Absence of zero-point entropy in a triangular Ising antiferromagnet

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.