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Page 10 of 18 Deng et al. Microstructures 2023;3:2023044 https://dx.doi.org/10.20517/microstructures.2023.42

Figure 8. (A) ZTE behavior of Mn Cu Ge 0.5 N [16] ; (B) local lattice distortion of Mn Cu Ge N [17] ; (C) the relationship between the
1-x
x
3
3
0.5
5g
anomalous change of the lattice and the atomic magnetic moments for Γ phase of Mn Zn N [20] .
x
3
spin-lattice coupling between the lattice constant and the atomic magnetic moment in Mn Zn N. In
x
3
addition, the strong spin-lattice coupling that can be tuned to achieve ZTE behavior was further confirmed
in antiperovskite Mn Ni N and Mn Zn N within Γ phase [15,21] . Meanwhile, in Mn Ga Sn N with Γ
5g
5g
3+x
1−x
x
3
1−x
3.19
0.77
0.94
phase, the increase of the phonon contribution to the thermal expansion induced by Sn doping and the
corresponding decrease of dm/dT are revealed to be the key parameters for tuning the magnetovolume
effect .
[22]
The first-principle calculations have been adopted for understanding the NTE behavior of antiperovskites.
The primary theoretical works focus on the comparison of differences in equilibrium volumes of
antiperovskites with different magnetic structures. Lukashev et al. found that the equilibrium volume of the
Γ AFM state in Mn GaN is larger than that of the PM state, which confirms that the magnetic transition in
5g
3
the material can lead to volume change (magnetovolume effect) . Qu et al. calculated the energy-lattice
[23]
curves of various magnetic configurations, and the results show that the Γ AFM state has the largest
5g
volume. This work also confirms that the Γ AFM state has the largest volume compared to other magnetic
5g
configurations . In addition, Mochizuki et al. constructed a classical spin model with frustrated exchange
[24]
interactions and magnetic anisotropy to study the nontrivial magnetic orders in the antiperovskite Mn AN.
3
5g
With a replica-exchange Monte Carlo technique, the Γ and Γ spin configurations, known to trigger the
4g
NTE, have been reproduced .
[25]
Electronic transport properties in antiperovskites
There is a strong correlation between the lattice, spin, and charge of Mn GaC. Therefore, a giant
3
magnetoresistance effect was found near its collinear AFM - collinear FM magnetic transition . The size of
[26]
magnetoresistance can be expressed by [ρ(H) - ρ(0)]/ρ(0), and ρ(H) and ρ(0) represent the resistivity when
the external magnetic field is finite and 0, respectively. As shown in Figure 9A, Mn GaC generates a
3