- Email: [email protected]
On the origin of the temperature dependence of spin susceptibility in correlated 2D electron system
Accepted Manuscript On the Origin of the Temperature Dependence of Spin Susceptibility in Correlated 2D Electron System V.M. Pudalov, M. Gershenson, A. Yu. Kuntsevich, N. Teneh, M. Reznikov PII: DOI: Reference:
S0304-8853(17)32172-8 https://doi.org/10.1016/j.jmmm.2017.10.077 MAGMA 63291
To appear in:
Journal of Magnetism and Magnetic Materials
Please cite this article as: V.M. Pudalov, M. Gershenson, A.Y. Kuntsevich, N. Teneh, M. Reznikov, On the Origin of the Temperature Dependence of Spin Susceptibility in Correlated 2D Electron System, Journal of Magnetism and Magnetic Materials (2017), doi: https://doi.org/10.1016/j.jmmm.2017.10.077
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
On the Origin of the Temperature Dependence of Spin Susceptibility in Correlated 2D Electron System V. M. Pudalova,b,1,, M. Gershensonc , A. Yu. Kuntsevicha,b , N. Tenehd , M. Reznikovd a P.N.
Lebedev Physical Institute of the RAS, Moscow, Russia 119991 Research University Higher School of Economics, Moscow, Russia 101000 c Serin Physics Lab, Rutgers University, Piscataway, NJ 08854, USA d Solid State Institute, Technion, Haifa, Israel 32000
b National
Abstract A dilute two-dimensional (2D) system of interacting electrons has tendency to spontaneous spin polarization with increase of interparticle interaction. This instability, anticipated to occur with lowering carrier density and temperature, in fact has never been observed. Here, we report temperature dependence of the spin susceptibility of a 2D electron system in Si-MOS structures measured by two different techniques: (i) χT (T ) by direct thermodynamic measurements, which are sensitive to all the electrons, and (ii) χ∗ (T ) from quantum oscillations in vector field, sensitive to the itinerant electrons only. In the former case, the susceptibility strongly diverges as 1/T 2 . In the latter case we found a weak χ∗ (T ) dependence, only a few percent over the range T = (0.1 ÷ 1) K, which seems to agree qualitatively with the predicted interaction corrections. We provide evidences for this difference to stem from the temperature- and magnetic field-dependent exchange with carriers between the localized and itinerant electrons coexisting in the two-phase state. Keywords: strongly correlated electron systems, spin magnetization
1. Introduction: Spin magnetization Dilute two-dimensional (2D) electron systems provide a unique opportunity for exploring the physics of electron-electron interactions, which are especially important in low dimensions. Although the 2D system of electrons under study resides near the surface of a purely nonmagnetic Si host lattice, the electronelectron interactions drive the system towards magnetic ordering, as the electron density n decreases. This trend is governed by the interplay between the Coulomb interaction and the Pauli principle, which is √ characterized by the ratio of the interaction and kinetic Fermi energies, rs ∝ 1/ n [1]. Email address: [email protected] (V. M. Pudalov)
Preprint submitted to Elsevier
October 20, 2017
Thus far, the ground state spin arrangement of the correlated electron system remained unsettled both for its liquid and solid state. The main question is whether or not the 2D electron system experiences a magnetic phase transition as interaction grows and temperature decreases. In the preceding transport and magnetotransport measurements [2, 3, 4, 5, 6, 7, 8], the spin susceptibility χ∗ was found to be strongly enhanced with lowering density (up to a factor of 7), and to be almost temperature independent. In contrast, thermodynamic measurements of the spin magnetization [9, 11] show strong density-dependent increase of the susceptibility χT with lowering the temperature. The strong χT (T )-dependence was interpreted in [11] as being due to localized “spin droplets” - spin polarized collective electron states with total spin of the order of 2. These easily polarizable “nanomagnets” exist as a minority phase in the background of the majority Fermi liquid phase even when the density and the dimensionless conductance are high, kF l ∼ 50. Such coexistence is nontrivial and represents a puzzle from the theoretical viewpoint, because the localized moments in the well-conducting state should be coupled by the RKKY interaction. Note, that the localized electrons in doped semiconductors, in the absence of the itinerant electrons, are known to align spins antiparallel rather than parallel. In this paper we report the first observation of the weak temperature dependence of the spin susceptibility χ∗ (T ) of itinerant electrons, clarify its origin, and explain qualitatively the above mentioned puzzle, namely the difference between the results of thermodynamic and transport measurements. 2. Results 2.1. Thermodynamic spin magnetization The data for the derivative of the susceptibility dχT /dn = ∂ 2 M/∂B∂n was obtained from the thermodynamic measurements of the chemical potential variations in response to a weak in-pane magnetic field modulation. The details of this experimental technique were provided in Refs. [9, 10, 11]. The derivative dχT /dn was then integrated from n = 0, taking into account that χT = 0 at n = 0. The results are presented in Fig. 1. One can see that χT strongly grows as temperature decreases (especially for low electron density), much exceeding the Pauli temperature-independent spin susceptibility value. Importantly, due to slow modulation (4 ÷ 12 Hz) of the magnetic field Bk , both itinerant and localized electrons got thermalized over the modulation period and contributed to the chemical potential variation. 2.2. Oscillatory magnetotransport AC (13 Hz) transport data for χ∗ was obtained from the period and phase of the beating patterns of the Shubnikov-de Haas (SdH) oscillations [4]. In the crossed-field (or vector-field) technique [12], the in-plane component of the magnetic field partially spin-polarizes the electron system, whereas a weak perpendicular component probes the density of electrons in the split spin-subbands 2
1.5
11
cm
-2
B
/T)
2.0
(10
1.0
0.5
0.0 0
2
n (10
4 11
6
-2
cm )
Figure 1: Thermodynamic spin susceptibility χT versus carrier density, determined from chemical potential. Different curves correspond to temperatures (from top to bottom): 2, 2.4, 2.7, 2.9, 3.1, 3.3, 3.8, and 5.7 K. Green line shows the Pauli spin susceptibility χP auli .
(for details, see Ref. [10]). The data was collected over the temperature range T = 0.1 ÷ 1 K and for electron densities n = (1.3 ÷ 10) × 1011 cm−2 ; this density range corresponds to the interaction strength rs = 7.3÷2.6, respectively [1]. AC current in the range (0.1 - 1) nA was supplied from a battery operated current source to avoid the electron overheating [13]. 1 B =2.5T ||
1
0
(
xx
/
LK
)
n=1.815
-1 8
12
16
20
Figure 2: Example of the normalized oscillatory magnetoresistance δρxx /(A1 ) measured for electron density n = 1.815×1011 cm−2 , at T = 0.4K and Bk = 2.5 T. Sample Si6-14, T = 0.4 K. Dots are the data and continuous line – the calculations.
An example of the beating pattern is shown in Fig. 2. For clarity, the δρxx (B⊥ ) data is normalized by the calculated amplitude δρLK 1 (B⊥ ) of the first harmonic of the oscillations [4, 14], and the inverse magnetic field is given in units of the Landau level filling factor, ν = nh/eB⊥ [1]. Figure 2 demonstrates that the oscillations can be fitted well by the Lifshitz-Kosevich (LK) formula [15, 14] using χ∗ as a fitting parameter; since interval of B⊥ is narrow, there is no need in using empirical corrections to the LK formula [14]. The χ∗ value is determined by the position of the beats and the phase of the oscillations. The uncertainty in the χ∗ values is rather small, 0.3 – 2%. 3
Figure 3 shows an example of the temperature dependencies of χ∗ for n = 2.08 × 1011 cm−2 , obtained from the beats for almost zero Bk (Fig. 3a), and for a relatively strong in-plane field Bk = 2.5 T (Fig. 3b). In the weak field δχ∗ (T ) is small, positive and, at least for densities, n > 1.6 × 1011 cm−2 , seems to agree with the calculated interaction corrections [16, 17, 18, 19, 20], both in the sign and magnitude. The striking difference between the weak χ∗ (T ) (Fig. 3) and the strong χT (T ) (Fig. 1) dependencies stems from their different origin: the former is the magnetic field response of the itinerate electrons, whereas the latter is the response of the whole electron system, in which the susceptibility of the localized spins dominate. 10
a)
*/
n=2.08 B =0.02T 0 10
b)
n=2.08 B =2.5T 0
0.4
0.8
Temperature (K)
Figure 3: Temperature dependence of the renormalized spin susceptibility for n = 2.08 × 1011 cm−2 . Dash-dotted line shows calculated interaction corrections in the ballistic regime [17]. The in-plane field Bk is indicated in each panel.
When a strong field Bk > 2T is applied, the χ∗ (T ) dependence does not vanish; it even changes sign and becomes stronger. Such a behavior is inconsistent with the predictions for the interaction corrections [21, 22]. Note that, in contrast with χ∗ (T ), the conductivity behaves as expected for the interaction corrections: the weakening of the temperature dependence of the conductivity with application of the in-plane field was confirmed experimentally for similar samples [8]. We, therefore, conclude that the temperature dependence of χ∗ should have a contribution from another mechanism, strongly dependent on both the field, and the temperature. We suggest that such mechanism originates from interaction between the itinerant electrons and localized ”spin droplets”. Understanding how it comes about is a challenging task. We did, however, explore and clarify the effect of the droplets on another property of the itinerant electrons which we extract from the SdH data, namely their density ni . In Fig. 4 we show the temperature and magnetic field dependence of ni , obtained from the period of SdH oscillations. Since the total density n in gated samples is effectively fixed by electrostatics, the temperature and magnetic field dependence of ni can come only from the particle exchange with the “spin droplets”, as illustrated schematically in the inset in Fig. 4. Magnetic-field dependence of ni is easily explained within this model: increase in magnetic field leads to polarization of the droplets and to reduction of their energy. This should attract itinerant electrons in order to equilibrate the chemical potential, and should lead to reduction of ni , as observed. The temperature dependence 4
density (10
11
-2
cm )
2.12
2.08
2.04 B =0 ||
2.5T
2.00
0.0
6T
0.2
0.4
0.6
0.8
1.0
Temperature (K)
Figure 4: Temperature dependence of the density of itinerant electrons (in units of 1011 cm−2 ), measured at various Bk fields. Upper inset shows schematic picture of the carriers exchange between the itinerant band and localized states.
of ni is more complicated, since magnetic field tends to polarize the droplets, and temperature to depolarize. The resultant behavior would depend on parameters, and constitutes a quest for theory, which is beyond the scope of this communication. To summarize, we observed that the spin susceptibility χ∗ of itinerant electrons in a strongly correlated 2D electron system in Si inversion layer weakly depends on temperature over the range (0.1 − 1) K. In low in-plane magnetic fields the temperature dependence of χ∗ is qualitatively consistent with the calculated Fermi liquid interaction corrections. However, in strong in-plane fields this dependence changes sign and becomes stronger, at odds with the predictions of the theory of interaction corrections. We also found weak variations δni (T ) of the mobile carriers density with temperature which is an evidence for the spatial separation in our low density 2D electron system. As a result of the separation, the χ∗ (T ) variations arise as a response of the itinerant subsystem to the interaction-coupled localized states which are much stronger affected by magnetic field and temperature. 3. Acknowledgements The work was supported in part by RSCF grant 16-42-01100, NSF grant 0077825 and the Israel Science Foundation. 4. References [1] T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54 4 (1982). [2] A. A. Shashkin, S. V Kravchenko, V. T. Dolgopolov, T. M. Klapwijk, Phys. Rev. Lett. 87, 086801 (2001). [3] S. A. Vitkalov, H. Zheng, K. M. Mertes, M. P. Sarachik, T. M. Klapwijk, Phys. Rev. B 87, 086401 (2001).
5
[4] V. M. Pudalov, M. E. Gershenson, H. Kojima, N. Butch, E. M. Dizhur, G. Brunthaler, A. Printz, and G. Bauer, Phys. Rev. Lett. 88, 196404 (2002). [5] E. Tutuc, S. Melinte, and M. Shayegan, Phys. Rev. Lett. 88, 036805 (2002). [6] M. P. Sarachik, S. A. Vitkalov, J. Phys Soc. Jpn., Suppl. A, 72, 5356 (2003). [7] J. Zhu, H. L. Stormer, L. N. Pfeiffer, K.W. Baldwin, and K.W.West, Phys. Rev. Lett. 90, 056805 (2003). [8] N. N. Klimov, D. A. Knyazev, O. E. Omel’yanovskii, V. M. Pudalov, H. Kojima, M. E. Gershenson, Phys.Rev. B 78, 195308 (2008). [9] O. Prus, Y. Yaish, M. Reznikov, U. Sivan, and V. M. Pudalov Phys. Rev. B 67, 205407 (2003). [10] M. Reznikov, A. Yu. Kuntsevich, N. Teneh, V. M. Pudalov, Pis’ma v ZhETF 92, 518 (2010). [JETP Lett. 92, 470 (2010)]. [11] N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev.Lett. 109, 226403 (2012). [12] M. E. Gershenson, V. M. Pudalov, H. Kojima, N. Butch, E. M. Dizhur, G. Brunthaler, A. Prinz, and G. Bauer, Physica E 12, 585 (2002). [13] O. Prus, M. Reznikov, U. Sivan, and V. M. Pudalov, Phys. Rev. Lett. 88, 016801 (2002) [14] V. M. Pudalov, M. E. Gershenson, and H. Kojima, Phys. Rev. B 90, 075147 (2014). [15] I. M. Lifshitz and A. M. Kosevich, Zh. Eks. Teor. Fiz. 29, 730 (1955). A. Isihara, L. Smrˇ cka, J. Phys. C: Solid State Phys. 19, 6777 (1986). [16] A. V. Chubukov, and D. L. Maslov, Phys. Rev. B 68, 155113 (2003). [17] V. M. Galitski, A. V. Chubukov, and S. Das Sarma, Phys. Rev. B 71, 201302(R) (2005). [18] J. Betouras, D. Efremov, and A. V. Chubukov, Phys. Rev. B 72, 115112 (2005). [19] A. V. Chubukov, D. L. Maslov, S. Gangadharaiah, and L. I. Glazman, Phys. Rev. Lett. 95 026402 (2005). [20] A. V. Chubukov, D. L. Maslov, and A. J. Millis, Phys. Rev. B 73, 045128 (2006). [21] B. L. Altshuler and A. G. Aronov, in Electron- Electron Interaction in Disordered Systems, edited by A. L. Efros and M. Pollak (North-Holland, Amsterdam, 1985). [22] G. Zala, B. N. Narozhny, and I. L. Aleiner, Phys. Rev. B 64, 214204 (2001); ibid 65, 020201 (2002). 6
S0304-8853(17)32172-8 https://doi.org/10.1016/j.jmmm.2017.10.077 MAGMA 63291
To appear in:
Journal of Magnetism and Magnetic Materials
Please cite this article as: V.M. Pudalov, M. Gershenson, A.Y. Kuntsevich, N. Teneh, M. Reznikov, On the Origin of the Temperature Dependence of Spin Susceptibility in Correlated 2D Electron System, Journal of Magnetism and Magnetic Materials (2017), doi: https://doi.org/10.1016/j.jmmm.2017.10.077
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
On the Origin of the Temperature Dependence of Spin Susceptibility in Correlated 2D Electron System V. M. Pudalova,b,1,, M. Gershensonc , A. Yu. Kuntsevicha,b , N. Tenehd , M. Reznikovd a P.N.
Lebedev Physical Institute of the RAS, Moscow, Russia 119991 Research University Higher School of Economics, Moscow, Russia 101000 c Serin Physics Lab, Rutgers University, Piscataway, NJ 08854, USA d Solid State Institute, Technion, Haifa, Israel 32000
b National
Abstract A dilute two-dimensional (2D) system of interacting electrons has tendency to spontaneous spin polarization with increase of interparticle interaction. This instability, anticipated to occur with lowering carrier density and temperature, in fact has never been observed. Here, we report temperature dependence of the spin susceptibility of a 2D electron system in Si-MOS structures measured by two different techniques: (i) χT (T ) by direct thermodynamic measurements, which are sensitive to all the electrons, and (ii) χ∗ (T ) from quantum oscillations in vector field, sensitive to the itinerant electrons only. In the former case, the susceptibility strongly diverges as 1/T 2 . In the latter case we found a weak χ∗ (T ) dependence, only a few percent over the range T = (0.1 ÷ 1) K, which seems to agree qualitatively with the predicted interaction corrections. We provide evidences for this difference to stem from the temperature- and magnetic field-dependent exchange with carriers between the localized and itinerant electrons coexisting in the two-phase state. Keywords: strongly correlated electron systems, spin magnetization
1. Introduction: Spin magnetization Dilute two-dimensional (2D) electron systems provide a unique opportunity for exploring the physics of electron-electron interactions, which are especially important in low dimensions. Although the 2D system of electrons under study resides near the surface of a purely nonmagnetic Si host lattice, the electronelectron interactions drive the system towards magnetic ordering, as the electron density n decreases. This trend is governed by the interplay between the Coulomb interaction and the Pauli principle, which is √ characterized by the ratio of the interaction and kinetic Fermi energies, rs ∝ 1/ n [1]. Email address: [email protected] (V. M. Pudalov)
Preprint submitted to Elsevier
October 20, 2017
Thus far, the ground state spin arrangement of the correlated electron system remained unsettled both for its liquid and solid state. The main question is whether or not the 2D electron system experiences a magnetic phase transition as interaction grows and temperature decreases. In the preceding transport and magnetotransport measurements [2, 3, 4, 5, 6, 7, 8], the spin susceptibility χ∗ was found to be strongly enhanced with lowering density (up to a factor of 7), and to be almost temperature independent. In contrast, thermodynamic measurements of the spin magnetization [9, 11] show strong density-dependent increase of the susceptibility χT with lowering the temperature. The strong χT (T )-dependence was interpreted in [11] as being due to localized “spin droplets” - spin polarized collective electron states with total spin of the order of 2. These easily polarizable “nanomagnets” exist as a minority phase in the background of the majority Fermi liquid phase even when the density and the dimensionless conductance are high, kF l ∼ 50. Such coexistence is nontrivial and represents a puzzle from the theoretical viewpoint, because the localized moments in the well-conducting state should be coupled by the RKKY interaction. Note, that the localized electrons in doped semiconductors, in the absence of the itinerant electrons, are known to align spins antiparallel rather than parallel. In this paper we report the first observation of the weak temperature dependence of the spin susceptibility χ∗ (T ) of itinerant electrons, clarify its origin, and explain qualitatively the above mentioned puzzle, namely the difference between the results of thermodynamic and transport measurements. 2. Results 2.1. Thermodynamic spin magnetization The data for the derivative of the susceptibility dχT /dn = ∂ 2 M/∂B∂n was obtained from the thermodynamic measurements of the chemical potential variations in response to a weak in-pane magnetic field modulation. The details of this experimental technique were provided in Refs. [9, 10, 11]. The derivative dχT /dn was then integrated from n = 0, taking into account that χT = 0 at n = 0. The results are presented in Fig. 1. One can see that χT strongly grows as temperature decreases (especially for low electron density), much exceeding the Pauli temperature-independent spin susceptibility value. Importantly, due to slow modulation (4 ÷ 12 Hz) of the magnetic field Bk , both itinerant and localized electrons got thermalized over the modulation period and contributed to the chemical potential variation. 2.2. Oscillatory magnetotransport AC (13 Hz) transport data for χ∗ was obtained from the period and phase of the beating patterns of the Shubnikov-de Haas (SdH) oscillations [4]. In the crossed-field (or vector-field) technique [12], the in-plane component of the magnetic field partially spin-polarizes the electron system, whereas a weak perpendicular component probes the density of electrons in the split spin-subbands 2
1.5
11
cm
-2
B
/T)
2.0
(10
1.0
0.5
0.0 0
2
n (10
4 11
6
-2
cm )
Figure 1: Thermodynamic spin susceptibility χT versus carrier density, determined from chemical potential. Different curves correspond to temperatures (from top to bottom): 2, 2.4, 2.7, 2.9, 3.1, 3.3, 3.8, and 5.7 K. Green line shows the Pauli spin susceptibility χP auli .
(for details, see Ref. [10]). The data was collected over the temperature range T = 0.1 ÷ 1 K and for electron densities n = (1.3 ÷ 10) × 1011 cm−2 ; this density range corresponds to the interaction strength rs = 7.3÷2.6, respectively [1]. AC current in the range (0.1 - 1) nA was supplied from a battery operated current source to avoid the electron overheating [13]. 1 B =2.5T ||
1
0
(
xx
/
LK
)
n=1.815
-1 8
12
16
20
Figure 2: Example of the normalized oscillatory magnetoresistance δρxx /(A1 ) measured for electron density n = 1.815×1011 cm−2 , at T = 0.4K and Bk = 2.5 T. Sample Si6-14, T = 0.4 K. Dots are the data and continuous line – the calculations.
An example of the beating pattern is shown in Fig. 2. For clarity, the δρxx (B⊥ ) data is normalized by the calculated amplitude δρLK 1 (B⊥ ) of the first harmonic of the oscillations [4, 14], and the inverse magnetic field is given in units of the Landau level filling factor, ν = nh/eB⊥ [1]. Figure 2 demonstrates that the oscillations can be fitted well by the Lifshitz-Kosevich (LK) formula [15, 14] using χ∗ as a fitting parameter; since interval of B⊥ is narrow, there is no need in using empirical corrections to the LK formula [14]. The χ∗ value is determined by the position of the beats and the phase of the oscillations. The uncertainty in the χ∗ values is rather small, 0.3 – 2%. 3
Figure 3 shows an example of the temperature dependencies of χ∗ for n = 2.08 × 1011 cm−2 , obtained from the beats for almost zero Bk (Fig. 3a), and for a relatively strong in-plane field Bk = 2.5 T (Fig. 3b). In the weak field δχ∗ (T ) is small, positive and, at least for densities, n > 1.6 × 1011 cm−2 , seems to agree with the calculated interaction corrections [16, 17, 18, 19, 20], both in the sign and magnitude. The striking difference between the weak χ∗ (T ) (Fig. 3) and the strong χT (T ) (Fig. 1) dependencies stems from their different origin: the former is the magnetic field response of the itinerate electrons, whereas the latter is the response of the whole electron system, in which the susceptibility of the localized spins dominate. 10
a)
*/
n=2.08 B =0.02T 0 10
b)
n=2.08 B =2.5T 0
0.4
0.8
Temperature (K)
Figure 3: Temperature dependence of the renormalized spin susceptibility for n = 2.08 × 1011 cm−2 . Dash-dotted line shows calculated interaction corrections in the ballistic regime [17]. The in-plane field Bk is indicated in each panel.
When a strong field Bk > 2T is applied, the χ∗ (T ) dependence does not vanish; it even changes sign and becomes stronger. Such a behavior is inconsistent with the predictions for the interaction corrections [21, 22]. Note that, in contrast with χ∗ (T ), the conductivity behaves as expected for the interaction corrections: the weakening of the temperature dependence of the conductivity with application of the in-plane field was confirmed experimentally for similar samples [8]. We, therefore, conclude that the temperature dependence of χ∗ should have a contribution from another mechanism, strongly dependent on both the field, and the temperature. We suggest that such mechanism originates from interaction between the itinerant electrons and localized ”spin droplets”. Understanding how it comes about is a challenging task. We did, however, explore and clarify the effect of the droplets on another property of the itinerant electrons which we extract from the SdH data, namely their density ni . In Fig. 4 we show the temperature and magnetic field dependence of ni , obtained from the period of SdH oscillations. Since the total density n in gated samples is effectively fixed by electrostatics, the temperature and magnetic field dependence of ni can come only from the particle exchange with the “spin droplets”, as illustrated schematically in the inset in Fig. 4. Magnetic-field dependence of ni is easily explained within this model: increase in magnetic field leads to polarization of the droplets and to reduction of their energy. This should attract itinerant electrons in order to equilibrate the chemical potential, and should lead to reduction of ni , as observed. The temperature dependence 4
density (10
11
-2
cm )
2.12
2.08
2.04 B =0 ||
2.5T
2.00
0.0
6T
0.2
0.4
0.6
0.8
1.0
Temperature (K)
Figure 4: Temperature dependence of the density of itinerant electrons (in units of 1011 cm−2 ), measured at various Bk fields. Upper inset shows schematic picture of the carriers exchange between the itinerant band and localized states.
of ni is more complicated, since magnetic field tends to polarize the droplets, and temperature to depolarize. The resultant behavior would depend on parameters, and constitutes a quest for theory, which is beyond the scope of this communication. To summarize, we observed that the spin susceptibility χ∗ of itinerant electrons in a strongly correlated 2D electron system in Si inversion layer weakly depends on temperature over the range (0.1 − 1) K. In low in-plane magnetic fields the temperature dependence of χ∗ is qualitatively consistent with the calculated Fermi liquid interaction corrections. However, in strong in-plane fields this dependence changes sign and becomes stronger, at odds with the predictions of the theory of interaction corrections. We also found weak variations δni (T ) of the mobile carriers density with temperature which is an evidence for the spatial separation in our low density 2D electron system. As a result of the separation, the χ∗ (T ) variations arise as a response of the itinerant subsystem to the interaction-coupled localized states which are much stronger affected by magnetic field and temperature. 3. Acknowledgements The work was supported in part by RSCF grant 16-42-01100, NSF grant 0077825 and the Israel Science Foundation. 4. References [1] T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54 4 (1982). [2] A. A. Shashkin, S. V Kravchenko, V. T. Dolgopolov, T. M. Klapwijk, Phys. Rev. Lett. 87, 086801 (2001). [3] S. A. Vitkalov, H. Zheng, K. M. Mertes, M. P. Sarachik, T. M. Klapwijk, Phys. Rev. B 87, 086401 (2001).
5
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