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Deng et al. Microstructures 2023;3:2023044 https://dx.doi.org/10.20517/microstructures.2023.42 Page 3 of 18

Figure 1. (A) Perovskite structure ABO ; (B) antiperovskite structure Mn XN.
3 3

Figure 2. The collinear (A) AFM structure and (B) FM structure of Mn GaC.
3
Mn GaC is k = (0, 0, 0), displaying m = 1.3 ± 0.1 μ /Mn at 193 K [53,54] . The direction [111] of easy
B
3
[56]
magnetization is also confirmed by the Mössbauer effect .
Mn ZnN is characterized by two first-order magnetic transitions: PM-AFM at 183 K and AFM-AFM at
3
140 K. As shown in Figure 3A, the low temperature AFM phase is collinear within a 2a sub-lattice
of manganese, exhibiting two inequivalent magnetic atoms with different ordered magnetic moments .
[57]
The values of moments 0.61 μ on Mn1 (000) and 1.03 μ on Mn2 (1/4, 1/4, 1/4) were clarified by
B
B
Fruchart et al. . In 2012, we determined the ordered moments of 1.40 μ on Mn1 and 2.44 μ on Mn2 at
[58]
B
B
80 K for Mn Zn N by neutron diffraction . Moreover, for Mn Zn N , we observed a collinear FIM
[20]
3.19
0.77
0.94
0.99
3
structure with a propagation vector k = (0, 0, 0) below 200 K [Figure 3B]. The magnetic moments alternate
along the [111] direction with different values, corresponding to 0.5(1) (face-centered atom) and
1.3(7) (corner atom) μ /Mn for Mn atoms at 120 K .
[21]
B
Non-collinear magnetic structures
It is worth noting that two non-collinear AFM phases belonging to Γ and Γ types, respectively, have been
5g
4g
studied extensively in antiperovskites. In this case, the compounds remain cubic with the propagation
5g
vector k = (0, 0, 0). For Γ type shown in Figure 4A, the magnetic moments of Mn atoms are located in the
(111) plane with a triangular arrangement. As seen from Figure 4B, the magnetic moments of Γ are
4g
4g
5g
triangularly located in the (111) plane achieved by rotating 90° coherently from Γ type. In Γ and Γ
5g
magnetic structures, two Mn atoms form an angle of 120° with each other in the (111) plane, and the
magnetic moments of the three atoms cancel each other out to generate a zero net magnetic moment.