Magnetic phase transitions to an incommensurate magnetic structure in FeGe$_{2}$ compound

A symmetry analysis of possible magnetic structures in an incommensurate magnetic phase in FeGe$_{2}$ compound, resulted from phase transitions from the paramagnetic phase, was performed based on a phenomenological consideration. It is shown that two possible approaches to a such an analysis, the first of which uses the magnetic representation of the space group, and the second one is based on the expansion of the magnetic moment in basis functions of irreducible representations of the space group of the paramagnetic phase, yield the same results. Space group irreducible representations are determined, according to which the transition to an incommensurate structure can occur. The set of these representations appears identical in both approaches. Ginzburg–Landau functionals for analyzing the transitions according to these representations are written. A renormalization group analysis of the second-order phase transitions from the paramagnetic state to the incommensurate magnetic structure is performed. It is shown that a helical magnetic structure can arise in the incommensurate phase as a result of two second-order phase transitions at the transitions temperature.