Transverse susceptibility and the $T^{3/2}$ law in the dynamic spin-fluctuation theory

We obtain explicit expressions for elements of the magnetic susceptibility tensor in the dynamic spin-fluctuation theory. Using an analytic continuation of the Green's functions, we show that the transverse susceptibility has spin-wave poles at low temperatures, yielding the asymptotic $T^{3/2}$ law for magnetization. We derive an explicit expression for the coefficient in the $T^{3/2}$ law based on the multiband Hubbard Hamiltonian and real band structure. We demonstrate the correct low-temperature behavior of magnetization in the example of iron.