Solid State Communications. Vol. 9, PP. 1971—1973, 1971. Pergamon Press. Printed in Great Britain IN STABILITY OF THE UNIFORM ANTIFERROMAGNETIC CHAIN P. Pincus* Department of Physics, University of California. Los Angeles, California 90024 (Received 9 September 1971 by A.A. Maradudin) It is shown that in the X—Y model the uniform antiferromagnetic chain spontaneously distorts into an alternating antiferrornagnet. This is a Jahn—Teller effect where the distortion lifts the degeneracy between the ground state and the k = 0 magnon. OVER the years, the prob~err of a one dimensional with the well-known Peierls instability. 79 In chain of spins coupled by nearest—neighbor anti- that case, the ground state energy of a half-filled ferromagnetic Heisenberg exchange has evoked one dimensional non-interacting electronic band considerable theoretical attention. ~ Recently this is lowered by dimerization into a two atom per interest has been reinforced by neutron scattering unit cell structure introducing a new zone investigations 2 of (CD 3)4NMriCl~,an apparently boundary and thus removing the zone boundary excellent approximation to a one dimensional degeneracy in the undistorted state. In our spin antiferromagnet, which clearly demonstrate problem the degeneracy which is lifted by the simultaneously both the spin wave excitations distortion is that between the ground state and and absence of long range magnetic order. There the k = 0 spin wave. also exists many organic solids, 3 some based, for example, on tetracyanoquinodimethane~ which crystallize in chainlike structures (Fig. 1). The magnetic resonance properties of these dirnerized 0 0 0 0 0 systems have been interpreted3 in terms of an alternating Heisenberg antiferromagnet with a large exchange i 1 between the closest near FIG. 1. A dimerized chain with distance alterna- neighbors and a weaker J2 between the more tion a — b -. a — h ... and exchange alternation distant near pairs (Fig. 1). J~ — Jz — Ji — The purpose of this communication is to show The X—Y model Hamiltonian for the alterna- that in the X—Y model, 4~ where the isotropic ting antiferromagnet is written: Heisenberg hamiltonian is replaced by a purely transverse coupling, the uniform antiferromagnet = i, ~ (S~, S~, -f S~ 1S~) + (J1 = j~) is unstable with respect to a lattice I distortion which dimerizes the chain into an - 1 alternating antiferromagnet. In this exactly J~ ~ (S~ S~, S~, S~,+1) (1) soluble model, this result is formally identical I where the chain consists of 2N spins (S = (eventually N —. ac). The transformation 4 Supported in part by the National Science Foundation, GP21,290, and the U.S. Office of N~va~ Research, Contract No. N00014-69-0200- 4032. 1971