Haldane Quantum Spin-1 Chain in a Magnetic FieldY. Chen and C. Broholm, Johns Hopkins University
Z. Honda, Saitama Univ., Japan
K. Katsumata, RIKEN, Japan
There are theoretical predictions that above their critical field, spin-1 chains should have a gapless excitation spectrum with soft points at q=ð and at an incommensurate wave vector whose displacement from ð varies in proportion to the magnetization. The effect is analogous to that for the uniform spin-1/2 chain, which we were the first to observe through experiments on copper benzoate. However, the effect has not yet been observed experimentally for one-dimensional spin-1 chains. Several factors make these experiments more difficult for spin-1 chains than for spin-1/2 chains. Firstly, higher magnetic fields are generally needed to magnetize spin-1 chains than spin-1/2 chains because of the Haldane gap. Secondly, spin-1 systems have single ion anisotropy terms that along with the strong applied magnetic field generally lead to Ising behavior in high fields. Finally, as for spin-1/2 chains, site symmetry alternation along spin chains leads to a staggered field that induces a gap in the spectrum and possibly disfavors soft incommensurate modes. We have performed extensive neutron scattering experiments in the magnetized states of the model spin-1 system NDMAP using the SPINS spectrometer. While the experiments do not provide direct evidence for incommensurate correlations, the q-dependence of quasi- elastic scattering in the high field phase is consistent with such.
NDMAP is a one dimensional spin-1 antiferromagnet with a T=0 critical field ranging from 3 to 6 Tesla depending on the field direction. Because there is only one Ni atom per unit cell, all spins experience the same Zeeman term when an external field is applied and this makes the material well suited for studies of the high field gapless phase of the Haldane spin chain. In addition, inter-chain coupling is weak enough that the system has a quantum-disordered phase in the low temperature and low field limit. The only problem with the material is the significant easy plane anisotropy that strongly affects the excitation spectrum and the high field properties of NDMAP.
To characterize the spin Hamiltonian for NDMAP we carried out a zero field neutron scattering study. The experiment determined the intra-chain coupling and the single ion anisotropy terms. These results have been published in the Physical Review B . We then examined the field induced ordered phase. As opposed to other Haldane systems such as, NENP, our data for NDMAP showed that there is a bona fide critical phase transition. For fields with a component perpendicular to the easy plane we found three-dimensional long-range order above the critical field. However, for fields in the easy plane we found a quasi-two-dimensional frozen state with long-range order in the a-c plane but no appreciable correlations detected along the b-axis where inter-chain interactions are weakest. It is unclear whether this frozen state is an intrinsic quantum glass phase or indicates an extreme sensitivity of the weakly interacting quantum spin chains in NDMAP to impurities .
With a critical field only half as large as for NENP and no staggered g-tensor, NDMAP is well suited for inelastic neutron scattering experiments to probe dynamic spin correlations above the critical field. The experiments carried out on 23 deuterated single crystals in a 9 T superconducting magnet system on SPINS, showed the Haldane gap closing at a critical field of 7.7 T for fields applied along the b-direction at a temperature of 2.5 K. An overview of data from above and below the critical field is shown in Figure 1. All aspects of the low field data are well accounted for by a perturbation theory that treats the excited state triplet as an effective spin-1 degree of freedom interacting with the applied field. Above the critical field, there is persistent quasi-elastic magnetic neutron scattering. This is not critical scattering associated with the imminent phase transition as the wave vector chosen was far from the corresponding critical wave vector. Rather this is a finite temperature quasi-elastic magnetic neutron scattering associated with the individual spin chains. Interestingly there is a finite width in q-space associated with these low energy fluctuations. The observed width is consistent with incompletely resolved incommensurate peaks at the locations anticipated from an independent fermion model of the high field phase (solid line in figure). A second interpretation is that this is scattering from a thermal ensemble of solitons. These are massive topological excitations known from the classical easy-plane antiferromagnet in a symmetry-breaking magnetic field, which may also be possible in this extreme quantum limit. A paper reporting these results has been accepted for publication in the Physical Review Letters  and further experiments are under way to distinguish these competing descriptions of the high field phase in the anisotropic spin-1 chain.
 Chen, Y. Y., Honda, Z., Zheludev, A., Broholm, C., Katsumata, K., Shapiro, S. M., "Haldane-gap excitations in the low Hc one-dimensional quantum antiferromagnet Ni(C5D14N2)2N3(PF6)," Phys. Rev. B 63, 104410 (2001).
 Chen, Y. Y., Honda, Z., Zheludev, A., Broholm, C., Katsumata, K., Shapiro, S. M., "Field-Induced Three-and Two-Dimensional Freezing in a Quantum Spin Liquid," Phys. Rev. Lett. 86 (8), 1618 (2001).
 Zheludev, A., Honda, Z., Chen, Y. Y., Broholm, C., Katsumata, K., Shapiro, S. M., Phys. Rev. Lett. (in press 2002).
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