Abstract

The spin-1 Heisenberg antiferromagnet on a triangular lattice with the nearest- and next-nearest-neighbor couplings, J1=(1−p)J and J2=pJ, J>0, is studied in the entire range of the parameter p. Mori's projection operator technique is used as a method which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature four second-order phase transitions are observed. At p≈0.038 the ground state is transformed from the long-range ordered 120° spin structure into a state with short-range ordering, which in its turn is changed to a long-range ordered state with the ordering vector Q′=(0,−2π3) at p≈0.2. For p≈0.5 a new transition to a state with a short-range order occurs. This state has a large correlation length which continuously grows with p until the establishment of a long-range order happens at p≈0.65. In the range 0.5<p<0.96, the ordering vector is incommensurate. With growing p it moves along the line Q′–Q1 to the point Q1=(0,−4π33) which is reached at p≈0.96. The obtained state with a long-range order can be conceived as three interpenetrating sublattices with the 120° spin structure on each of them.

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