Entropy change reversibility in MnNi1−x Co x Ge0.97Al0.03 near the triple point

The nature of the phase transition has been studied in MnNi1−x Co x Ge0.97Al0.03 (x= 0.20–0.50) through magnetization, differential scanning calorimetry and x-ray diffraction measurements; and the associated reversibility in the magnetocaloric effect has been examined. A small amount of Al substitution for Ge can lower the structural phase transition temperature, resulting in a coupled first-order magnetostructural transition (MST) from a ferromagnetic orthorhombic to a paramagnetic hexagonal phase in MnNi1−x Co x Ge0.97Al0.03. Interestingly, a composition-dependent triple point (TP) has been detected in the studied system, where the first-order MST is split into an additional phase boundary at higher temperature with a second-order transition character. The critical-field-value of the field-induced MST decreases with increasing Co concentration and disappears at the TP (x= 0.37) resembling most field-sensitive MST among the studied compositions. An increase of the hexagonal lattice parameter a hex near the TP indicates a lattice softening associated with an enhancement of the vibrational amplitude in the Ni/Co site. The lattice softening leads to a larger field-induced structural entropy change (structural entropy change≫ magnetic entropy change, for this class of materials) with the application of a lower field, which results in a larger reversibility of the low-field entropy change (|ΔS rev| = 6.9 J kg−1 K for Δμ 0 H = 2 T) at the TP.


Introduction
Phase transitions in magnetic materials always draw special attention of the scientific community due to the fascinating fundamental insights they provide while being the origin of different application-oriented functional properties, such as magnetoresistance [1], magnetic shape memory [2], barocaloric [3] and magnetocaloric effects (MCEs) [4].Among the wide variety of magnetic phase transitions and their delicate balance, they are broadly classified into two categories, namely second-order (SOMT) and first-order (FOMT) magnetic phase transitions.The nature of phase transitions is relatively well explored for materials exhibiting a pure SOMT from a ferromagnetic (FM) to a paramagnetic (PM) state.The discontinuous variation of the order parameter associated with the FOMT makes it rather complicated to explain the phase transition considering a well-defined representation.Still, a consistent effort has been dedicated to explore magnetic materials exhibiting a FOMT due to their enhanced functional properties in comparison to those presenting SOMTs.
The magnetostructural (magnetostructural transition (MST)) or magnetoelastic FOMT between an ordered FM to a disordered PM state acquired surplus attention because of their attractive multifunctional properties associated with large magnetization jumps [3][4][5][6][7][8][9].It has also been extensively studied that the FOMT between two ordered states can give rise to large magnetization changes and result in large multifunctional properties [1,2,10].However, the unavoidable thermal hysteresis associated with FOMT often limits the reversibility of these functional properties.There are several intrinsic (e.g.nature of magnetic ordering, spin fluctuations) and extrinsic (e.g.microstructure) components of the observed hysteresis associated with the FOMT [11].Often it is hard to determine their origin and which component is dominant.Many different routes have been applied in order to reduce the thermal hysteresis and to improve the reversibility of functional properties.The improvement of the structural compatibility at MSTs is one of the most prominent [12].
In this context, let us imagine a hypothetical scenario where thermal hysteresis remains almost invariant upon compositional variation.Could it still be possible to further improve the functional properties' reversibility?To get more insight, a systematic study of phase transitions has been conducted in MnNi 1−x Co x Ge 0.97 Al 0.03 compounds and the reversibility of the MCE, in terms of the isothermal entropy change (∆S) has been examined.The determination of this system's phase diagram revealed a composition-dependent triple point (TP) due to the separation of a single MST line into SOMT and FOMT boundaries.An improvement of the low-field reversible entropy change |∆S rev | has been observed near the TP and the possible origin of the effect has been discussed.
Stoichiometric MnNiGe and MnCoGe compounds exhibit antiferromagnetic (AFM) with a spiral magnetic structure and FM ordered states below their respective SOMT temperatures, Néel temperature T N (∼346 K) [13] and Curie temperature T C (∼345 K) [14].A structural transition between a low-temperature TiNiSi-type orthorhombic to a high-temperature Ni 2 In-type hexagonal structure occurs in the PM state.Therefore, increasing the substitution of Co for Ni in MnNi 1−x Co x Ge can weaken the AFM order and stabilize a higher magnetization state (such as FM, ferrimagnetic, FM spiral) with a magnetic instability near 50:50 substitutions, as reported in the literature [15,16].The previously generated phase diagram also indicates that the magnetic and structural transitions remain decoupled in MnNi 1−x Co x Ge, while only the nature of magnetic ordering changes [15,17].Although, Ren et al reported a coupled MST in the intermediate composition range of Mn(Co 1 − x Ni x )Ge, this could be related with the different sample preparation and annealing procedure [18].A hydrostatic-pressure-induced TP has also been previously reported for the studied class of materials [16,19].However, the composition-dependent TP is not well studied and deserves more attention, especially in view of related functional properties.Pressure-induced TPs are very interesting from a fundamental point of view.However, a composition-dependent TP is more relevant for applications.Moreover, the comparison of the materials' properties around pressure-induced and composition-dependent TPs can yield interesting information on the nature of the MST.To investigate the composition-dependent TP, we selected the MnNi 1−x Co x Ge 0.97 Al 0.03 system for our study.In addition to the already described characteristics, in this system the substitution of a small amount of Al for Ge results in a coupled MST even for higher Ni-concentration due to the decrease of the structural transition temperature.A similar effect on the structural stability and realization of the MST has been observed earlier for the Al-substituted MnNiGe system [20,21] and it is also consistent with the proposed stabilization of the hexagonal phase in MnNiGe by isostructural substitution of MnNiAl through DFT calculation [22].

Experimental methods
All polycrystalline MnNi 1−x Co x Ge 0.97 Al 0.03 (x = 0.20-0.50)samples were prepared by arc melting of the constituent elements of purity better than 99.9% in an argon atmosphere.To compensate the weight loss due to the high vapor pressure of Mn, 2 wt% extra Mn was added during melting for all the studied samples.The as-cast samples were further sealed inside a pre-evacuated partially argon-filled quartz tube and annealed at 900 • C for 2 d followed by furnace cooling.To determine the crystal structure, room-temperature x-ray diffraction (XRD) measurements were carried out on a Philips X'Pert Pro MPD diffractometer using Cu K α radiation.An XPERT-PRO diffractometer with Cu K α radiation source and a TTK-450 low temperature chamber were used for the temperature-dependent XRD measurements.Structural refinement of the XRD data was executed using the FullProf software to estimate the lattice parameters [23].The chemical compositions of selected samples have been estimated using elemental analysis in FEI Helios NanoLab 600i DualBeam Focused Ion Beam with EDAX addon.The scan area of the measurement was about 1 mm 2 .The results are summarized in the supplementary material.The magnetization measurements were performed using a Quantum Design MPMS 3 magnetometer for the temperature interval of 5-360 K with applied magnetic fields up to µ 0 H = 7 T. High-temperature (up to 950 K) magnetization measurements were carried out using the oven option of the MPMS 3 magnetometer.In order to avoid artifacts in the estimation of the ∆S of a FOMT [24], isofield M(T) data have been used for calculations using the Maxwell relation: ) represent the values of magnetization in a magnetic field µ 0 H at temperatures T i + 1 and T i , respectively.The reversible |∆S rev | is the effective entropy change excluding the unavoidable thermal hysteresis loss due to the FOMT, which can be exploited for a cyclic magnetic cooling application and is estimated as the overlap of the temperature-dependent entropy change curves on heating and cooling [25].Differential scanning calorimetry (DSC) measurements were executed using a DSC25 (TA Instruments) with a temperature sweep rate of 10 K min −1 during heating and cooling.

Results and discussion
From the room temperature XRD measurements, it has been found that all the compositions crystalize in a hexagonal Ni 2 In-type crystal structure.Rietveld refinements of the XRD data for all studied compositions are included in the supplementary material.The composition-dependent variation of the hexagonal lattice parameters (c hex and a hex ) is shown in figure 1(a).A decrease of c hex has been observed with increasing x with a significant change between the x = 0.35 and 0.40 compositions.A peak-like feature has been detected in the variation of a hex within the composition range 0.30 ⩽ x ⩽ 0.40, exhibiting a maximum at x = 0.37.Significantly larger vibrational amplitude for Co atoms along a hex has been identified earlier for the MnCoGe system in its hexagonal Ni 2 In-type crystal structure [26].Therefore, the observed increase in a hex for x = 0.30-0.37 is associated with an enhancement of the vibrational amplitude in the Ni/Co site.In turn, the composition-dependent increase of a hex results in an increase of the hexagonal unit cell volume (V hex ) (as shown in figure 1(b)) and, consequently, makes the hexagonal lattice softer (indicating that a transformation from a high-temperature hexagonal to a low-temperature orthorhombic martensitic phase is easier upon external perturbation) [26].The plot of c hex /a hex (x) is shown in figure 1(c).Similar to c hex (x), the c hex /a hex ratio decreases with increasing x with a slightly larger variation in between the compositions x = 0.35 and 0.37.Temperature-dependent XRD measurements were carried out to identify the low-temperature crystal structure for the compositions x = 0.30, 0.37 and 0.40.The XRD patterns as measured at different constant temperatures for x = 0.30, 0.37 and 0.40 are shown in figures 2(a)-(c), respectively.At low-temperature a TiNiSi-type orthorhombic phase has been detected similar to that observed in this class of material [21].The orthorhombic lattice parameters at 100 K were found to be a orth = 6.014(3), 6.005(1), 5.996(3) Å, b orth = 3.754(1), 3.752(1), 3.755(2) Å and c orth = 7.089(3), 7.086(1), 7.074(3) Å for x = 0.30, 0.37, 0.40, respectively.Rietveld refinements profiles at 100 K can be found in the supplementary material.The composition-dependent variation of magnetization (M) as a function of temperature (T) is shown in figure 3(a) for a µ 0 H = 0.1 T applied magnetic field.The thermal hysteresis between heating and cooling M(T) curves indicates the first-order nature of the phase transition, which is associated with a MST from a low-temperature TiNiSi-type orthorhombic to a high-temperature Ni 2 In-type hexagonal phase.Moreover, an increase of M in the low-temperature phase due to the MST signifies that the FOMT occurs between a FM orthorhombic to a PM (or lower magnetization state) hexagonal phase.The FOMT was also detected in the DSC heat flow curve (shown in figure 3(b)) as evident from the clearly visible endothermic/exothermic peaks during heating/cooling and thermal hysteresis.The latent heat (L) as estimated from the DSC heat flow curve decreases monotonically with increasing x and then a saturation tendency has been observed for x ⩾ 0.4, as shown in figure 3(c) (right axis) for heating.However, the variation of the total transition entropy change (∆S tr = L/T M , where T M is transition temperature corresponding to the MST) as a function of x shows a clear change near the composition x = 0.37 (figure 3

(c) (left axis)).
The composition-dependent magnetic phase diagram as depicted in figure 3(d) was generated using M(T) curves measured applying a µ 0 H = 0.1 T magnetic field.A single spiral-FM to PM MST has been observed for x ⩽ 0.37 [27].The orthorhombic FM state transforms to an AFM-like state at temperatures below the MST for all the studied compositions, which is consistent with the literature for similar materials classes [15,17,18,28].For x > 0.37, the single MST splits into two transitions: one second-order in character followed by a FOMT at lower temperature.In this case, the SOMT starts during cooling, but is not complete: the partial magnetic transition is completed through the coincidence with the structural transition (T st ) in a cooperative manner if T st falls at the edge (or intermediate region) of the magnetic transition [29,30].The overlap of the second-order FM transition (T C ) line with the first-order MST phase boundary results in a 'triple point' (TP) for x = 0.37.A similar type of TP was previously reported induced by hydrostatic pressure [16,19] and sometimes observed in elemental substituted MnTX (T=Co, Ni and X=Ge, Si) systems [29,30].
Magnetic field (µ 0 H) dependent magnetization data has been collected for all studied compositions in the close vicinity of their respective phase transition temperatures (FM to PM MST), T M , during heating as shown in figure 4(a) (see left axis).A magnetic-field-induced MST has been detected for x ⩽ 0.35.The critical field value (µ 0 H C ) of the field-induced MST has been estimated by considering the maximum value of dM/d(µ 0 H) as plotted in figure 4(a) (see right axis).The variation of µ 0 H C (x) is shown in figure 4(b).To examine the composition-dependent variation of the saturation magnetization (M S ), isothermal magnetization measurements as a function of µ 0 H were carried out at 5 K, these are plotted in figure 5(a).A field-induced metamagnetic transition from an AFM-like state to a FM state has been observed in the low-temperature orthorhombic state, which is more pronounced for lower x.The critical field value of the metamagnetic transition decreases with increasing x and almost disappears for x = 0.50, indicating a progressive destabilization of the AFM state with increasing Co-concentration.The temperature-dependent variation of the inverse susceptibility (1/χ) for µ 0 H = 0.1 T in the hexagonal PM state is shown in figure 5(b) for the x = 0.37 and 0.40 compositions (the details of the 1/χ(T) plot for all compositions are included in the supplementary material), which is used to estimate the effective magnetic moment (µ eff ) in the PM state.A modified Curie-Weiss expression, χ = χ 0 + C/(T-θ P ) was employed to fit the 1/χ(T) data, where C, θ P and χ 0 are the Curie constant, PM Curie temperature and T-independent susceptibility, respectively [31].From the fitting, the values of C and θ P have been evaluated.The variation of the µ eff (as estimated from C) as a function of x is illustrated in figure 5(c  The variation of |∆S rev | under high-field is a valuable information to gain more insight about the nature of the phase transition.Moreover, a large |∆S rev | at fields up to 2 T is desirable for applications such as magnetic cooling, since it can be achieved using a permanent magnet.The composition-dependent variation of |∆S rev | for ∆µ 0 H = 2 T is shown in figure 6(d).Interestingly, |∆S rev | reaches a maximum value (|∆S rev | = 6.9 J kg −1 K for ∆µ 0 H = 2 T) at the TP (x = 0.37).The observed |∆S rev | for ∆µ 0 H ⩽ 2 T is large for this class of materials (e.g.|∆S rev | = 2 and 1.9 J kg −1 K for ∆µ 0 H = 1 T in Mn 1 − x Fe 2x Ni 1 − x Ge [12], MnNi 1−x Co x Ge [17], respectively, which is 3.6 J kg −1 K for the same field change in case of the presently studied system) and is comparable to that of Gd [32] and NiMn-based Heusler alloys [10].However, the value is moderate in comparison to other well-known giant magnetocaloric materials, such as Fe 2 P-based and La(Fe 1 − x Si x ) 13 compounds [33].The major focus in the present study is not just to report the absolute value of the reversible |∆S rev |, rather to understand the origin of the enhanced reversibility near the TP; these are discussed as follows.
The representative diagram of the variations of the entropy change (∆S) as a function of temperature in the presence of magnetic field up to 7 T for x = 0.37 in the vicinity of MST is shown in figure 6(a) for heating and cooling, respectively.A large direct MCE has been observed, which is associated with a MST between a low-temperature FM TiNiSi-type orthorhombic to a high-temperature PM Ni 2 In-type hexagonal phase.An inverse MCE has also been detected due to the spiral-AFM to FM transition near T N AFM-FM (as shown in the insets of figure 6(a)), similar to that observed in earlier studies [17,18].
Two types of dependence in T M have been reported for the MnTX system: a nearly linear variation with (i) valence electron concentration (e/a) [34][35][36][37] or (ii) a orth /b orth ratio (≡c hex /a hex ) [12,37].The substitution of small elements or application of hydrostatic pressure usually results in a decrease of c hex /a hex and also a reduction of T M associated with the stabilization of the high-temperature hexagonal phase at lower temperature [37][38][39][40].The stabilization of the hexagonal phase can also be accomplished by substituting bigger elements with fewer valence electrons [18,20,21,41].In this case, a more complicated dependence of T M has been observed, which is associated with a competition between the variation of the e/a ratio and chemical pressure (as generated due to the modification of the local environment by substituting different size elements).The situation is similar in the present studied MnNi 1−x Co x Ge 0.97 Al 0.03 system.Partial substitution of the bigger elements Al and Co (with fewer valence electrons than Ge and Ni, respectively) for smaller Ge and Ni, respectively, results in a coupled MST in MnNi 1−x Co x Ge 0.97 Al 0.03 .A small primary Al substitution for Ge can establish a coupled MST in Ni-rich MnNi 1−x Co x Ge 0.97 Al 0.03 as observed earlier for Al and In-substituted MnNiGe systems [20,21,41,42].With increasing Co-concentration, T M initially decreases with decreasing e/a ratio.With further increase of Co-concentration (x ⩾ 0.3), the chemical pressure (as generated by the substitution of bigger Co for smaller Ni) starts to compete with the variation in e/a to modify the T M .As a result, a deviation from the linear dependence of T M with e/a has been observed (x ⩾ 0.37).The negative chemical pressure starts to expand the hexagonal unit cell for x > 0.3 and reaches a maximum value at the TP (x = 0.37).The increase of V hex is associated with an increase of the hexagonal lattice parameter a hex (however, a progressive decrease is accounted for by c hex ) due to the enhancement of the vibrational amplitude in the Ni/Co site [26], which results in a lattice softening near the TP.
After crossing the TP for x = 0.4, an abrupt contraction of V hex associated with the decrease of both a hex and c hex generates a positive chemical pressure and decreases T M due to the stabilization of the low-volume hexagonal phase.The effect of chemical pressure likely has a lower impact on the magnetic transition temperature, T C, in agreement with the effect of pure hydrostatic pressure [16].As a result, the T C remains almost unchanged, only T M moves to lower temperature.Eventually, the splitting of T C and T M results in a TP at x = 0.37.A similar TP has been observed earlier for related systems with the application of hydrostatic pressure [16,19].The TP has been also realized in the elemental-substituted MnCoGe system [21,30,38,43] and the existence of the effect has been explained as a result of the reduction in the magnetostructural coupling constant [43].A pronounced increase of M S for x > 0.37 likely excludes the possibility of band hybridization, which can stabilize a non-collinear magnetic structure by modifying the electronic density of states at the Fermi level.However, based on the sudden reduction of µ eff in the PM state, a slight variation of the electronic state cannot be ignored for the composition with x = 0.4.The modification of the electronic state could improve the bond strength at the expense of magnetism by the formation of a non-collinear magnetic state [18].A similar type of competition between magnetism and bonding has been observed in Mn(Co 1 − x Ni x )Ge by Ren et al [18] and is considered as the driving force of the FOMT in transition metal Fe 2 P-based giant magnetocaloric materials [44].constant similar to that observed earlier [16,43]

Conclusions
The substitution of bigger-size elements with fewer valence electrons can establish a coupled MST in the MnNiGe-based system.The stability of the MST and therefore the variation of T M depends on the delicate balance between the modification of the valence electron concentration e/a and chemical pressure as induced by elemental substitution in MnNi 1−x Co x Ge 0.97 Al 0.03 .The competition of the above-mentioned two factors results in a composition-dependent TP for x = 0.37.Interestingly, a better low-field reversibility in |∆S rev | has been observed near the TP.It has been found that the combined effects of lattice softening and a higher field sensitivity of the magnetic-field-induced MST can transform a larger fraction of the FM orthorhombic phase near the TP with the application of a lower field.Consequently, the contribution of ∆S st to ∆S is enhanced at low-field, which leads to a better |∆S rev | near the TP.The present study indicates that the investigation of the magnetocaloric properties near the TP could be of interest for the studied class of materials with an expectation to realize a better reversible entropy change.

Figure 1 .
Figure 1.(a) The variation of hexagonal lattice parameters (c hex and a hex ) at room-temperature as a function of composition (x) in MnNi 1−x CoxGe0.97Al0.03.(b) Change of hexagonal unit cell volume V hex with composition.(c) The composition-dependent modification of the ratio c hex /a hex is plotted.

µ 0 H
C decreases almost linearly with increasing x and disappears at x = 0.37 indicating a better field-sensitivity of the magnetic-field-induced MST near the TP.
) (right axis) and qualitatively compared with M S (x).A sharp increase in M S has been observed for a slight variation in composition from x = 0.37-0.40near the TP, however, µ eff decreases suddenly in the same compositional range.|∆S|(T) curves during heating and cooling are shown in figure 6(b) for x = 0.37 with ∆µ 0 H = 2 T as a representing figure for evaluating the reversible entropy change |∆S rev |.The details of the variation in ∆S(T) and concomitant |∆S rev | up to µ 0 H = 7 T for all studied compositions can be found in the supplementary material.The composition-dependent variation in |∆S rev | as a function of µ 0 H is plotted in figure 6(c).A change of curvature in |∆S rev |(µ 0 H) for lower x is a characteristic feature of a field-induced MST, which disappears at the TP.With the application of a magnetic field µ 0 H > µ 0 H C , a relatively faster increase (nearly linear) in |∆S rev | has been observed for x ⩽ 0.3, which is consistent with the observed larger total transition entropy change ∆S tr of the respective composition (see figure 3(c)).As a result, a large |∆S rev | of 17.2 J kg −1 K (24.5) for ∆µ 0 H = 5 T (7) has been observed for x = 0.30, which is comparable with the largest reversible reported value in this class of materials (|∆S rev | = 18.6 J kg −1 K for ∆µ 0 H = 5 T) as well as other well-known giant magnetocaloric materials [12].

Figure 3 .
Figure 3. (a) Temperature dependence of the magnetization (M) during heating and cooling for MnNi 1−x CoxGe0.97Al0.03 in the presence of magnetic fields µ0H = 0.1 T. Inset: plot of M(T) in the close vicinity of MST for x = 0.20 and 0.25.(b) DSC heat flow curves as a function of temperature during heating and cooling for MnNi 1−x CoxGe0.97Al0.03.(c) (left axis) Transition entropy (∆Str) and (right axis) latent heat (L) are plotted as a function of x for heating.(d) The magnetic phase diagram as generated using M(T) data measured in the presence of µ0H = 0.1 T. The triple point (TP) as detected for the composition x = 0.37 is indicated by the arrow.

Figure 4 .
Figure 4. (a) Magnetization isotherms as a function of magnetic field (shown by solid symbols as connected with lines) near MST of the respective composition, x (left axis).Plot of dM/d(µ0H) (shown by dashed lines), as used to determine the critical field value (µ0HC) of field-induced MST (right axis).(d) µ0HC as a function of x.Field-induced MST disappears at TP (x = 0.37).Solid line through the data points is a guide to the eye.
For a MST, there are two entropy contributions, namely structural entropy change |∆S st | and magnetic entropy change |∆S M |, to the total isothermal entropy change |∆S| [45].The addition of |∆S st | and |∆S M | results in a total |∆S| as |∆S| = |∆S st | + |∆S M | for the MnTX system [45].Usually, a much larger |∆S st | has been observed in the MnTX system when compared to |∆S M | due to a large volume change at the MST resulting in |∆S| ∼ |∆S st | [46, 47].Therefore, a large |∆S| can be realized for a large change in |∆S st |.The lattice softening due to the enhancement of the vibrational amplitude in the Ni/Co site along a hex (which favor the low-temperature orthorhombic martensitic phase) and a better field-sensitivity of the magnetic-field-induced MST near the TP (as shown in figure 4(a)), make it easier to transform a larger FM orthorhombic martensitic phase fraction with the application of a lower magnetic field in comparison to the other compositions and result in a better low-field reversibility in |∆S rev |.Above the TP (x ⩾ 0.4), the decrease of the low-field |∆S rev | could be related with the reduction in the magnetostructural coupling

Figure 5 .
Figure 5. (a) Field-dependent magnetization as measured at 5 K.(b) Plot of inverse susceptibility (1/χ) as a function of temperature in the presence of µ0H = 0.1 T for the compositions x = 0.37 and 0.40.Solid lines through the data points are the corresponding fitting in the temperature interval of 400-950 K. (c) Variations of saturation magnetization (MS) and effective magnetic moment (µ eff ) as a function of composition.
. The decrease of the Zeeman energy in the FM martensitic phase (the field-induced MST is incomplete for x = 0.2 as µ 0 H C > 2 T) diminishes the low-field value of |∆S rev | (due to a smaller change in ∆M across the MST) with increasing Ni-concentration below the TP.

Figure 6 .
Figure 6.(a) Entropy change (∆S) as a function of temperature for x = 0.37 during heating and cooling with the application of magnetic field (µ0H) up to 7 T. Inset: inverse MCE for heating (upper inset) and cooling (lower inset) are shown by ∆S(µ0H) plots, which is associated with a phase transformation from a spiral-AFM to FM transition near TN AFM-FM below the MST.(b) Temperature dependence of |∆S| for x = 0.37 with a change of magnetic field of µ0H = 2 T. The reversible region of ∆S (|∆Srev|) is highlighted in gray.(c) The maximum reversible entropy change (|∆Srev|) as a function of magnetic field variation up to 7 T for all the studied compositions.(d) Composition dependent |∆Srev| for µ0H = 2 T.