GGA+$U$ calculation of the magnetic ground state of GdB$_{4}$

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