Critical behavior study of antiferromagnetism in isostructural La$_{2}$CuO$_{4+\delta }$ and La$_{2}$NiO$_{4+\delta }$

Neutron diffraction [1] and nuclear quadruple resonance [2] experiments coupled with theory calculations provide substantial evidence to support the widely-accepted belief that the two-dimensional Heisenberg model describes the antiferromagnetic interactions in La$_{2}$CuO$_{4}$ (S = $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} )$ and La$_{2}$NiO$_{4}$ (S = 1). The heat capacity critical exponent $\alpha $, which could provide further evidence, has never been studied in these two compounds because of the weak nature of the anomalies at T$_{N}$. [3] We will present heat capacity and high-resolution thermal expansion measurements of La$_{2}$CuO$_{4}$ and La$_{2}$NiO$_{4}$ single crystals, grown by the floating-zone method, and an analysis of $\alpha $ within the context of predicted values for a variety of universality classes. This material is based upon work supported by the NSF (DMR-0504769) and US DOE Office of Basic Energy Sciences (DE-FG-06ER46269) [1] Y. Endoh et al., PRB 37, 7443 (1988); G. Aeppli and D.J. Buttrey, PRL 61, 203 (1988). [2] P. Carretta, A. Rigamonti, and R. Sala, PRB 55, 3734 (1997). [3] T. Kyomen et al., PRB 60, 14841 (1999); K. Sun et al., PRB 43, 239 (1991).