Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η  , is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η⩾1.82η⩾1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.

Research highlights
► We study the ground state of frustrated rectangular and triangular magnets.
► The ground states depend on the ratio of vertical and horizontal lattice spacings.
► The rectangular lattice has two long-range ordered ground states.
► The triangle lattice has both short-range and long-range ordered states.