⇦Chinese Physics Letters, 2017, Vol. 34, No. 11, Article code 116701 Spin Dynamics in Ferromagnet/10-nm-Thick N-Type GaAs Quantum Well Junctions Xiao-Chen Ji(纪晓晨)1,2, Chao Shen(申超)1,2, Yuan-Jun Wu(吴元军)1,2, Jun Lu(鲁军)1,2, Hou-Zhi Zheng(郑厚植)1,2** Affiliations 1State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 2College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 101408 Received 13 July 2017 **Corresponding author. Email: hzzheng@red.semi.ac.cn Citation Text: Ji X C, Shen C, Wu Y J, Lu J and Zheng H Z 2017 Chin. Phys. Lett. 34 116701 Abstract Spin dynamics in several different types of ferromagnetic metal (FM)/10-nm-thick n-type GaAs quantum well (QW) junctions is studied by means of time-resolved Kerr rotation measurements. Compared with the MnGa/in-situ doped 10-nm-thick n-type GaAs QW junction, the spin lifetime of the MnGa/modulation-doped 10-nm-thick n-type GaAs QW junction is shorter by a factor of 5, consistent with the D'yakonov–Perel' spin relaxation mechanism. Meanwhile, compared with the spin lifetime of the MnAs/in-situ doped 10-nm-thick n-type GaAs QW junction, the MnGa/in-situ doped 10-nm-thick n-type GaAs QW junction is of a spin lifetime longer by a factor of 4.2. The later observation is well explained by the Rashba effect in the presence of structure inversion asymmetry, which acts directly on photo-excited electron spins. We demonstrate that MnGa-like FM/in-situ doped 10-nm-thick n-type GaAs QW junctions, which possess relatively low interfacial potential barriers, are able to provide long spin lifetimes. DOI:10.1088/0256-307X/34/11/116701 PACS:67.30.hj, 73.21.Fg, 73.30.+y © 2017 Chinese Physics Society Article Text Ferromagnetic proximity polarization (FPP) is a specific phenomenon, observed by the time-resolved Faraday or Kerr rotation (TRFR or TRKR) measurements in ferromagnetic metal (FM)/n-typed semiconductor (100–200 nm in thickness) junctions.[1-3] It is well established that an initially non-polarized electron spin distribution, excited by linearly polarized light, was found to acquire a spin polarization.[1,3] In the case of circularly polarized pump beam with its wave vector normal to the applied magnetic field, a modified Larmor frequency has also been observed. This is attributed to a process that the excited spin polarized electrons act like a magnetic field in the direction of the pump beam, and then rotate to the applied magnetic field in the fireball duration before the Larmor precession starts. That is why the Larmor frequency changes in this kind of measurement.[2] Nearly at the same time, Ciuti et al.[4] theoretically studied the spin dependence of a two-dimensional electron gas (2DEG) passing through the channel portions underneath ferromagnetic gates. It turns out that the tunneling coupling of the electron wave function of the 2DEG to the exchange-split band states in the ferromagnetic metal produces a spin-dependent broadening and split of the quantized electron energy in the 2DEG itself. To check this theoretical prediction, one has to reduce the thickness of n-type doped GaAs layer from 100–200 nm down to 10–20 nm, thus both size quantization effects and the tunneling coupling across FM/n-type GaAs start to play a role. As a first step, one must check if spin lifetime in FM/10-nm-thick n-type GaAs quantum-well (QW) junctions could still be long enough for observing the mentioned coupling. In the present work, we focus on spin dynamics in specific quantum confined structures, composed of FM, n-type GaAs QW and AlGaAs plus AlAs composite barrier. Unlike the standard Al$_{x}$Ga$_{1-x}$As/GaAs/Al$_{x}$Ga$_{1-x}$As QW, the barrier close to FM side is formed by the Schottky barrier instead of Al$_{x}$Ga$_{1-x}$As barrier, thus our FM/10-nm-thick n-type GaAs/Al$_{x}$Ga$_{1-x}$As heterostructure is asymmetric, and of naturally structural inversion asymmetry (SIA). We investigate the dynamics of spin coherence in different types of FM/n-type GaAs QWs, and analyze spin relaxation mechanisms. It is concluded that it is possible to construct an FM/n-type GaAs QW junction which possesses high spin coherence. As usual, electron spin dynamics in our experiments were studied by time-resolved Kerr rotation (TRKR) using a mode-locked Ti:sapphire laser that emits $\sim$230 fs pulses at a 76 MHz repetition rate. Its output, with the energy tuned slightly above the band gap of n-type doped GaAs layer at $T\sim70$ K, was split into circularly polarized (CP) pump beam and linearly polarized (LP) probe beam. They were focused on the same spot of the sample. In the previous work, both pump and probe beams radiate from the back side of the sample. To avoid the loss of both pump and probe beams, the usual method is first mounting the measured sample on fused silica with transparent epoxy. Then the substrates were removed up to a etching stop layer (400 nm AlGaAs layer) by a selective etch.[5] To avoid the difficulty in preparing such samples, we adopted a new measurement skill, and let both pump and probe beams radiate directly onto the front side of samples without the need to remove the thick substrate portion. In addition, by chopping the pump beam and using lock-in detection, we measured the response of Kerr rotation caused only by photo-excited electrons on the side of n-type GaAs. However, in principle, sub-picosecond laser pulses (especially pump pulse) have the interaction with magnetic materials, for example, changing their magnetic order. That involves the complex interaction of photons with charges, spins, lattice, and the angular momentum transfer.[6] To check if the mentioned complex interactions have their influence on our measured TRKR signal, we measured TRKR signal of the MnGa film itself by tuning the wavelength of both pump and probe beams down to 850 nm, where no signal came from n-type GaAs. It was found that the measured TRKR, excited by left-, right-circularly and linearly polarized pump beams, were essentially horizontal lines except a very tiny sharp peak appears within initial 10 ps. As a matter of fact, the mentioned phenomena exist as well when the pump and probe beams excite from the back side of the samples, and then penetrate out off the front side. On the other hand, it is well known from the Maxwell equation that the wave vector $k$ is defined as $$ k^2=\frac{\varepsilon\mu}{c^2}\omega ^2+i\frac{4\pi \sigma \omega \mu }{c^2}, $$ where $\varepsilon $ is the permittivity, and $\mu$ is the permeability. The other quantities are defined as usual. Here a nonzero conductivity $\sigma \ne 0$ gives rise to attenuation to the penetrating light beams. Next, we have to check that the attenuations of right-circularly and left-circularly polarized pump beams by the ferromagnetic film are the same when they pass through the MnGa film. Therefore, we have measured the TRKR responses at 70 K, when the pump beam is left-, right-circularly and linearly polarized in a particular sample. The layer structure consists of MnGa/10 nm n-type GaAs QW ($1\times10^{18}$ cm$^{-3}$)/20 nm undoped Al$_{0.3}$Ga$_{0.7}$As/50 nm undoped AlAs/800 nm undoped i-GaAs/SI-GaAs substrate. Figures 1(a) and 1(b) give the TRKR responses in the absence and presence of magnetic field, excited with left-circularly (blue), right-circularly (red) and linearly-polarized (green) pump beams by turning $1/4\lambda$ wave plate. The polarization accuracy of linear polarized pump beam may be better than 10$^{-4}$. The others have less accuracy. The black curve represents the results by summing the TRKR responses from left-circularly (blue) and right-circularly (red) excitation. One can find that the black and green curves are in good consistence, as required by the relationship between them. Spin dynamics of photo-excited carriers in normal GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells have been intensively investigated in terms of well-width and temperature dependences. For example, it was found that the electron spin-relaxation rate in wide wells follows that for bulk GaAs, which varies approximately as $T^{2}$. For narrow wells, the relaxation rate varies quadratically with the confinement energy.[7] The spin lifetime of 2DEG and their dependence on the electron density were also investigated in gate-controlled QWs. A markedly enhanced 2DEG spin lifetime was observed in the voltage range where the QW features a transition from an insulating to a conducting state at 3.5 K.[8] Hereafter, we concentrate on the spin dynamics in specific quantum confined structures, composed by ferromagnetic metal (FM), 10 nm n-type GaAs QW and AlGaAs plus AlAs composite barrier.
cpl-34-11-116701-fig1.png
Fig. 1. The TRKR responses excited by linearly polarized (LP), left- and right-circularly polarized (LCP and RCP) pump beams in the absence (a) and the presence (b) of magnetic field.
We first investigate and compare the spin dynamics behaviors in two kinds of samples at 70 K by time-resolved Kerr rotation (TRKR). The wavelength of both pump and probe beams is 800 nm, which is tuned to the band gap of 10 nm GaAs QWs. Sample 1 consists of the layer structure (from top to down): 2 nm Al/10 nm MnGa/10 nm n-type GaAs QWs ($1\times10^{18}$ cm$^{-3}$)/20 nm undoped AlGaAs/50 nm undoped AlAs/800 nm undoped GaAs/SI-GaAs substrate. Sample 2 is composed by the layers: 2 nm Al/10 nm MnGa/10 nm undoped GaAs QWs/10 nm undoped AlGaAs/2 nm n-type AlGaAs ($1\times10^{18}$ cm$^{-3}$)/10 nm undoped AlGaAs/50 nm undoped AlAs/800 nm undoped i-GaAs/SI-GaAs substrate. The major difference between samples 1 and 2 is that sample 1 has an in-situ doped QW, while the QW of sample 2 is a modulation-doped one. The spin relaxation and Larmor precession, measured at 70 K in the absence and presence of applied magnetic field (1.4 T), are shown in Figs. 2(a) and (b) for the samples 1 and 2. The extracted $g$ factors are $-$0.35 and $-$0.39, respectively. The spin lifetime, extracted from sample 1, is longer than 474 ps. In contrast, its value from sample 2 is as low as 96 ps. To explain the experimental results, two possible mechanisms are considered. Firstly, the maximum values of cold electrons in 10-nm-thick n-type GaAs QWs, which could be provided in samples 1 and 2, are different. Sample 1 has maximum cold electrons of $1\times10^{12}$ cm$^{-2}$, and sample 2 has $2\times10^{11}$ cm$^{-2}$. One possibility might be that photo-holes, excited by the pump beam, are not completely recombined by enough cold electrons in sample 2. As a result, photo-excited electrons' spins still have chance to be depolarized due to their exchange interaction with the residual holes in sample 2. However, it looks unlikely unless photo-excitation is very strong. The other possibility is purely due to the D'yakonov–Perel' (DP) mechanism, which is considered to be the dominant mechanism for spin relaxation, particularly in n-type samples and at higher temperature.[9] In the DP mechanism the driving force for spin reorientation is the intrinsic tendency of electron spins to precess in the effective magnetic field which they experience as a result of spin–orbit interaction. The corresponding spin relaxation rate is determined by $\tau _{{\rm S},i}^{-1}=\langle {{\it \Omega}_\bot^2 } \rangle \tau _{\rm p}^\ast$ ($\langle {| {{\it \Omega} _\bot ^2}|} \rangle \tau _{\rm p}^\ast < 1$), where $|{{\it \Omega}_\bot ^2}|$ is the square of the component of precession vector ${\it \Omega}_\bot$ perpendicular to the axis $i$, averaged over the spin-oriented population, and $\tau _{\rm p}^\ast$ is the momentum scattering time of a single electron.[10] Obviously, the longer $\tau _{\rm p}^\ast$ is, the larger the spin relaxation rate $\tau _{{\rm S},i}^{-1}$ is. That gives a good reason why the modulation-doped QW has a shorter spin lifetime compared with the in-situ doped QW, because the remote ionized impurity scattering is much less effective. On the other hand, it is known that, at a temperature of 70 K, a transition from Fermi–Dirac to Maxwell–Boltzmann electron distribution leads to faster electron momentum scattering by charged impurities in the higher doped samples. That is also in favor of a longer spin relaxation time.[11]
cpl-34-11-116701-fig2.png
Fig. 2. Spin relaxation (black squares) and Larmor precession (red circles) were measured at 70 K in the absence and presence of applied magnetic field (1.4 T). Black and red lines are corresponding fitting curves. (a) Sample 1 is in-situ doped. (b) Sample 2 is modulation-doped.
Next, we check the spin dynamics behavior of MnAs/n-type GaAs junctions. The layer structure of sample 3 is composed by 10 nm MnAs/200 nm n-type GaAs ($1\times10^{18}$ cm$^{-3}$)/100 nm undoped Al$_{0.3}$Ga$_{0.7}$As/500 nm undoped GaAs buffer/SI-GaAs substract. Sample 4 has the same layer structure except that 200 nm n-type GaAs ($1\times10^{18}$ cm$^{-3}$) is replaced by 10 nm n-type GaAs QWs ($1\times10^{18}$ cm$^{-3}$). For samples 3 and 4, the wavelengths of both pump and probe beams are adjusted to 830 nm and 800 nm, respectively. For the MnAs/200-nm-thick n-type GaAs ($1\times10^{18}$ cm$^{-3}$) junction (sample 3), as seen in Fig. 3(a), the spin lifetime is longer than 376 ps at 70 K with very clear Larmor oscillations, seen in a magnetic field of 1.4 T. Under the excitation of circularly polarized pump beam, the spin dynamics, seen in sample 3, mainly reflect the intrinsic spin dynamics of the thick n-type GaAs layer. The fireball effect at the MnAs/GaAs interface is negligible.[12] In contrast, the spin dynamics of the MnAs/10-nm-thick n-type GaAs QW ($1\times10^{18}$cm$^{-3}$) junction (sample 4) only has one period of Larmor precession discernible with a spin lifetime of 112 ps, as seen in Fig. 3(b). The spin dynamics of sample 4 is also in sharp contrast with sample 1. From the experimental side, we find that the Schottky barriers, formed at the MnGa/10-nm-thick n-type GaAs QW junction and at the MnAs/10-nm-thick n-type GaAs QW junction, respectively, are quite different. The $I$–$V$ curve of the former junction shows a turn-on voltage as low as +0.1 V. The latter has very high barrier near MnAs/10-nm-thick n-type GaAs QW interface, thus there is no free electron in the 10-nm-thick n-type GaAs layer in the absence of the pump beam. This is neither due to usual depletion of electrons, because there is no way for them to escape through the thick barrier on the bulk GaAs side, nor a transition from a conducting to an insulating state, which occurs at much low temperature, like 3.5 K.[8] In the case of n-type GaAs QWs, one has to remember that the energy for electrons to ionize into conduction band increases. It is no longer equal to the energy difference between the bottom of conduction band and the donor level. Instead, it becomes the difference between the lowest quantized level in n-type GaAs QWs and the donor level. As a result, the electrons in 10-nm-thick n-type GaAs QWs are in fact frozen in the donor impurities in such a MnAs/10-nm-thick n-type GaAs QW junction even at 70 K. Nevertheless, these frozen electrons can still play a role to kill photo-excited hole in n-type GaAs QWs, and diminish the spin relaxation by spin exchange scattering between electrons and holes. However, a small momentum scattering rate by neutral donors gives rise to a higher spin relaxation rate according to the DP mechanism. In addition to the DP spin relaxation mechanism, the Rashba effect plays an important role on the dynamics of photo-excited electron spins in asymmetric QWs due to structure inversion asymmetry (SIA).[13] It acts directly on photo-excited electron spins.[14] Kikkawa and Awschalom[15] measured the coherent transport length of spins by shining pump beam, for example, at $x$ point on n-type GaAs and probing them at $x+\Delta x$ point by probe beam at 1.6 K. They found that over a distance of 100 μm the spin coherence still remains. The density of the spin polarized electrons, excited by the circularly polarized pump beam, is highest at the excitation position and causes the electrons to diffuse around. Such lateral diffusion motion gives rise to a special Rashba dephasing effect due to SIA. As shown in Fig. 4, the spin-polarized electrons, created by the pump beam at $x$ point, are going to diffuse away following a pattern like sun shining lines in the plane. Then, these electrons are eventually recombined with holes somewhere away from the excitation point. In such a way, the pump beam creates stable motions of electrons in the plane within the photo-luminescence lifetime. Although, our measurements were performed at 70 K, and the spin diffusion length may be shorter. Such spin diffusive motion does exist in our present case. Then, an electric field, created along the growth direction, will induce a Rashba effective magnetic field in a direction perpendicular to both the electric field and in-plane diffusive motion. Such an SIA induced Rashba effect leads to effective spin de-coherent action directly on photo-excited electron spins. A sensitive variation of spin coherence with changing electric field should feature such spin de-coherent process.
cpl-34-11-116701-fig3.png
Fig. 3. Spin Larmor precession (black circles), measured at 70 K in an applied magnetic field of 1.4 T. Black lines are corresponding fitting curves: (a) for sample 3 and (b) for sample 4.
To verify the spin dynamics, the MnAs/10-nm-thick n-type GaAs ($1\times10^{18}$ cm$^{-3}$) junction (sample 4) was measured at 70 K and in a magnetic field of 0.9 T by TRKR under different biases, as seen in Fig. 5. In Fig. 5(a), one can clearly see that by changing the junction bias from $-$1 V to 0 V, +1 V, +2 V, the amplitudes of the Larmor precession are continuously enhanced, then decrease after +2 V. To extract the detail message about spin lifetimes $\tau$ and $g$ factors, we further adopt exponentially decaying sine functions to fit the measured Larmor precession curves. As shown in Fig. 5(b), the spin lifetime increases rapidly from a value of 75 ps at $-$1 V up to 275 ps at +2 V. Then, it is reduced again to $\sim$200 ps at +4 V. In the meantime, as seen in Fig. 5(c), the absolute value of $g$ factor increases from 0.373 at $-$1 V to 0.386 at +2 V. Afterwards, it decreases continuously to a value of 0.353 at +4 V. An approximately 3.7 increase in the spin lifetime is most likely attributed to the suppression of the Rashba effect on the photo-excited electron spins by positive bias, as mentioned previously.
cpl-34-11-116701-fig4.png
Fig. 4. Diffusion motions in the $x$–$y$ plane, as indicated by long black arrows, created by a local spin excitation of circularly polarized pump beam in the presence of SIA. Red short arrows denote spin polarization directions in conjugation with different directions of in-plane diffusion motions, respectively. The downward large blue arrows are the electric field directions.
cpl-34-11-116701-fig5.png
Fig. 5. (a) Spin Larmor precession of sample 4, measured at 70 K in an applied magnetic field of 0.9 T. Different colored dots and lines represent measured and fitting Larmor precessions under different biases. (b) Spin lifetimes, extracted at different biases. (c) The $g$ factors, extracted at different biases.
The variation of the $g$ factor is easily understood. Firstly, one has to remember that the $g$ value of the bulk GaAs is $-$0.44, while the $g$ value of the bulk Al$_{0.3}$Ga$_{0.7}$As is +0.4. Secondly, the electron wave function is not completely confined in QWs, and the penetration of the electron wave function into the quantum well barriers (like Al$_{0.3}$Ga$_{0.7}$As) will make the absolute value of $g$ factor decrease from 0.44 downward.[16] At high negative bias, such wave function penetration into Al$_{0.3}$Ga$_{0.7}$As barrier is deep. This leads to a smaller absolute $g$ factor at high negative biases. With increasing the bias towards about +2 V, it reaches a maximum value of 0.388. Afterward, it decreases again and down to 0.353. Such decrease may be related to the wave function penetration into the MnAs ferromagnetic layer.[4] It is beyond the present scope, and will be discussed elsewhere. In conclusion, we have investigated the dynamics of spin coherence in different types of FM/n-type GaAs QWs. It turns out that the spin lifetime in an FM/in-situ doped n-type GaAs QW junction is much longer than its value in an FM/modulation-doped n-type GaAs QW junction by a factor of 5. This is explained by the DP spin relaxation mechanism. By choosing different ferromagnetic metals, e.g., MnGa or MnAs, and composing an FM/in-situ doped n-type GaAs QW junction, the spin lifetime of the former is longer than the latter by a factor of 4.2. This is attributed to a specific Rashba effect in the presence of SIA, which acts directly on spin polarized electrons, excited by a circularly polarized pump beam. From our work, we conclude that it is possible to construct an FM/n-type GaAs QW junction, which possesses high spin coherence by choosing proper ferromagnetic metal. Moreover, by biasing the FM/in-situ doped n-type GaAs QW junction, the spin lifetime can be adjustable in a controllable way by a factor of 3.6. The present work provides a basis for future study on the spin dependence of a two-dimensional electron gas passing through the channel portions underneath ferromagnetic gates.[4] References Ferromagnetic Imprinting of Nuclear Spins in SemiconductorsSpontaneous spin coherence in n -GaAs produced by ferromagnetic proximity polarizationVoltage control of nuclear spin in ferromagnetic Schottky diodesSpin-dependent properties of a two-dimensional electron gas with ferromagnetic gatesEtching and Optical Characteristics in GaAs/GaAlAs Surface Emitting Laser Fabrication Using a Novel Spray EtchUltrafast optical manipulation of magnetic orderSpin relaxation in G a A s / A l x Ga 1 − x As quantum wellsEnhanced spin-polarization lifetimes in a two-dimensional electron gas in a gate-controlled GaAs quantum wellExciton spin dynamics in quantum wellsDynamic Ferromagnetic Proximity Effect in Photoexcited SemiconductorsElectric Field Control of Interface Related Spin Splitting in Step Quantum WellsAll-optical measurement of Rashba coefficient in quantum wellsLateral drag of spin coherence in gallium arsenideMagnetic g factor of electrons in GaAs/ Al x Ga 1 − x As quantum wells
[1] Kawakami R K, Kato Y, Hanson M, Malajovich I, Stephens J M, Johnston-Halperin E, Salis G, Gossard A C and Awschalom D D 2001 Science 294 131
[2] Epstein R J, Malajovich I, Kawakami R K, Chye Y, Hanson M, Petroff P M, Gossard A C and Awschalom D D 2002 Phys. Rev. B 65 121202
[3] Epstein R J, Stephens J, Hanson M, Chye Y, Gossard A C, Petroff P M and Awschalom D D 2003 Phys. Rev. B 68 041305
[4] Ciuti C, McGuire J P and Sham L J 2002 Appl. Phys. Lett. 81 4781
[5] Tanobe H, Koyama F and Iga K 1992 Jpn. J. Appl. Phys. 31 1597
[6] Kirilyuk A, Kimel A V and Rasing T 2010 Rev. Mod. Phys. 82 2731
[7] Malinowski A, Britton R S, Grevatt T, Harley R T, Ritchie D A and Simmons M Y 2000 Phys. Rev. B 62 13034
[8] Anghel S, Singh A, Passmann F, Iwata H, Moore J N, Yusa G, Li X and Betz M 2016 Phys. Rev. B 94 035303
[9] Maialle M Z, de Andrada e Silva E A and Sham L J 1993 Phys. Rev. B 47 15776
[10]D'yakonov M I and Perel' V I 1971 Sov. Phys. JETP 33 1053
[11]Awschalom D D, Loss D and Samarth N 2002 Semiconductor Spintronics and Quantum Computation (Berlin: Springer) chap 4 p 107
[12] Bauer G E W, Brataas A, Tserkovnyak Y, Halperin B I, Zwierzycki M and Kelly P J 2004 Phys. Rev. Lett. 92 126601
[13] Hao Y F, Chen Y H, Hao G D and Wang Z G 2009 Chin. Phys. Lett. 26 077104
[14] Eldridge P S, Leyland W J H, Lagoudakis P G, Karimov O Z, Henini M, Taylor D, Phillips R T and Harley R T 2008 Phys. Rev. B 77 125344
[15] Kikkawa J M and Awschalom D D 1999 Nature 397 139
[16] Snelling M J, Flinn G P, Plaut A S, Harley R T, Tropper A C, Eccleston R and Phillips C C 1991 Phys. Rev. B 44 11345