Magnetism and Peierls distortion in Dirac semimetal CaMnBi$_2$
Dirac semimetals of the form $A$Mn$X_2$ ($A =$ alkaline-earth or divalent rare earth; $X =$ Bi, Sb) host conducting square-net Dirac-electron layers of $X$ atoms interleaved with antiferromagnetic Mn$X$ layers. In these materials, canted antiferromagnetism can break time-reversal symmetry (TRS) and produce a Weyl semimetallic state. CaMnBi$_2$ was proposed to realize this behavior below $T^{*}\sim 50$ K, where anomalies in resistivity and optical conductivity were reported. We investigate single-crystal CaMnBi$_{2}$ using polarized and unpolarized neutron diffraction, x-ray diffraction, and density functional theory (DFT) calculations to elucidate the underlying crystal and magnetic structures. The results show that the observed anomalies do not originate from spin canting or weak ferromagnetism; no measurable uniform Mn spin canting is detected. Instead, CaMnBi$_2$ undergoes a coupled structural and magnetic symmetry-lowering transition at $T^{*} = 46(2)$ K, from a tetragonal lattice with C-type antiferromagnetism to an orthorhombic phase with unit-cell doubling along the $c$ axis and minimal impact on magnetism. Analysis of superlattice peak intensities and lattice distortion reveals a continuous second-order transition governed by a single order parameter. The refined atomic displacements correspond to a zigzag bond-order-wave (BOW) modulation of Bi-Bi bonds, consistent with an electronically driven Peierls-type instability in the Dirac-electron Bi layer, long anticipated by Hoffmann and co-workers [W.~Tremel and R.~Hoffmann, \textit{J. Am. Chem. Soc.} \textbf{109}, 124 (1987); G.~A.~Papoian and R.~Hoffmann, \textit{Angew. Chem. Int. Ed.} \textbf{39}, 2408 (2000)]. %\textcite{TremelHoffman_JACS1987} [JACS {\bf 109}, 124 (1987)].