Available online at www.sciencedirect.com

Physica E 17 (2003) 320 – 321 www.elsevier.com/locate/physe

Temperature dependence of electrically detected ESR at #lling factor
= 1 in a 2DEG Eugene Olshanetskya;∗ , Manyam Pillaa , Joshua D. Caldwella , Cli.ord R. Bowersa , Jerry A. Simmonsb , John L. Renob a Chemistry

Department and National High Magnetic Field Laboratory, University of Florida, Gainesville, FL 32611-7200, USA b Sandia National Laboratories, MS 1415, Albuquerque, NM 87185, USA

Abstract Electrically detected electron spin resonance (ESR) was measured as a function of temperature for 0.3–4:2 K in a AlGaAs/GaAs multiple quantum well sample at #lling factor
= 1. The ESR amplitude exhibits a maximum at about 2:2 K and vanishes with increased or decreased temperature. To explain the observed temperature dependence of the signal amplitude, the signal amplitude temperature dependence is calculated assuming a model based on heating. ? 2002 Published by Elsevier Science B.V. PACS: 73.43.−f; 73.63.Hs Keywords: Electron spin resonance; Quantum Hall e.ect

1. Introduction In the physics of a two-dimensional electron system (2DES) the electron spin resonance (ESR) has the potential to serve as a tool for directly probing the electron spin order and dynamics that cannot be obtained by standard transport measurements. However, there are serious technical di>culties that make direct microwave absorption detection of ESR quite problematic in the case of a 2DES due to the comparatively small number of electron spins. On the other hand, it has been previously demonstrated [1] that high sensitivity can be obtained if the ESR absorption is detected electrically via a change induced in the magnetoresis∗ Corresponding author. Grenoble High Magnetic Field Laboratory, B.P. 166, 38042 Grenoble Cedex 9, France. Fax: 0476855610. E-mail address: [email protected] (E. Olshanetsky).

tance that can be observed under certain conditions in the regime of the quantum Hall e.ect. The present work focuses on an experimental study of electrically detected ESR (EDESR) and its temperature dependence in AlGaAs/GaAs heterostructure at #lling factor
= 1. 2. Samples and experiment The EDESR signals were detected from both multiple and single Al1−x Gax As=GaAs quantum well samples with mobilities between  = 4:4 × 105 and 1:2 × 106 cm2 =V s and electron densities per layer of Ns = (7–25) × 1010 cm−2 . Samples were patterned with a conventional Hall bar geometry. The behavior of the EDESR in all of these samples was found to be qualitatively the same. The sample was mounted on a rotation stage in a He3 cryostat allowing the ESR

1386-9477/03/$ - see front matter ? 2002 Published by Elsevier Science B.V. doi:10.1016/S1386-9477(02)00823-8

E. Olshanetsky et al. / Physica E 17 (2003) 320 – 321

8

T, K

1.0 ESR amplitude. (a.u.)

0.4

δRxx, Ω

6 4 2 0 5.1

2.2 2.9 3.2 3.8 4.3 5.2

321

0.8

spin-waves

0.6

non-interacting electrons

0.4 0.2 0.0 0

5.3

5.4

5.5

5.6

5.7

5.8

B, T Fig. 1. The EDESR signal at di.erent temperatures.

condition to be obtained at a desired #lling factor and magnetic #eld. The ESR signals were detected via a change in the longitudinal resistance HRxx due to the spin resonance absorption of the microwaves by the 2DES using the standard double lock-in technique. 3. Experimental results and discussion Fig. 1 shows the typical EDESR traces measured at di.erent temperatures. These data represent the raw HRxx signals that include a nonresonant background contribution. The ESR line position is given by h
0 = gB B0; ESR , where
0 is the microwave resonance frequency, B0; ESR is the magnetic #eld at which the resonance is observed and g is the bare g-factor for single spin Iips. It is apparent that the EDESR amplitude measured in the vicinity of
= 1 has a pronounced maximum at about 2 K, decreasing sharply at higher or lower temperatures. The aim of the present work is to explain the observed temperature dependence of the EDESR. We propose a mechanism for EDESR whereby excitation of ESR produces a change in the longitudinal magnetoresistance, HRxx . This model involves heating of the 2DES via the dissipation of the MW power absorbed due to ESR excitation of the k = 0 spin waves. The heating results in a corresponding change of the 2DEG temperature and, as a consequence, in a change of Rxx observed in the experiment:

Rxx = R0 (HE=2kT 2 ) exp(−HE=2kT 2 ) T , where HE is the activation energy gap at
= 1. The power

2

4

6 T, K

8

10

12

Fig. 2. The EDESR amplitude versus temperature. The circles are experimental data.

dissipated in the 2DEG is directly proportional to P, the electron spin polarization, a quantity of interest for comparison with theory. We #t the experimental data with a magnetization calculation assuming that the low-lying spin excitations are spin waves. The spin polarization is calculated using the dispersion relation from [2]. In Fig. 2, the experimental data is compared with the calculated temperature dependence of the EDESR for both the spin waves and the noninteracting electron model. The qualitative agreement of the model with the experimental data con#rms the validity of the heating mechanism for EDESR. The model indicates that the position of the maximum ESR response depends primarily on the activation energy gap, HE, determined from transport, and is given by kB T ≈ HE=4. As is also evident from Fig. 2, electron correlations do a.ect the position of the maximum and the shape of the temperature dependence. In summary, the heating model correctly predicts the experimental temperature dependence of EDESR. It appears that EDESR may provide experimental access to the dispersion function and may be useful to characterize low-lying spin excitations of the 2DES in the QHE regime. References [1] D. Stein, G. Ebert, K. von Klitzing, G. Weimann, Surf. Sci. 142 (1984) 406. [2] Y.A. Bychkov, et al., JETP Lett. 33 (1981) 143; C. Kallin, B.I. Halperin, Phys. Rev. B 30 (1984) 5655.