Magnetic susceptibility and inelastic neutron scattering experiments have been performed in the nearly ideal one-dimensional Heisenberg antiferromagnet with spin one, Ni(C2H8N2)2NO2ClO4. The experimental results are consistent with the recent theoretical predictions for a quantum energy gap between the ground state and the first excited states.

Following the Haldane conjecture, the antiferromagnetic (AF) Heisenberg chain of integer spins has a singlet ground state separated from the excited states by an energy gap. Recent numerical calculations on finite AF chains with S = 1 supported this conjecture and provided an approximate value for the energy gap: EG "",0.41 J I, where J is the intrachain exchange interaction. We report experimental studies on two Ni (II) quasi-one-dimensional (ID) AF with large intrachain interaction, J /k= -50 K, Ni(C2HgNzhNOz(CI04) (NENP) and NHC3HwN2)2N02(Cl04)' (NINO). In both compounds, the magnetic susceptibility along the three crystal axes steeply decreases below T"", 15 K and no 3D long-range magnetic order could be detected down to 1.2 K. These features are consistent with the Haldane conjecture. This result, which is rather surprising owing to the rotational invariance of the Heisenberg hamiltonian, is now well supported by numerical calculations on finite rings for S = 1. 3 -6 For the S = 1, ID-HAF, a reliable estimation of the energy gap, Eo = 0.41 i J I, where J is the nearest-neighbor exchange integral, has been obtained from Monte Carlo calculations up to 32 spins. 7 The effect of magnetic anisotropy has also been studied on the following Hamiltonian: a) Present address: Kamerlingh Onnes Laboratorium. P.O. Box 9506,2300 RA Leidcn, The Netherlands.where J is the intrachain exchange interaction, 1 -A. the exchange anisotropy, and D the single ion anisotropy. It appears that the symmetry breaking terms do not destroy Haldane's gap if they are sufficiently small with respect to the isotropic coupling J.The existence of such a gap would greatly affect the lowtemperature magnetic properties. As the temperature decreases below EGlk, the magnetic susceptibility must decrease rapidly and tend to a value close to zero, independently of the magnetic field orientation. In addition, since the 1D correlation length is severely limited as T ..... 0, the interchain interaction J' which is always present in real quasi-lD magnetic systems would be unable to induce threedimensional long-range order (JD-LRO), below a critical value of the ratio I J '/ J i. 8 This situation is very different for the gapless ID-HAF which achieves 3D-LRO at TNH =2S2( I J XJ' /k I) 1/2. Furthermore, it must be pointed out than an anisotropy gap induced by an additional Ising-like term would increase the correlation length for spin components along the easy axis and induce 3D-LRO at a temperature still higher than T NH • 3538

Extensive neutron inelastic scattering measurements of the frequencies of normal modes in strontium titanate propagating in the crystallographic directions [0, 0, [I, [l, [, 01, [ ;. [, ;I, [4, +, i] and [c, [, 31 are reported. The temperature dependence of the 'soft' modes at points r a n d R have been investigated with particular emphasis on the mode of symmetry A2, propagating in the direction [+, 4, ; I ; quantitative estimates of the isotropy of the dispersion surface at r and R are given. Rigid ion, rigid shell, and deformable shell models of the crystal dynamics have been developed. Based on these, the frequency distribution, specific heat, one-phonon x ray scattering intensity, Debye-Waller factor, and two-phonon Raman spectrum have been calculated; where possible, these are compared with the available experimental measurements.

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The neutron scattering function for liquid 3 He at 120 mK and pressures of 0, 0.5, 1, and 2 MPa has been determined for wave vectors in the range 3 nm -1 < Q < 20 nm _1 . This represents the first experimental information on the density dependence of the zero-sound frequency and damping at finite wave vectors, and should serve as a useful test of theories on excitations in neutral Fermi liquids. The results are in qualitative agreement with extensions of the Landau Fermi-liquid theory to finite wave vectors.PACS numbers: 67.50.Dg Neutron inelastic scattering offers a unique method to examine directly the elementary excitations in liquid 3 He on a microscopic scale, i.e., for wave vectors of order 10 nm -1 . Through their spin-dependent interaction with the 3 He nuclei, neutrons probe the nuclear spin fluctuations, in addition to the density fluctuations which are probed by the spin-averaged interaction. In the neutron scattering function, one distinguishes three components: the excitation of single particle-hole (p-h) pairs, a collective density mode (zero sound), and a broad distribution corresponding to multiple p-h excitations. The current theoretical and experimental situation in this area has recently been reviewed by Glyde. l Previous neutron-scattering experiments 2 " 5 have shown that the single p-h spectrum resembles the one expected for a noninteracting Fermi gas but with an effective mass m* ~ 3mo which lowers the energy of the p-h band compared with that of the noninteracting system. For Q < 10 nm -1 , the single-pair spin fluctuations are enhanced and are well described by the paramagnon model. 6 The zero-sound mode is well resolved for wave vectors less than 10 nm -1 and shows anomalous dispersion, i.e., the energies are above those corresponding to linear dispersion co^coQ, where Co is the ultrasonic zero-sound velocity. It broadens considerably with increasing wave vector even before the mode overlaps with the p-h band. All the results published so far at saturated-vapor pressure (SVP) are in good general agreement with the predictions of the polarization-potential theory developed by Pines and co-workers. 7 Here the potential parameters, obtained by a fitting to the neutron-scattering results and to the Landau parameters, have been used to calculate transport properties for both normal and superfluid 3 He which are in excellent agreement with measured values. 8 The effective interactions in the polarization-potential theory are expected to be sensitive to the density, as discussed by Aldrich and Pines 7 and as shown by the Landau parameters, which are the low-(? limits of the effective interactions.While in an earlier experiment 9 the scattering function for pressurized liquid 3 He could only be measured for wave vectors larger than 12 nm -1 , the present experiment explores the wave-vector range 3 nm ~l < Q < 20 nm" 1 . This therefore represents the first measurement of the zero-sound mode at elevated pressures.The measurements were made at the time-of-flight spectrometer 10 IN6 at the high-flux...