Antiferromagnetic Heisenberg spin-1 chain: magnetic susceptibility of the Haldane chain described using scaling

Abstract

The phenomenological expression χT/(Ng²μ_B²/k)=C_1n exp(-W_1n/T)+C_2n exp(-W_2n/T) describes very accurately the temperature dependence of the magnetic susceptibility computed for antiferromagnetic rings of Heisenberg spins S=1, whose size n is even and ranges from 6 to 20. This expression has been obtained through a strategy justified by scaling considerations together with finite size numerical calculations. For n large, the coefficients of the expression converge towards C₁=0.125, W₁=0.451J, C₂=0.564, W₂=1.793J (J is the exchange constant), which are appropriate for describing the susceptibility of the spin-1 Haldane chain. The Curie constant, the paramagnetic Curie-Weiss temperature, the correlation length at T=0 and the Haldane gap are found to be closely related to these coefficients. With this expression, a very good description of the magnetic behavior of Y₂BaNiO₅ and of Ni(C₂H₈N₂)₂NO₂ClO₄ (NENP), the archetype of the Haldane gap systems, is achieved over the whole temperature range.