Spin-dependent Smoluchowski effect

Abstract

Electron charge near atomically sharp corrugations at the surfaces of a solid tends to spill out and smoothen the abrupt variation of the positions of the positively charged atomic nuclei. The reason is that electrons are much less localized than nuclei. This has been discussed already some 70 years ago by Smoluchowski [R. Smoluchowski, Phys. Rev. 60, 661 (1941)], and the corresponding effect of charge redistribution near surface corrugations bears his name. The Smoluchowski effect focuses on the total electron charge density. It neglects that electrons-in addition to charge-also carry a spin. We discuss spin-dependent electron spill out and demonstrate in a combined theoretical and experimental work that compelling consequences for spin-polarization and spin-dependent transport arise at the edges of magnetic nanostructures due to the spin-dependent Smoluchowski effect. We find a variation of the tunnel magnetoresistance ratio of more than 20% on a length scale of a few atomic diameters.

On the critical behaviour of two-dimensional liquid crystals

“…We compare now the values measured for η for a system (the 2D Heisenberg model) which does not exhibit any transition, at least for temperatures above T = 0.1 [10] (see figure 4)). Then, we can expect the behaviours of η to be quite different in the two cases.…”

“…The 2D Heisenberg model is expected not to exhibit any phase transition [10,11,12,13]. The magnetic susceptibility strongly diverges when the temperature van-ishes [10].…”

“…We will consider hereafter the 2D XY-model [8], the 2D Heisenberg model [10], and the 2D Lebwohl-Lasher model [20]. The simulations will be performed using Monte Carlo (MC) Wolff cluster algorithm [34] appropriately adapted to the model under consideration [22], in order to avoid most of the critical slowing down behaviour close to transition, if any.…”

“…The 2D Heisenberg model is expected not to exhibit any phase transition [10,11,12,13]. The magnetic susceptibility strongly diverges when the temperature van-ishes [10]. However, some authors argued in favour of a transition [14,15,16,17] and possibly an effective quasilong-range-ordered phase [18,19] at very low temperatures, at least in large but finite systems.…”

“…On the other hand, the 2D Heisenberg model (O(3), non-Abelian symmetry) has no transition at any finite temperature (asymptotic freedom) [10,11,12,13]. The longitudinal modes of the O(3) model are frozen for the low temperatures, and only the transverse modes are activated, leading essentially to two Gaussian modes.…”