Introduction

Giant magnetoresistance (GMR) denotes a large change in the electrical resistance under the application of a magnetic field and the GMR effect observed in magnetic metallic multilayers (MMM) has now become the canonical GMR effect since it transformed the magnetic hard disk storage and memory industries1,2,3,4,5,6. Physically, the MMM-GMR arises as an applied magnetic field re-aligns the magnetic moments of the successive ferromagnetic layers, which are separated by the nonmagnetic layers1,2,5,6. Although not as well known, GMR also occurs in both magnetic and non-magnetic semiconductor systems3. Semiconductor GMR is particularly interesting for applications because of the expected ease of integration of associated devices with typical semiconductor electronics3. As a consequence, the study of potential new mechanisms for realizing GMR in semiconductors has been a useful line of basic research7,8,9,10. Semiconductor GMR in disordered 2D electronic systems has also been a topic of interest from the fundamental physics perspective11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28, providing insight into weak localization11,17, weak anti-localization11,17, electron-electron interaction-induced magnetoresistance11,14,15,16,18,19,22,23, metal-insulator transitions induced by a magnetic field29, and GMR in the quantum Hall regime30,31.

Here, we study and model an interesting new mechanism for inducing- and controlling- GMR in a two-dimensional semiconductor system. While previous studies have examined electric field control of magnetoresistance7,9,10, we show that a supplementary dc-current-bias and associated carrier heating in an ac- and dc- current biased high mobility 2DES provides for a current dependent “non-ohmic” decrease in the conductivity with increasing dc current bias in the absence of a magnetic field, and this effect leads to a dc-current tunable GMR in the presence of 100’s-of-millitesla-type magnetic fields. Thus, the effect identifies a simple new method for setting the magnitude of the GMR effect as desired, in a semiconductor system.

The ultra high mobility GaAs/AlGaAs system has been the subject of intense magnetotransport studies at high filling factors or low magnetic fields because improvements in material quality in this 2D electron system have led to a steady stream of spectacular new phenomena such as the microwave radiation-induced zero-resistance states and associated magnetoresistance oscillations32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72, magnetoresistance that depends on the electron-electron interactions14,15,16,18,23, device size19,21,26, scatterer type20,22,24,27, temperature, carrier density24, and orientation of magnetic field25, giant resonances at the second harmonic of cyclotron resonance73,74,75, etc. The negative magnetoresistance observed in the GaAs/AlGaAs system was initially viewed as a manifestation of disorder-induced electron-electron interaction effect14,15,16. However, features such as the concurrent absence of a Hall-effect correction26, dependence upon scattering type27, etc., have led to new experimental and theoretical interest. Following upon this interest, we report on an effect which is unexpected within the context of previous theory - a current tunable, carrier-heating-induced negative GMR in the GaAs/AlGaAs 2D system.

Results

Figure 1(a) shows the magnetoresistance at T = 1.7 K, as Idc is varied from 0 to 19 μA. The figure shows that Rxx below B = 0.05 T is hardly influenced by the Idc. We found that this part could be simply represented by ΔRxx = Aln(B0/B)26. On the other hand, above B = 0.05 T, the Rxx vs B traces change substantially with the applied Idc. In particular, the observed positive magnetoresistance above B = 0.05 T at Idc = 0 μA progressively decreases with increasing Idc and results in ≥90% negative GMR at Idc = 19 μA and B = 0.3 T. Above B = 0.05 T, the magnetoresistance traces also exhibit, to B ≈ 0.2 T, magnetophonon oscillations76 which increase in amplitude with increasing Idc. This feature, to be examined elsewhere, is one signature of Idc-induced heating. Finally, at the highest B, B ≥ 0.2 T, Fig. 1(a) shows Shubnikov de Haas (SdH) oscillations, which appear to be reduced in amplitude with increasing Idc - yet another signature of Idc induced electron heating.

Figure 1
figure 1

Tunable giant magnetoresistance induced by a dc current bias in a GaAs/AlGaAs heterostructure 2DES.

(a) Magnetoresistance, Rxx, vs. the magnetic field, B, at different dc currents. The inset shows a schematic of the measurement. (b) The resistivity (red) and conductivity (blue) vs. Idc in the absence of magnetic field.

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In order to convey the variation of the resistivity (ρ) and conductivity (σ) under the influence of Idc, Fig. 1(b) exhibits the ρ (in red) and σ (in blue) vs. Idc at B = 0 T. Without heating, one expects ρ and σ to remain constant under changing Idc, as a consequence of “Ohm’s Law”. The figures show, however, that σ is reduced with increasing Idc, roughly by 1.3% for ΔIdc = 19 μA. Thus, the total current-dependent conductivity in the absence of a magnetic field can be written as σ(I) = σ0 + σ1′(Idc), where σ(I) is the current dependent conductivity. Here, the effect of the ac-current is not included since it is relatively small in magnitude.

To fit the B-dependent GMR results of Fig. 1(a), following previous work26, σ → σxx, resulting in . [Similarly, ]. Here, μ1 is a parametric mobility in the Drude model26. Since L/W = 1, we set the diagonal resistance Rxx = ρxx, the diagonal resistivity, and (similarly, the off-diagonal resistivity is ). Here, σ0 = n0μ0e, where n0 and μ0 are the electron density and mobility in the 2D electron system. To account for the Idc independent magnetoresistance for B ≤ 0.05 T, the afore-mentioned additional ln(B0/B) term was included. Hence, the magnetoresistance data trace was fit to . Here, A and B0 were pre-determined by fitting the B ≤ 0.05 T data, n0 is held constant versus Idc and T, while μ0 is held constant versus Idc but allowed to vary with T. Note that σ1 and μ1 are the fundamental parameters that serve to characterize the giant magnetoresistance (GMR) and its change with Idc. Although there are four parameters, n0, μ0, σ1 and μ1 here, at a given T, only σ1 and μ1 were allowed to vary with Idc. The fits to the 1.7 K data of Fig. 1(a) are presented in Fig. 2(a), and the fit parameters are summarized in Table (1). Figure 2(a) indicates a good description of the non-oscillatory portion of the data by this empirical fit.

Table 1 Fit parameters extracted from empirical data fit at 1.7 K.
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Figure 2
figure 2

Model fits of the magnetoresistance in a GaAs/AlGaAs 2D electron device.

(a) Multi-conduction model fits of giant magnetoresistance for various Idc. Solid lines represent data, and symbols represent fit. (b) Fit parameter σ1 vs. Idc. Dashed line is a guide to the eyes. (c) Model parametric mobility, μ1, vs. Idc.

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The variation of the fit-obtained parameters σ1 and μ1, vs. Idc, are shown in Fig. 2(b) and (c), respectively. Figure 2(b) shows that σ1 is initially positive, then it gradually decreases, and turns negative above around Idc = 11 μA while continuing the trend at higher Idc. Thus, dσ1/dIdc ≤ 0 recalls the observed dσ/dIdc ≤ 0 in Fig. 1(b). The observed variation in the σ1 vs. Idc correlates with the progressive Idc induced change in Rxx from overall positive- to overall negative GMR to B = 0.3 T. Note also that Idc ≥ 11 μA allows for negative conductivity in σ1, i.e., σ1 ≤ 0. Since the parameters in Table 1 suggest that |σ1| < < |σ0|, the negative σ1 is manifested as a resistance correction at B = 0 T and a B-dependent (negative) magnetoresistance26. Figure 2(c) conveys that the fit parameter μ1 increases gently with Idc.

Similar measurements of Rxx vs. B were carried out at higher temperatures. Figure 3 shows Idc parametrized Rxx vs B data-traces at T = 1.7 K, 2.7 K, 3.4 K, and 4.2 K, with each data set sequentially offset by 2 Ω. At each T, overall positive magnetoresistance is observable at the highest B for Idc = 0 μA. However, as Idc is increased, the positive magnetoresistance is progressively reduced and transformed into negative magnetoresistance at the highest Idc (the characteristic T for this crossover depends on whether or not one includes the weak-localization-like term in the vicinity of B = 0 in the consideration). Further, at T = 4.2 K, magnetophonon oscillations are apparent at Idc = 0 μA and they are progressive reduced in amplitude with increasing Idc. On the other hand, at T = 1.7 K, magnetophonon oscillations are not readily apparent at Idc = 0 μA and become more apparent with increasing Idc. Both these features can be understood as a consequence of the well-known non-monotonic variation of the magnetophonon oscillation amplitude with T76. That is, while the magnetophonon oscillations vanish in the “low-T” limit, they increase in the amplitude with increasing temperature up to some characteristic temperature, while further temperature increase then leads to a reduction in the oscillation amplitude. Since the 4.2 K traces suggests strong amplitude at Idc = 0 μA, and the increase of Idc leads to a reduction in the oscillation amplitude, it is apparent that this data set represents the “optimally heated” to the “over-heated” regime, where the magnetophonon oscillation amplitude decreases with a further increase in the temperature, due to the dc-current induced heating. On the other hand, Fig. 3 shows that at 1.7 K, the magnetophonon oscillations are barely perceptible at 1.7 K and they become stronger with increasing Idc. Thus, this data set represents the “under-heated” to “optimally heated” regime, where increasing the temperature with the Idc increases the oscillation amplitude. Thus, the observed trends in the amplitude of the magnetophonon oscillations also confirm that the Idc serves to heat the system, as reasoned earlier.

Figure 3
figure 3

Temperature dependence of the magnetoresistance and its dependence on Idc.

This panel shows the Rxx vs. B, at various bath temperatures, with the Idc = 0, 3, 7, 11, 15 and 19 μA as the parameter. Here, the data sets at different T have been sequentially offset by 2Ω, for the sake of presentation. In addition, the percentage change in the magnetoresistance to B = 0.1 Tesla, at the highest current, is indicated for each temperature.

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The non-oscillatory part of the T-dependent data sets of Fig. 3 were also fit with the multiconduction model; the results are shown in Fig. 4(a) while the fit parameters are summarized in Table 2. Here, symbols represent the fit while the lines represent data. As indicated by Fig. 4, the empirical model succeeds in describing the data at all temperatures and Idc. The extracted fit parameter σ1 is shown in Fig. 4(b) as a function of Idc. Similar to its behavior at T = 1.7 K, the fit extracted σ1 decreases with increasing Idc at all T. However, the magnitude of the decrease in σ1 with increasing Idc is more pronounced at lower T. Further, the crossover from positive to negative GMR at B = 0.3 T is only observed T = 1.7 K and T = 2.7 K, while at higher T, there is only mostly positive GMR. This feature can be correlated with the point that negative magnetoresistance is only observable when σ1 < 0. As mentioned, the fit extracted μ1 was only allowed to vary with Idc but not with T. As a consequence, the fit extracted μ1 vs. Idc traces at all T, not shown, were identical to the Fig. 2(c). Figure 4(c) exhibits the T-dependence of σ1 at various Idc. At small Idc, σ1 is essentially independent of T. On the other hand, at Idc = 19 μA, σ1 decreases strongly with decreasing temperature, and the crossover from positive- to negative- σ1 occurs around T = 3 K. Thus, at Idc = 19 μA, negative magnetoresistance due to heating becomes observable below T = 3.0 K.

Table 2 Summary of the temperature dependence of the fit parameters extracted from the data fits.
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Figure 4
figure 4

Data fits of the magnetoresistance at different Idc and temperatures.

(a) The Idc-dependent magnetoresistance is shown for various T with Idc = 0, 3, 7, 11, 15 and 19 μA, along with the empirical data fits. Here, solid lines represent data and symbols represent fits. (b) This plot shows σ1, which is extracted from data fits, vs. Idc, at different temperatures. (c) This plot shows σ1 vs. T, at different Idc.

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Discussion

The experimental results shown here in Fig. 1(b) indicate that steady state specimen heating induced by the application of a supplementary Idc gives rise to a “non-ohmic” current-dependent conductivity with dσ/dIdc ≤ 0. Under the same steady state Idc-induced non-equilibrium conditions, the specimen exhibits a Idc dependent magnetoresistance to B = 0.3 T, which can be successfully described by a two-term Drude model including a second conduction term with the parameters σ1 and μ1. Data fitting helps to extract these parameters and shows that dσ1/dIdc ≤ 0, similar to dσ/dIdc ≤ 0. While dσ/dIdc ≈ 102Ω−1/A, the fit parameters show that dσ1/dIdc ≈ 1Ω−1/A. This point suggests that all the conductivity change induced by the dc-current in Fig. 1(b) does not contribute towards the modification of the magnetoresistance described by σ1 in Fig. 2(b). Thus, it appears that the dc-current modifies σ via several modes and not all these modes influence the magnetoresistance. Further, Fig. 4(b) shows that dσ1/dIdc varies strongly with T. This feature suggests a role for the inelastic scattering length in influencing the GMR, as suggested previously19, and its dependence on the Idc and T. The previous fit-study indicated that a negative conductivity term with associated parametric mobility in a multiconduction model is sufficient to realize negative GMR in this 2D electron system26. This study shows that the application of Idc helps to realize such a conductivity correction as a by-product of heating, leading to the observed negative GMR.

Previous theoretical and experimental studies on the effect of steady state heating on the energy distribution of electrons offer insights for our study. For example, experimental photoluminescense studies at a low lattice temperature (e.g., TL = 10 K) have shown that the photoluminescence lineshape at the fixed lattice temperature broadens and red-shifts with the steady state heating due to terahertz radiation, while lineshape fits utilized to extract an effective (electron) temperature indicate the electron temperature, Te, exceeds the lattice temperature, TL, and the difference Te − TL becomes larger with increased terahertz photoexcitation77. Remarkably, concurrent studies of the electrical conductivity under the same steady state terahertz drive showed a monotonic decrease in the conductivity with increased terahertz photoexcitation which could also be described in terms of an effective (electron) temperature that exceeds TL. Indeed, the Te determined through the two different experiments showed good agreement. Thus, the energy distribution of electrons under steady state terahertz excitation induced heating could be characterized by an electron temperature that is elevated with respect to the lattice temperature, i.e., Te > TL77. Theoretical studies based on a steady state Boltzmann equation solution of the momentum and energy-balance equations taking into account the electron-LO phonon78 and electron-deformation potential acoustic phonon interaction79 confirmed that in such steady state drive experiments (i) the electron energy distribution can be characterized by an effective- and elevated- Te, (ii) the electron-phonon interaction dominates both momentum and energy relaxation, (iii) hot electrons relax by emitting or absorbing phonons, which changes phonon number and leads to a phonon number that depends on the electron temperature, and (iv) phonon-drift is negligible78,79.

Another detailed study of the energy loss mechanism in a low temperature 2DES including ballistic hot electron injection suggested that injecting mono-energetic hot electrons into a 2DES thermalizes the 2D electronic system to a temperature Te that exceeds TL when electron-electron scattering rate is large compared to inelastic scattering rate80. For hot electron injection energies below the LO phonon energy ELO = 36meV, all the injected power is transferred via electron-electron scattering to a thermalized 2DES at an elevated Te, and the associated energy is subsequently lost by energy balance to acoustic phonons. In such a situation, Te is a proportional measure of the injected power, or vice-versa. For hot electron injection energies above the LO phonon energy, injected hot electrons could emit LO phonons before interacting with the 2DES, depending upon the LO phonon emission time, τLO, and the energy transferred to the 2DES per hot electron could then become the difference between the hot electron energy and the LO phonon energy80.

In our experiment, the steady state heating is realized by injecting the supplementary dc current, not by terahertz photoexcitation or by mono-energetic hot electron injection. Yet, the above mentioned results imply that, since we are using the same GaAs/AlGaAs material system in the same low temperature limit, the electron-electron scattering rate likely exceeds the inelastic scattering rate, leading to Idc heated electron system characterized by a Te > TL. Further, since the applied supplementary dc currents are modest, Idc ≤ 19 μA, the effective energies associated with the injected electrons in the supplemental dc current are likely small compared to ELO = 36 meV. (For Idc = 19 μA, and an upper bound resistance estimate based the Hall resistance Rxy ≈ 1 kΩ at B = 0.3 T, it turns out that eIRxy = 19 meV, which is less than the ELO = 36 meV). As a consequence, energy loss is expected to be through acoustic phonons. In this regime, the Te should increase monotonically with increased Idc. Since electron heating has been shown the reduce the electrical conductivity77, and we observe and report a reduction in the conductivity with the increase of the supplementary Idc, while correlating this observation with the characteristic heating-like reduction in the Shubnikov-de Haas oscillation amplitude with increased Idc (Fig. 1), and the characteristic Idc induced changes in amplitude of the magnetophonon oscillations (Figs 1 and 3), it is clear that the observed dσ/dIdc < 0 (Fig. 1(b)) is a manifestation of electron heating induced correction to the conductivity, where the Idc parametrically represents the electron temperature.

When the heating by Idc produces a “non-ohmic” correction to the conductivity σ (Fig. 1(b)), the correction affects the second term in the two-term Drude model modifying, as shown by the modeling presented here, the character of the magnetoresistance. Simply put, the supplementary Idc heats the electron system, producing a “non-ohmic” decrease in the conductivity. The decrease in the conductivity has the effect of progressively converting the positive magnetoresistance to the negative giant magnetoresistance because the non-ohmic term strongly influences the second term in the Drude model. The magnetoresistance then becomes manifest through the mathematical character of the model.

The practical interest in these results rests upon the possibility of tuning the magnetoresistance in the 2D electron system simply with the application of a supplementary Idc. This suggests the possibility of GMR devices, without a gate-electrode, where the response may be set as desired after manufacture by adjusting dc-current bias with external circuitry. While it is not yet clear which physical channel influenced by the dc-current heating affects the magnetoresistance, these results show that such a channel exists in the 2D electron system. Identification of this channel and the optimization of the physical platform, which are topics for future study, are likely to result in improved control of the giant-magnetoresistance in the 2D electron system.

Methods

The high-mobility GaAs/AlGaAs heterostructures used in this study were grown by molecular-beam epitaxy (MBE), and patterned into Hall bar devices by photolithography. The 200 μm wide Hall bars included voltage probes spaced by 200μm, which set the effective Length-to-Width (L/W) ratio L/W = 1. Electrical measurements were carried out using standard low frequency lock-in techniques. The electron mobility at temperature T = 1.7 K was μ ≈ 107 cm2/Vs and the density was n = 2.4 × 1011 cm−2. The ac- and dc- currents were applied as shown in the inset of Fig. 1. The lock-in sourced ac current source was held constant at 2 μA, as a dc current was varied as desired under computer control. Typically, at a fixed T, magnetic field (B) sweeps of the lock-in detected diagonal voltage Vxx were collected at a series of constant Idc. The data traces plotted in the Figs 1a, 2a, 3 and 4a report the magnetoresistance . The sample was immersed in pumped liquid helium for these measurements over the range 1.7 K ≤ T ≤ 4.2 K.

Additional Information

How to cite this article: Wang, Z. et al. Tunable electron heating induced giant magnetoresistance in the high mobility GaAs/AlGaAs 2D electron system. Sci. Rep. 6, 38516; doi: 10.1038/srep38516 (2016).

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