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arXiv:cond-mat/0409100 · Physical Review Letters

Pauli Spin Susceptibility of a Strongly Correlated Two-Dimensional Electron Liquid

A. A. Shashkin, S. Anissimova, Mohammed R. Sakr, S. V. Kravchenko, Valerii T. Dolgopolov, T. M. Klapwijk

Published Jan 24, 2006• 66 citations
arXivHTMLPDF

Abstract

Thermodynamic measurements reveal that the Pauli spin susceptibility of strongly correlated two-dimensional electrons in silicon grows critically at low electron densities--behavior that is characteristic of the existence of a phase transition.
DOI
10.1103/physrevlett.96.036403

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Comment on "Critical behavior of the Pauli spin susceptibility..." by A. A. Shashkin et. al

M. I. Reznikov, Sarit Sara Sivan

The paper by A. A. Shashkin et al. [cond-mat/0409100] reports measurements of the thermodynamic magnetization of two-dimensional electrons in silicon. Although the experimental data is very similar to that reported by us more then two years ago, the authors arrive at an opposite conclusion regarding the spin susceptibility "critical behavior" and spin instability in the vicinity of the metal-insulator transition. We show that this interpretation is based on a flawed analysis of the experimental data.

arXiv:cond-mat/0410409•Oct 17, 2004•0 citations

R1.6 The thermodynamic spin magnetization of strongly correlated 2d electrons in a silicon inversion layer

J.H Davies, A.R Long

The nature of the ground state of degenerate two dimensional (2D) fermions at zero magnetic field is an outstanding open problem, which has not been deciphered despite decades of research. In the absence of disorder, the ground state is believed to be determined by the interplay between the kinetic energy, E f, and the inter-particle interaction energy, Ec = e2/ica, where a = (nn)~1^ 2 is the typical inter-particle distance, n is the areal particle density, and k is the host dielectric constant. The relative importance of the two energy scales is characterized by rs = a/ao, with ao being the Bohr radius. For electrons in a single band, rs = Ec/ E f while for the (100) surface of silicon rs = Ec/2E p , due to the two-fold valley degeneracy. At very high densities (rs <£ 1) a 2D system approaches the paramagnetic limit of a non-interacting degenerate gas characterized by the Pauli susceptibility, xo • As the density is reduced, the growing ferromagnetic correlations lead to substantial enhancement of the spin susceptibility, The system is predicted to remain paramagnetic up to rs « 20, where numerical calculations [1] find a quantum phase transition to a ferromagnetic liquid phase [2]. At lower density, rs & 37 [3], the Coulomb correlations are predicted to lead to a second phase transition to an anti-ferromagnetic quantum Wigner crystal. The energy balance between the ferro and paramagnetic states is very subtle, therefore the density window where ferromagnetism can take place is small [1].

CRC Press eBooks•May 1, 2003•0 citations
Electrons in two-dimensional (2D) layers at semiconductor interfaces may be driven to a solid phase by reducing their density. Understandmg of this electron liquid-solid transition at mK-temperatures and the origin of the 2D electron solid phase remain challenging. The experimental system under study is subject to strong interactions and disorder. Charge transport in the electron solid phase demonstrates many features anticipated for the pinned crystal, though no direct imaging of a spatial charge- or magnetic-ordering is available by now. Rich information has been recently obtained for dilute electron liquid phase on strong renormalization of the Pauli spin susceptibility, magnetization, and the effective mass. These data provide a set of the Fermi-liquid coupling parameters for densities down to and at the transition. The steep density dependence of the susceptibility is intriguing because it might indicate a developing magnetic transition, though it is more likely reflects a tendency to crystallization.
The paper by A. A. Shashkin et al. [cond-mat/0409100] reports measurements of the thermodynamic magnetization of two-dimensional electrons in silicon. Although the experimental data is very similar to that reported by us more then two years ago, the authors arrive at an opposite conclusion regarding the spin susceptibility "critical behavior" and spin instability in the vicinity of the metal-insulator transition. We show that this interpretation is based on a flawed analysis of the experimental data.
The nature of the ground state of degenerate two dimensional (2D) fermions at zero magnetic field is an outstanding open problem, which has not been deciphered despite decades of research. In the absence of disorder, the ground state is believed to be determined by the interplay between the kinetic energy, E f, and the inter-particle interaction energy, Ec = e2/ica, where a = (nn)~1^ 2 is the typical inter-particle distance, n is the areal particle density, and k is the host dielectric constant. The relative importance of the two energy scales is characterized by rs = a/ao, with ao being the Bohr radius. For electrons in a single band, rs = Ec/ E f while for the (100) surface of silicon rs = Ec/2E p , due to the two-fold valley degeneracy. At very high densities (rs <£ 1) a 2D system approaches the paramagnetic limit of a non-interacting degenerate gas characterized by the Pauli susceptibility, xo • As the density is reduced, the growing ferromagnetic correlations lead to substantial enhancement of the spin susceptibility, The system is predicted to remain paramagnetic up to rs « 20, where numerical calculations [1] find a quantum phase transition to a ferromagnetic liquid phase [2]. At lower density, rs & 37 [3], the Coulomb correlations are predicted to lead to a second phase transition to an anti-ferromagnetic quantum Wigner crystal. The energy balance between the ferro and paramagnetic states is very subtle, therefore the density window where ferromagnetism can take place is small [1].