A-type antiferromagnetic order in MnBi4Te7 and MnBi6Te10 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 ${\mathrm{MnBi}}₂{\mathrm{Te}}₄$.