Tuning the range, magnitude, and sign of the thermal expansion in intermetallic Mn${}_3$(Zn, $M$)${}_x$ N($M$ $=$ Ag, Ge)

Neutron diffraction is used to reveal the origin and control of the thermal expansion properties of the cubic intermetallic compounds Mn${}_3$Zn${}_x$N and Mn${}_3$[Zn-(Ag,Ge)]${}_x$N. We show that the introduction of Zn vacancies induces and stabilizes an antiferromagnetic phase with huge spin-lattice coupling that can be tuned to achieve zero thermal expansion (ZTE) over a wide temperature range. We further show that the antiferromagnetic ordering temperature ($T_N$) that controls this ZTE can be tuned by chemical substitution, again on the Zn site, to adjust the span of ZTE temperatures from well above room temperature to well below. This establishes a quantitative relationship and mechanism to precisely control the ZTE of a single material, enabling it to be tailored for specific device applications.

Figure 1

(a)–(c) Observed crystal and magnetic phases for Mn${}_3$Zn${}_x$N. (d)–(f) Temperature dependence of the cubic lattice constant for three values of Zn vacancies. All three samples are paramagnetic (PM) above 185 K with a cubic crystal structure. The $M_{\mathrm{NTE}}$ phase has the magnetic structure shown in (b), which for Zn99 is present between 185 and 135 K. (e) $M_{\mathrm{NTE}}$ temperature range is enlarged (185–120 K) for the Zn96 sample, with a complete PM to $M_{\mathrm{NTE}}$ transformation. The $M_{\mathrm{PTE}}$ phase is stable below 120 K. (f) For the Zn93 sample the $M_{\mathrm{NTE}}$ phase is stabilized in the entire temperature range below the PM-$M_{\mathrm{NTE}}$ transition at 185 K. In all three compounds the $M_{\mathrm{NTE}}$ phase has very small thermal expansion with α < 10${}^{-6}$ K${}^{-1}$. An external pressure of 0.55GPa (△) converts $M_{\mathrm{NTE}}$ to $M_{\mathrm{PTE}}$, or $M_{\mathrm{PM}}$ at higher $T$, where $a_{\mathrm{PM}}$ and $a_{\mathrm{PTE}}$ form the usual smooth curve observed in the Zn99 and Zn96 samples, without a detectable anomaly at the $M_{\mathrm{PTE}}$-PM transition.

Figure 2

Relationship between the lattice variation and phase fractions for sample Zn99. The $M_{\mathrm{NTE}}$ phase is present between 185 and 135 K. The transition from PM to $M_{\mathrm{NTE}}$ is incomplete; an 83$\%$ M${}_{\mathrm{NTE}}$ phase coexists with the PM phase between 185 and 160 K, and the $M_{\mathrm{NTE}}$ phase fraction decreases gradually on further cooling and coexists with the $M_{\mathrm{PTE}}$ phase between 160 and 135 K. Solid symbols represent phase fractions and open symbols depict lattice constants. Curves are guides to the eye.

Figure 3

(a)–(c) Relationship between the lattice variation $a_{\mathrm{NTE}}$-$a_T$, ordered magnetic moments, and $r$($T$) for three Zn occupancies. The data for (a) Zn99, (b) Zn96, and (c) Zn93 show that the temperature variation of the lattice parameter is proportional to the ordered magnetic moment in the $M_{\mathrm{NTE}}$ phase due to the presence of strong magnetoelastic coupling.

Figure 4

Temperature dependence of the cubic lattice parameter and ordered moment in Mn${}_3$Zn${}_{0.41}$Ag${}_{0.41}$N and Mn${}_3$Zn${}_{0.5}$Ge${}_{0.5}$N. (a) shows the lattice parameter and (b) the ordered magnetic moment for Mn${}_3$Zn${}_{0.41}$Ag${}_{0.41}$N, demonstrating the ZTE behavior, with $r$($T$) essentially constant. (c) Lattice parameter and phase fraction for Mn${}_3$Zn${}_{0.5}$Ge${}_{0.5}$N, with an antiferromagnetic ordering temperature adjusted to 530 K.