Comparative analysis of magnetic and caloric determinations of the magne-tocaloric effect in Mn 0 . 99 Co 0 . 01 As

The results from direct and indirect determinations of the magnetocaloric parameters of Mn0.99Co0.01As have been analyzed. The isothermal entropy change (ΔS T ) due to external magnetic field changes has been determined through direct measurements of the heat absorbed by the sample when the field is removed under isothermal conditions. It has also been calculated from isothermal magnetization and isofield heat capacity measurements. In addition to that, the adiabatic temperature change (ΔTS ) has been obtained from direct measurements and from isofield heat capacity measurements. The different results of both ΔS T and ΔTS are compared. Due to the presence of a first-order phase transition, the studied sample exhibits giant magnetocaloric effect at room temperature. The observed maximum values, −ΔS T,max = 32.1 J/kg·K and ΔTS ,max = 17.7 K for a field change from 0 to 6 T, suggest that the Co-doped MnAs compounds are promising candidates for the preparation of useful materials for magnetic refrigeration near room temperature.


Introduction
Magnetic refrigeration based on the magnetocaloric effect (MCE) has been proposed as a competitive cooling technology to replace the conventional vapor-compression refrigeration due to low environmental impacts and high energy efficiency.In the past years, much attention has been paid to magnetic refrigeration near room temperature.To achieve that, one of the most important subjects is to find out materials with large MCE.Normally, anomalous MCE is expected to be observed at the Curie temperature in a ferromagnet, since the first derivative of magnetization M with respect temperature T , at a constant magnetic field B, |(∂M/∂T ) B |, reaches a maximum, leading to a large value of the isothermal entropy change (ΔS T ), according to the thermodynamic Maxwell's relation: (∂S /∂B) T = (∂M/∂T ) B .In particular, materials undergoing first-order phase transitions (FOPT) exhibit giant MCE, because in this case the derivative (∂M/∂T ) B becomes infinite.Therefore, a great deal of attention has been focused on materials with FOPT [1][2][3][4].
In most papers, ΔS T is obtained from magnetization measurements based on the Maxwell relation.However, it has been proved that the quite common careless use of the Maxwell relation leads to very high and spurious peaks of ΔS T in the transition region for materials with hysteresis [5][6][7].Hence, the use of alternative methods, such as direct and specific-heat techniques, becomes very a Corresponding author: burriel@unizar.esvaluable in the MCE determinations.Moreover, the MCE is quantified with two fundamental parameters [8], ΔS T and the adiabatic temperature change (ΔT S ), where ΔT S is the temperature change of the material induced by a field change ΔB.An evaluation of ΔS T alone, without considering ΔT S , does not provide the information needed for cooling applications.Thus, both parameters are required to be precisely characterized in order to identify a material being good enough as a refrigerant or not.Measurements of the heat capacity (C p,B ) at different constant magnetic fields are advisable since, from them, both parameters can be deduced.The binary compound MnAs undergoes a FOPT from ferromagnetic (FM) phase to paramagnetic (PM) phase combined with a structural transition from the hexagonal NiAs-type structure to the orthorhombic MnP-type structure at 317 K upon increasing temperature.The inverse transition takes place at 306 K on a cooling process at zero field [9].The MCE of MnAs and its derivatives, with slight substitutions of Fe, Cu, and Cr for Mn, or Si and Sb for As [3,[10][11][12][13][14][15][16], have been extensively studied using magnetization data.As a result of an incorrect application of the Maxwell relation, some fallacious conclusions saying that the MnAs-based compounds exhibit "huge" or "colossal" MCE (|ΔS T,max | ∼ 300 J/kg•K) were made [11,12,15].In this paper, we report on a giant MCE at room temperature (∼295 K) in Mn 0.99 Co 0.01 As, using three different methods, i.e., isothermal magnetization, heat capacity, and direct measurements.The resulting values of ΔS T and ΔT S from the three methods are compared and analyzed.

Experimental
The compound was arc melted under argon atmosphere, then heat treated in a resistive furnace at 1,340 K, followed by annealing at 1,070 K and water quenched to ambient temperature, as described in detail elsewhere [11].The Xray diffraction pattern at room temperature indicates that the sample crystalizes in a single hexagonal phase.The heat capacity was measured under magnetic field in an adiabatic calorimeter through step points at equilibrium temperatures and also with a quasi-static scanning technique, called thermograms [17].The second technique has some advantages for studying materials undergoing FOPT, e.g., allowing to obtain C p,B not only on heating processes but also on cooling ones, and also providing more precise C p,B values at the transition.The direct measurements of ΔS T and ΔT S were carried out using the same calorimeter.Magnetization as a function of temperature and magnetic field was measured with a Quantum Design SQUID (PPMS) magnetometer.
In the present study, three different measuring protocols have been used in the magnetization and direct measurements, described as follows: (1) Protocol 1: A measurement is performed a field change from 0 to B and then back to 0 at a low starting temperature T l , at which the sample is in fully FM phase at zero field.Then the sample is heated to T i at zero field and then a measurement is performed following the same field sequence as used at T l .The procedure is repeated until the temperature reaches T h , at which the sample is in fully PM phase at zero field.
(2) Protocol 2: The sample is heated from T l to T i at a constant field B. A measurement is performed when the magnetic field is brought back to 0 at T i .After that, the sample is cooled down to T l again, and then heated up to the next temperature T i+1 (T i < T i+1 ) at constant B. A measurement is performed at T i+1 following the same field sequence as used at T i .The procedure is repeated until the temperature reaches T h .
(3) Protocol 3: The sample is cooled at zero field from T h to T i .Then, a measurement is performed adiabatically with a field change from 0 to B starting at T i .After that, the sample is heated up to T h again, and then cooled down to the next temperature T i+1 (T i < T i+1 ) at zero field.A measurement is carried out at T i+1 following the same field sequence as used at T i .The procedure is repeated until the temperature reaches T h .

Results and discussion
Fig. 1 shows the temperature dependence of C p,B obtained near the FOPT at constant magnetic fields of 0, 1, 3, 5, and 6 T on heating and cooling processes for Mn 0.99 Co 0.01 As.An excellent agreement is observed between the data determined with the step method and the thermograms at 0 T and 6 T, but the thermograms data are more informative, in particular, at the transition.For all the studied fields, the C p,B curves exhibit sharp peaks and large hysteresis, implying the occurrence of FOPT.
For each C p,B curve, the transition temperature T t is taken at the corresponding peak.The resulting values of T t are listed in Table 1.We found that with 1% at.substitution of Co for Mn, the transition temperature on heating (T h t ) decreases from 317.0 K for MnAs to 294.7 K, which is desirable for magnetic refrigeration at room temperature.However, the hysteresis is enlarged by the Co doping, which is disadvantageous for high efficiency refrigeration.T t shifts to high temperature with applying magnetic field at a rate of dT c t /dB = 4.7 K/T for cooling processes, and dT h t /dB = 3.7 K/T for heating processes.These values are similar in MnAs [18].The faster increase of T t on cooling than on heating leads to a reduction of the hysteresis, specifically, from 17.1 K at 0 T to 10.1 K at 6 T. The enthalpy change at the transition (or latent heat) was calculated using )dT , where T s and T f are the starting and finishing temperatures of the transition, respectively; C FM p,B and C PM p,B are the heat capacities in the FM and PM phases near the transition, respectively.Then, the entropy change at the transition for these sharp peaks is written as ΔS t = ΔH t /T t .The resulting values of ΔH t and ΔS t for different fields are listed in Table 1.It is found that the values of ΔH t and ΔS t on cooling are higher than on heating at a given magnetic field, whereas both, simultaneously, decrease with increasing field for heating and cooling processes.The magnitudes of ΔH t and ΔS t are close to those for MnAs [10].The observation of large values of ΔH t and ΔS t foretells a giant MCE in Mn 0.99 Co 0.01 As.
The isothermal entropy change of Mn 0.99 Co 0.01 As has been determined independently with the following three methods: (1) using the Maxwell relation in the form , where the isothermal magnetization data was measured following protocol 1; (2) using the expression ΔS T = Q/T , valid for equilibrium thermodynamics, where Q represents the heat absorbed by the sample when removing the field isothermally, what we call direct determination of ΔS T , and was carried out following protocol 2; (3) using the equation dT , where C p,0 and C p,B are the heat capacity data measured at magnetic fields 0 and B.
To be precise, for irreversible processes as happen in first-order transitions, there is an entropy dissipation to be added to ΔS T , such as ΔS diss = E diss /T , where E diss is the dissipated energy, that can be estimated from the magnetization loops or the entropy loops obtained from the corresponding heating and cooling cycles of M(B) and C p,B (T ).In the present case, the correction values E diss /T calculated for the direct determinations and the calorimetric derivations of ΔS T were found to be smaller than 0.5 J/kg•K.Figs.2(a) and (b) display the plots of ΔS T for field changes of 1, 3, 5, and 6 T derived from C p,B on cooling and heating processes, respectively.The cooling curves exhibit higher maxima than the heating curves, as seen in Table 1.For a field change of 6 T, the maxima of |ΔS T | are found to be 26.9J/kg•K and 32.1 J/kg•K for heating and cooling processes, respectively.These values are quite reasonable when compared with the latent heats of the transition at zero field.For the sake of comparison, the ΔS T data determined from direct measurements, for a field change from 6 T to 0, are also plotted in Fig. 2(b).One can see that there is an excellent coincidence for the data obtained using these two techniques.
Figures 2(c) and 2(d) show the plots of ΔS T calculated from the magnetization data with increasing and decreasing fields, respectively, following protocol 1.In order to compare with ΔS T derived from C p,B , here we only present the data for field changes of 1, 3, 5 and 6 T (the measurements were carried out with maximum fields up to 9 T).The expected spurious peaks of ΔS T are observed in Fig. 2(c), due to inadequate application of the Maxwell relation to the magnetization data, using the expression previously shown.The observed maximum value, −ΔS T,max = 138 J/kg•K for a field change of 6 T, is comparable to the literature values for Mn 1−x Fe x As [11] and Mn 1−x Cu x As [12].On decreasing field, no spurious ΔS T peaks are obtained, since each demagnetization curve starts from a fully FM state in the phase transition region and only the data below 6 T are considered.Thus, these ΔS T values on decreasing field are well consistent with the results obtained from C p,B and the direct measurements, shown in Fig. 2(b).These slightly higher values than the results derived from the calorimetric measurements can be argued as coming from a higher contribution of the correction term in the magnetic derivation of ΔS T .
Figure 3 shows the temperature dependence of the adiabatic temperature change for Mn 0.99 Co 0.01 As obtained by directly measuring the temperature increment in the sample upon an adiabatic application of field.It also shows the calculated ΔT S from the entropy curves derived from the C p,B data.Since the direct measurements were carried out on increasing field using protocol 3, the resulting ΔT S values coincide with those from the cooling C p,B curves.The values obtained for ΔT S are higher than those reported for MnAs [3,10], and also higher than those for Gd [19], that has been regarded as one of the best materials for magnetic refrigeration at room temperature.For some typical field changes, the values of ΔT S ,max are listed in Table 1.
Such a giant MCE of Mn 0.99 Co 0.01 As originates from the occurrence of a field-induced magneto-structural FOPT.The giant room-temperature MCE suggests that the Co-doped MnAs compounds are potential candidates for the derivation of useful refrigerants near room temperature.A decrease of the large hysteresis would be necessary through some processing or additional doping.

Conclusions
The presence of hysteresis in the C p,B and magnetization curves indicates that the nature of the transition is firstorder.The large latent heat of the FOPT together with its T t field dependence imply a giant MCE in Mn 0.99 Co 0.01 As.Three different methods, including magnetization, C p,B , and direct measurements, have been employed to determine the MCE of the studied compound.Application of the Maxwell relation on the magnetization data measured using protocol 1 produces spurious peaks in the resulting ΔS T curves.The direct measurements of ΔS T and ΔT S gave results coinciding with those derived from C p,B measurements.The compound exhibits giant MCE with maximum values, −ΔS T,max = 32.1 J/kg•K and ΔT S ,max = 17.7 K for a field change from 0 to 6 T, which indicates these Co-doped compounds are potential candidates for obtaining good materials for room-temperature magnetic refrigeration.

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences, 2014

Figure 1 .
Figure 1.(Color online) Temperature dependence of C p,B for Mn 0.99 Co 0.01 As at constant fields.Open circles: data determined using the step technique.Solid and dotted lines: heating and cooling thermograms, respectively.R is the gas constant.

Figure 2 .
Figure 2. (Color online) Temperature dependence of the isothermal entropy change for Mn 0.99 Co 0.01 As for several field changes.(a) ΔS T obtained from isofield C p,B measurements on cooling.(b) lines: ΔS T obtained from isofield C p,B measurements on heating; open symbols: the ΔS T data obtained from the direct measurements.(c) and (d) the ΔS T data obtained from magnetization measurements on increasing and decreasing fields, respectively.

Figure 3 .
Figure 3. (Color online) Temperature dependence of the adiabatic temperature change for Mn 0.99 Co 0.01 As with different field changes.The solid and dotted lines denote the data determined from the isofield C p,B on heating and cooling, respectively.The symbols denote the data obtained from direct measurements.

Table 1 .
Transition temperatures, transition enthalpies, and transition entropies on heating and cooling processes.Maximum isothermal entropy changes and maximum adiabatic temperature changes derived from the entropy curves for Mn 0.99 Co 0.01 As.
and c denote heating and cooling processes, respectively.in and de denote increasing and decreasing fields, respectively. h