Improving barocaloric properties by tailoring transition hysteresis in Mn₃Cu$_{1-x}$Sn$_{x}$N antiperovskites

The variation of the transition temperature as a function of x, determined using either magnetometry, DSC or X-ray diffraction, is shown in figure 1(a) and is in excellent agreement with previously reported data [14].

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Lab-based x-ray diffraction confirmed the presence of Bragg reflections consistent with the antiperovskite structure for all samples, with a minority phase of MnO that is challenging to eliminate in these materials. Further analysis of the crystal structure was performed for $0.35 \lt x \lt 0.465$ using powder synchrotron diffraction as a function of temperature. A typical diffractogram and Rietveld refinement is shown in figure 1(b) for the sample x = 0.435. An excellent fit is achieved with the expected antiperovskite structure ($Pm\overline{3}m$, Cu/Sn Wyckoff 1a, N 1b and Mn 3c) and the refined fractional occupancies of Sn and Cu were close to the nominal values for all samples (see table S1 in the SI).

Synchrotron data were collected as a function of temperature in order to determine the relative volume change, $\Delta V/V$, for each sample. A typical thermodiffractogram is shown in figure 1(c), demonstrating a phase transition with a large peak position shift and a phase coexistence region where two clear peaks are evident. The refined volume change, $\Delta V/V$, for all measured samples is shown in figure 1(d). All samples demonstrate similar temperature dependence with $0.5 \lt \Delta V/V \lt 0.7$% at the PM-AFM transition However, it is clear that the transitional volume change decreases with increasing x (see table 1), as expected from previous results [14]. A remarkable observation from this plot is that the paramagnetic phase of all samples shows a significantly enhanced thermal expansion in the phase coexistence region (see dash dot lines in figure 1(d)). We had observed signs of similar behaviour in the material Mn₃Zn_0.5In_0.5N, although it was inconclusive [18]. Here, the behaviour is much clearer although its origin remains an open question.

Table 1. Properties relevant to the barocaloric effects of Mn antiperovskites and other metallic barocaloric systems. For the latter, where a number of related materials exist, the member with the lowest hysteresis is shown here. Transition temperature, $T_{\mathrm{t}}$; relative transitional volume change, $\Delta V/V$; sensitivity of the transition to pressure, $\frac{\mathrm{d}T_{\mathrm{t}}}{\mathrm{d}p}$; thermal hysteresis of materials studied in this work were determined as described in the text, $\Delta T_{\mathrm{hys}}$; transitional entropy change, $\Delta S_{\mathrm{t}}$; minimum reversible pressure calculated from the ($T,p$) phase diagram, $p_{\mathrm{rev}}$, as the value for which the endothermic transition temperature is equal to the exothermic transition temperature at atmospheric pressure. Values of $p_{\mathrm{rev}}$ in parenthesis were estimated from $p_{\mathrm{rev}} = \Delta T_\mathrm{hys}(\mathrm{d}T/\mathrm{d}p)^{-1}$ according to [20].

	$T_{\mathrm{t}}$ (K)	$\lvert\Delta V/V\rvert$ ($\%$)	$\frac{\mathrm{d}T_{\mathrm{t}}}{\mathrm{d}p}$ (K GPa−1)	$\Delta T_{\mathrm{hys}}$ (K)	$\lvert\Delta S_{\mathrm{t}}\rvert$ (J K−1 kg−1)	$p_{\mathrm{rev}}$ (MPa)	References
Mn3NiN	262	0.40	13.5	4	52	600	[12]
Mn3GaN	290	1.00	−65	6	22	(92)	[11]
Mn3ZnN	180	1.50	−70	8	39	(114)	[14, 18, 21]
Mn3PdN	290	0.20	−14	2	30	150	[22]
Mn3Zn0.5In0.5N	300	0.9	−33	1	37	240	[18]
Mn3Cu0.65Sn0.35N	220	0.75	−42	1.3	25	40	This work
Mn3Cu0.58Sn0.42N	253	0.65	−40	0.5	22	20	This work
Mn3Cu0.565Sn0.435N	262	0.62	−39	0.5	22	20	This work
Mn3Cu0.55Sn0.45N	271	0.60	−37	0.3	22	50	This work
Mn3Cu0.535Sn0.465N	283	0.55	−37	0.4	21	80	This work
Ni0.85Fe0.15S	303	1.6	−75	11.5	53	(153)	[23]
MnNiSi0.61FeCoGe0.39	311	2.7	−70	4	63	175	[24]
MnCoGe0.99In0.01	310	4.4	−77	8	52	(104)	[25]
Fe49Rh51	310	1	60	10	12	150	[26]
Ni35.5Co14.5Mn35Ti15	249	1.6	58	7	40	$\gt$100	[27]
Ni1.99Mn1.37In0.64	329	0.6	19.5	4	40	$\gt$250	[7]
La1.2Ce0.8Fe11Si2H1.86	310	1.7	−260	∼1	—	50	[28]

Atmospheric pressure DSC measurements were performed to investigate the entropy changes at the magnetic transition across the series. The DSC data, as a function of temperature, for samples $0.35 \lt x \lt 0.465$ are shown in figure 2(a). The transition becomes broader with increasing x, particularly for x > 0.35, indicating increased phase coexistence in these samples. The measured transitional entropy change, $\Delta S_{\mathrm{t}}$, as a function of x is shown in figure 2(b). The trend of decreasing $\Delta S_{\mathrm{t}}$ with increasing x is perhaps expected based on both (i) the increased transition temperature and (ii) the observed trends in both $\Delta V/V$ and the width of the DSC peak in figure 2(a). Nonetheless, the changes in $\Delta S_{\mathrm{t}}$ are only 10%–20% across this range of samples, and the absolute value of $\Delta S_{\mathrm{t}}$ for the x = 0.465 sample is very similar to that found in Mn₃GaN ($\Delta S_{\mathrm{t}} = 22$ J kg⁻¹ K⁻¹, see table 1).

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For all samples, a striking feature of the DSC data in figure 2(a) is the remarkably small hysteresis of the transition. Measurement of the hysteresis was performed by taking data at different temperature ramp rates between 0.5 and 10 K min⁻¹. A linear fit to these datasets allowed extrapolation of the hysteresis to 0 K min⁻¹ (see figure S8). All samples have an extrapolated hysteresis of $\Delta T_{\mathrm{hys}} \lt 1.5$ K, with most samples having a hysteresis of ∼0.5 K. It is noteworthy that the transition temperature has a weak and linear dependence on the ramp rate (see SI figure S8) which indicates that the transition has a significant athermal character [29]. This is in stark contrast to the plastic crystal neopentyl glycol, which has recently been characterised as a promising barocaloric material [3]. Organic plastic crystals and other barocaloric pure compounds in general show significant isothermal character with a strong dependence of both the peak maximum temperature and peak width on the ramp rate.

To further characterise the samples at a microstructural level we performed EBSD along with EDS on a mechanically polished sample of Mn₃Cu_0.5Sn_0.5N (x = 0.5). An EBSD image with a horizontal field width of ∼100 µm captured over 1800 grains (see figure 3(a)) with a mean grain size of ∼4 µm, demonstrating that particle sizes were relatively large and disordering due to nanostructural effects can be ruled out. EDS data collected across this whole region gives a Mn:(Cu,Sn) ratio of 2.98:1 and a ratio of Cu:Sn of 1.05:1, demonstrating an excellent agreement to the nominal Mn₃Cu_0.5Sn_0.5N composition (N peaks in EDS lie at too low energy for reliable quantification). EDS data collected on a reduced region of ∼100 grains are shown in figures 3(b)–(f). The element with most variation across this region is Cu. From the colour scale in figure 3(c), it is clear that this variation occurs only in small regions (${\lt}5~\mu$m), localised between the larger antiperovskite grains. This is further demonstrated by the elemental variation line profile indicated in figure 3(f), which is plotted in figure 3(g). Here one can see that increase in Cu across the regions of smaller grains coincides with a decrease in Mn and little change in Sn; we propose that this is caused by a very small percentage of a separate third phase. The same line profile at the centre of the larger grains shows the expected 3:0.5:0.5 Mn:Cu:Sn ratio within error expected of the antiperovskite phase. Finally, a ternary phase diagram of Mn/Cu/Sn from the EDS data presented is shown in figure 3(h). Here one can see that the distribution of the stoichiometry is centred quite closely on the expected 3:0.5:0.5 Mn:Cu:Sn ratio. The slightly larger distribution in the Mn concentration is due to the presence of MnO particles. Taken together, the EBSD and EDS analyses demonstrate that the stoichiometry is close to that expected and that inhomogeneity in the Cu and Sn mixing between grains is not the cause of the low hysteresis.

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We now turn to pressure dependent heat flow measurements in order to explore the BCE. Measurements were performed for samples with $0.35 \lt x \lt 0.465$. Representative datasets for sample x = 0.435 are shown in figure 4. The remaining datasets are included in figure S3 and extracted parameters for all samples are provided in table 1. The background subtracted heat flow measurements are plotted in figure 4(a) for applied pressures $0 \lt p~(\mathrm{GPa}) \lt 0.6$. From these data we can plot the pressure-temperature phase diagram, figure 4(b), which (i) shows that the small hysteresis is maintained at high pressure due to the similarity of $\frac{\mathrm{d}T}{\mathrm{d}p}$ for endothermic and exothermic transitions and (ii) allows us to calculate the sensitivity of the transition, $\frac{\mathrm{d}T}{\mathrm{d}p} \sim -39$ K GPa⁻¹. Extracted from the data in figure 4(a) with the method explained in the SI, the entropy plotted as a function of temperature on cooling and heating is shown in SI figure S4 (see figure S5 for all analysed samples). Finally, using quasi-direct methods [3], we calculate the associated barocaloric isothermal entropy change, $\Delta S$, and adiabatic temperature changes, $\Delta T$. For each sample these values are plotted in SI figures S6 and S7.

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The reversible BCEs are summarised in figures 4(c)–(e). It can be noted that $\Delta S_\mathrm{rev}$ below the transition is very small (consistent with the nearly inverse behaviour in this temperature interval), $\Delta S_\mathrm{rev}$ across the transition is positive upon compression (consistent with the inverse effects due to $\frac{\mathrm{d}T}{\mathrm{d}p} \lt 0$) and $\Delta S_\mathrm{rev}$ above the transition is negative upon compression (consistent with the positive thermal expansion of the high-temperature phase). In turn, $\Delta T_\mathrm{rev}$ is displayed in figure 4(d) for decompression processes, for which it shows the same sign as $\Delta S_\mathrm{rev}$. Whilst the magnitudes of the BCEs are similar to previously reported values for Mn antiperovskites [11, 12, 22], the low hysteresis demonstrated in these Mn₃Cu$_{1-x}$Sn_x N samples results in reversible values of $\Delta S_{\mathrm{rev}}$ (figure 4(c)) and $\Delta T_{\mathrm{rev}}$ (figure 4(d)) being significantly larger.

Furthermore, we find significant reversible BCE even at pressures below 100 MPa due to the very low hysteresis, as demonstrated in figure 4(e) where $\Delta T_{\mathrm{rev}}$ for p = 80 and 140 MPa are shown. $\Delta T_\mathrm{rev}$ peaks at ∼1 K and ∼2 K for those pressure values.

We start by discussing the potential mechanisms underlying the low hysteresis of Mn₃Cu$_{1-x}$Sn_x N. It is useful to compare our results with other Mn₃ AN and Mn₃(A,B)N. As has previously been demonstrated, the end-members (x = 0 and x = 1) of the series Mn₃Cu$_{1-x}$Sn_x N do not display a 1st-order magnetic transition and therefore no concomitant volume change occurs [14]. As x is increased above ∼0.1, a sharp and large volume change occurs at the transition, which gradually weakens with increasing x although still remains until x = 0.7 [14]. Consequently, one might also expect the hysteresis to decrease with increasing x in this manner. The measured values of the transition hysteresis for all samples are shown in figure 5(a). A reduction of $\Delta T_{\mathrm{hys}}$ is observed on increasing x from low values, reaching a minimum at $x \sim 0.5$ and then increasing with further x doping. This suggests that $\Delta T_{\mathrm{hys}}$ is not simply linked to parameters related to the strength of the first-order transition, e.g. the magnitude of $\Delta V/V$, $\mathrm{d}T/\mathrm{d}p$ or $\Delta S_{\mathrm{t}}$ (see table 1). This behaviour is most apparent when plotting $\Delta V/V$ and $\mathrm{d}T/\mathrm{d}p$ against $\Delta T_{\mathrm{hys}}$, as we show in figure 5(b). Here we can see that for Mn₃ AN, $\Delta T_{\mathrm{hys}}$ correlates extremely well with both $\Delta V/V$ and $\mathrm{d}T/\mathrm{d}p$. In stark contrast is the behaviour of Mn₃Cu$_{1-x}$Sn_x N, where $\Delta V/V$ and $\mathrm{d}T/\mathrm{d}p$ are both comparable to those of Mn₃GaN and Mn₃NiN, yet $\Delta T_{\mathrm{hys}}$ is an order of magnitude smaller. Taken together these results suggest an additional mechanism underlies the x-dependence of $\Delta T_{\mathrm{hys}}$, unrelated to the magnetovolume coupling. A similar type of hysteresis reduction as a function of composition has been shown in austenite/martensite systems, in which low hysteresis was linked to minimisation of strain between the austenite and martensite phases [30]. Unlike the austenite/martensite system however, Mn₃Cu$_{1-x}$Sn_x N does not undergo a change in lattice symmetry through the solid–solid phase transition. Nonetheless, it has been shown that Vegard's law is not obeyed in Mn₃Cu$_{1-x}$Sn_x N system and an inflection is observed in the data for lattice constant as a function of concentration, x, around x = 0.5 [14]. It was argued that the cause of this was due to magnetic frustration suppressing spin fluctuations above $T_{\mathrm{N}}$ and therefore reducing the paramagnetic lattice volume. Thus, the magnetic frustration might assist the lattice contraction at $T_{\mathrm{N}}$, facilitating the transition between the two states and therefore reducing the hysteresis. This could be seen as analogous to the strain related mechanism in the austenite/martensite systems. On a fundamental level, investigating the cause of the low hysteresis in Mn₃Cu$_{1-x}$Sn_x N should be of great interest in the broader context of magnetostructural materials, given that the transitions in many of the materials listed in table 1 are magnetostructural in origin (except Ni_0.85Fe_0.15S) with largely similar transitional entropy changes.

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We continue the discussion by comparing our results for the Mn₃Cu$_{1-x}$Sn_x N series with other metallic barocaloric materials. To do so, table 1 contains $\Delta T_{\mathrm{hys}}$ for $A =$ Ni, Ga and Zn samples measured using the same method, in addition to several other metallic barocaloric systems obtained from recent reviews [1, 2]. From table 1 it is clear that Mn₃Cu$_{1-x}$Sn_x N materials display the smallest hysteresis among the metallic barocaloric systems studied so far. The only materials with $\Delta T_{\mathrm{hys}}$ of a similar order of magnitude are those of Mn₃PdN and La_1.2Ce_0.8Fe₁₁Si₂H_1.86 from recent studies [22, 28]. In Mn₃PdN, reversible effects are also observed at 90 MPa with $\Delta T_{\mathrm{rev}} \sim 1$ K. Interestingly, for this pressure the absolute change of $\Delta T_{\mathrm{rev}}$ in our study is ∼2 K, however the peak is reduced due to the different thermal expansion properties away from the transition (see figure 4(c)). In La_1.2Ce_0.8Fe₁₁Si₂H_1.86, a key difference is that the hysteresis increases significantly with applied pressure. Nonetheless, $\Delta T_{\mathrm{rev}}$ peaks at 8 K for this material under 100 MPa, although a direct comparison is made difficult due to the use of direct methods (unlike the quasi-direct method used in the present study). However, it should be noted that the Mn₃Cu$_{1-x}$Sn_x N system has reversibility pressures as low as 20 MPa (based on the ($T,p$) phase diagram) for x = 0.42 and 0.435. This is significantly lower than other comparable metallic systems that we were able to identify in the literature.

In general, our results further demonstrate that significant reversible BCE can be achieved in metallic systems driven by moderate pressures of p < 100 MPa. The extremely small hysteresis that can be engineered, combined with other properties such as high thermal conductivity, large density and chemical tunability, makes them attractive for potential applications. Specifically within the Mn₃(A,B)N family it has now been shown that the chemical flexibility allows the transition temperature, BCE and now the transition hysteresis to be tuned. However, only a small part of this chemical phase space has been explored and further improvements may be possible.