J. Phys. D: Appl. Phys. 44 (2011) 395001

V Sanchez´-Alarcos et al

Figure 7. Magnetically induced entropy change (Sm) at the MT under an applied field of 60 kOe, as a function of the temperature.

are plotted in figure 7 as a function of the temperature. In both cases Sm show a negative peak (direct MCE) around 300 K associated with the negative value of ∂M/∂T at the paramagnetic–ferromagnetic transition (see figure 5), as well as a positive peak (inverse MCE) in the temperature range

corresponding to the reverse MT. The maximum values areSm = 8.4 J kg−1 K−1 and Sm = 1.4 J kg−1 K−1 for the ternary and quaternary alloys, respectively. The MCE in

the ternary alloy is similar to the MCE values observed in other Ni–Mn–In alloys showing similar compositions [11, 39], although somewhat lower than the maximum values reported in Ni–Mn-based metamagnetic shape memory alloys, Sm 30 J kg−1 K−1 [9]. Nevertheless, it can be seen that the MCE in Ni–Mn–In is also considerably reduced by the Cr addition, thus leading to an undesirable reduction in the refrigerant capacity of these alloys.

The entropy change due to the application of a magnetic field in a system undergoing a first-order magnetostructural MT is associated with the transformation entropy change at the magnetically induced MT, in such a way that the limit value of the MCE is Sm = S. Therefore, the MCE depends on the applied magnetic field, the field-induced MT temperature shift and the width of the MT temperature range, as recently proposed [39]. In our case, the MT spreads over T = 27 K and T = 46 K in the Cr0 and Cr4 alloys, respectively. Likewise, the fractions of the magnetically induced reverse MT estimated from the ratios between the MT temperature shift under a 60 kOe magnetic field ( Tm) and the MT temperature range ( T )

are ( Tm/ T ) =	5.4	= 0.2 and ( Tm/ T ) =	3.6	= 0.08 for
	27		46

the Cr0 and Cr4 alloys, respectively (where Tm has been calculated from the respective dTm/dH values). Now, if we compare the magnetic entropy change calculated from equation (2) with the total transformation entropy changes in

table 2, the corresponding ratios are ( Sm/ S) =				8.4	= 0.23
				36
and ( Sm/ S) =	1.4	= 0.05,	for the Cr0 and Cr4 alloys,
	28

respectively, which are in very good agreement with theTm/ T values. Then, the assumption that the magnetically

induced entropy change is linked to the induction of the MT is confirmed in the studied alloys. In this sense, the low MCE observed in the Cr-doped alloy can be attributed to a low induction of the MT, which results from both the low dTm/dH and the high T (with respect to the Cr0 alloy) associated with the appearance of a second phase and to the negative effect of Cr in the ferromagnetic exchange. Therefore, it can be concluded that the addition of high amounts of chromium to Ni–Mn–In may be highly detrimental to the achievement of large MCE and large magnetically induced MT shifts, and thus to the potential applicability of these alloys.

4. Summary and conclusions

The effect of the partial substitution of Mn by Cr on the structural and magnetic properties of Ni–Mn–In metamagnetic shape memory alloys has been investigated. It is found that a Cr-rich second phase appears for Cr concentrations as low as 2% (at%), pointing to an extraordinary low solubility of Cr in Ni–Mn–In. The fraction and the morphology of the appearing second phase drastically evolve with the increasing amount of Cr. In turn, the MT temperature of the doped alloys can be related to the variation in the electron concentration in the matrix phase, just as it occurs in the ternary Ni–Mn–In system, irrespective of the Cr concentration. The effect of magnetic field on the structural transformation has been evaluated on both a ternary and a quaternary alloy. It is shown that the presence of the second phase reduces the magnetically induced shift of the MT and the associated MCE, thus limiting the potential applicability of Ni–Mn–In alloys. The obtained results prevent the addition of high amounts of Cr to Ni–Mn–In.

Acknowledgments

This work has been carried out with the financial support of the Spanish ‘Ministerio de Ciencia y Tecnolog´ıa’ (Project number MAT2009-07928).

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