Reentrant Bloch ferromagnetism

Abstract

An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagneticto-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density (n) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field (B), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, B ∼ n p . For p < pc, with pc = 1(2/3) in 2(3)D, the system remains either fully spin-polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin-polarized or fully spin-polarized. However, for p > pc, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first order transition back to the fully spin-polarized phase again with a single Fermi surface.

Valley polarization transition in a two-dimensional electron gas

“…1(b) and 1(c), we present the unbiased fitting of our theoretical results to the measured experimental resistivity in both experimental samples (Samples 1 and 2) presented in Ref. [9], finding the best fit impurity densities to be; n i2d = 3.71 × 10 11 cm −2 (6.44 × 10 11 cm −2 ) and n i3d = 2.22 × 10 4 cm −3 (2.34 × 10 4 cm −3 ) in Samples 1 (2). Note that the unbiased best fit value for the background unintentional impurity density is basically zero, which is consistent with the known extreme high quality of the AlAs 2DEG system used in the experiment.…”

“…Whether a Bloch-type strictly density-driven paramagnetic-toferromagnetic spin transition happens or not is still an open question, but any such transition can only occur at extreme low carrier densities which are inaccessible in any 3DEG systems. Recently, such a Bloch spin transition has been experimentally reported in 2D composite fermions at the half Landau level filling [2,3].…”

“…Introduction.-The possibility of a density-driven spin-polarization transition in an electron gas from a paramagnetic spin-unpolarized (i.e., spin degeneracy 2) to a ferromagnetic spin-polarized (i.e., spin-degeneracy 1) system with the decreasing of density was predicted by Bloch almost 100 years ago, and is historically the first quantum many body prediction [1]. The basic idea is that at high density the electrons occupy both spin states equally so as to minimize the kinetic energy whereas at low density, electrons occupy only one spin state so as to minimize the exchange energy [2]. Although Bloch's original hope of explaining the metallic ferromagnetism of Fe, Ni, Co has turned out to be incorrect since it is now known that the narrow band nature of the transition metals plays a crucial role in metallic ferromagnetism, the fact that exchange (kinetic) energy enhances ferromagnetism (paramagnetism) by preferring 2-spin (1spin) electron occupancy is well-established.…”

“…1 and 2 are our central findings, we now discuss their salient features: (1) Experiment and theory agree exactly at high densities (n > n c ), and the agreement is semi-quantitative at lower densities, which is understandable since the dimensionless k F l parameter becomes progressively smaller with decreasing carrier density making the Boltzmann theory less applicable in the low-density n < n c regime-we emphasize that our fit uses the high-density regime where the theory is exact. (2) The most important aspect of our results in the current context is that the theory well reproduces the experimentally observed resistive discontinuity at the critical density with an abrupt jump or drop in the resistivity at n = n c depending on the direction of transport (because of the mass anisotropy)-the importance of this finding is that the theory has the valley polarization transition at n = n c explicitly included in the calculations, thus manifestly validating the experimental claim of a spontaneous valley polarization transition at n = n c . (3) The theoretical resistivity discontinuity at n = n c is in reasonable quantitative agreement with the experiment with the experimental discontinuity being slightly smaller and somewhat smoother than the sharp theoretical discontinuity, most likely because of thermal broadening.…”