SPIN-WAVE THEORY OF THE TRIANGULAR-LATTICE HEISENBERG-ANTIFERROMAGNET

The spin-wave analysis proposed in the previous study for the square-lattice Heisenberg antiferromagnet, in which the second time derivative of the z-component spin was taken into account and the existence of a long-range order (LRO) was not always assumed, is applied to the triangular case. With the aid of a sum rule, the spin-correlation function at the absolute zero of temperature is calculated and the existence of LRO in the ground state is suggested. The calculation of the spin-correlation function at finite temperatures is performed and the nonexistence of LRO is shown for finite temperatures. Then the expression for the correlation length is given in the explicit form. Also the estimations of the ground-state energy and the magnitude of LRO are attempted on the basis of our spin-wave approximation. The obtained results are reasonable.