Magnetic gap excitations in a one-dimensional mixed spin antiferromagnet Nd 2 BaNiO 5 A. Zheludev, J. M. Tranquada, and T. Vogt Brookhaven National Laboratory, Upton, New York 11973-5000 D. J. Buttrey University of Delaware, Newark, Delaware 19716 Received 10 January 1996; revised manuscript received 4 March 1996 Magnetic excitations in a Nd 2 BaNiO 5 powder sample were investigated by inelastic neutron scattering. Well-defined one-dimensional 1D gap modes were observed above and below the Ne ´el temperature T N =24 K. In both temperature regimes the measured dynamic structure factor was found to be consistent with that calculated for transverse Haldane gap modes in a quantum-disordered S =1 linear-chain antiferromagnet. The energy gap does not show any appreciable T dependence at T T N . However, in the ordered phase the spin gap increases. The observed behavior is totally different from that found in other Haldane gap systems undergoing 3D antiferromagnetic ordering, such as CsNiCl 3 . S0163-18299606134-6 I. INTRODUCTION Since the pioneering work of Haldane 1,2 much attention has been given to quantum magnetism of quasi-one- dimensional 1D integer-spin Heisenberg antiferromagnets AF. If the interaction between the AF chains is substan- tially weaker than the in-chain exchange coupling, such sys- tems have a nonmagnetic ground state i.e., with no long- range order in the spin pair correlation function and an exchange-induced gap in the magnetic excitation spectrum. The low-lying magnetic excitations are singlet to triplet, and the dispersion has a minimum referred to as the Haldane gap at the 1D AF reciprocal space point. Fortunately, this unique, purely quantum behavior is relatively robust. Weak easy-plane single-ion anisotropy does not destroy the non- magnetic ground state or eliminate the energy gap, although it does indeed split the excitation triplet into a lower-energy doublet of transverse modes with spin fluctuations perpen- dicular to the chain direction and a higher-energy longitudi- nal mode spin fluctuations along the chains. 3–5 Moreover, the gap can be observed at finite temperatures. This robust- ness made it possible to study the Haldane gap experimen- tally in quite a number of real quasi-1D compounds, and inelastic neutron scattering proved to be the most informa- tive technique for a comprehensive reference list see, for example, Refs. 6–8. In this work we focus on the isostructural family of quasi- 1D materials with the general formula L 2 BaNiO 5 . Members with L =Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, and Tm are known. 9,10 In these species the high-spin ( S =1) Ni 2 + ions are arranged in linear chains along the a axis of the ortho- rhombic structure, and the in-chain antiferromagnetic ex- change constant is relatively large ( | J | 250 K. 11,12 For nonmagnetic L ( L =Y the interchain interaction is negli- gible. Y 2 BaNiO 5 is a good example of a Haldane-gap system 13,14,11 and does not exhibit any long-range magnetic order down to 1.2 K. The L sites being positioned in between the Ni chains, substituting magnetic ions for L leads to an increased interchain coupling and all the L Y members or- der antiferromagnetically with T N ranging from 24 to 50 K Ref. 15 and references therein. It is known that the onset of 3D long-range order at low temperature does not eliminate the possibility of Haldane-like behavior. 16–19,8 However, purely 1D systems appeared to be of greater immediate fun- damental interest. Much of the experimental work, especially inelastic neutron scattering, was focused on Y 2 BaNiO 5 and until recently the L Y members were largely neglected. Our studies of Pr 2 BaNiO 5 which orders at T N =24 K have re- vealed interesting and unique dynamic properties of this mixed spin system. 12 In particular, well-defined Haldane-like gap excitations were observed at T T N and shown to persist in the 3D AF phase. Moreover the gap mode retains its purely 1D dispersion in the ordered phase. In contrast with the behavior observed in such materials as CsNiCl 3 , 17,16,8 no softening is observed in the gap mode at any wave vector. The gap excitations are distinct from acoustic spin waves in the ordered state. It was also demonstrated that these excita- tions represent spin fluctuations in the Ni-chain subsystem, with hardly any contribution from the rare-earth sites. Herein we report the results of inelastic neutron-scattering experiments on Nd 2 BaNiO 5 . We show that a well-defined 1D magnetic transverse gap mode is present in Nd 2 BaNiO 5 both above and below the Ne ´ el temperature T N =48 K Ref. 15. It corresponds to the Haldane-gap excitations in Y 2 BaNiO 5 . Unlike those in the extensively studied CsNiCl 3 compound, 17,16,8 the gap modes in Nd 2 BaNiO 5 do not expe- rience any softening at T N at any wave vector and are appar- ently not related to the gapless antiferromagnons Goldstone modes in the ordered phase. The results are discussed in comparison with those previously obtained for Pr 2 BaNiO 5 . II. EXPERIMENTAL The preparation of Nd 2 BaNiO 5 samples is described elsewhere. 15 We have utilized the same single-crystal sample 321 mm 3  that was used by Sachan et al., 15 for the stud- ies of the magnetic structure and a newly synthesized 15 g powder sample. The crystal structure of Nd 2 BaNiO 5 is orthorhombic space group Immm ), with cell constants PHYSICAL REVIEW B 1 SEPTEMBER 1996-II VOLUME 54, NUMBER 10 54 0163-1829/96/5410/72106/$10.00 7210 © 1996 The American Physical Society