Nonlinear magnetic field dependence of spin polarization in high-density two-dimensional electron systems

Abstract

The spin polarization (P) of high-density InSb two-dimensional electron systems (2DESs) has been measured using both parallel and tilted magnetic fields. P is found to exhibit a superlinear increase with the total field B. This P-B nonlinearity results in a difference in spin susceptibility between its real value χ s and χ gm ∝ m * g * (m * and g * are the effective mass and g factor, respectively) as routinely used in experiments. We demonstrate that such a P-B nonlinearity originates from the linearly P-dependent g * due to the exchange coupling of electrons rather than from the electron correlation as predicted for the low-density 2DES. 71.27.+a, 73.43.Qt Direct experimental evidence of the P-B nonlinearity has so far been reported in low-density GaAs 2DESs with a relatively large r s ~ 5.6 at P < 0.5 [11], where the correlation energy is believed to determine the P-B nonlinearity [11,12]. We here, however, present a similar nonlinear P-B dependence via a high-density InSb 2DES with a small r s ~ 0.2. The large g * (over 39 in magnitude) of the InSb 2DES makes the P = 1 state achievable at easily accessible fields and the magnetization curve (P vs. its corresponding field B p ) observable over a wide range of P from 0.07 to 1. P is found to be superlinear in B p , which is analogous to the findings in Ref. 11. This P-B nonlinearity is fit well by a simple empirical equation. Note that χ gm calculated by this equation can also be used to fit the non-monotonic n 2D -χ gm data in Ref. 11. However, the P-B nonlinearity in the high-density specimen does not arise from the electron correlation because of the small r s . Further experiments demonstrate that this P-B nonlinearity is attributed to a linear P dependence of g * . PACS: Samples and methodsUnless otherwise noted, the employed InSb 2DES in a Hall bar (80 μm ×30 μm) is confined to a 30 nm wide InSb quantum well (QW) with δ-doped Al 0.09 In 0.91 Sb barriers on each side of the well [15].The parallel and tilted-field measurements were performed at 200 mK in a dilution refrigerator with an in situ rotator. The tilt angle θ between B and the sample normal (inset, figure 1(a)) was determined from the Hall resistance with an accuracy of at least 0.1 ○ . A low-frequency AC lock-in technique (13.3 Hz, 3 nA) was used to measure the longitudinal resistance R xx . Magnetotransport measurements gave n 2D = 1.83 × 10 15 m -2 and an electron mobility of μ = 14.3 m 2 /Vs in this sample. Experimental results and discussionAs shown in the inset of figure 1(b), the energy space between Landau levels (LLs) with spin-up (↑) and spin-down (↓) electrons is enhanced with increasing the tilted angle. Because the cyclotron energy (where is the reduced Planck's constant h, * / m eB E perp C

Effects of spin polarization in the HgTe quantum well

“…Noteworthy is that the found difference in spin-polarization properties of InSb and HgTe QW is not due to a small effective mass in InSb, as was suggested in Ref. 8, since the corresponding mass here m * /m 0 = 0.024 12 is not radically different from that for the InSb QW m * /m 0 = 0.018÷0.026. 7 This is a topic for future investigations to understand whether this difference is due to the Γ 6 and Γ 8 characters of conduction bands in these materials or due to a relatively wide QW of 30 nm in InSb 8 when the magnetic length equals the well width already at 0.75 T. Second, another system of straight traces along the coincidences, descending from a single point B 0…”

“…Here B 1 = hn S /e is the ρ xx (B ⊥ ) minimum position for ν = 1. Notable is that similar equation for a B(B ⊥ ) graph, usually built in other works (e.g., in Ref. 8), holds exactly for the whole range of θ. The descending straight beams in Fig.…”

“…7 with MR in a pure B || and seen is that just the field of a full spin polarization separates two kinds of dependences in ρ xx (B = B || ): a somewhat complicated function at lower fields, where two spin subbands are filled, from a monotonously increasing one, for a single subband filled, at higher fields as has been observed in a number of studies. 7,8,15,16 …”

Interplay of spin and orbital magnetogyrotropic photogalvanic effects in InSb/(Al,In)Sb quantum well structures

“…As a possible origin of this effect, we consider exchange interaction between electrons, which is known to lead to a nonlinearity of the Zeeman splitting on the external magnetic field at moderate fields. 11,14 In this case, the effective g * factor besides g 0 , the Landé factor like at B = 0, contains a contribution linear in the spin polarization…”

“…4 This novel material is the subject of numerous experimental studies of transport, optical, magneto-optical, and spin-related phenomena. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] The characteristics driving the interest in this novel narrow gap material are the high carrier mobility, small effective masses, large Landé g * factor, possibility of the mesoscopic spindependent ballistic transport, and a strong spin-orbit coupling. The latter gives rise to a number of optoelectronic effects such as, e.g., terahertz photoconductivity 15 and the circular photogalvanic effect [16][17][18][19][20][21][22] recently observed in InSb QWs.…”