Magnetic frustration in cubic antiferromagnet studied by means of the constraint function: Application to FeF3

We propose a simple way to determine the frustration rate in simple cubic ordered frustrated magnetic structure, based upon the calculation of the reduced energy of the system. The case where the magnetic frustration phenomena based on the competing of nearest and next nearest neighbours interactions is considered. The constraint function is described neglecting all quantum fluctuations effects. The application to FeF3 frustrated magnetic system is presented. Two kinds of magnetic frustrated configurations originating a magnetic phase transition were evidenced according to the values of exchange interactions between first (JAB1v) and second nearest neighbours (JAA(BB)2v). We report on the evolution of the constraint function Fc, versus ratios JAB1v/JAA2v and JAB1v/JBB2v.