Longitudinal Spin Density Wave Order in a Quasi-1D Ising-like Quantum Antiferromagnet

From neutron diffraction measurements on a quasi-1D Ising-like ${\mathrm{Co}}^{2+}$ spin compound ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$, we observed an appearance of a novel type of incommensurate ordering in magnetic fields. This ordering is essentially different from the Néel-type ordering, which is expected for the classical system, and the peculiar spin structure is caused by quantum fluctuation inherent in the quantum spin chain. A Tomonaga-Luttinger liquid nature characteristic of the gapless quantum 1D system is responsible for the realization of the incommensurate ordering.

Figure 1

Spin correlations in the TLL phase of the $S=1/2$ 1D $XXZ$ antiferromagnet. (a) The staggered correlation of the transverse spin components, which is expressed as $⟨S_0^x{S}_r^x⟩\simeq (-1{)}^r{r}^{-{\eta }_x}$. (b) The incommensurate correlation of the longitudinal spin component, expressed as $⟨S_0^z{S}_r^z⟩-m^2\simeq \cos (2k_{F}r)r^{-{\eta }_z}$. $r$ is a distance between the spins. ${\eta }_x$ and ${\eta }_z$ are Tomonaga-Luttinger exponents, which satisfy a relation ${\eta }_x{\eta }_z=1$.

Figure 2

Phase diagram of ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ in magnetic fields applied along the $c$-axis. Neutron scattering measurements are conducted in the region, shown by arrows.

Figure 3

Magnetic field dependence of neutron diffraction profiles of $(4,0,l)$ scan measured at temperature $T=0.85\mathrm{K}$ (a), 1.5 K (b,) and 2 K (c). Solid lines are the results of fits to Gaussian functions. The experimental points are partly eliminated to make the fitting lines more visible.

Figure 4

Magnetic field dependence of the peak position of the observed neutron scan profile. The data are extracted from the least-square fits to the neutron scan profile. Inset shows the field dependence of a normalized incommensurate modulation $2k_F/\pi$. The theoretical curve is obtained by the calculation based on the Bethe ansatz exact theory.