Magnetism in a Wigner solid and the Aharonov-Bohm effect: Experiment and theory

Okamoto, Tohru; Kawaji, Shinji

doi:10.1103/physrevb.57.9097

Cited by 44 publications

(35 citation statements)

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“…Application of a magnetic field [20] transforms the exchange frequencies to J p e 2πieB ⊥ ap/h where a p is the area of the exchange (see table I) and B ⊥ the magnetic field. Experiments with magnetic fields will allow exploration of this AharonovBohm effect and thereby provide direct information on ring exchanges.…”

Section: Figmentioning

confidence: 99%

Exchange Frequencies in the 2D Wigner Crystal

2001

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Using Path Integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3 He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for rs ≤ 175±10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.PACS Numbers: 73.20Dx, 67.8Jd The uniform system of electrons is one of the basic models of condensed matter physics. In this paper, we report on the first exact calculations of the spin Hamiltonian in the low density 2 dimensional Wigner crystal (2dWC) near melting. This system is realized experimentally with electrons confined at an semiconductor MOS-FET's and heterostructures [1], and for electrons on the surface of liquid helium [2].A homogeneous charged system is characterized by two parameters: the density given in terms of r s = a/a 0 = (m * /mǫ)(πa 2 0 ρ) −1/2 and the energy in effective Rydbergs Ry * = (m * /m e ǫ 2 )Ry where m * is the effective mass and ǫ the dielectric constant. Figure 1 summarizes the 2d phase diagram. At low density (large r s ) the potential energy dominates over the kinetic energy and the system forms a perfect triangular lattice, the Wigner crystal [3]. Tanatar and Ceperley [4] determined that melting at zero temperature occurs at r s ≃ 37 ± 5. Recent calculations [5] have shown that the low temperature phase is free of point defects for densities with r s ≥ 50 but defects may be present very near melting. At densities for r s ≥ 100 the melting is classical, and occurs for temperatures T melt = 2Ry/(Γ c r s ) where Γ c ≈ 137 [6].We determine the spin-spin interaction in the Wigner crystal, using Thouless' [8] theory of exchange. According to this theory, in the absence of point defects, at low temperatures the spins will be governed by a Hamiltonian of the form:where the sum is over all cyclic (ring) exchanges described by a cyclic permutation P , J P is its exchange frequency andP spin is the corresponding spin exchange operator. Path Integral Monte Carlo (PIMC) as suggested by Thouless [8] and Roger [9]has proved to be the only reliable way to calculate these parameters. The theory and computational method have been tested thoroughly on the magnetic properties of bulk helium obtaining excellent agreement with measured properties [10]. Rather surprisingly, it has been found [11] that in both 2d and 3d solid 3 He, exchanges of 2, 3 and 4 particles have roughly the same order of magnitude and must all be taken into account. This is known as the multiple spin exchange model(MSE). A WKB calculation of the exchange frequencies in the 2dWC by Roger [9] predicted that the three electron J 3 nearest neighbor exchange would dominate, leading to a ferromagnetic(F) ground state. It has be...

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Section: Figmentioning

confidence: 99%

Exchange Frequencies in the 2D Wigner Crystal

2001

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“…It has been found to be important in several materials such as two-leg ladder compound La x Ca 14−x Cu 24 O 41 , [1][2][3][4] two-dimensional antiferromagnet La 2 CuO 4 , 5,6 magnetism of two-dimensional quantum solids, e.g., solid 3 He films, 7 and Wigner crystals. 8 Four-spin ring exchange plays an essential role in several models to give rise to exotic phases due to its frustration, e.g., the vector-chirality phases, 9 nematic orderings, 10 and octapolar order. 11 Especially, the two-leg ladder model with the multiplespin exchange interactions has been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

2009

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A spin-1 2 two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as localorder parameters. Reflecting local objects, nontrivial ͑͒ Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topologically invariant for gapped systems with the time-reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveal that the local objects are a local singlet and a plaquette singlet, respectively.

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“…The ground state of the insulating phase of high mobility Si-MOSFET's is considered to be a pinned Wigner solid (WS) [10,11]. Magnetic field dependence of the thermal activation energy observed for various angles of the magnetic field was essentially explained by a model based on magnetic interactions in the pinned WS [12,13]. Although the quantum fluctuations change the 2D system into a liquid at higher-N s , electron-electron (e-e) interaction is expected to be still important.…”

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“…In the previous work [12,13], we have investigated the activation energy in the insulating phase which depends on B ⊥ and B tot . Oscillatory behavior linked with B ⊥ /N s φ 0 was explained using a model based on the Aharonov-Bohm effect on the exchange of electrons localized in the pinned Wigner solid [19].…”

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Spin Degree of Freedom in a Two-Dimensional Electron Liquid

et al. 1999

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We have investigated correlation between spin polarization and magnetotransport in a high mobility silicon inversion layer which shows the metal-insulator transition. Increase in the resistivity in a parallel magnetic field reaches saturation at the critical field for the full polarization evaluated from an analysis of low-field Shubnikov-de Haas oscillations. By rotating the sample at various total strength of the magnetic field, we found that the normal component of the magnetic field at minima in the diagonal resistivity increases linearly with the concentration of "spin-up" electrons. 71.30.+h, 73.40.Qv, 73.40.Hm A metal-insulator transition (MIT) observed in Si metal-oxide-semiconductor field-effect transistors [1,2] (Si-MOSFET's) and other systems [3-6] attracts a great deal of attention since it seems to contradict an important result of the scaling theory by Abrahams et al. [7] that the conductance of a disordered two-dimensional (2D) system at zero magnetic field goes to zero for T → 0. In the metallic phase in Si-MOSFET's with high peak electron mobilities of µ peak > ∼ 2 m 2 /V s, the diagonal resistivity ρ xx shows a sharp drop with decreasing temperature from about 2 K [1]. Recent experiments [8,9] show that magnetic fields applied parallel to the 2D plane suppress the low temperature metallic conduction in Si-MOSFET's. Since the parallel magnetic field does not couple the orbital motion of electrons, this fact suggests an important role of the spin of electrons. However, the mechanism of the conduction in the anomalous metallic phase is not clear yet.The 2D systems that show the MIT [1-6] are characterized by strong Coulomb interaction between electrons. The mean Coulomb energy per electron U = (πN s ) 1/2 e 2 /4πε 0 κ is larger than the mean kinetic energy K = πh 2 N s /m * by an order of the magnitude around the critical point for the MIT. Here, N s is the electron concentration, κ is the relative dielectric constant at the interface, and m * is the effective mass of electron. It is estimated that U = 120 K, K = 14 K and the ratio r s = U/K = 8.3 for κ = 7.7 and m * = 0.19m e at N s = 1 × 10 15 m −2 in Si-MOSFET's. The ground state of the insulating phase of high mobility Si-MOSFET's is considered to be a pinned Wigner solid (WS) [10,11]. Magnetic field dependence of the thermal activation energy observed for various angles of the magnetic field was essentially explained by a model based on magnetic interactions in the pinned WS [12,13]. Although the quantum fluctuations change the 2D system into a liquid at higher-N s , electron-electron (e-e) interaction is expected to be still important.In the conduction band of silicon, the spin-orbit interaction is negligible and the spin polarization p = (N ↑ − N ↓ )/N s can always be given in the direction to the magnetic field. Here N ↑ and N ↓ are the concentrations of electrons having an up spin and a down spin, respectively (N s = N ↑ + N ↓ ). In the present work, we investigate the low temperature conduction in a high mobility Si-MOSFET for vario...

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Magnetism in a Wigner solid and the Aharonov-Bohm effect: Experiment and theory

Cited by 44 publications

References 35 publications

Exchange Frequencies in the 2D Wigner Crystal

Exchange Frequencies in the 2D Wigner Crystal

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

Spin Degree of Freedom in a Two-Dimensional Electron Liquid

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