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Deng et al. Microstructures 2023;3:2023044 https://dx.doi.org/10.20517/microstructures.2023.42 Page 9 of 18

it to low temperatures [Figure 7E]. When x = 0.6, the Mn Ag N compound shows ZTE with
3.6
0.4
α = -0.48 × 10 K (temperature range 5 - 87 K). Moreover, Lin et al. revealed a giant NTE covering room
-1
-6
temperature in nanocrystalline Mn GaN . By reducing the average grain size to ~10 nm, the temperature
[10]
3
x
window ΔT for NTE exceeds 100 K, and α remains as large as -30 ppm/K (-21 ppm/K) for x = 1.0 (x = 0.9).
The influence of Ge and Sn doping on the thermal expansion behavior of Mn Zn Ge(Sn) N has been
1-x
3
x
investigated by us [11,12] . Figure 7F shows the variation of lattice constant with temperature in Mn Zn Ge N.
3
x
1-x
The doping of Ge broadens the magnetovolume effect of Mn Zn Ge N and moves the temperature zone to
3
x
1-x
the higher one, thereby realizing the regulation of NTE behavior. A similar behavior was also observed in
Sn-doped Mn Zn Sn N compounds . On the other hand, the regulation of the thermal expansion
[12]
x
1-x
3
behavior of Mn NiN-based compounds has also been reported [13,14] . Antiperovskite Mn Ni Ag N shows
3
3
0.5
0.5
-1
NTE behavior in a wide temperature range (260-320 K) near room temperature with α = -12 × 10 K . The
-6
Mn Ni Cu N exhibits NTE in the temperature range of 160-240 K (ΔT = 80 K) with α = -22.3 × 10 K .
-6
-1
0.5
3
0.5
[15]
Interestingly, a new type of Invar-like material exhibiting ZTE has been revealed in Mn Ni N .
1-x
3+x
Song et al. revealed the ZTE behavior of Mn Cu Ge N due to the size effect . When Mn Cu Ge N was
[16]
0.5
0.5
0.5
3
3
0.5
prepared from polycrystalline samples (average size of 2.0 μm) to ultra-nanocrystals (average size of 12 nm),
the occupancy rate of Mn in the sample changed from 100% to 78.7% [Figure 8A]. Meanwhile, the ultra-
nanocrystalline sample exhibits ZTE behavior in a wide temperature range ΔT = 218 K (12-230 K) with
α = 1.18 × 10 K .
-7
-1
The mechanism for the NTE of antiperovskites was investigated by Iikub et al. The neutron diffraction
5g
results indicate that the non-collinear Γ AFM structure plays a key role in the magnetovolume effect of
Mn Cu Ge N, which leads to the appearance of NTE behavior. Moreover, Iikub et al. further revealed that
x
3
1-x
[17]
the local lattice distortion plays a very important role in the NTE of Mn Cu Ge N [Figure 8B]. As
1-x
x
3
suggested by the pair distribution function (PDF) analysis, Mn Cu Ge N maintains a cubic structure within
x
1-x
3
a certain doping range, while the Mn N octahedrons in Mn Cu Ge N rotate along the z-axis with Ge
3
1-x
6
x
doping to form a local lattice distortion. This structural instability displays a strong correlation with the
broadness of the growth of the ordered magnetic moment, which is considered as a trigger for broadening
the volume change . Moreover, Tong et al. studied the magnetic transition broadening and local lattice
[18]
distortion in Mn Cu Sn N with NTE . The PDF results indicate that the distribution of Cu/Sn-Mn bonds
[19]
x
1-x
3
is linked to the fluctuations of the AFM integral. This may account for the broadening of the volume change
in antiperovskites.
Through the study of Mn (Zn, M) N(M = Ag, Ge), we revealed the quantitative relationship between
x
3
thermal expansion and atomic magnetic moments in antiperovskites and realized the regulation of thermal
expansion . A collinear AFM structure M and a non-collinear AFM structure Γ are observed in
[20]
5g
PTE
Mn Zn N. Herein, the M phase displays PTE behavior, while the Γ configuration shows NTE behavior.
5g
x
3
PTE
5g
The NTE of Γ phase can balance the contributions from PTE generated by the anharmonic vibration in the
sample, producing the ZTE of antiperovskites. By introducing vacancies into Mn Zn N, the existence of a
x
3
temperature range for Γ configuration can be effectively regulated, thereby obtaining a ZTE material with a
5g
wider temperature range. In addition, we also discussed the quantitative relationship between the
anomalous change of the lattice and the atomic magnetic moments for the Γ phase. As shown in Figure 8C,
5g
both the lattice change a - a and the atomic magnetic moment m in Mn Zn N gradually decrease with
3
x
T
NTE
the increase of temperature, and the change trends for both factors are consistent. By defining
r(T) = (a - a )/m, it is obtained that r(T) hardly changes with temperature where a , a and m are the
NTE
T
T
NTE
lattice constants and magnitude of the ordered magnetic moment, which confirms that there is a strong