The advent of free electron lasers (FELs) in the soft and hard X-ray spectral region has opened the possibility to probe electronic, magnetic and structural dynamics, in both diluted and condensed matter samples, with femtosecond time resolution. In particular, FELs strongly enhanced the capabilities of several analytical techniques, which took advantage of the high degree of transverse coherence provided. FELs based on the harmonic up-conversion of an external seed laser are characterised also by a high degree of longitudinal coherence, since electrons inherit the coherence properties of the seed. At the present state of the art, the shortest wavelength delivered to user experiments by an externally seeded FEL light source is about 4 nm. We show here that pulses with a high longitudinal degree of coherence (first and second order) covering the water window and with photon energy extending up to 790 eV can be generated by exploiting the so-called nonlinear harmonic regime, which allows generation of radiation at harmonics of the resonant FEL wavelength. Moreover, we report the results of two proof-of-principle experiments: one measuring the oxygen K-edge absorption in water ($\sim$ 530 eV), the other analysing the spin dynamics of Fe and Co through magnetic small angle x-ray scattering at their L-edges (707 eV and 780 eV)

The extension of four-wave mixing (FWM) technique to the extreme ultraviolet and soft X-ray ranges allows to monitor the dynamics of coherent excitations of matter, when realized with the exquisite coherent property of bright FEL pulses. We show for the first time a scheme to provide transversally separated pulses with parallel or crossed linear polarizations, realized at FERMI FEL. This configuration paves the way to explore additional features of pump&probe and FWM techniques, and, in particular, the possibility to excite a transient polarization grating on the sample. For this reason, such a technique is important the detection of circular dichroism and chiral properties of matter and the characterization of spin waves and magnons. By tailoring the electrons trajectory along the undulator line, we demonstrate the possibility of deliver balanced and stable couple of pulses with an horizontal separation of the order of millimeters at the experimental station.