Abstract
The square Bi layers in $A$MnBi$_2$ ($A =$ Sr, Ca) host Dirac fermions which coexist with antiferromagnetic order on the Mn sublattice below $T_\mathrm{N} = 290\,$K (Sr) and $270\,$K (Ca). We have measured the spin-wave dispersion in these materials by triple-axis neutron spectroscopy. The spectra show pronounced spin gaps of 10.2(2)$\,$meV (Sr) and 8.3(8)$\,$meV (Ca) and extend to a maximum energy transfer of 61 - 63$\,$meV. The observed spectra can be accurately reproduced by linear spin-wave theory from an Heisenberg effective spin Hamiltonian. Detailed global fits of the full magnon dispersion are used to determine the in-plane and inter-layer exchange parameters as well as on the magnetocrystalline anisotropy constant. To within experimental error we find no evidence that the magnetic dynamics are influenced by the Dirac fermions.
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