Magnetic structures of the anisotropic Dirac metals AMnBi$_{2}$ (A $=$ Ca, Sr)

Magnetism is potentially important in the Dirac materials AMnBi$_{2}$ (A $=$ Sr and Ca) because long-range magnetic order of the Mn spins provides an additional periodic potential that could influence the Fermi surface and hence the behavior of the Dirac fermions. We report powder and single crystal neutron diffacraction measurements of the magnetic order in AMnBi$_{2}$ (A $=$ Sr and Ca), two layered manganese pnictides with anisotropic Dirac fermions on a Bi square net. Both compounds are found to order in k $=$ 0 antiferromagnetic structures, with ordered Mn moments at T $=$ 10 K of approximately 3.8 $\mu_{\mathrm{B}}$ aligned along the c axis. The magnetic structures are N\'{e}el-type within the Mn-Bi layers, consistent with density functional theory predictions, but the interlayer ordering is different in the two materials, being antiferromagnetic in SrMnBi$_{2}$ and ferromagnetic in CaMnBi$_{2}$. This allows a mean-field coupling of the magnetic order to the Dirac fermions in CaMnBi$_{2}$, but not in SrMnBi$_{2}$.