Momentum relaxation of the spin distribution function caused by electron-electron scattering in a two-dimensional Fermi gas

The influence of Coulomb interaction on the relaxation of the spin distribution function over the directions of electron momenta is studied by calculating the angular harmonics of the linearized electron-electron collision integral at low temperatures, when the electron gas is degenerate. It is shown that the relaxation rates of the spin distribution function of two-dimensional electron gas are substantially different for even and odd angular harmonics. For even harmonics, the relaxation rate of the spin distribution function is equal to the relaxation rate of the density distribution function, demonstrating a logarithmic increase with the number of harmonic and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mi>T</a:mi><a:mn>2</a:mn></a:msup></a:math> temperature dependence. For odd harmonics, the relaxation rate does not depend on the number of harmonic and depends on temperature as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msup><b:mi>T</b:mi><b:mn>2</b:mn></b:msup><b:mo form="prefix">ln</b:mo><b:mrow><b:mo>(</b:mo><b:msub><b:mi>ɛ</b:mi><b:mi>F</b:mi></b:msub><b:mo>/</b:mo><b:mi>T</b:mi><b:mo>)</b:mo></b:mrow></b:mrow></b:math>, where <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>ɛ</d:mi><d:mi>F</d:mi></d:msub></d:math> is the Fermi energy. The results are used for theoretical investigation of the temperature dependence of spin accumulation rates relating the intensity of external spin pumping with nonequilibrium spin polarization in the electron gas with spin-orbit coupling. This dependence has a maximum when the collisional broadening energy governed by electron-electron scattering exceeds the spin splitting energy, and is sensitive to the difference in the relaxation rates for even and odd harmonics.