Magnetic order and magnon coherent state in double exchange image lattices Original Research Article

Starting from trial wave functions and by minimizing the total energy, we obtain the ground state (GS) of a magnetic system in which there is competition between two exchange interactions: one of them between localized and unlocalized spins and another one among the spins of a Heisenberg image lattice. This analysis allows us to analyze directly a particular case of a magnetic ground state: a magnon gas whose collective wave function presents similarities with the coherent state of the electromagnetic field which is the basis for the laser. The Kondo coupling becomes concomitant with the external magnetic field which can control the number of magnons. The corresponding Zeeman effect provoked by the magnetic external field plus the Kondo interaction energy compete with the spin–spin Heisenberg exchange of the localized magnetic lattices. The fruit of the competition of these three interactions is the existence of a collective state which can be represented with an oscillation with one only frequency which has a minimum uncertainty and therefore it is a most similar quantum state to a classical wave. This collective state for determined crystal conditions, values of Kondo coupling strength, external B values and Heisenberg image-parameters tends to be a minimal energy state, and then, this coherent state, can transit to a magnon Bose–Einstein condensate (BEC). The passing from the minimal coherent state towards the BEC condensation is thermodynamically analyzed and we have deduced the critical temperature of this phase transition.