Enhancement of paramagnetic effects during spin alignment in 2D semiconductors

An Effect of the Space Dimension of Electron Fermi Gas upon the Spin Ordering in Clusters and Nanoparticles

“…Their influence on the character of the spin ordering in such a system plays a crucial role. Before we considered the polarization effects in the Fermi system, we present our results in the more appropriate form using the dimensionless parameter r s (see [2,4,5]). Let us introduce this dimensionless parameter as a ν-dimensional concentration of particles, messed in the atomic units:…”

“…where the coefficients C 1ν for each space dimension are presented in Table 3. The detailed computation of the exchange contributions for the different space dimensions can be seen in [2,4,5]. Then, the total mean value of the energy per electron has the following general form in the atomic units accounting for the space dimension ν:…”

“…Commonly, we call the system dynamic one-or two-dimensional if the electron motion is free only in one (or two) spatial dimensions and their motion in the second and third (or only third) dimensions corresponds to the discrete energy states. Practically, samples with quantum scale (films and wire) [4][5][6] have size approximately equal to 50-100 atomic units (a.u.). The experimentally obtained quasi-one-dimensional system on the (114) surface of the bismuth semimetal has a size of about 60-100 a.u.…”

“…As underlined in [2], in a real system with non-zero width, the results remain qualitatively valid, but require a quantitively detailed consideration. The total energy takes into account the negative maximal exchange contribution in the case of complete (100%) polarization of spin, as compared in [3,4,[8][9][10][11][12][13][14] with the energy of degenerate electron gas in the case of complete depolarization. Such a comparison leads to the conjecture that a state with spontaneous polarization of electrons in a quasi-two-dimensional semiconductor is formed only when the exchange energy exceeds the kinetic energy, which is possible only when the electron concentration in a quasi-two-dimensional system is σ~7.6 × 10 10 -5 × 10 11 1/cm 2 (see experimental work [12]).…”

“…The giant Zeeman effect [27] occurring in these systems allows for the creation of a highly polarized 2D electron gas in which the spin quantization occurs without direct modification of the orbital motion. Effects of magnetic ordering associated with the Coulomb exchange interaction of free electrons in a 2D Fermi system are considered in [4,29], which has shown that the paramagnetic response is substantially enhanced by Fermi liquid effects. The phase transition to a state with spontaneous polarization of spins has been described.…”