Inelastic neutron scattering study of the anisotropic $S=1$ spin chain $\left[\mathrm{Ni}\right({\mathrm{HF}}_2\left)\right(3-\text{Clpyridine}\left){}_4\right]{\mathrm{BF}}_4$

$\left[\mathrm{Ni}({\mathrm{HF}}_2\right)(3-\text{Clpyridine}){}_4]{\mathrm{BF}}_4$ (NBCT) is a one-dimensional, $S=1$ spin chain material that shows no magnetic neutron Bragg peaks down to temperatures of 0.1 K. Previous work identified NBCT as being in the Haldane phase and near a quantum phase transition as a function of $D/J$ to the large-$D$ quantum paramagnet phase (QPM), where $D$ is the axial single-ion anisotropy and $J$ is the intrachain superexchange. Herein, inelastic neutron scattering results are presented on partially deuterated, ${}^{11}\mathrm{B}$-enriched NBCT polycrystalline samples in zero magnetic field and down to temperatures of 0.3 K. Comparison to density matrix renormalization group calculations yields $D/J=1.51$ and a significant rhombic single-ion anisotropy $E$ ($E/D\approx 0.03, E/J\approx 0.05$). These $D, J$, and $E$ values place NBCT in the large-$D$ QPM phase but precipitously near a quantum phase transition to a long-range ordered phase.

Figure 1

NBCT crystal structure and chain motif. (a) The NBCT unit cell; ${\mathrm{NiF}}_2{\mathrm{N}}_4$ (black) and ${\mathrm{BF}}_4$ (green) polyhedrons are shown. (b) A chain portion along the crystallographic $c$ axis and the $z$ axis of Eq. (1), with atoms not linking the chain suppressed. The dashed lines illustrate the relative canting between the two ${\mathrm{NiF}}_2{\mathrm{N}}_4$ moieties along the $z$ ($c$) axis.

Figure 2

Intensity maps of reverse-power-averaged NBCT experimental data and the DMRG model. (a) $E_i=3.32\mathrm{meV}, T=0.3\mathrm{K}$ data minus $T=13\mathrm{K}$ data. White regions are where the scattering condition is not satisfied by the spectrometer. (b) $E_i=3.32\mathrm{meV}$ model that is calculated at $T=0$ but includes a $T=0.3\mathrm{K}$ Bose factor correction. For (a) and (b) the intensity scale has $\min =-2\times {10}^{-4}$ and $\max =5\times {10}^{-4}$ with scaled units. (c) $E_i=1.00\mathrm{meV}, T=0.3\mathrm{K}$ data. (d) $E_i=1.00\mathrm{meV}$ that is calculated at $T=0$ but includes a $T=0.3\mathrm{K}$ Bose factor correction. For (b) and (d) the intensity scale has min = 0 and $\max =2\times {10}^{-4}$ with scaled units.

Figure 3

Intensity versus energy transfer for reverse-power-averaged NBCT experimental data and the DMRG model. (a) Data and model of $E_i=1.00\mathrm{meV}, T=0.3\mathrm{K}$ are shown for $Q_{1D}$ = $[0.44,0.57]{}^{-1}$. Data and model of $E_i=3.32\mathrm{meV}, T=0.3\mathrm{K}$ are shown for (b) $Q_{1D}=[0.41,0.65]{}^{-1}$ centered on the $\pi$ point, (c) $Q_{1D}=[0.66,0.90]{}^{-1}$ centered on the $3\pi /2$ point, and (d) $Q_{1D}=[0.91,1.15]{}^{-1}$ centered on the $2\pi$ point. The negative intensities in $E_i=3.32\mathrm{meV}$ are most likely due to oversubtraction of the $T=13\mathrm{K}$ data that has quasielastic magnetic scattering.

Figure 4

Anisotropic spin chain phase diagram. The theoretical phase boundary is from Ref. [10]. The $D/J=1.51$ line is shown along with a marker for $E/J=0.05$, which places NBCT in the large-$D$ QPM phase but close to a long-range ordering transition.

Figure 5

Local mode in NBCT. (a) $E_i=1.55\mathrm{meV}, T=0.3\mathrm{K}$ data, with min = 0 and $\max =2\times {10}^{-2}$ intensity scale. (b) $E_i=1.55\mathrm{meV}, T=0.3\mathrm{K}$ data minus $T=13\mathrm{K}$ data with min = $-1\times {10}^{-5}$ and $\max =1\times {10}^{-4}$ intensity scale. In (a) and (b), white regions are where the scattering condition is not satisfied by the spectrometer. (c) Intensity versus energy transfer for $E_i=1.55\mathrm{meV}$ powder averaged data near $q_{1D}=\pi$ ($Q_{1D}$ averaged between $[0.4,0.6]{}^{-1}$).