ga0.75N / GaN heterostructures were grown by means of metal-organic chemical vapor deposition. A lowtemperature GaN buffer layer was initially deposited on the 共0001兲 surface of the sapphire substrate, followed by a 2 ␮m thick GaN layer. Then an unintentionally doped 28 nm thick Al0.25Ga0.75N layer was grown. The 2DEG mobility of the samples varies from 1500 to 1800 cm2 / V s. All the samples were cut into stripes with the same size as shown in the inset of Fig. 1. Two 0.5 mm diameter circle electrodes, with a distance of 3 mm, and two 共0.5 mm⫻ 4.0 mm兲 strip electrodes, with the same distance, were made by annealing the Ti/Al/Ni/Au metal layers. The AHE measurements were performed at room temperature. A 400 mW solid state laser with a wavelength of 1064 nm was used to excite the electrons to the high energy states out of the triangular quantum well 共QW兲 at the heterointerface. The laser beam passed through a rotatable quarter wave plate, which is used to modulate the helicity of the incident light Pcirc, and then irradiated normally on the samples at the center of the four electrodes, with a diameter

FIG. 1. 共Color online兲 The total photocurrent measured with the longitudinal electric field Edc = 20 V / cm in an Al0.25Ga0.75N / GaN heterostructure, which is well fitted with Eq. 共1兲. 98, 122104-1

© 2011 American Institute of Physics

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FIG. 2. 共Color online兲 The schematic diagrams of the photoinduced AHE: 共a兲 under right-rotation and 共b兲 under left-rotation circularly polarized radiation.

of 1 mm. The longitudinal electric field was applied by the two strip electrodes, and the current signal was collected by a lock-in amplifier through the two circle electrodes. When the right-rotation circularly polarized light irradiates on the samples, as shown in Fig. 2共a兲, the electrons in the 2DEG with the spin ms = −1 / 2 are excited to the upper band with the spin ms = +1 / 2, inducing the spin imbalance. According to the intrinsic and extrinsic AHE mechanisms, the spin polarized electrons driven by the longitudinal electric field will lead to a transverse AHE current. While the left-rotation circularly polarized light irradiates on the sample as shown in Fig. 2共b兲, the spin polarized electrons will lead to an opposite transverse AHE current. Apparently, the amount of the spin polarized electrons is proportional to the helicity of the incident light Pcirc so that the AHE current is proportional to Pcirc. Besides the AHE, the circular photogalvanic effect 共CPGE兲 and the spin galvanic effect 共SGE兲 are also sensitive to the circularly polarized light so that they might contribute similar transverse currents.11 However, we find that the CPGE and the SGE do not contribute a detectable current proportional to Pcirc in our measurements. First, the spin polarization directions of the 2DEG in Al0.25Ga0.75N / GaN heterostructures are within 共0001兲 plane, so the normally incident light will induce neither CPGE nor SGE current.11 Second, the longitudinal electric field will lead to a transverse pure spin current, and then induces the asymmetric spin distribution in momentum space, which may induce a CPGE current.12 However, the pure spin current induced CPGE current will lead to a stronger absorption of the circularly polarized light with the electric field increasing. We measured the photocurrent in both-sides polished Al0.25Ga0.75N / GaN heterostructures but found no considerable change in transmission light intensity with the varied electric fields. So the photocurrent component proportional to Pcirc is not supposed to be attributed to the pure spin current, either. Therefore, the total photocurrent can be described by the following formula: j = jAHE sin 2␸ + jL sin 2␸ cos 2␸ + j0 ,

共1兲

where ␸ is the rotation angle of the optical axis of the quarter wave plate with respect to the polarized plane of the laser beam, and the helicity of the incident light is Pcirc = sin 2␸; jAHE, sensitive to the circularly polarized light, is the ampli-

FIG. 3. 共Color online兲 The amplitude of the circularly polarized light sensitive current as a function of the longitudinal electric field in an Al0.25Ga0.75N / GaN heterostructure. Inset: the schematic diagram of the verifying experiment geometry.

tude of the AHE current; jL, sensitive to the linearly polarized light, is the amplitude of the linear photogalvanic effect 共LPGE兲 current; j0 is the background current, which can be attributed to the transverse component of the longitudinal current, the Dember effect, and other photovoltaic effects.13 Figure 1 shows the total photocurrent with the longitudinal electric field Edc = 20 V / cm, which is fitted with Eq. 共1兲, where the dashed line and the dotted line represent AHE and LPGE current components, respectively. The AHE current, with an amplitude of jAHE = 3.6 nA, achieves the maximum at about ␸ = ⫾ 45°, which is completely consistent with the phenomenology we discussed above. The two circle electrodes, as shown in the inset of Fig. 1, may not be strictly normal to the longitudinal electric field, so there will be a current component due to the asymmetric electrodes, which might contribute to a circularly polarized light sensitive current. We exaggerate the current component due to the asymmetric electrodes, as shown in the inset of Fig. 3. So the current component is much larger than that of Fig. 1. But the circularly polarized light sensitive current jAHE is too small to be detected, so the contribution to jAHE from the asymmetric electrodes is negligible. In addition, the electric field applied on the samples shown in Fig. 3 cannot be added as large as that shown in Fig. 1 because the lock-in amplifier will overload due to the large background current j 0. Figure 4 shows the amplitudes of the AHE current detected in Al0.25Ga0.75N / GaN heterostructures with varied longitudinal electric fields applied. The amplitude of the AHE current changes linearly with the varied longitudinal electric fields, and the anomalous Hall conductivity of the 2DEG in Al0.25Ga0.75N / GaN heterostructures is ␴AH = 9.0 ⫻ 10−10 ⍀−1, obtained from the linear fit line in Fig. 4. The anomalous Hall conductivity is a little smaller than the theoretical value in the n-type GaAs QW,14 which is probably because the photoinduced transition in our measurement is quite different from that in the n-type GaAs QW. The photoinduced anomalous Hall conductivity is proportional to the optical absorption coefficient.14 In the n-type GaAs QW, the anomalous Hall conductivity is estimated to be ␴AH = 4 ⫻ 10−9 ⍀−1 with the photo energy 1.55 eV of the incident light, which induces the interband transition between the heavy hole valence band and the conduction band.14 How-


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FIG. 4. 共Color online兲 The amplitude of the photoinduced AHE current as a function of the longitudinal electric field in an Al0.25Ga0.75N / GaN heterostructure. The solid line is the linear fit.

ever, the anomalous Hall conductivity of the 2DEG in Al0.25Ga0.75N / GaN heterostructures is measured with the photo energy 1.17 eV of the incident light. Considering that the height of the triangular QW is only about 0.37 eV,15 the electrons in the 2DEG are excited to the high energy states out of the QW, so the optical absorption coefficient is obviously smaller than that of the inter band transition. Accordingly, the photoinduced anomalous Hall conductivity ␴AH = 9.0⫻ 10−10 ⍀−1 is a reasonable value for the measurement in Al0.25Ga0.75N / GaN heterostructures. The Rashba SOC of the 2DEG in Al0.25Ga0.75N / GaN heterostructures is very strong as we proved in former works.10,16 The Rashba SOC coefficient is about 2.6 ⫻ 10−12 eV m,10 and the Dresselhaus SOC coefficient, induced by the bulk inversion asymmetry of the bulk film, is about 0.20⫻ 10−12 eV m.10 Therefore, the Rashba SOC of the 2DEG in Al0.25Ga0.75N / GaN heterostructures will lead to a stronger intrinsic AHE than the former SHE/AHE experiments in bulk films. Furthermore, the shielding effect due to the high 2DEG density will weaken the scattering mechanism of extrinsic AHE. Considering the two reasons above, we believe that there should be considerable intrinsic AHE due to the Rashba SOC in the photoinduced AHE measurements. The photoinduced AHE measurement we proposed in this study is very simple and effective. The photoinduced AHE current is detected at room temperature, and the measurement demands much lower longitudinal electric fields than the former AHE measurements in nonmagnetic

materials.1,7 Furthermore, the AHE current is modulated by the helicity of the incident light and thus oscillates with the rotation angle ␸ in a period of ␲ while the other components of the photocurrent oscillate with ␸ in different periods. As a result, the AHE current is precisely obtained among the other signals and the noises by fitting to Eq. 共1兲, and the uncertainties for the experimental points shown in Fig. 4 are very small. In summary, the photocurrent has been measured in Al0.25Ga0.75N / GaN heterostructures at room temperature, and the photoinduced AHE was observed. The AHE current changes linearly with the varied longitudinal electric fields, and the anomalous Hall conductivity is determined to be ␴AH = 9.0⫻ 10−10 ⍀−1. Due to the strong Rashba SOC of the 2DEG in Al0.25Ga0.75N / GaN heterostructures, the intrinsic mechanism is supposed to contribute to the AHE observed in this study. It is worth noting that the photoinduced AHE measurement used in this study is very simple and effective, and it could be used to other spin related measurements. This work was supported by the National Natural Science Foundation of China 共Grant Nos. 60990313, 60890193, 60806042, and 60736033兲, the Research Fund for the Doctoral Program of Higher Education in China 共Grant No. 200800011021兲, and the Wuhan National High Magnetic Field Center 共WHMFCKF2011004兲. 1

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