  Frustrated Ising magnets host exotic excitations, such as magnetic monopoles
in spin ice. The ground state (GS) in this case is characterized by an
extensive degeneracy and associated residual entropy going back to the
pioneering work by G. Wannier who established large residual entropy of nearly
50%Rln2 per mole spins in a triangular Ising antiferromagnet (TIAF) already in
1950. Here, we endeavor to verify this result experimentally using TmMgGaO4, a
novel rare-earth-based frustrated antiferromagnet with Ising spins arranged on
a perfect triangular lattice. Contrary to theoretical expectations, we find
almost no residual entropy and ascribe this result to the presence of a weak
second-neighbor coupling J2zz ~ 0.09J1zz that lifts the GS degeneracy and gives
rise to several ordered states, the stripe order, 1/3-plateau, and 1/2-plateau.
TmMgGaO4 gives experimental access to these novel phases of Ising spins on the
triangular lattice.
