Angular dependence of nonclassical magnetic quantum oscillations in a quasi-two-dimensional multiband Fermi liquid with impurities

The semiclassical Lifshitz-Kosevich-type description is given for the angular dependence of quantum oscillations with combination frequencies in a multiband quasi-two-dimensional Fermi liquid with a constant number of electrons. The analytical expressions are found for the Dingle, thermal, spin, and amplitude (Yamaji) reduction factors of the nonclassical combination harmonics, where the latter two strongly oscillate with the direction of the field. At the “magic” angles those factors reduce to the purely two-dimensional expressions given earlier. The combination harmonics are suppressed in the presence of the nonquantized (“background”) states, and they decay exponentially faster with temperature and/or disorder compared to the standard harmonics, providing an additional tool for electronic structure determination. The theory is applied to ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$