DFT+U search for the energy minimum among eight collinear and noncollinear magnetic structures of GdB4

We have studied eight collinear and noncollinear magnetic orientations of ${\text{GdB}}_{4}$ using the $\text{GGA}+U$ method, without and with spin-orbit coupling, for values of $U\ensuremath{-}J$ between 0 and 6. For $U\ensuremath{-}J=6$, the value which had been found to yield the correct Gd lattice constants, we obtain ${\text{GdB}}_{4}$ lattice constants within 0.26% of experiment. We find that the magnetization lies in plane but is collinear, in disagreement with the most recent experimental determination.