Nuclear ferromagnetism induced Fulde-Ferell-Larkin-Ovchinnikov state

We present a theoretical study of the influence of the nuclear ferromagnetism on superconductivity in the presence of the electron-nuclear spin interaction. It is demonstrated that in some metals, e.g. Rh, W, the BCS condensate imbedded in a matrix of ferromagnetically ordered nuclear spins should manifest the FFLO (Fulde-Ferell-LarkinOvchinnikov) state. We outline that the optimal experimental conditions for observation of FFLO could be achieved by creation, via adiabatic nuclear demagnetisation, of the negative nuclear spin temperatures. In this case the nuclear polarisation points in the opposite to the external magnetic field direction and the electromagnetic part of the nuclear spin magnetisation compensates the external magnetic field, while the exchange part creates the non-homogeneous superconducting order parameter.