Incommensurate magnetic ordering in ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathit{X}}_2$ $(X=\mathrm{Cl},\mathrm{Br})$ studied by single crystal neutron diffraction

Polarized and unpolarized neutron-diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{X}_2$ $(X=\mathrm{Cl}$,Br). A model of the magnetic structure associated with the propagation vectors ${{\mathbf{k}}^{\prime }}_{\mathrm{Cl}}\approx (-0.150,0.422,\frac{1}{2})$ and ${{\mathbf{k}}^{\prime }}_{\mathrm{Br}}\approx (-0.172,0.356,\frac{1}{2})$ and stable below $T_N=18\mathrm{K}$ for $X=\mathrm{Cl}$ and $T_N=11\mathrm{K}$ for $\mathit{X}=\mathrm{Br}$ is proposed. A feature of the model, common to both the bromide and chloride, is a canted coplanar motif for the four ${\mathrm{Cu}}^{2+}$ spins on each tetrahedron which rotates on a helix from cell to cell following the propagation vector. The ${\mathrm{Cu}}^{2+}$ magnetic moment determined for $\mathit{X}=\mathrm{Br},0.395\left(5\right){\mu }_B$, is significantly less than for $\mathit{X}=\mathrm{Cl},0.88\left(1\right){\mu }_B$ at $2\mathrm{K}$. The magnetic structure of the chloride associated with the wave vector ${\mathbf{k}}^{\prime }$ differs from that determined previously for the wave vector $\mathbf{k}\approx (0.150,0.422,\frac{1}{2})$ [O. Zaharko et al., Phys. Rev. Lett. 93, 217206(E) (2004)].

Figure 1

The $hk0$ and $hk\frac{1}{2}$ layers of reciprocal space of a ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathit{X}}_2$ crystal. Black circles correspond to magnetic reflections $\left\{hk\frac{1}{2}\right\}$ of ${\mathbf{k}}^{\prime }$ and gray circles to those of $\mathbf{k}$ wave vectors. The circle radii are proportional to intensities of magnetic reflections. Dashed circles with center at 000 connect reflections with intensity $I_1$ and $I_2$.

Figure 2

(Color online) The $ac$ (top) and $ab$ (bottom) view on the layer of spin tetrahedra of the ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2{\mathbf{k}}^{\prime }$ magnetic structure. The origin is shifted by [0 0 $1∕2$] relative to the crystallographic unit cell.

Figure 3

(Color online) The $ac$ layer of spin tetrahedra of the ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Br}}_2{\mathbf{k}}^{\prime }$ magnetic structure.

Figure 4

The $ac$ layer of resultant moment of tetrahedra of the ${\mathrm{Cu}}_2{\mathrm{Te}}_2{\mathrm{O}}_5{\mathrm{Cl}}_2{\mathbf{k}}^{\prime }$ magnetic structure.