It is the purpose of the present report to discuss a particular case of competing AF and superconducting orders within the framework of the Hubbard model, which is relevant for understanding the mechanism of unconventional superconductivity in the heavy fermion materials and high­Tc cuprates. Experimental data indicates that under variation of certain parameters of the system, such as pressure or doping fraction, the AF order eventually disappears in favor of superconductivity. We focus on a concrete way this suppression of the antiferromagnetism occurs. In particular, it is argued that there is no abrupt transition; instead an inhomogeneous intermediate state of the system sets up. The latter was extensively discussed in the context of high­Tc materials (the so-­called striped phase), but never before in the heavy fermions. We show that (in the weak coupling regime) this state is naturally analogous to the well known Larkin-­Ovchinnikov-­Fulde-­Ferrell state of conventional superconductors. The existence of the modulation with a particular wavelength straightforwardly leads to the incommensurate structure of the transverse magnetic response function, a feature which received a lot of attention recently.

Generalization of this analysis to the strong coupling case (the t­J model) represents a formidable problem. Here we report our preliminary considerations of this issue. In particular, a new representation of the original degrees of freedom, which may be useful in addressing this problem, will be discussed.