Possible Ground States and Magnetic-Field-Tuned Phase Transitions of a Geometrically Frustrated Ising Antiferromagnet on a Triangular Lattice

Possible average alignments of the spins in the ground state and the phase transitions of a geometrically frustrated Ising antiferromagnet in the presence of magnetic fields on a triangular lattice are studied in a mean field approximation. Starting from a zero-field clock phase, we can determine the phase boundaries from the curves of magnetic moments and their derivatives as functions of the fields. We also analyze the behavior of sublattice magnetic moments under the effect of the fields. The experimental relevances for TmMgGaO ₄ and SrEr ₂ O ₄ are discussed. Besides, using a functional integral method, we have calculated a functional for free energy to obtain the contribution of spin fluctuations. From this, we can find that the role of the quantum spin fluctuations at very low temperatures is only prominent in the vicinity of the transition points. It can therefore be seen that the results, although given in the mean field approximation, describe quite well the phase transitions and rearrangements of the magnetic moment per spin under the effect of both the transverse and longitudinal fields.