Recently, orthorhombic CuMnAs has been proposed to be a magnetic material where topological fermions exist around the Fermi level. Here we report the magnetic structure of the orthorhombic Cu0.95MnAs and Cu0.98Mn0.96As single crystals. While Cu0.95MnAs is a commensurate antiferromagnet (C-AFM) below 360 K with a propagation vector of k = 0, Cu0.98Mn0.96As undergoes a second-order paramagnetic to incommensurate antiferromagnetic (IC-AFM) phase transition at 320 K with k = (0.1,0,0), followed by a second-order IC-AFM to C-AFM phase transition at 230 K. In the C-AFM state, the Mn spins order parallel to the b-axis but antiparallel to their nearest-neighbors with the easy axis along the b axis. This magnetic order breaks Ry gliding and S2z rotational symmetries, the two crucial for symmetry analysis, resulting in finite band gaps at the crossing point and the disappearance of the massless topological fermions. However, the spin-polarized surface states and signature induced by non-trivial topology still can be observed in this system, which makes orthorhombic CuMnAs promising in antiferromagnetic spintronics.Dirac cones have been proposed and observed in many non-magnetic materials, including Cd 3 As 2 [1, 2] and Na 3 Bi [3,4]. By breaking inversion symmetry (P) or time-reversal symmetry (T ), a Dirac point can be split into a pair of Weyl points. To break T , we can either apply an external magnetic field or use the spontaneous magnetic moment inside the material. For the latter case, the correlation between spontaneous magnetism and Weyl fermions has been studied in the AMnPn 2 (A = rare earth or alkali earth and Pn = Sb or Bi) system [5][6][7][8][9][10][11][12] and the half-Heusler compound GdPtBi [13,14]. Recently, CuMnAs was proposed to be an interesting material with non-trivial topology. CuMnAs has two polymorphs; the tetragonal (TET) CuMnAs, which crystalizes in the space group P 4/nmm, and the orthorhombic (ORT) CuMnAs crystalizing in the non-symmorphic P nma space group. The TET phase consists of alternating layers of edge-sharing CuAs 4 and MnAs 4 tetrahedra. It has been proposed to be a candidate with favourable applications in spintronics [18,19] and a topological metal-insulator transition driven by the Néel vector [17]. On the other hand, the ORT phase consists of a 3D network of edge-sharing CuAs 4 and MnAs 4 tetrahedra (Fig. 2(c)), where the Mn atoms form a 3D distorted honeycomb lattice (Fig. 2(d)). ORT CuMnAs was proposed to be an antiferromagnetic topological semimetal when the spin-orbit coupling is fully considered [15,17]. In such a system, two gapless points, named as coupled Weyl fermions, are robust if the combination of PT is * Corresponding author: nini@physics.ucla.edu reserved and the non-symmorphic screw symmetry S 2z is not broken. Thus, the anti-ferromagnetic ORT CuMnAs provides an ideal system to study the interplay between antiferromagnetism (AFM) and Dirac fermions [15]. In this paper, we will focus on the ORT CuMnAs. We experimentally determine its magnetic order, which breaks th...