Half-ordered state in the anisotropic Haldane-gap antiferromagnet $\mathrm{Ni}{\left({\mathrm{C}}_5{\mathrm{D}}_{14}{\mathrm{N}}_2\right)}_2{\mathrm{N}}_3\left({\mathrm{PF}}_6\right)$

Neutron diffraction experiments performed on the Haldane gap material $\mathrm{Ni}{\left({\mathrm{C}}_5{\mathrm{D}}_{14}{\mathrm{N}}_2\right)}_2{\mathrm{N}}_3\left({\mathrm{PF}}_6\right)$ in high magnetic fields applied at an angle to the principal anisotropy axes reveal two consecutive field-induced phase transitions. The low-field phase is the gapped Haldane state, while at high fields the system exhibits a three-dimensional long-range Néel order. In a peculiar phase found in intermediate fields only half of all the spin chains participate in the long-range ordering, while the other half remain disordered and gapped.

Figure 1

Crystal structure of NDMAP in projection onto the $\left(ac\right)$ crystallographic plane and the geometry of the present experiment. Only the N-ions (small balls) and Ni-ions (large balls) are shown. The local magnetic anisotropy axes $x$ and $z$ are tilted in the $\left(ac\right)$ plane by $\alpha =16°$ relative to the $c$ axis. The tilt direction is opposite for type-$A$ and type-$B$ chains. The field $H$ is applied at an angle $\psi$ relative to the $c$ axis of the crystal and forms unequal angles ${\varphi }_A$ and ${\varphi }_B$ with the anisotropy axes $z_A$ and $z_B$, respectively.

Figure 2

Main panels: field dependence of two magnetic Bragg peak intensities measured in NDMAP at $T=35\mathrm{mK}$. The magnetic field is applied in the $(a,c)$ crystallographic plane at an angle 14.2° to the $c$ axis. The solid lines are as described in the text. Insets: $h$-scans across the two magnetic Bragg peaks at $H=6\mathrm{T}$.