Charge fluctuation effects on the Néel temperature and spin waves in NaV₂O₅

At room temperature NaV₂O₅ exhibits the Pmmn structure with V^4.5+. Here, we use the P2₁mn structure, which exhibits linear chains along the b-direction as a model with separate V⁴⁺ and V⁵⁺ to study the effect of charge disproportionation on the exchange interactions, critical temperature and spin waves.  The exchange interactions are calculated by a linear response method from the quasiparticle self-consistent GW band structure. We find the P2₁mn  structure to have lower total energy but the disproportionation is not complete, leading to small and large magnetic moment vanadiums. In P2₁mn the exchange interactions are essentially limited to an isolated chain with antiferromagnetic coupling between nearest neighbors of the large moment V⁴⁺, while in Pmmn  the coupling J₁ between the V^4.5+ are smaller along the chain but have a strong FM coupling J ₂ across the V-O-V rung. This leads to a higher critical temperature T_N=(2/3k_B)S(S+1)[-2J₁+J₂] in mean field theory for the Pmmn structure than in the P2₁mn structure, T_N=(2/3k_B)S(S+1)[-2J₁]. We interpret the Pmmn structure as the dynamical average of a fluctuating structure and these fluctuations  are crucial to obtain a Néel temperature of order 320K.  The spin waves including only the large magnetic moments of the P2₁mn structure show the expected |2MJ₁ sin(qb/2)| behavior along the chain. However, in the Pmmn structure an additional optic spin wave excitation with energy of 0.2 eV is obtained corresponding to opposite precession of the spin density across a rung.