Experimental techniques

A polycrystalline ingot of Ni₄₅Mn₄₃CoSn₁₁ was prepared by arc-melting in a high-purity argon atmosphere. The ingot was re-melted four times, subsequently annealed at 1123 K for 24 h under vacuum, and then slowly cooled to room temperature. The magnetic properties were measured at temperatures ranging from 5 to 400 K in magnetic fields up to 5 T using a Quantum Design superconducting quantum interference device magnetometer (SQUID). Differential scanning calorimetry (DSC) measurements were carried out employing a Perkin-Elmer DSC 8000 instrument in the temperature range 123–473 K. The latent heat (L) was estimated from the endothermic peak of the heat flow curve from the DSC measurements. During the hydrostatic pressure measurements, the value of the applied pressure was calibrated by measuring the shift of the superconducting transition temperature of Pb used as reference manometer (T _C ≈ 7.2 K at ambient pressure).^[ Reference Eiling and Schilling ^{13 ]} Heat capacity measurements were done in fields up to 5.0 T using a Physical Properties Measurement System (PPMS) by Quantum Design. Samples were affixed using a thin layer of grease to the sample platform, which was mounted on a vertical adapter to conduct the measurements in non-zero magnetic fields.

Results and discussion

The magnetization data M(T) for Ni₄₅Mn₄₃CoSn₁₁ measured in 0.01 T applied magnetic fields obtained at different applied hydrostatic pressures are shown in Fig. 1. The sharp changes in magnetization in the M(T) curves above 200 K are associated with a MST from a low-magnetization MP to a high-magnetization ferromagnetic AP. The first-order transition temperature (T _M) was highly sensitive to pressure, with shift of about +40 K for a pressure P = 1.06 GPa (or about +4 K/Kbar). The applied pressure shifts the MST temperature close to room temperature (T _M = 298 K at P = 0.73 GPa). With the increase in pressure, the temperature of martensitic transition is also found to linearly increase.

Figure 1.

The magnetization versus temperature M(T) curves of Ni₄₅Mn₄₃CoSn₁₁ measured at different applied hydrostatic pressures (P) in applied magnetic field of H = 0.01 T.

The MST occurred at a lower temperature with the application of higher field as shown in Fig. 2(a). External magnetic field found to act opposite of pressure direction and shift MST to low temperature region. A shift in T _M by about 15 K has been detected with H = 5 T [see Fig. 2(a)]. Therefore, the magnetic field and applied hydrostatic pressure provide shifts T _M in opposite directions, as the applied pressure stabilizing the martensite phase at higher temperature and the applied magnetic field attempts to stabilize the cubic austenite phase. Figure 2(b) shows the M(H) curves at low temperature (5 K) obtained under applied pressures up to 1.06 GPa. These M(H) data indicates that the ground state in the MP are characterized by a magnetization of 33–35 emu/g, which is much lower than of the austenitic phase. Increasing pressure results in an increase in magnetization. Hence, the application of pressure changes the magnetic ground state and increases the temperature stability of the MP. These results are consistent with those obtained for Ni-Co-Mn-Sb, where the application of external pressure kept T _C constant and resulted in a significant increase in the martensitic transformation temperature.^[ Reference Nayak, Suresh, Nigam, Coelho and Gama ^{14 ]}

Figure 2.

(a) M(T) curves of Ni₄₅Mn₄₃CoSn₁₁ measured at atmospheric pressure and applied pressure P = 1.06 GPa in applied magnetic field of H = 5 T. (b) The M(H) curves at T = 5 K obtained at different applied pressures.

The first order nature of the phase transitions was also detected in the DSC measurements [see Fig. 3(a)]. The well-defined peaks during heating and cooling cycles are related to the latent heat of the first-order MST. The thermal hysteresis between heating and cooling cycles verifies the first order nature of the martensitic transition. The latent heat of the MST and corresponding total entropy changes estimated from the DSC curves were 8.7 J/g and 30 J/(kgK), respectively. These values are similar to those observed in Ni-Mn-In based Heusler alloys.^[ Reference Pandey, Aryal, Quetz, Samanta, Dubenko, Stadler and Ali ^{15 ]} Also, the total entropy changes calculated from the DSC data are in good agreement with the “universal” temperature dependence of entropy changes.^[ Reference Gottschall, Skokov, Benke, Gruner and Gutfleisch ^{16 ]}

Figure 3.

(a) DSC heat flow curves as a function of temperature for Ni₄₅Mn₄₃CoSn₁₁ obtained for cooling (open symbols) and heating (closed symbols) cycles. (b) Magnetization curves in the vicinity of T _M and T _C of Ni₄₅Mn₄₃CoSn₁₁ measured with increasing temperature for atmospheric pressure (open symbols) and applied pressure P = 0.73 GPa (closed symbols).

Isothermal magnetization curves M(H) curves of Ni₄₅Mn₄₃CoSn₁₁ at atmospheric pressure (P _atm) and applied pressure P = 0.73 GPa are shown in Fig. 3(b). The magnetization isotherms were found to be metamagnetic-like at temperatures near the MST and show behavior typical for ferromagnetic-paramagnetic transitions near T _C. The critical field of the direct metamagnetic transition increases under pressure. The initial susceptibility (dM/dH) in the low magnetic field region decreases with pressure. Such behavior can be related to an increase in the antiferromagnetic interaction due to a decrease in interatomic distance.

Figure 4(a) shows the thermal variation of the magnetic entropy change (∆S _M) for magnetic field changes ∆H = 2 T, 5 T and at pressures P = P _atm and 0.73 GPa. From the M(H) curves shown in Fig. 3(b), the ∆S _M values were estimated by using an integrated Maxwell relation.^[ Reference Tishin and Spichkin ^{17 ]} The sample exhibits inverse and direct MCEs at MST (T _M) and Curie temperature (T _C), respectively. Since the applied pressure affects the interatomic separation, and therefore the magnetic interactions, the magnetocaloric properties are expected to change with pressure. We found for Ni₄₅Mn₄₃CoSn₁₁ that the peak value of ΔS _M at the martensitic transition significantly increases under applied hydrostatic pressure. Positive magnetic entropy changes (i.e., inverse MCE) of 24 and 42 J/kg K were observed at martensitic transition for P = P _atm and 0.73 GPa, respectively for ∆H = 5 T. Ni₄₅Mn₄₃CoSn₁₁ alloy shows a larger magnetic entropy change with pressure (2.5 J/kgK/Kbar) in comparison with other reported Ni_21.5Mn_0.85Ga,^[ Reference Albertini, Kamarad, Arnold, Pareti, Villa and Right ^{18 ]} Ni₅₀Mn₃₄In₁₆,^[ Reference Sharma, Chattopadhyay and Roy ^{8 ]} Ni-Mn-Sn^[ Reference Muthu, Kanagaraj, Singh, Sastry, Ravikumar, Rao, Raja and Arumugam ^{19 ]} Heusler alloys. As it can be seen from Fig. 2(a), the magnetization of the AP at MST temperature increases with pressure. The reason for such behavior may be due to the decrease in crystal cell volume of the alloy under pressure. The change in the volume results in an increased stability of the MP with respect to temperature while the Curie temperature of martensitic (T _CM) and AP (T _C) remain almost unchanged [see Figs. 1 and 2(a)]. The applied pressure shifts the martensitic transition temperature to higher temperature with a paramagnetic or low magnetization MP, and the MST from the paramagnetic MP to the ferromagnetic AP occurs [see Fig. 2(a)]. The changes in the magnetic entropy produced by the transitions from the paramagnetic MP to the ferromagnetic AP were found to be larger than those from the ferromagnetic martensitic to the ferromagnetic AP. The inset of Fig. 4(a) shows that the inverse martensitic transition found to increase nearly linearly with increasing of pressure for field change of 0.1 and 5 T. The ΔS _M values were found to increase monotonically at FOT with external magnetic field for P = P _atm and 0.73 GPa [see Fig. 4(b)].

Figure 4.

(a) Magnetic entropy changes (∆S _M) as a function of temperature for Ni₄₅Mn₄₃CoSn₁₁ for a magnetic field changes of 2 T and 5 T at atmospheric pressure and applied pressure P = 0.73 GPa. The inset shows the inverse martensitic transition at different applied pressure for field change of 0.1 and 5 T. (b) Magnetic entropy changes as a function of applied magnetic field at the FOT and second order transition (SOT) for P = P _atm and 0.73 GPa.

The refrigeration capacity (RC) is one useful parameter used to quantify MCE properties. The maximum RC at a magnetic field 5 T at atmospheric pressure was found to be 240 and 130 J/kg at T _C and T _M, respectively. At P = 0.73 GPa, the RC values were found to be 260 and 180 J/kg at T _C and T _M, respectively. The refrigerant capacity increases under the effect of hydrostatic pressure.

For Mn-based alloys, the magnetic entropy changes calculated by the Clausis–Clapeyron and the Maxwell relations are observed to be similar.^[ Reference Zhang, Zhang, Yu, Liu, Xu, Liu, Chen, Cao and Wu ^{20 ]} The total entropy change using the Clausius–Clapeyron ratio is

(1) $$\displaystyle{{\Delta T} \over {\mu _0 \Delta H}} = - \displaystyle{{\Delta {\rm M}} \over {\Delta S_{\rm M}}} $$

where ∆T/μ _o∆H is the derivative of the temperature to the magnetic field, and ΔM is the change in the magnetization. Using the Clausius–Clapeyron equation, the maximum values of ΔS _M obtained were found to be 19.4 and 33 J/(kg K) for P = P _atm and 0.73 GPa, respectively. The MCE values obtained at MST are similar to those obtained from the DSC curves at ambient pressure.

The temperature dependent heat capacity (C _p) data of Ni₄₅Mn₄₃CoSn₁₁ at a magnetic field of 0 and 5 T are shown in Fig. 5(a). The heat capacities are characterized by λ-type anomalies typical for FOT at T = 270 K and 258 K at H = 0 and 5 T, respectively. Applied magnetic field suppresses the peak of the λ-type anomaly and shifted it to the lower temperature. The temperature of the MST obtained from the heat capacity and magnetization measurements are in good agreement. Because of the diffusionless character of the martensitic transition, configurational contributions to the specific heat are absent,^[ Reference Khovailo, Oikawa, Abe and Takagi ^{21 ]} thus the specific heat can be written as:

(2) $$C_{\rm P} = C_{{\rm el}} + C_{{\rm vib\;}} + C_{{\rm mag}} $$

where C _el, C _vib, C _mag represents the electronic, vibrational, and magnetic contributions, respectively. The electronic contribution based on the linear-T term^[ Reference Mizutani ^{22 ]} is

(3) $$C_{{\rm el}} = \displaystyle{\pi \over 3}^2 N_{\rm A} k_{\rm B}^{\rm 2} D(E_{\rm F} )T = \gamma T$$

where D(E _F) is the density of states at Fermi energy. The vibrational effect can be described using the Debye model^[ Reference Mizutani ^{22 ]} as,

(4) $$C_{{\rm vib\;}} = 9R(\theta _{\rm D} {\rm \vert} T)^3 \int_0^{\theta _{\rm D} /T} {\displaystyle{{x^4 e^x} \over {(e^x - 1)^2}} dx} \; $$

where θ _D is the Debye temperature and R is the ideal gas constant. Since the magnetic contribution is found to be very small at low temperature,^[ Reference Chernenko, Fujita, Besseghini and Perez-Landazabal ^{23 ]} we plotted C _p/T versus T ² at low temperature [see the inset of Fig. 5(a)] and fitted the data using the equation C _p(T) = γT + βT ², where γ and β are the electronic and vibrational coefficients, respectively. For zero external magnetic field, γ and β were found to be 0.0178 J/mol K² and 0.000232 J/mol K⁴, respectively. The obtained value of γ is similar to those observed in Ni₄₈Co₂Mn₃₅In₁₅ ^[ Reference Pathak, Dubenko, Xiong, Adams, Stadler and Ali ^{24 ]} and Ni₅₀Mn₃₆In₁₄.^[ Reference Chen, Bruno, Karaman, Huang, Li and Ross ^{25 ]} From the fitted values of γ and β, and using Eqs. (3) and (4), values of 7.5 states/eV/f. u. and 310 K were found for the density of electronic states and the Debye temperature, respectively.

Figure 5.

(a) Heat capacity (C _p) of Ni₄₅Mn₄₃CoSn₁₁ as a function of temperature at H = 0 and 5 T. The inset shows the low temperature C _p/T versus T ² linear fit data for H = 0 T. (b) The adiabatic temperature change as a function of temperature obtained from heat capacity data.

The adiabatic temperature change (∆T _ad) at ambient pressure was estimated from the temperature-dependent heat capacity measurements. The magnetic entropy changes were obtained from the heat capacity using

(5) $$S(T)_{0,H} = \int_0^H {\displaystyle{{C_{\rm p} (T,H) - C_{\rm P} (T,0)} \over T}\; dT} $$

where C _p(T, 0) and C _p(T, H) represent the heat capacity in a field zero and H, respectively. Note that this relation comes from the fundamental thermodynamics without using Maxwell or Clausius–Clapeyron relations. Hence, it is valid whether the transition is first or second order. From S(T)_0,H , ∆T _ad can be obtained by taking the difference of T (S, H) at different fields at constant entropy.^[ Reference Gschneidner, Pecharsky and Tsokol ^{1 ]} Figure 5(b) shows the estimated ΔT _ad from heat capacity measurements for a field change of 5 T. An inverse ΔT _ad with a value of 4 K was calculated at T _M. This value of ΔT _ad is consistent with the large adiabatic temperature changes (about 1.2 K/T) obtained from direct measurements of ∆T _ad for the Ni-Mn-In-B system.^[ Reference Pandey, Quetz, Aryal, Dubenko, Blinov, Rodionov, Prudniko, Mazumdar, Granovsky, Stadler and Ali ^{26 ]}