Magnetic susceptibilities of rectangular Heisenberg S=1/2 antiferromagnets

Rectangular antiferromagnets are two-dimensional systems with inequivalent exchange strengths (J', J) along the two principle axes with J' $\equiv $ $\alpha $J, $\alpha \quad <$1. They have an intermediate dimensionality that can vary continuously from 1D ($\alpha $ = 0 ) to square 2D ($\alpha $ = 1). There exist a number of physical realizations of rectangular antiferromagnets (CuPzBr$_{2}$, CuPzCl$_{2}$, CuPz(N$_{3})_{2}$ where Pz = pyrazine) but there has been no previous mechanism for interpreting their susceptibilities in terms of two exchange parameters. We have simulated the susceptibility of the rectangular S=1/2 Heisenberg antiferromagnet using the stochastic series expansion quantum Monte Carlo method [1] and used the results to interpret our experimental data. For example, copper pyrazine diazide, CuPz(N$_{3})_{2}$, has a primary exchange of 15.5 K and an anisotropy parameter $\alpha $ = 0.4. The stronger exchange is due to the superexchange pathway through the pyrazine molecule and the weaker corresponds to the azide bridges. [1] A. Sandvik, PRB 59, R14157 (1999).