Ferromagnetism in the austenitic and martensitic states of Ni-Mn-In alloys

The magnetic and structural transformations in the Heusler-based system Ni0.50Mn0.50−xInx are studied in the composition range 0.05 x 0.25. While the cubic phase is preserved in the range 0.165 x 0.25, we find the presence of martensitic transformations in alloys with x 0.16. In a critical composition range 0.15 x 0.16, the magnetic coupling in both austenitic and martensitic states is ferromagnetic. Magnetic field-induced structural transitions are also found in the x=0.16 alloy, whereby the structural transition temperature shifts by 42 K in a field of 50 kOe.


I. INTRODUCTION
Heusler-based ferromagnetic ͑FM͒ Ni-Mn-Ga alloys with concentrations close to that of the stoichiometric compound Ni 2 MnGa undergo martensitic transformations.In the martensitic state, the application of a magnetic field can cause strains up to about 10%. 1 This field-induced strain is known as the magnetic shape memory effect and is caused by the reorientation of martensite variants by twin boundary motion.The driving force for the reorientation is provided by the difference in the Zeeman energy of neighboring variants ⌬M • H. 2 High saturation magnetization and high magneto-crystalline anisotropy are favorable for moving twin boundaries in low as possible external magnetic fields.In Ni-Mn-Ga alloys that transform martensitically, the magnetic ordering in both parent and product phases are FM, however with different exchange. 3ith the aim of searching for other ferromagnetic Heusler alloys that transform martensitically, we have studied in a previous work the structural and magnetic properties of Ni 0.50 Mn 0.50−x Sn x alloys. 4Martensitic transformations were observed in alloys with concentrations up to 15 at % Sn.Similar results were also reported by Sutou et al. 5 In the narrow concentration range 0.13ഛ x ഛ 0.15, ferromagnetism and lattice instabilities were found to coexist, and an investigation of the magnetic properties had shown that the magnetic exchange in both parent and product phases are also FM as in Ni-Mn-Ga.However, in Ni-Mn-Sn, it was found that the magnetization of the low-temperature phase is smaller than that in the parent phase as opposed to the case in Ni-Mn-Ga alloys. 3or a systematic understanding of the properties of structural and magnetic transitions in Ni-Mn-based FM Heusler alloys, it is necessary to extend the studies to materials that incorporate other group IIIA-VA elements.In the present work, we examine the structural and magnetic properties of Ni 0.50 Mn 0.50−x In x alloys by use of calorimetry, x-ray diffraction, optical microscopy, and magnetization.

II. EXPERIMENT
Ingots of about 3 g were prepared by arc melting the pure metals under argon atmosphere in a water-cooled Cu crucible and were remelted several times.The ingots were subsequently encapsulated under argon in quartz glass and annealed at 1073 K for 2 h.They were then quenched in ice water.The compositions of the alloys were determined by energy dispersive x-ray photoluminescence analysis ͑EDX͒ and are summarized in Table I.The corresponding valence electron concentration e / a is also given in the table.This is calculated as the concentration weighted sum of the number of 3d and 4s electrons of Ni and Mn and the number of 4s and 4p electrons of In.An estimated error of ±0.1% in determining the concentration leads to an error of ±0.007 in the value of e / a.
Polycrystalline samples of 30-100 mg cut from the ingots using a low-speed diamond saw were used as samples for magnetization and calorimetric studies.For the differential scanning calorimetry ͑DSC͒ measurements, one side of the samples was ground with 1200 grid SiC abrasive to insure proper thermal contact.Calorimetric measurements were carried out in the temperature range 120 K ഛ T ഛ 830 K in a DSC ͑TA Instruments MDSC 2920͒.For DSC measurements, the cooling and heating rates were 2 -5 K / min.We have also used a second high sensitivity calorimeter for measurements in the temperature range 100 K ഛ T ഛ 350 K.A third calorimeter was used for measurements under magnetic field. 6The cooling rate in these measurements was 0.5 K / min.The temperature dependence of the magnetization M͑T͒ in a low external magnetic field ͑H =50 Oe͒ was measured in the temperature range 5 K ഛ T ഛ 380 K using a superconducting quantum interference device magnetometer.Prior to the measurements, the sample was prepared in a zero-fieldcooled state ͑ZFC͒ by cooling it from 380 to 5 K in the absence of a magnetic field.Subsequently, the external field was applied and the data were taken on increasing temperature up to 380 K.Then, without removing the external field, the data were taken on decreasing temperature, i.e., fieldcooled ͑FC͒.As a last step, again without removing the external field, the magnetization was measured on increasing temperature.The last step is denoted as the field-heated ͑FH͒ sequence.Any hysteresis in the FC and FH sequences is expected to be associated with a structural transition, whereas any splitting of the ZFC and FC curves below the FM transition temperatures is expected to be associated with pinning due to coexisting antiferromagnetic ͑AF͒ exchange, or pinning due to noncollinear magnetic structures that reside within twin boundaries if the system is martensitic.To further characterize the magnetic properties, the magnetic field dependence of the magnetization M͑H͒ was measured in fields up to 50 kOe.
Room-temperature structural analyses were carried out with conventional x-ray techniques using Cu K␣ radiation.The microstructure of the specimens was examined by optical microscopy.For this study, the samples with x = 0.25 and 0.15 were polished and etched in Cr͑IV͒ oxide solution with 5 V dc bias.For x ഛ 0.15, nitric acid with 2% alcohol was used.

A. Calorimetric studies and identification of the transition temperatures
The results of calorimetric studies for the alloys with 0.16ജ x ജ 0.05 are plotted in Figs.1͑a͒-1͑e͒ in the temperature vicinity of the martensitic transformation.The heating and cooling cycles are indicated by arrows.For alloys with x Ͼ 0.16, no structural transformation is observed.On the other hand, alloys with 0.16ജ x ജ 0.05 exhibit a first-order structural transformation, for which the transition temperature increases with decreasing In concentration.We collect in Table II the characteristic transition temperatures at which martensite start and finish ͑M s , M f ͒, and austenite start and finish ͑A s , A f ͒ and the width of the hysteresis ⌬T determined as the difference between the temperatures corresponding to the peak positions of the forward and reverse transitions.The superscripts DSC and M refer to the method used in determining the transition temperatures.For the alloys with 0.155ജ x ജ 0.05, the transition temperatures are taken as the temperatures where dQ / dT begin to deviate from the baselines.An example of the identification of the transition temperatures is shown in Fig. 1͑b͒ with the vertical arrows.The transition temperatures determined in this manner from the calorimetry data are in very good agreement with those determined from the magnetization data ͑Sec.III C͒.The magnetization data allow only M s and A f to be identified.
The features in dQ / dT of the sample with x = 0.16 seen in Fig. 1͑a͒ are unlike those of the other samples.Here, the broad shoulder below the ferromagnetic Curie temperature of the austenitic state T C A Ϸ 300 K ͑Sec.III C 2͒ overlaps with the features of the first-order structural transformation.This makes it difficult to determine the exact positions of M s and A f , whereas M f and A s can be identified.Also, the presence of multiple peaks observed in dQ / dT both in the forward and reverse transitions, especially the double-peak structure with nearly identical separations in the heating and cooling curves, suggests that intermartensitic transitions could be occurring.The observed data can be understood to be due to the superposition of the contributions from the features associated with the magnetic and structural transitions.The dashed lines are guides representing the overlapped contributions, and it would be expected that M s lies within the temperature range of the bracket shown in the figure.This range falls within ±10 K of M s M , the martensite start temperature determined from the magnetization data ͑Sec.III C 2͒.
The entropy and enthalpy changes ͑⌬S and ⌬H, respec-tively͒ around the structural transitions are calculated from the baseline-corrected calorimetry data. 4The values of ⌬H and ⌬S, determined as the average obtained from the cooling and heating experiments, are also included in Table II.
As will become evident from the magnetization data presented in Sec.III C, the sample with x = 0.16 exhibits a mag- netic field-induced transformation.Therefore, we have studied dQ / dt vs T for this sample under various constant magnetic fields.The measurements were done on cooling only.The results plotted in Fig. 2 show the data in the full temperature range of the measurements and in the temperature region of the major feature around the martensitic transition ͑inset͒.The rate of shift in the position of the major peak ͑and thereby the position of M s ͒ with respect to field amounts to −0.8 K kOe −1 ͑−8 K T −1 ͒.This value is also found in temperature-dependent magnetization measurements measured in 50 kOe presented at the end of this paper.

B. Structural properties
Figure 3 shows x-ray diffraction patterns taken at room temperature for the alloys with x = 0.25 and x = 0.16.For x = 0.25, superstructure reflections of the L2 1 phase ͑Fm3m͒ are also observed.By replacing In with Mn, the lattice constants of the austenitic phase become smaller, and the peak positions shift to larger angles.The superstructure reflections are not present for x = 0.16.The crystal structure in this case is B2 ͑Pm3m͒, for which the lattice constants are half as large as that of the L2 1 phase.
The alloys with x ഛ 15.5 are martensitic at room temperature in agreement with the calorimetric measurements.The samples with x = 0.155 and x = 0.15 have a 10 M modulated martensite structure.Figure 4 shows the diffraction pattern with the inset showing the details in the range 40°ഛ 2 ഛ 44.5°.The unit cells are monoclinic with ␤ = 88.45°and88.93°for x = 0.155 and x = 0.15, respectively.
The diffraction pattern of the alloy with x = 0.10 ͑Fig.5͒ is related to that of a 14 M martensitic structure.The inset shows the details in the range 40°ഛ 2 ഛ 46.5°.The unit cell here is also monoclinic with ␤ = 93.67°.For x = 0.05, the martensite has an unmodulated tetragonal L1 0 structure as seen in Fig. 6.
8][9] The crystal structures and the lattice constants obtained from x-ray diffraction experiments are collected in Table III.
The room-temperature microstructure of the alloys is shown in Figs.7͑a͒-7͑e͒.These show optical microscopy images of the surface of the alloys with x = 0.05, 0.10, 0.15, 0.155, and 0.25.Figure 7͑a͒ shows the surface of the sample with x = 0.25, for which the grain size varies between 50 and 300 m.The black spots are voids caused by the etch process during surface preparation.
Figures 7͑b͒-7͑e͒ show the microstructure of the samples that are martensitic at room temperature.No phase separation can be identified, in agreement with the x-ray diffraction patterns.The grain size in all images lies within 50-300 m.Although the crystal structures are different, the morphologies of the 10M, 14M, and the unmodulated   As Mn is substituted for In, excess Mn atoms occupy In sites.In such spatial configurations, Mn-Mn neighbors have a smaller separation than that in the stoichiometric compound.This can introduce AF exchange, which can pin the FM domains in various configurations depending on whether the sample is cooled through T C in a small ͑H Ϸ 50 Oe͒ external field or not. 10,11This causes a separation of the FC and ZFC curves, which is seen in the M͑T͒ data of the samples with x = 0.20 and x = 0.17 in Figs.8͑a͒ and 9͑a͒, respectively.However, contrary to what is expected, the splitting weakens with decreasing In concentration, from x = 0.20 to x = 0.17, and at x = 0.165, the splitting vanishes ͓Fig.9͑b͔͒.There is also a marginal increase in T C from 290 K for x = 0.25 to 310 K for x = 0.165, indicating a strengthening of the FM exchange interaction.
In Fig. 10͑a͒, M͑H͒ at 5 K measured on samples with 0.25ജ x ജ 0.165 are compared.All data show saturation  above 15 kOe.Furthermore, the saturation magnetization increases with decreasing In concentration from about 80 emu g −1 ͑x = 0.25͒ to about 119 emu g −1 ͑x = 0.165͒.The increase is effectively linear in concentration as seen for the saturation magnetization per formula unit s plotted in Fig. 10͑b͒.However, if it is assumed that Ni and In carry essentially no moment, the moment on the Mn atom remains constant throughout the studied concentration range.Generally, one would expect s to decrease as Mn-Mn neighbors appear with decreasing In concentration, as in the case of other Ni-Mn-based Heusler alloys.We discuss this point in Sec.IV.

Samples with compositions 0.16Ð x Ð 0.15: Identification of transition temperatures in M"T…
As the In concentration is further decreased, we reach the situation shown in Fig. 11͑a͒, where M͑T͒ is plotted for the sample with x = 0.16.The FH data do not retrace the FC data but show a hysteresis ͓Fig.11͑b͔͒, indicating a first-order structural transition as found in the results of the calorimetric measurements.At high temperatures, in the austenitic state, the sample is paramagnetic and orders ferromagnetically below T C A = 300 K.However, as the temperature decreases, instead of M͑T͒ running at a constant value, as expected from a ferromagnet, it begins to decrease after reaching a maximum.Below this point the austenitic state begins to lose stability.Therefore, the temperature corresponding to this maximum is taken as M s .Its value of 264 K corresponds approximately to the temperature at which the feature associated with the structural transition in the cooling DSC curve approaches the base line ͓vertical arrow in Fig. 1͑a͔͒.Similarly, in the reverse transformation, A f is identified as the maximum in M͑T͒ lying at about 275 K. Below M s , M͑T͒ decreases with decreasing temperature and reaches a minimum as the proportion of FM austenite progressively decreases.Since the martensitic state is not ferromagnetic in this temperature regime ͑ferromagnetism appears below T C M ͒, the total magnetization of the mixed austenite-martensite decreases.Namely, the martensite acts as a nonferromagnetic entity lowering the total magnetization.As the sample is further cooled, a second FM transition occurs at T C M Ϸ 200 K, which lies close to M f determined from the DSC measurements.Below T C M , a large separation between FC and ZFC curves ͓Figs.11͑a͒ and 11͑b͔͒ is found.Due to the reduced symmetry of the martensitic state with respect to the cubic austenitic state, the number of easy axes can decrease, which in turn can be accompanied by an increase in the magnetic anisotropy.The increase in anisotropy can be seen in the low-field region of M͑H͒ shown in detail in Fig. 11͑d͒, where the initial slope of the magnetization decreases with decreasing temperature.Under these circumstances, the magnetic domain configuration below T C M will depend on the external cooling field conditions as the sample is cooled through T C M .This leads to the observed splitting in the FC and ZFC curves.A similar effect has also been observed in the Ni-Mn-Ga system. 12͑H͒ for x = 0.16 is plotted in Fig. 11͑c͒ at various temperatures.Here, it is seen that M͑H͒ does not saturate at temperatures in the range M s ഛ T ഛ T C A , indicating that even at these temperatures within the austenitic phase, the FM state incorporates nonferromagnetic entities.The M͑H͒ data shown with closed symbols at 186, 214, and 226 K in Fig. 11͑c͒ indicate the presence of a field-induced transition, whereby at 50 kOe, M͑H͒ at 214 and 226 K approach values similar to those of M͑H͒ at 250 K.Although 186 K is lower than M f determined from DSC measurements, an upturn in the curve associated with the field-induced transition is also found in M͑H͒ at about 40 kOe.
M͑T͒ and M͑H͒ for x = 0.155 are shown in Fig. 12. Around room temperature the sample undergoes a martensitic transformation, whereby the positions of the maxima in the FC and ZFC M͑T͒ curves correspond to M s and A f respectively ͓Fig.12͑b͔͒.Other than this, there is a second feature in M͑T͒ about 20 K below M s indicated as T * .To understand the nature of this feature, it is necessary to examine M͑H͒ ͓Fig.12͑c͔͒ at various temperatures and M͑T͒ in 50 kOe ͓Fig.12͑d͔͒.M͑H͒ at 330 and 290 K, i.e. on both sides and in the vicinity of M s , show linear behavior.However, the data at 330 K reach higher values than those at 290 K at the same field values.Namely, the magnetic shortrange correlations in the paramagnetic L2 1 state at 330 K are stronger than those at 290 K, which is below M s .Indeed, considering the high-temperature end of the curve in Fig. 12͑d͒, M͑T͒ increases with decreasing temperature in a manner that would approach an austenitic Curie temperature T C A as shown by the dashed guideline.However, before T C A can be reached, the structural transformation takes place at M s -the value of which is not altered in 50 kOe.M͑T͒ data show that hysteresis between FC and FH M͑T͒ curves prevails at temperatures around T * , and persists to temperatures down to below 70 K.This suggests that the martensitic transition is not complete and austenite coexists in the sys- With regard to T * , a similar situation occurs for the alloy with x = 0.15, which we discuss next.
M͑T͒ and M͑H͒ for x = 0.15 are plotted in Fig. 13.The features in the data are similar to those for the data of the x = 0.155 alloy, but M͑T͒ in 50 Oe is about 2 orders of mag-nitude smaller.Here also, the values of M s and A f are in good agreement with those obtained from the DSC measurements.M͑H͒ at temperatures above and below M s have similar character with those for the x = 0.155 alloy, i.e., the magnetic correlations in the austenitic state are stronger than those in the martensitic state.The tendency of the austenitic state to order magnetically is also observed in M͑T͒ for this sample.However, the sample transforms martensitically before magnetic ordering can occur.Similar to the situation for x = 0.155, there is hysteresis between the FC and FH M͑T͒, showing that austenite is present in the sample.Here also, the position of T * could be related to T C A .
3. Samples with compositions x = 0.10 and x = 0.05 At lower In concentrations, long-range FM ordering no longer occurs.This can be seen in the M͑T͒ and M͑H͒ data for the samples with x = 0.10 and x = 0.05 in Fig. 14.These samples transform martensitically above room temperature.The magnetization of these samples are about 3 orders of magnitude smaller in 50 Oe than in the case for the samples with well-defined FM ground states.For x = 0.10, M͑H͒ seen in Fig. 14͑b͒ is essentially linear at 350 K, but at 100 and 5 K an upward curvature is observed with respect to the linear reference line drawn in the figure.Such behavior can be attributed to the gradual reorientation of noncollinear spins in the direction of the magnetic field.For x = 0.05, M͑H͒ is linear at all temperatures, whereby it can be expected that the interactions become AF at this concentration as the composition of the antiferromagnet Ni 0.50 Mn 0.50 is approached.

IV. DISCUSSION
The Ni-Mn-In system near the Heusler composition shows marked differences in the magnetic properties from those of other Ni-Mn-based Heusler alloys.The major feature that particularly stands out is the increase of s with increasing Mn concentration.As for other Ni-Mn-based Heuslers, one would expect a weakening of the magnetic moment with increasing Mn concentration due to the decreased distance of the Mn-Mn bonds, thus leading to AF exchange.It appears that the considerably larger size of the In atom as compared to other group IIIA and group IVA elements ͑other than Tl͒ leads to a Mn-Mn separation that is large enough so that AF exchange of substantial strength cannot develop.In Ni-Mn-Sn and Ni-Mn-Ga Heusler alloys, where Sn has a smaller atomic radius than In, and the lattice constants of the alloys are smaller than in Ni-Mn-In at similar compositions, AF interactions do appear with increasing Mn content. 4,20ny weak AF exchange that develops in Ni 0.50 Mn 0.50−x In x , as evident in the separation of ZFC and FC curves for the alloys with compositions 0.25ജ x ജ 0.165, is essentially suppressed by the magnetization of the ferromagnetic matrix in high magnetic fields, so that M͑H͒ reaches saturation ͓Fig.10͑a͔͒.This property is found in the alloys that do not undergo a martensitic transformation.However, to understand the exact cause of the increase of s with increasing Mn concentration, the band structure giving the details of the overlap of p and d states is required.This would also explain why the ZFC-FC splitting weakens with increasing Mn concentration in the range 0.20ജ x ജ 0.17 and vanishes for x = 0.165.
In the case of the alloys that undergo martensitic transformations, one observes that high external fields do not wash out the features around the martensitic transitions as observed in Figs. 12 and 13.Instead, the features are accentuated.This is also the case for the alloy with x = 0.16, for which M͑T͒ in 50 kOe is shown in Fig. 15.However, unlike the other two samples with x = 0.155 and x = 0.15 that transform martensitically and show no shift in the transition temperatures, this alloy shows a strong shift of about 40 K in M s on applying a field of 50 kOe amounting to a rate of change of M s with respect to field of −0.8 K kOe −1 .This value is the same as that found in the calorimetric measurements in field ͑Fig.2͒.M s in 50 kOe ͑M s 50 kOe = 225͒ K and 50 Oe ͑M s 50 Oe = 264͒ K are shown in the figure.These data, along with the calorimetric data, indicate that the upturn in the M͑H͒ curves observed in the data of Fig. 11͑c͒ is attributed to a field-induced transition from the martensitic to the austenitic state.This situation is opposite to what is observed for Ni-Mn-Ga alloys, where an external field causes M s to shift to higher values. 13or alloys that undergo martensitic transformations around and below room temperature, a good agreement can be reached in the transition temperatures determined by M͑T͒ measurements in small magnetic fields and DSC measurements.The agreement is observed in the values of M s and A f for x = 0.155 and x = 0.15 collected in Table II and corresponds to the onset of the deviation from "normal" ferromagnetic behavior in M͑T͒ and the onset of the deviation from the baseline in dQ / dT.However, in the latter case, the uncertainty in the positioning of the baseline can make a difference in determining M s DSC .On the other hand, determining the position where M͑T͒ deviates from normal behavior requires no reference and is easily observed if considerable difference in strength of magnetic exchange accompanies the structural transition.Once M s M has been determined, M s DSC can be self-consistently cross checked, and the DSC results for the alloys with lower In concentrations ͑x = 0.10 and 0.05͒ can then be used to estimate their martensitic transition temperatures.
On the other hand, determining and cross checking M f and A s is not as straightforward.The prevalence of the hysteresis observed in FC and FH M͑T͒ down to low temperatures suggests that the austenitic phase is still present in a broad temperature range, whereas DSC measurements cannot resolve the presence of an austenitic state at the same temperatures.For practical purposes, however, M f and A s are estimated from the DSC measurements as described in the preceding paragraph.Neutron diffraction studies are required to confirm that the hysteresis in M͑T͒ is linked to the presence of austenite at low temperatures.
The high-field M͑T͒ results, together with the DSC, and low-field magnetization studies show that x = 0.16 is a critical concentration that separates alloys that transform martensitically from those that are stable in the L2 1 or the B2 phase.It is also the only composition that exhibits a field-induced transition.For a better understanding of the magnetic and structural changes occurring around the martensitic transition, magnetic field-dependent neutron diffraction experiments and magnetic field-dependent calorimetric measurements on the alloys with concentrations in the critical region are required.
Figure 16 shows the structural and magnetic transition temperatures as a function of the valence electron concentration.This diagram resembles that of the Ni-Mn-Sn system. 4 Whereas T C M shows very little change with e / a, the change in

T C
M is relatively rapid.The temperatures corresponding to T * of the x = 0.155 and x = 0.15 alloys are also included as T C A data in the diagram.M s , on the other hand, decreases with deceasing e / a and is expected to vanish around x = 0.17.In the critical composition range 0.16ജ x ജ 0.15, which corresponds to about 7.92ജ e / a ജ 7.87, the martensitic phase is FM at low temperatures.
The e / a dependence of the M s temperatures of Ni-Mn-based Heusler systems is plotted in Fig. 17.6][17] Instead of the data following a single curve, which would have supported e / a to have a universal character for the Heusler al-loys, 18,19,21 they have different slopes originating from their common point corresponding to Ni 0.50 Mn 0.50 ͑e / a = 8.5͒.Therefore, a simple choice of e / a as the concentration weighted valence electron per atom can only be considered to be a guideline for examining systematic changes only within a single-alloy system.A study on isoelectronic alloys obtained by substituting In for Ga to obtain Ni-Mn-Ga-In shows that, although e / a remains unchanged, the structural and magnetic transition temperatures vary considerably. 22he entropy and enthalpy changes at the martensitic transition calculated from the heat flow data are plotted in Fig. 18.Both ⌬S and ⌬H decrease with increasing In concentration.For systems where the main contribution to ⌬S is vibrational, such as in Cu-based Heusler alloys, there is no significant concentration dependence. 23On the other hand, a similar concentration dependence has been reported for Ni-Mn-Sn alloys, where the difference in the magnetic exchange interactions below and above M s is large. 4In fact, this large difference gave rise to a positive magnetic entropy change in the vicinity of the martensitic transformation leading to a large inverse magnetocaloric effect. 24A similar effect can also be expected to occur in the Ni-Mn-In system.
For a magnetic shape memory effect to occur at all, the presence of ferromagnetism in the martensitic state is necessary.The alloy with x = 0.16 is a particularly interesting candidate, since M s lies around room temperature and the alloy becomes FM at a lower temperature.The present study will also be complemented by magnetic field-induced strain studies to address the question as to whether a magnetic shape memory effect occurs in these alloys.

V. CONCLUSION
The type of modulated structure of martensite in Ni 0.50 Mn 0.50−x In x is found by x-ray studies to depend on the In composition.The structure changes in a 10M, 14M, and L1 0 sequence as the In concentration decreases.In a critical composition range 0.15ഛ x ഛ 0.16, the austenitic and martensitic phases are FM.However, the ferromagnetism of the parent and product phases is characterized by separate magnetic transition temperatures.The lowtemperature phase incorporates ferromagnetic components with complex magnetic domain structures which are coupled to the lattice degree of freedom.This is suggested by the splitting of the ZFC and FC curves measured in low external magnetic fields.For x = 0.16 a magnetic field-induced transitions at temperatures T Ͻ M s are observed.The strong shift in M s M suggests that the induced transition is structural.Due to the induced structural transition, the x = 0.16 sample is likely to exhibit large field-induced strains.We furthermore find that the features found in the low external magnetic field M͑T͒ data, especially the rapid decrease of the magnetization below M s , are retained when the measurements are performed in high magnetic fields.

FIG. 1 .
FIG. 1. dQ / dT vs temperature for the alloys undergoing martensitic transformations ͑a͒ x = 0.16; ͑b͒ x = 0.155; ͑c͒ x = 0.15; ͑d͒ x = 0.10; and ͑e͒ x = 0.05.Horizontal arrows indicate direction of temperature change.The temperature region indicated by the bracket in part ͑a͒ is where the austenitic state begins to lose stability.Vertical arrows in part ͑b͒ exemplify the positions of the martensitic and austenitic transition temperatures.

FIG. 2 .
FIG. 2. ͑Color online͒ dQ / dt vs T taken on cooling and under various magnetic fields.The inset shows the data in the temperature region of the major feature around the martensitic transition.The rate of shift in M s with respect to field amounts to −0.8 K kOe −1 .

FIG. 10 .
FIG.10.͑a͒ M͑H͒ at 5 K of samples with 0.165ഛ x ഛ 0.25.͑b͒ The magnetic moment per formula unit and the magnetic moment on Mn determined by assuming no moment on Ni and In for the samples with 0.165ഛ x ഛ 0.25.

FIG. 12 .
FIG. 12. ͑a͒ ZFC, FC, and FH M͑T͒ of the sample with x = 0.155 in H =50 Oe. ͑b͒ M͑T͒ plotted in a temperature range around the martensitic transition.͑c͒ M͑H͒ at selected temperatures given at the right of the figures in kelvin.Closed symbols pertain to data for T Ͼ M s .Prior to each M͑H͒ measurement, the samples were taken above 380 K and prepared in the ZFC state.͑d͒ M͑T͒ in 50 kOe.

FIG. 16 .
FIG. 16.The structural and magnetic transition temperatures as a function of the valence electron concentration for Ni-Mn-In.The open symbols represent values obtained from literature ͑Refs.5 and 14͒.

FIG. 18 .
FIG. 18. ⌬S and ⌬H as a function of e / a.

TABLE I .
Compositions of the Ni 0.50 Mn 0.50−x In x samples determined by EDX analysis and the valence electron concentrations per atom e / a.

TABLE II .
Martensite start and finish temperatures ͑M s , M f ͒, austenite start and finish temperatures ͑A s , A f ͒ determined by DSC and M͑T͒ measurements ͑DSC and M in superscript͒ and the enthalpy and entropy changes ͑⌬H , ⌬S͒ around the transition.

TABLE III .
Crystal structures and lattice parameters of Ni 0.50 Mn 0.50−x In x at room temperature.The structures of the samples with x = 0.155, x = 0.15, and x = 0.10 are monoclinic with ␤ = 88.45°,88.93°, and 93.67°, respectively.