Experimental percolation studies of two-dimensional honeycomb lattice:   Li2Mn1-xTixO3
  Li2MnO3 with a S=3/2 two-dimensional Mn honeycomb lattice has a Neel-type antiferromagnetic transition at TN=36 K with a broad maximum in the magnetic susceptibility at TM=48 K. We have investigated site percolation effects by replacing Mn with nonmagnetic Ti, and completed a full phase diagram of Li2Mn1-xTixO3 solid solution systems to find that the antiferromagnetic transition is suppressed continuously without a clear sign of changes in the Neel-type antiferromagnetic structure. The magnetic ordering eventually disappears at a critical concentration of xc=0.7. This experimental observation is consistent with percolation theories for a honeycomb lattice when one considers up to 3rd nearest-neighbor interactions. This study highlights the importance of interaction beyond nearest neighbors even for Mn element with relative localized 3d electrons in the honeycomb lattice. 
Sanghyun Lee, Junghwan Park, Jiyeon Kim, Kun-Pyo Hong, Youngmi Song,   and Je-Geun Park
cond-mat.str-el