Unusual physical behaviors of strongly correlated rare earth dialuminides*

We present electronic, magnetic, and magnetostructural behaviors of rare earth dialuminides calculated by first principles. Total energy calculations show that CeAl$_{2}$ and EuAl$_{2}$ adopt antiferromagnetic ground states while dialuminides formed by other magnetic lanthanides have ferromagnetic ground states. The magnetic moment of CeAl$_{2}$ indicates that the 4f orbital moment of Ce in CeAl$_{2}$ is quenched. Eu in EuAl$_{2}$ and Yb in YbAl$_{2}$ are divalent. PrAl$_{2}$ exhibits a tetragonal distortion near ferromagnetic transition. HoAl$_{2}$ shows a first order magnetostructural transformation while DyAl$_{2}$ shows a second order transformation. The dialuminides formed by Nd, Tb, and Er are simple ferromagnet without additional anomalies in the ferromagnetic state. SmAl$_{2}$ orders ferromagnetically with less than 1 $\mu_{\mathrm{B}}$ indicating the cancellation of 4f spin moment by its orbital counterpart. Due to substantially high 4f crystal field splitting TmAl$_{2}$ shows 4f spin magnetic moment lower than expected.