Pressure dependence of magneto-structural properties of Co-doped off-stoichiometric Ni 2 MnGa alloys

A strong effect of pressure on magnetization and paramagnetic moment of the Co-doped Mn-rich Ni50-xCoxMn25+yGa25-y (x = 5,7,9 and y = 5,6,7,8) Heusler alloys is presented and compared with very weak pressure sensitivity of magnetization of the stoichiometric Ni2MnGa alloy. The effects of both, the pressure and the magnetic field, on temperature of the structural martensitic transition in the alloys are discussed with a use of the Clausius-Clapeyron relations. An analysis of pressure and field effects provides a possibility to evaluate structural and magnetic parts of latent heat of the martensitic transitions in the studied alloys. The Curie temperature of martensite phase of the Co-rich alloys is not affected by pressure.


Introduction
The huge shape memory effects and the magnetocaloric effects (MCE) in the Heusler Ni 2 MnGa alloy are a consequence of the first order magneto-structural transition from the high temperature cubic austenite (A) to the low temperature tetragonal martensite (M) crystal structure [1,2].In the case of off-stoichiometric or doped Ni-Mn-Ga alloys, the martensitic transition is accompanied by very pronounced changes of their volume and magnetization and so, a large family of these alloys is a subject of long-lasting and extended research not only at ambient but even under high pressure [3][4][5][6][7][8].During decades, the effect of high hydrostatic pressure on the Curie temperature T C A [3,5,8] and on temperatures of the martensitic transformation T M-A and T A-M [4,6] of the Heusler stoichiometric as well as the off-stoichiometric Ni-Mn-Ga alloys was determined.We present the results of pressure investigation of a set of the Co-doped Mn-rich Ni-Co-Mn-Ga alloys that exhibit extraordinary magnetic and structural properties that were studied in detail at ambient pressure recently [9].

Experimental details
The polycrystalline Co-doped Ni 50-x Co x Mn 25+y Ga 25-y (x = 0, 5, 7, 9 and y = 0, 5, 6, 7, 8) alloys were prepared by arc melting under protective Ar atmosphere and consequently annealed at 900 K for 72 hours with quenching in water [9].The final compositions of alloys were verified by EDAX.Temperature and high pressure dependences of magnetization of the alloys were measured with the use of the SQUID magnetometer (MPMS-7T with oven, Quantum Design Inc.) and of the miniature Cu-Be pressure cell [10], (see also Figure 1) in temperature range from 5 K up to 500 K at ambient pressure and up to 400 K in pressure range up to 1.2 GPa at magnetic fields up to 7 T.The magnetic properties of the alloys at ambient conditions are described in detail in our recent papers [9,11,12] and hence, we keep the similar labeling of the samples that expresses a content of Co and Mn ('at.%Co-at.%Mn') in the studied alloy.Due to a restricted temperature range that is available for high pressure measurements, four samples were selected from a prepared set of alloys, '5-30' (Ni 45.5 Co 4.8 Mn 30.1 Ga 19.6 ), '7-31' (Ni 42.9 Co 7.1 Mn 31.3Ga 18.7 ), '9-32' (Ni 41.9 Co 9.1 Mn 32.0 Ga 17.0 ) and '9-33' (Ni 41.9 Co 9.3 Mn 33.1 Ga 15.7 ).

Results and Discussion
The effect of pressure on magnetization of the Co-free Ni-Mn-Ga alloys and their structural transitions was studied recently [5,7].We compare here the results of the pressure study of the Co-doped Mn-rich Ni 50-x Co x Mn 25+y Ga 25-y alloys with the effect of pressure on magnetization and structural transition of the stoichiometric '0-25' (Ni 50.5 Mn 25.5 Ga 24 ) alloy.

Magnetization
Both, the substitution of Co for Ni and the introduction Mn for Ga, induce a significant decrease of saturated magnetization of martensite phase, M M , of all the studied samples.Magnetization of austenite phase, M A (H,T A ), at temperature T A just above the martensitic transition temperature T M-A , seems to be slightly affected by the substitutions and consequently, a paramagnetic gap appears in the Co-doped compounds with higher values of x and y.The Figure 2 (increasing temperature is shown only) shows the paramagnetic gap in '9-32' and '9-33' alloys together with a universal dependence of saturated magnetization of austenite phases M A (5T) of the Codoped alloys on the normalized T/T C A temperature.In the stoichiometric '0-25' alloy, magnetization decreases in course of the martensitic M-A transition and the change of magnetization, M M-A , is negative in all the Co-free alloys [7].However due to the rapid decrease of M M in Co-doped alloys, M M-A becomes positive and increases with the increasing content of Co when the content of Mn is kept constant, as it is seen in Figure 2 and presented in [9].Temperature T M-A of the martensitic transition increases with increasing Co-content, but due to the positive value of M M-A , T M-A strongly decreases with increasing magnetic field in all the Co-doped alloys.In the case of '9-33' alloy, T M-A is higher than its T C A and the martensitic transition occurs in paramagnetic state of the austenite phase of the alloy.Due to this, temperature T M-A of the '9-33' alloy is not dependent on magnetic field what was verified by measuring of dT M-A /dH.The very weak negative effect of pressure on magnetization M M of the stoichiometric '0-25' alloy is accompanied by a slight increase of M A (H,T A ) under pressure in this alloy.The last effect is induced by an increase of the Curie temperature of the austenite phase T C A [5].In contrast to the '0-25' alloy, the Co-doped Mn-rich alloys exhibit very pronounced decrease of M M under pressure, see Table 1.In the case of the '5-30' alloy, the decrease of M M , dlnM M /dP = -29*10  under pressure, dlnM A (5T, 360K)/dP = -3.7*10 - GPa -1 , see Figure 3.As a consequence of this big difference between the pressure effects on M M and M A (H,T A ), the change of magnetization M M-A increases with increasing pressure in the '5-30' alloy.
A similar extraordinarily different pressure behavior of magnetization has been observed and described in ordered Ni 3 Mn and disordered Ni 75 Mn 25 alloys [13].The theoretical ab-initio calculations revealed a relatively slight effect of pressure on magnetic Mn-moments, but, a substantial pressure effect on a number of anti-parallel Mn-moments of atoms that are shifted out of their regular lattice positions in the disordered alloys.As a consequence, low magnetization of the disordered alloys is accompanied by the high sensitivity of magnetization to external pressure.A presence of paramagnetic state in the Co-rich alloys at a temperature range below the temperature of M-A transition, T M-A , was verified by linear dependence of  dc (T) -1 .Figure 4 shows this dependence in case of the Joint European Magnetic Symposia 2012 was calculated by using a standard formula: ( where, k, C and N are Boltzmann, Curie and Avogadro constants, respectively, and  is density.Due to a relatively narrow temperature range of linear part of  dc (T) -1 , the values of C and m eff were determined with an accuracy of about 5% of their nominal values.The presented values of m eff of all alloys (including the stoichiometric '0-25' alloy) were determined from 1Tcurves of  dc (T) -1 .They lie in an interval from 5.08 µ B to 5.65 µ B and they agree well with values in reference [3].
The values of m eff also follow the phenomenological relation m eff = n V -24, where n V is a number of valence electrons [14].The values of m eff are identical for both, the martensite and the austenite phases of alloys and they decrease slightly with increasing field, see Figure 4. We have observed a relatively strong effect of pressure on paramagnetic moments of the stoichiometric '0-25' and Co-doped '9-33' alloys with dlnm eff /dP = -17*10 -3 GPa -1 and -24*10 -3 GPa -1 , respectively.

Curie temperature
The Curie temperature of austenite phase of the stoichiometric '0-25' alloy increases with pressure by a rate of dT C A /dP = + 5.9 K/GPa.This value of the pressure parameter dT C /dP agrees well with data in literature [3,8].A saturation of the pressure shift of T C A was observed in pressure range above 6 GPa [8].Unfortunately, T C A of the Co-doped alloys lies above a today's temperature limit of our pressure measurements.The Curie temperature T C M of martensite phase of the Codoped (x 7) alloys that decreases with the increasing content of Co (as can be seen on Figure 2) is practically insensitive to pressure.The pressure parameter dT C M /dP is 0 ± 1 K/GPa.

Temperature of structural transition
The temperature of structural transition from martensite to austenite, T M-A , increases with increasing of both, the Co-and the Mn-doping in all the studied alloys, see Table1.However as it was stressed recently, a thermal treatment of the Ni-Co-Mn-Ga has a great influence on both, the transition and the Curie temperatures of these alloys [15].Similarly as in the case of magnetization, very great difference (more than one order) has been observed between the pressure effect on T M-A of the stoichiometric '0-25' alloy and one of the Co-doped Mnrich alloys.However, the pressure shift of T M-A is always positive verifying a lower volume of martensite phase with respect to austenite phase in all alloys.The mentioned high sensitivity of magnetization M M of the alloys to composition induces a change of sign of M M-A from negative in '0-25' alloy to positive in the Co-doped alloys.As a consequence, the small positive effect of magnetic field on T M-A in the '0-25' alloy changes into very pronounced negative field effect on T M-A of the Codoped Mn-rich alloys.Values of a parameter dT M-A /dH that are presented in Table 1 are in good agreement with recent results of high field experiments [16].
Table 1.The values of magnetization M M , its change M M-A and its pressure derivation, effective paramagnetic moment m eff , transition temperature T M-A of noticed samples with its pressure and field dependence that was used to a determination of S m .S m (J /kgK) +3.1 +6.9 +12.0 +12.9

0-
A use of the Clausius-Clapeyron (C-C) relations ( 2) and (3) provides a possibility to analyse an evolution of entropy and/or latent heat of the martensitic transition with increasing doping of the Mn-rich alloys by Co. ( Entropy changes S m and S s are relevant to changes of magnetization, M M-A , and volume, V M-A , that occur during the transition from martensite to austenite.The positive values of S m in the Co-doped alloys means that an inverse magnetocaloric effect (MCE) should be observed in these alloys and this was really verified experimentally [11,12].However, it is necessary to take into account that due to negative value of dT value of dT M-A /dH, ensures in this case that the structural transition is not induce by field even at T M-A and a very weak standard MCE connected with arrangement of magnetic domains (with an increase of magnetization) in ferromagnetic phase is observed by a direct MCE measurements [17].An increase of the entropy change S m in the Co-doped alloys reflects an increasing magnetic disorder with increasing Co-doping that is also a possible source of the significant decrease of magnetization M M in these alloys.We tried to use the measured values of pressure parameter dT M-A /dP together with values of V/V presented in [11] to the calculation of entropy change S s by the C-C relation (3).We have obtained S s = 23.2J/kgK and latent heat L s = 9.2 J/g in the case of '7-31' alloy.Both values are in a good agreement with data in literature [4,15,18,19].Values of S s determined for both, the '0-25' and the '5-30' alloys were higher than 75 J/kgK.These values seem to be unrealistic in comparison with the calorimetric measurements of the transition latent heat in the Ni-Mn-Ga alloys [19].

Conclusions
The saturated magnetization M M of martensite phase of the studied Co-doped Mn-rich Ni-Co-Mn-Ga alloys decreases significantly with increasing Co-and Mncontent as well as with increasing pressure in contrast to a relevant behavior of magnetization of austenite phase of these alloys.A paramagnetic gap appears in the Codoped compounds and a change of magnetization M M-A that accompanies the structural M-A transition becomes positive and very pronounced with increasing Co-content.Effects of pressure and magnetic field on transition temperature T M-A were used to evaluate structural and magnetic parts of entropy changes to draw attention to a possible misleading interpretation of experimental results with respect to thermo-dynamical data given by the C-C relations.

Fig. 2 .
Fig. 2. Magnetization of selected alloys at field 5 T as a function of T/T C A .

Ni 45.5 Co 4.8 Mn 30.1 Ga 19.6
-3GPa -1 , is accompanied by a very slight decrease of M A (H,T A )