A-type antiferromagnetic order in MnBi 4 Te 7 and MnBi 6 Te 10 single crystals

${\\mathrm{MnBi}}_{4}{\\mathrm{Te}}_{7}$ and ${\\mathrm{MnBi}}_{6}{\\mathrm{Te}}_{10}$ are two members with $n=2$ and 3 in the family of ${\\mathrm{MnBi}}_{2n}{\\mathrm{Te}}_{3n+1}$ where the $n=1$ member, ${\\mathrm{MnBi}}_{2}{\\mathrm{Te}}_{4}$, has been intensively investigated as the first intrinsic antiferromagnetic topological insulator. Here we report the A-type antiferromagnetic order in these two compounds by measuring magnetic properties, electrical and thermal transport, specific heat, and single-crystal neutron diffraction. Both compounds order into an A-type antiferromagnetic structure as does ${\\mathrm{MnBi}}_{2}{\\mathrm{Te}}_{4}$ with ferromagnetic planes coupled antiferromagnetically along the crystallographic $c$ axis. While no evidence for any in-plane ordered moment is found for ${\\mathrm{MnBi}}_{2}{\\mathrm{Te}}_{4}$ or ${\\mathrm{MnBi}}_{6}{\\mathrm{Te}}_{10}$, weak reflections at half-$L$ positions along the [0 0 $L]$ direction are observed for ${\\mathrm{MnBi}}_{4}{\\mathrm{Te}}_{7}$ suggesting an in-plane ordered moment around $0.15{\\ensuremath{\\mu}}_{B}/\\mathrm{Mn}$. The ordering temperature, ${T}_{N}$, is 13 K for ${\\mathrm{MnBi}}_{4}{\\mathrm{Te}}_{7}$ and 11 K for ${\\mathrm{MnBi}}_{6}{\\mathrm{Te}}_{10}$. The magnetic order is also manifested in the anisotropic magnetic properties. For both compounds, the interlayer coupling is weak and a spin-flip transition occurs when a magnetic field of around 1.6 kOe is applied along the $c$ axis at 2 K. As observed in ${\\mathrm{MnBi}}_{2}{\\mathrm{Te}}_{4}$, when cooling across ${T}_{N}$, no anomaly was observed in the temperature dependence of thermopower. On the other hand, critical scattering effects are observed in thermal conductivity although the effect is less pronounced than that in ${\\mathrm{MnBi}}_{2}{\\mathrm{Te}}_{4}$.