Classical antiferromagnet on the pyrochlore lattice

Abstract Classical Heisenberg antiferromagnet on the pyrochlore lattice is studied using the nonequilibrium relaxation method. Effects of farther neighbor interactions are investigated. We found two ordered phases stabilized by the second- and the third-neighbor interactions.One is a commensurate phase where both k = 0 mode and k = π mode appear. It occurs when J 3 is more ferromagnetic than J 2 . The other one is a double-incommensurate phase which is characterized by two incommensurate wave numbers. It occurs when J 2 is more ferromagnetic than J 3 . No long range ordered state is realized when J 2 = J 3 .