Spin Excitations in an Anisotropic Bond-Alternating Quantum $S=1$ Chain in a Magnetic Field: Contrast to Haldane Spin Chains

Inelastic neutron scattering experiments on the $S=1$ quasi-one-dimensional bond-alternating antiferromagnet $\mathrm{Ni}({\mathrm{C}}_9{\mathrm{D}}_{24}{\mathrm{N}}_4)({\mathrm{NO}}_2){\mathrm{ClO}}_4$ have been performed under magnetic fields below and above a critical field $H_c$ at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below $H_c$ has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at $q_{\parallel }=\pi$ that is present in dimerized chains but absent in uniform ones. Above $H_c$, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].

Figure 1

(a) Field dependence of the magnetic Bragg peak intensity at $\mathbf{q}=(1,0,0)$. The solid line is a fit of the experimental data to the expression $a(H-H_c{)}^{2\beta c}$ with $H_c=11.35\mathrm{T}$ and ${\beta }_c=0.316$ between 11.3 and 12 T. The ${\beta }_c$ value is close to the expected 3D-$XY$ value. The dashed line is a guide for the eyes. (b) Field dependence of the gap energies measured in NTENP. Solid lines are calculated triplet branches in a magnetic field, and a vertical thin broken line indicates the critical field $H_c$. The line above $H_c$ is a guide for the eyes.

Figure 2

Inelastic energy scans near $\mathbf{q}=(1,0,1.5)$ at 100 mK and $H=0$, 2, and 4 T. Thin lines represent contributions of three excitation modes. The arrow indicates the higher mode.

Figure 3

Measured dispersion relation of magnetic excitations in NTENP (open circles). Solid symbols show the positions of peaks in the in-plane (squares) and out-of-plane (circles) dynamic structures obtained by Lanczos calculations for 20 spins using the parameters $(\delta ,J/D)=(0.45,0.25)$ and the periodic boundary condition. Note that the size dependence of the dispersion curve is so small around 20 spins. Solid and broken lines are the results of fitting to the form $(\hslash \omega {)}^2={\Delta }^2+{\omega }_{\max }^2{sin}^2\pi h$. Inset: excitation continuum (shaded area), as calculated for NTENP. The lower bound (thin solid line) coincides with the observed position of the observed $z$ axis mode (the highest excitation mode). The in-plane modes are shown by a heavy solid line.

Figure 4

Inelastic energy scans at $\mathbf{q}=(1.1,0,1.5)$ and 100 mK for $H=8.5$ $(<H_c)$, 11.5 $(\sim H_c)$, and 14.5 T $(>H_c)$. Thin lines represent contributions of excitation modes.