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Current and strain-induced spin polarization in InGaN/GaN superlattices

H. J. Chang, T. W. Chen, J. W. Chen, W. C. Hong, W. C. Tsai, Y. F. Chen, and G. Y. Guo

Department of Physics, National Taiwan University, Taipei 106, Taiwan The lateral current-induced spin polarization in InGaN/GaN superlattices (SLs) without an applied magnetic ?eld is reported. The fact that the sign of the nonequilibrium spin changes as the current reverses and is opposite for the two edges provides a clear signature for the spin Hall e?ect. In addition, it is discovered that the spin Hall e?ect can be strongly manipulated by the internal strains. A theoretical work has also been developed to understand the observed strain induced spin polarization. Our result paves an alternative way for the generation of spin polarized current.

PACS numbers: 71.20.-b, 72.25.Dc, 78.20.Hp, 78.55.Cr

arXiv:cond-mat/0702583v1 [cond-mat.mes-hall] 26 Feb 2007

It has been proposed theoretically that a transverse spin current, the so called spin Hall current, can be generated in strongly spin-orbit coupling systems by external electric ?eld [1, 2, 3, 4, 5, 6, 7]. This novel phenomenon o?ers the exciting possibility of pure electric driven spintronics in semiconductors, which can be more readily integrated with current industry. Recently, the observations of the spin Hall e?ect have been reported [8, 9, 10] in GaAs based devices, which has generated an intensive research [11, 12, 13, 14, 15, 16]. However, up to now, most of the experimental measurements were concentrated on GaAs system. More clear evidences to con?rm the spin Hall e?ect in other semiconductors are still needed [17]. Nitride semiconductors probably represent the most studied material system in semiconductor community for the last decade. InGaN/GaN superlattices have become particularly attractive because of their wide applications in light-emitting diodes (LEDs) [18] and high e?ciency laser diodes (LDs) [19]. In this letter, we provide the ?rst experimental observation of currentinduced spin polarization in InGaN/GaN superlattices. In addition, we discover that the spin Hall e?ect can be strongly manipulated by the internal strains. In order to have a fundamental understanding of the strain-induced spin Hall e?ect, a theoretical investigation has also been performed. Because strains are commonly present in semiconductor multilayers and superlattices due to lattice mismatch, our result therefore provides a convenient way to control the magnitude of the spin Hall e?ect, which should be very useful for the future applications. Furthermore, this strain dependence enables to resolve the intensive debate about whether the intrinsic spin Hall e?ect remains valid beyond the ballistic transport regime. The n-type InGaN/GaN superlattices were grown by a horizontal ?ow metalorganic chemical vapor deposition on (0001) sapphire substrate. All structures consist of 30 nm bu?er layer, followed by a 2 ?m epitaxial GaN layer and then 50 periods of InGaN/GaN superlattices. Superlattices are composed of periods of alternating 30 ? GaN A barriers and 50 ? Inx Ga1?x N wells with x ? 0.15. The A superlattices was doped with Si, and the electron concentration is 2x1012 cm?2 according to the Hall measurement. For the cross sectional photoluminescence (PL) measurement, the sample was excited by a He-Cd laser

FIG. 1: The schematic diagram of the edge photoluminescence measurement with di?erent angle of polarizer

working at 325 nm, dispersed by a SPEX 0.85 m doublegrating spectrometer, and the spectra was detected by a photomultiplier tube. Figure 1 shows the experimental arrangement for measuring the current-induced spin polarization. The current ?ow was stabilized with a value of 80 mA. The laser light was incident along the c-axis, which in turn was normal to the growth surface, and the polarized PL spectra were collected along the edge direction of the sample. The cross sectional PL spectra with right-handed (σ + ) and left-handed (σ ? ) modes were analyzed with a λ/4 wave plate and linear polarizer. For applying an electric ?eld, ohmic contacts were formed by depositing indium drops and a constant current was applied by Keithley 236 source measure unit. Figure 2(a) shows the cross sectional PL spectra with σ + and σ ? polarizations of the InGaN/GaN superlattices without current ?ow. The main PL signal originates from the recombination of electron-hole pairs in the quantum wells, and the weak modulation on the spectrum is due to the interference e?ect [20]. The PL spectra were carefully checked by recording zero di?erence between P Lσ+ and P Lσ? spectra when no current was delivered through the sample. Figures 2(b) shows the intensity variation of the cross sectional PL spectra at 13 K with di?erent orientation of polarization when the current ?ow is turned on. Here, the angle of 0 degrees is de?ned as the polarization is parallel to the c-axis of the sample. As can be seen in Figs. 2(b), it reveals a dramatic change in the PL intensity with respect to the polarized angle when the current ?ow is turned on. With the positive current ?ow (along the y-direction), the PL signal of the σ ? polarization is dominant as compared to that of the σ +

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FIG. 2: (a) Cross sectional photoluminescence spectra with σ + and σ ? polarizations of the InGaN/GaN superlattices in absence of a current. (b) shows the intensity variation of the cross sectional PL spectra with di?erent orientation of polarization when the current ?ow ( I = +/- 80 mA ) is turned on at 13 K.

FIG. 3: Di?erential spectra of polarized photoluminescence. Base line is taken with the current turned o?.

polarization. On the other hand, the σ + polarization PL intensity is dominant for the negative current ?ow (along the -y-direction), i.e., the PL polarization is inverted. To illustrate the e?ect of the current ?ow on the PL spectra in more detail, the di?erence of the PL intensity between σ + and σ ? polarizations is shown in Fig. 3. The base line (dotted) is taken with the current turned o?. The result seems containing a large ?uctuations, which may arise from the e?ect of scattering due to a large defect density existing in nitride semiconductors [8]. Even with the large ?uctuations, it reveals an important feature that the di?erence of the edge PL spectra inverses its sign as the electric current is reversed. In other words, the PL polarization is inverted as the direction of the current ?ow is reversed. This is a direct evidence of the current-induced spin orientation, in complete agreement with the results on the spin photocurrents in previous reports [8, 9, 10]. It is also worth noting that we did not detect a measurable anisotropy for the in-plane PL spectra with the current ?ow, and there is also no measurable anisotropy in the edge PL spectrum for the band to band emission when the current is turned o?. Thus, the optical anisotropy is a unique property related to the current-induced spin polarization. In addition, to further con?rm that the detected optical anisotropy is indeed due to nonequilibrium spin accumulation at sample edges, we have performed and found that the PL polarization is opposite for the two edges. Let us now brie?y outline the underlying mechanism that the nonzero di?erential edge polarized PL spectra detected in the absence of an external magnetic ?eld is indeed an experimental demonstration of the spinpolarization e?ect caused by asymmetric band occupation due to the current ?ow [21]. When a σ-spin electron in the k state of the conduction band makes a radiative transition to the topmost heavy-hole subband, the probability of this process depends on σ because the population of hole at the k state in the split up subband may

be di?erent from that in the split down subband. Hence, at k the conduction-band electron spin will be polarized along the σ direction if an electron with (σ) spin has a higher recombination rate. However, since the hole spin orientation at -k is reversed with respect to that at k, the spin polarization of the conduction band electron at the -k state will be along the -σ direction. Consequently, if the momentum distributions of both the electron gas and the hole gas are isotropic, there will be no net spin polarization of the conduction-band electrons. On the other hand, if such momentum distributions are anisotropic, the generation of spin polarization becomes possible. To further elucidate the unique behaviors of the spin Hall e?ect in the InGaN/GaN superlattices, we have measured the edge polarized PL spectra under di?erent excitation power as shown in Fig. 4. We can clearly see that the degree of circular polarization P decreases with increasing pumping power, where P is de?ned as P = Iσ+ ? Iσ? , Iσ+ + Iσ? (1)

This interesting result is quite subtle. To understand this intriguing behavior, let us recall the reported photoelastic e?ect in InGaN/GaN multiple quantum wells [20]. It has been shown that increasing excitation intensity will enhance the screening of piezoelectric (PZ) ?eld due to spatial separation of photoexcited electrons and holes. At the ?rst glance, it seems clear that our observation can be simply explained in terms of the reduced Rashba e?ect due to the screened electric ?eld. However, one has to keep in mind that nitride semiconductors are excellent piezoelectric materials. Through the converse PZ e?ect, a change in the built-in electric ?eld can induce a sizable change in the strain. According to the previous study [15, 22], a small change of strain can have a signi?cant in?uence on the Rashba e?ect, which has been considered as one of the main causes for the spin Hall e?ect [1, 2, 3, 4, 5, 6, 7]. Therefore, to complete our understanding, it will be worthwhile to take the strain e?ect into account. In order to demonstrate that the pumping laser can indeed change the internal strain in the studied sample, we have measured the Raman scattering of

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FIG. 4: The degree of circular polarization as a function of excitation density and corresponding strain. The strain is calculated by the Raman spectra in Fig. 5.The in-plane electric ?eld is applied in -y direction.

the InGaN/GaN superlattices under di?erent excitation density as shown in Fig. 5. It clearly indicates that the phonon frequency decreases with increasing pumping power, which implies that the internal strain of the heterostructure due to lattice mismatch can be changed by external excitation. The redshift in Raman spectra is unlikely due to local heating of the sample, because the corresponding PL peak has a blueshift, instead of a redshift (not shown here). If local heating is signi?cant, the band gap will be shrinked, which will result in a redshift of the PL spectra. In addition, the fact that the PL peak of GaN layer remains unchanged further supports a negligible heating e?ect. The strain ? change can be calculated according to phonon shift ?ω by the expression [23] ?= ?ω , C13 2a ? 2b C33 (2)

FIG. 5: Raman shift as a function of excitation density. In the inset, the calculated strain as a function of excitation density. It shows that the internal strain in InGaN/GaN superlattices can be manipulated by external excitation.

0.02 αe (eV?) 0.1 0.05 0 5 0 -5 -10 -2 -1.5 -1 -0.5 Strain (%) 0 CP (%) β (eV? ) 0.015 0.01 0.005

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σ xy [(e/8π)(2m/h ) ]

2 2 s

0 0.0005 0.0004 0.0003 0.0002 0.0001

where a and b are phonon deformation potentials ,and C13 and C33 are the elastic constants, respectively. The calculated strain is shown in the inset of Fig. 5, where the deformation potentials a, b and the elastic constants C13 , C33 were estimated by the extrapolation of the data for GaN and InN [23]. To establish the fundamental background of the straindependent spin Hall e?ect in InGaN/GaN superlattices, a theoretical investigation of the spin Hall current in n-type two-dimensional (2D) wurtzite structure is performed. Taking into account of the strong polarization ?eld at the interface alone the c-axis of wurtzite structure and the bulk inversion asymmetry (BIA), the 2D Hamiltonian can be written as [24] H= k2 + (αe + βk 2 )(σx ky ? σy kx ), 2m (3)

FIG. 6: (a) The theoretical e?ective Rashba coupling αe = λ + α (eV ?) (open circle) and BIA coupling β (eV ?3 ) (solid A A circle) vs. the in-plane strain. (b) the theoretical spin Hall s conductivity (σxy ) (solid square) and the degree of circular polarization (CP) (solid triangle) vs. the in-plane strain. The in-plane electric ?eld is applied in -y direction.

where αe = λ + α is the e?ective Rashba coupling. The coupling λ is induced by the built-in electric ?eld due to the piezoelectric e?ect. The coupling α and β are due to the BIA e?ect. To estimate the coupling parameters αe and β, we have performed ab initio relativistic

band structure calculations for GaN under several compressive in-plane strains (0 ? -2.0 %) using the highly accurate all-electron full-potential linearized augmented plane wave (FLAPW) method [25]. The details of the calculations will be reported elsewhere [26]. By ?tting the 2D Hamiltonian (Eq. 3) to the calculated spin-orbit coupling splitting of the lowest conduction bands near k = 0 as a function of the wavevector kx , we obtain the theoretical αe and β, as shown in Fig. 6(a) as a function of the in-plane strain. We note that the theoretical αe values are in the same order of magnitude of the e?ective Rashba coupling measured on AlGaN/GaN [27]. Since the magnitude of the in-plane strain in InGaN/GaN is close to that in AlGaN/GaN, the magnitude of built-in electric ?eld is found to be in the same order of magnitude in both systems (? 1M V /cm) [28, 29]. Therefore, we may expect InGaN/GaN and AlGaN/GaN to have similar coupling parameters αe and β, and hence the the-

4 oretical αe and β (Fig. 6a) will be used in the following spin Hall conductivity calculations. Within the linear-response Kubo formalism (see, e.g., [30]), we ?nd that the spin Hall conductivity for the 2D Hamiltonian of Eq. (3) is given by

s0 s0 σxy = ?σyx ≈

2 2m e [1 + αe β( 2 )2 ], 8π 3

(4)

plane strain is in good qualitative agreement with our experimental observation as shown in Fig. 6(b). This correlation implies that the circularly polarized PL spectra observed above are indeed due to the spin accumulation, which can be ?ne tuned by the internal strains. We therefore open a new possibility to manipulate the spin Hall e?ect in semiconductor heterostructures. In conclusion, we have investigated the currentinduced spin polarization in InGaN/GaN superlattices (SLs). It is found that the degree of polarization changes sign as the direction of the current ?ow is reversed. In addition, we also found that the internal strain in InGaN/GaN superlattices can be used to manipulate the magnitude of the spin Hall e?ect. The corresponding theoretical calculation has also been developed to interpret the strain dependence of the spin Hall e?ect. The strain-induced spin Hall e?ect discovered here paves an alternative way for the creation of spin polarized current, which should be useful for the realization of the future applications in spintronics. In view of the wide range of applications in nitride semiconductors, our study shown here should be very useful and timely. This work was supported by the National Science Council and Ministry of Education of the Republic of China.

under the condition that αe (? 10?2 eV ?) is larger than A 2 βk± (10?3 ? 10?4 eV ?), where the k+ and k? are the A Fermi momenta of the two spin-split bands, respectively. The spin Hall conductivity would be a universal constant, as found before [7], if we set β = 0. However, it is well known [31] that in the presence of scattering due to, e.g., the disorder, the spin Hall conductivity due to the klinear coupling term would vanish. Therefore, the observed spin Hall e?ect would be predominantly due to e 2 s the k-cubic term, i.e., σxy ≈ 8π 3 ( 2m )2 αe β. This clearly 2 shows that the spin Hall e?ect in the wurtzite semiconductor superlattices and multilayers could be enhanced by manipulating the spin-orbit coupling parameters αe and β which in term can be tuned by the compressive inplane strain via the piezoelectric ?eld, as demonstrated by our ab initio relativistic band structure calculations (Fig. 6a). The monotonic increase of the calculated spin Hall conductivity as a function of the compressive in-

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