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Observation of Spin-Orbit Interaction Parameter Over a Wide Temperature Range Using Potentiometric Measurement Youn Ho Park1;2 , Hyun Cheol Koo1;2 , Kyung Ho Kim1 , Hyung-jun Kim1;2 , Joonyeon Chang1;2 , Suk Hee Han1 , and Hijung Kim1 Nano Convergence Device Center, Korea Institute of Science and Technology, Seoul 136-791, Korea Department of Nano Electronics, University of Science and Technology, Daejeon 305-333, Korea Spin-orbit interaction parameter ( ) can be obtained by measuring the Shubnikov-de Haas oscillation, but this method is valid at only very low temperature. The current induced spin polarization in a 2-D electron gas layer is measured by potentiometric geometry which measures spin dependent chemical potential shifts. Subsequently, a spin-orbit interaction parameter can be extracted up to = 250 K. In an inverted In0 52 Al0 48 As In0 53 Ga0 47 As In0 52 Al0 48 As quantum well system, of 5 65 10 12 eVm and 3 85 10 12 eVm are obtained at = 1.8 and 250 K, respectively. Index Terms—2-D electron gas (2DEG), potentiometric measurement, Rashba effect, spin-orbit interaction.
I. INTRODUCTION PIN-ORBIT interaction in a semiconductor layer has become of great interest in the field of spin electronics because it is a key mechanism in implementing the spin field effect transistor (spin-FET) [1]. Previous studies [2]–[7] have shown that the spin transport and gate modulation in a semiconductor channel are detected via an electrical or an optical method. However, the electrical spin detection efficiency is still very low and the spin transport with gate modulation is implemented at a low temperature. In a spin-FET, an electric field applied by a gate electrode modulates the spin-orbit interaction, and hence controls the amount of the spin precession. in a perpendicular electric field Moving electrons experience an effective magnetic field in the -direction due to a mechanism known as the Rashba effect. This induced magnetic field in turn interacts with the magnetic moment of the electrons, resulting in spin orientation control. Generally, an electric field induces spin-orbit interaction in the relativistic frame, but structural asymmetry of a quantum well has the same effect. The Rashba-effect-induced spin splitting energy between spin-up and -down electrons can be expressed as , where is the Fermi wave number [8]. Note that is a function of the carrier concentration.
S
II. RESULTS AND DISCUSSION In order to observe Shubnikov-de Haas oscillation (SdH) [8], [9] and potentiometric signals [10]–[12], we utilize an inverted high electron mobility transistor (HEMT) structure [3], [7], [8] with an channel. Fig. 1 shows the calculated energy diagram and the electron distribution of the heterostructure used in this experiment. For the band calculation we utilized WinGreen [13] simulator with its data file. As shown in Fig. 1, the quantum well is not symmetric and the charge is concentrated on the side of the carrier supply layer, which is
Manuscript received October 30, 2009; revised January 14, 2010; accepted March 03, 2010. Current version published May 19, 2010. Corresponding author: H. C. Koo (e-mail:
[email protected]). Digital Object Identifier 10.1109/TMAG.2010.2045241
Fig. 1. Energy band structure and carrier distribution of an inverted heterostructure. The distance from the top surface is denoted by z . The solid and dotted lines are the energy band structure and the carrier distribution, respectively.
located below the channel layer. This asymmetry induces a strong internal electric field and zero field spin splitting. The total carrier concentration and mobility of the cm and 2-D electron gas (2DEG) are cm V s at 1.8 K. Fig. 2 shows the potentiometric geometry and measurement results. When the bias current is applied to the 2DEG channel, the voltage is measured between the ferromagnetic electrode (FM) and the end of the channel as shown in the inset of Fig. 2. pattern is used for FM and the lateral An 80 nm thick m m. The length of FM is marginally dimension is longer than the 2DEG channel width of 8 m so that the stray field effect from the ends of FM can be disregarded. The moving flowing in the quantum well channel feel the elecelectrons and produce the spin-orbit interaction intric field duced magnetic field. In this geometry the asymmetric quantum well produces an electric field whose direction is perpendicular to the 2DEG plane. This induced magnetic field shifts the spin subbands of the up and down spins in the 2DEG and causes a net magnetization [10]–[12]. The alignment between the magnetization direction of FM and the induced field direction of 2DEG determines the measured potential as shown in Fig. 2. In the parallel (antiparallel) alignment, the voltage probe reads the lower (higher) spin subband chemical potential of 2DEG.
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PARK et al.: OBSERVATION OF SPIN-ORBIT INTERACTION PARAMETER
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Fig. 2. Results of the potentiometric measurement at T 1.8 K. The bias current is 0.1 mA and the channel width is 8 m. Arrows on the curves are the field sweep direction. The curves are shifted for clarity.
Therefore, the detected potential depends on the magnetization status of FM and shows a hysteresis loop-like curve. The direction of the spin-orbit interaction field depends on the direction . When the direction of the bias current is of the bias current reversed, the opposite direction of the spin orbit interaction field should arise. Thus the low and high potential states are inverted , is as shown in Fig. 2. The measured signal, 1.8 K. The detected potential is proportional to 0.239 at the amount of the Fermi level shift which is increased with the bias current. The results of the SdH measurements for various tempera1.8 K the clear beat pattern tures are shown in Fig. 3(a). At is observed for measuring the resistance of the channel with a perpendicular field. From the node positions denoted by arrows eVm is oband the carrier concentration, 4 K the oscillation and beat pattern still remain tained. At but the node positions cannot be precisely decided. The beat pattern rapidly becomes unclear as the temperature increases. 10 K due to the thermal The beat pattern disappears above agitation which makes it difficult to detect the Rashba effect induced spin splitting in this method. However, the clear signals 250 K for the pontentiometric measureare observed up to ment [see Fig. 3(b)]. The detected signals are 0.246 and 20 and 250 K, respectively. In the potentiometric 0.161 at geometry, the FM detects the chemical potential which is not seriously distorted in the detection process even at higher temperature. The critical field, where low (high) to high (low) potential changes occur, is matched with the coercive field of FM. This critical field decreases with increasing temperature because the coercivity of the FM becomes lower at higher temperatures. of the The next issue is the relationship between potentiometric measurement and spin splitting induced by the spin-orbit interaction. The dispersion relationship can be described by the spin splitting parameter, . Spin splitting energy induced by spin-orbit interaction is given by [10]
(1)
Fig. 3. Shubnikov-de Haas oscillations (a) and potentiometric signals (b) at various temperatures.
where is a mean Fermi wave vector. From (1) we can determine the spin-orbit interaction parameter in terms of as (2) is a function of the fractional The potentiometric signal, and the spin splitting parameter . The polarization expression is [10] (3) is the resistance of the 2DEG channel of the length where equal to the average mean free path and is a scattering time related parameter which is generally negligible. Here, the mean free path cannot be precisely determined so we utilized obtained from the SdH oscillation to calculate . Typically is around 0.4 for . Using the experimental data of a potentiometric measurement, we can find at a higher temperature. Since the experimental value of is known at 1.8 K, we can obtain and finally decide at the same temperature. From (2) and eVm which is determined by the SdH oscillation, of 49.9 at 1.8 K is obtained. Usually is and therefore inversely proportional to which is linear to as a function of the temperature can be determined. Fig. 4 illustrates the temperature dependence of the measured
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makes it possible to estimate only at very low temperature, we can clearly obtained spin subband shifts at higher temperature by using the potentiometric measurement. From this method, of eVm and eVm are obtained at 1.8 and 250 K, respectively. These values are positive signals for developing spin-FET, because the spin-orbit interaction, which is essential for the spin-FET operation, does not seriously weaken at a higher temperature.
ACKNOWLEDGMENT Fig. 4. Temperature dependence of rameter .
1R =R
and spin-orbit interaction pa-
which is normalized to . Using (2) and (3), is directly calculated and finally is determined. The temperature dependence of is also shown in Fig. 4. As increasing the temperature, is slowly decreased but is still eVm at 250 K. This value is considered to be large enough to drive the spin precession in a sub micron-scaled channel. One may argue that the stray field induces the Hall effect which can be detected by the voltage probe. In order to investigate the temperature depen100 dence of Hall effect, we measured Hall voltage with mT. The Hall resistance is almost constant and the variation is 250 K. This resistance variation is only 5% at 1.8 K much smaller than that of potentiometric signal shown in Fig. 4. Therefore the Hall effect does not contribute to the measured signal. We now consider the origin of the temperature dependence of the spin orbit-interaction parameter. The spin-orbit interac, where is the tion parameter has a relationship of electric field applied to the quantum well and is a coefficient which is inversely proportional to the effective mass and energy gap of the channel [8]. In this case, is almost constant and the energy band gap slightly decreases with temperature. How77 K. The possible reason is the ever, becomes smaller at thermal agitation induced spin randomization [12] and the mo250 K, bility reduction at the higher temperature. At above is not easy due to the base line noise. the estimation of The spin-orbit interaction parameter, however, would not be reduced significantly even at room temperature considering the tendency of temperature dependence of effective mass and energy band gap. III. CONCLUSION In conclusion we fabricated an inverted heterostructure with an channel and obtained using the potentiometric measurement. While the Shubnikov-de Haas oscillation
This work was supported by the KIST Institutional Program and the KRCF DRC Program.
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