Non-Fermi-liquid behavior of quantum magnetooscillations near a quantum critical point

We study many-body effects in quantum magnetooscillations of a 2D strongly correlated system near ferromagnetic and antiferromagnetic quantum critical points (QCP). The amplitude of magnetooscillations is determined by the electron self-energy $\Sigma(\pi T, \mathbf{k};T)$ averaged over the Fermi surface, at the Matsubara frequency $\omega=\pi T$ for $T>\omega_c$, where $\omega_c$ is the cyclotron frequency. The major contribution of the bosonic propagator to the electron self-energy comes from static spin fluctuations. In the spin-fermion model, the self-energy behaves as $\Sigma \propto \sqrt{T}$ in the ferromagnetic system and as $\Sigma \propto T\ln{T}$ in the antiferromagnetic system. This shows the non-Fermi-liquid temperature dependence of the self-energy near the QCP and the oscillation amplitude $A\propto \exp{\left[-2\pi (\pi T + \Sigma)/\omega_c\right]}$ can be very different from the Lifshitz-Kosevich form. The momentum dependence of the self-energy contribution to the oscillation amplitude is also discussed.