Inﬂuence of Thermal and Magnetic History on Direct ∆ T ad Measurements of Ni 49 + x Mn 36 − x In 15 Heusler Alloys

: In the present work, using Heusler Ni 49 + x Mn 36-x In 15 (with x = 0 and 0.5) alloys, it is shown that the choice of the appropriate measurement protocol (erasing the prior state of the sample in between experiments) in ∆ T ad ﬁrst shot characterization is crucial for obtaining reliable results. Unlike indirect measurements, for which incorrect protocols produce overestimates of the characteristics of the material, erroneous direct measurements underestimate ∆ T ad in the region close to its ﬁrst order phase transition. The error in ∆ T ad is found to be dependent on the temperature step used, being up to ~40% underestimation, including a slight shift in its peak temperature.


Introduction
Magnetic materials, when adiabatically subjected to magnetic field changes, can undergo significant adiabatic temperature change (∆T ad ) ascribed to the magnetocaloric (MC) effect [1][2][3]. This effect constitutes the basis of magnetic refrigeration, an emergent environmental-friendly refrigeration alternative (50% more energy efficient than conventional systems) [4]. Nowadays, the basic study and optimization of MC materials and devices is a hot topic for the scientific community [5][6][7]. The maximum MC response is obtained close to a thermomagnetic phase transition, either first-(FOPT) or second-order (SOPT), being this a common criterion categorizing the materials. In the former case, it corresponds to a discontinuity in the first derivative of the free energy (with phase coexistence during the transition and hysteretic behavior) while a SOPT is associated to a discontinuity in the second derivative of the free energy (in this case, its resultant phase variation is continuous and reversible) [8]. To date, there are several promising MC materials being considered. Historically, Gd was the first material to demonstrate that magnetic refrigeration can serve as a real alternative to the conventional refrigeration systems though its high price and limited availability impeded further advances in commercialization of magnetic refrigerators [9]. Nowadays, there are other well-regarded MC material candidates with large MC responses that can surpass that of Gd, which include Gd 5 (Si,Ge) 2 [10], MnFe(P,As) [11,12], La(Fe,Si) 13 [13,14], or Heusler alloys [15][16][17][18]; all of them belong to the FOPT type.
Hence, the appropriate performance evaluation is crucial for MC materials as that would determine their suitability for their technological application [19]. For FOPT MC materials, temperature and field variations are irreversible due to the intrinsic hysteresis of the transition [20,21]. This implies that the Metals 2019, 9, 1144 2 of 8 partial transformation of the sample from previous measurement conditions could persist for subsequent measurements within its hysteretic range. This has been brought up when performing the continuous measurements for the indirect MC determination of the isothermal entropy change (∆S iso ) as spurious peaks are found [22,23]. Therefore, it is important to consider the effects of partial transformations after each measurement and erase them to obtain physically meaningful data (usually termed as discontinuous protocols). This is made by cooling/heating well below/above the transition before proceeding to the next measurement. This process is also accompanied with an appropriate value of the magnetic field (depending on the particular phase to be stabilized). It should be stressed that these protocols refer to a first shot characterization to obtain information about the material's nature, however, it can be also evaluated in cycled conditions to examine the technological capacities [24,25].
In this work, the effect of the different measurement protocols on the direct ∆T ad measurements is studied for two polycrystalline Heusler alloys (nominal compositions Ni 49 Mn 36 In 15 and Ni 49.5 Mn 35.5 In 15 ) exhibiting martensitic (FOPT) and Curie (SOPT) transitions (being a good test material for our purpose). We observe that ∆T ad values can be severely underestimated when using continuous protocols instead of discontinuous ones, whereby discrepancies as high as up to 40% are observed in the region close to the martensitic transition. In addition, it is found that the protocol application becomes more crucial with increasing thermal hysteresis span as compared to the temperature step used in the measurements.

Methods
The direct MC effect of the samples was characterized using a direct ∆T ad measurement system, whereby the sample chamber is maintained in vacuum (10 −5 mbar) and its temperature is controlled by a Lake Shore Cryotronics temperature controller. The variable magnetic field generator is composed of two concentric Hallbach cylinders with a maximum magnetic field of 1.76 T. The temperature change of the sample produced by the application/removal of a magnetic field is registered using a type T thermocouple in differential configuration, with its reference weld located in contact with the sample holder. Due to their composition, type T thermocouples do not have a magnetic field-dependent response. The other weld of the thermocouple is located between two pieces of sample with rectangular shape. The different measurement protocols were automated using our in-house implemented software with appropriately adjusted PID (Proportional-Integral-Derivative) parameters for the temperature controller (to avoid thermal oscillations around the selected temperature).

Results and Discussion
The chosen alloys exhibit low-temperature martensite transforming to austenite at higher temperatures from both microstructural and magnetic observations. Further details of their synthesis, structural characterization, and magnetocaloric properties can be found in References [26,27]. Their temperature dependence of magnetization is shown in Figure 1a for which various magnetic phase transitions upon heating can be observed: a martensitic (martensite to austenite) transition (FOPT) followed by a Curie transition of the austenitic phase at higher temperatures (SOPT). It can be observed that small compositional changes can significantly affect the martensitic transition (in agreement with literature) [28]. With respect to direct ∆T ad measurements, Table 1 shows the different discontinuous protocols used in this work to perform the direct measurements. In the case of continuous protocols, the samples are neither cooled down nor heated up to the end of the transformation after the measurement at a selected temperature. The protocols have been selected taking into account that the martensitic transition of the alloys is shifted to lower temperatures under an applied magnetic field (magnetic field stabilizes the austenitic phase) [15]. It can be noted that the characterization protocols used are in conjunction with those proposed for indirect MC measurements of FOPT MC materials. results of Ni49.5Mn35.5In15 show slight differences for the two measurement protocols in the region close to the martensitic transition while in the region close to the ferro-paramagnetic transition there are no differences. This is further magnified in the inset of Figure 2 using the temperature dependence of δΔTad (where δΔTad = ΔTad (continuous) − ΔTad (discontinuous)), however, the error bars avoid any detailed discussion. In addition, similar features are observed for the ΔTad results using both protocols while heating (not shown).

Heating
Cooling Set the temperature well below the martensitic transition at low field Set the temperature well above the martensitic transition at high field Set the desired measurement temperature Set the desired measurement temperature Measure ΔTad from low to high field Measure ΔTad from high to low field Repeat the steps before measurement at a different temperature Repeat the steps before measurement at a different temperature Figure 3 shows the temperature dependence of ΔTad at 1.76 T while heating using discontinuous and continuous measurement protocols with a temperature step of 5 K for Ni49Mn36In15 alloy. In this case, the heating protocol was used with a reset temperature of 200 K and zero field, well below the martensitic transition around 260 K. For this sample, significant differences in the two curves with and without accounting for its history are observed (further magnified by δΔTad in the inset of Figure  3). The ΔTad values associated to the martensitic transition are underestimated using the continuous protocol (maximum differences ≈ 20% are obtained around the peak temperature of ΔTad, ), while

Heating Cooling
Set the temperature well below the martensitic transition at low field Set the temperature well above the martensitic transition at high field Set the desired measurement temperature Set the desired measurement temperature Measure ∆T ad from low to high field Measure ∆T ad from high to low field Repeat the steps before measurement at a different temperature Repeat the steps before measurement at a different temperature The temperature dependence of ∆T ad at 1.76 T while cooling using discontinuous (i.e., erasing the memory of the sample between measurements) and continuous (i.e., not erasing it) measurement protocols with a temperature step of 5 K for Ni 49.5 Mn 35.5 In 15 sample is shown in Figure 2. Two peaks are clearly observed, which correspond to the martensitic and Curie transitions (around 295 K and 320 K, respectively). The former response is larger than the second one, although it happens in a narrower temperature range (as expected from the characteristics of each transition, i.e., an abrupt change for FOPT and a gradual change for SOPT). A magnetic field sweep rate of 0.5 T s −1 was selected for both samples. The discontinuous protocol was applied by subjecting the sample to a reset temperature of 350 K and 1.76 T (which is well above its martensitic transition of~295 K). Error bars correspond to the precision of the system (close to room temperature ≈ 0.06 K). The different ∆T ad results of Ni 49.5 Mn 35.5 In 15 show slight differences for the two measurement protocols in the region close to the martensitic transition while in the region close to the ferro-paramagnetic transition there are no differences. This is further magnified in the inset of Figure 2 using the temperature dependence of δ∆T ad (where δ∆T ad = ∆T ad (continuous) − ∆T ad (discontinuous)), however, the error bars avoid any detailed discussion. In addition, similar features are observed for the ∆T ad results using both protocols while heating (not shown). sample, explaining why the differences between discontinuous and continuous protocols are more significant for this alloy (the discussion of the different hysteresis mechanisms is beyond the scope of this work). Furthermore, in agreement with the previous argument, the observed thermal hysteresis span between cooling and heating curves is larger for the Ni49Mn36In15 sample than for the Ni49.5Mn35.5In15 one, ≈12 and 6 K, respectively, which in the latter case is quite close to the selected temperature steps. To evaluate the influence of the temperature step on the direct measurements, a finer temperate step resolution of 2.5 K was used. It can be observed that the influence of the protocol on ΔTad while cooling becomes more significant near the martensitic transition of Ni49Mn36In15 sample (for which the effects are more evident) with decreasing the temperature step (5 and 2.5 K are used for comparison), as shown in Figure 4. For the cooling protocol, a reset temperature of 350 K and a magnetic field of 1.76 T were chosen. The underestimation of ΔTad peak associated to martensitic transition increases to ~40% (a two-fold increase in comparison to the 5 K step measurements). With this finer resolution of the ΔTad curves, the peak temperature slightly shifts to higher temperatures when using continuous protocols. In addition, in the case of using discontinuous protocols (either for cooling or heating curves), the different ΔTad measured points are independent of the temperature step resolution, as expected.  Figure 3 shows the temperature dependence of ∆T ad at 1.76 T while heating using discontinuous and continuous measurement protocols with a temperature step of 5 K for Ni 49 Mn 36 In 15 alloy. In this case, the heating protocol was used with a reset temperature of 200 K and zero field, well below the martensitic transition around 260 K. For this sample, significant differences in the two curves with and without accounting for its history are observed (further magnified by δ∆T ad in the inset of Figure 3). The ∆T ad values associated to the martensitic transition are underestimated using the continuous protocol (maximum differences ≈ 20% are obtained around the peak temperature of ∆T ad , T pk ), while the curves are relatively similar in the region close to the ferro-paramagnetic SOPT. In addition, the differences between their cooling ∆T ad (T) curves using both protocols are also notable, in agreement to those observed from the heating protocol. To establish a comparison between both samples, it is important to note that the mass and shape of both samples are quite similar, in order to avoid the influence of these parameters in the general conclusions. With respect the hysteretic behavior, Figure 1b shows the magnetization/demagnetization curves at selected temperatures close to the martensitic transition for both samples. The hysteresis can be associated with the area enclosed between magnetization/demagnetization curves, being 50.2 and 9.6 A m 2 kg −1 T −1 for the Ni 49 Mn 36 In 15 and Ni 49.5 Mn 35.5 In 15 , respectively. According to this, the magnetic hysteresis is larger for the Ni 49 Mn 36 In 15 sample, explaining why the differences between discontinuous and continuous protocols are more significant for this alloy (the discussion of the different hysteresis mechanisms is beyond the scope of this work). Furthermore, in agreement with the previous argument, the observed thermal hysteresis span between cooling and heating curves is larger for the Ni 49 Mn 36 In 15 sample than for the Ni 49.5 Mn 35.5 In 15 one, ≈12 and 6 K, respectively, which in the latter case is quite close to the selected temperature steps.    To evaluate the influence of the temperature step on the direct measurements, a finer temperate step resolution of 2.5 K was used. It can be observed that the influence of the protocol on ∆T ad while cooling becomes more significant near the martensitic transition of Ni 49 Mn 36 In 15 sample (for which the effects are more evident) with decreasing the temperature step (5 and 2.5 K are used for comparison), as shown in Figure 4. For the cooling protocol, a reset temperature of 350 K and a magnetic field of 1.76 T were chosen. The underestimation of ∆T ad peak associated to martensitic transition increases to~40% (a two-fold increase in comparison to the 5 K step measurements). With this finer resolution of the ∆T ad curves, the peak temperature slightly shifts to higher temperatures when using continuous protocols. In addition, in the case of using discontinuous protocols (either for cooling or heating curves), the different ∆T ad measured points are independent of the temperature step resolution, as expected.
It should be noted that, in contrast to the case of indirect ∆S iso measurements, wherein an overestimation of the response is obtained when using continuous protocols, the effect on direct ∆T ad measurements is a reduction of the response. This difference is due to the application of the Maxwell relation for determining ∆S iso . The different fraction of phase transformation (due to a temperature variation) at the initial magnetic field, when compared to the one in an isofield curve, leads to an artificial increment of the magnetization change that produces a spurious spike in ∆S iso data. In contrast, for ∆T ad measurements, the deviations are ascribed to the irreversibility of the magnetization/demagnetization path which leads to a reduction of the transformed para-ferro fraction, reducing the ∆T ad values. Using a finer temperature step, the differences of the amount of transformed fraction ascribed to the irreversibility increases as the number of measurements increase (each measurement contributing to the total amount of transformed phase), magnifying the error of the continuous protocol.

Conclusions
To conclude, the effect of the measurement protocols on the direct measurement of ∆T ad has been studied using Ni 49+x Mn 36-x In 15 Heusler alloys (x = 0 and 0.5). For measurement protocols that do not take into account the history of the sample (i.e., continuous protocols), underestimations of ∆T ad values were obtained in the region close to the martensitic FOPT, including a slight shift in its peak temperature. These errors in the measurement are shown to be highly dependent on the hysteretic temperature span with respect to the temperature step used for the measurements (discrepancies up to 40% are observed for the studied sample). Reducing the temperature step, instead of enhancing the reliability of the results, enhances the problem, which is counter-intuitive and relevant for designing appropriate characterization methods. This reduction of the experimentally measured ∆T ad when a continuous protocol is used is in contrast with the overestimation of ∆S iso when the history of the sample is also neglected. The results presented here clearly illustrate the importance of considering discontinuous measurement protocols to accurately determine the magnetocaloric response of FOPT materials even for direct methods.