Journal of Physics and Chemistry of Solids 74 (2013) 158–165

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Thermal strain and magnetization of the ferromagnetic shape memory alloyNi52Mn25Ga23 in a magnetic field

T. Sakon a,b,n, H. Nagashio b, K. Sasaki b, S. Susuga b, D. Numakura b, M. Abe b, K. Endo c, S. Yamashita c,H. Nojiri d, T. Kanomata e,f

a Department of Mechanical and Systems Engineering, Faculty of Science and Technology, Ryukoku University, Otsu 520-2194, Japanb Department of Mechanical Engineering, Graduate School of Engineering and Resource Science, Akita University, Akita 010-8502, Japanc Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japand Institute for Materials Research, Tohoku University, Sendai 980-8577, Japane Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo 985-8537, Japanf Department of Materials Research, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

a r t i c l e i n f o

Article history:

Received 3 August 2011

Received in revised form

27 August 2012

Accepted 2 September 2012Available online 10 September 2012

Keywords:

A. Alloys

B. Crystal growth

C. X-ray diffraction

D. Thermal expansion

D. Magnetic properties

97/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.jpcs.2012.09.004

esponding author at: Department of Mechani

of Science and Technology, Ryukoku Unive

1 77 543 7443; fax: þ81 77 543 7457.

ail address: sakon@rins.ryukoku.ac.jp (T. Sako

a b s t r a c t

The objective of this paper is the investigation of the correlations between crystal structure and the

magnetization of Ni–Mn–Ga Heusler alloy. Thermal strain, permeability, and magnetization measure-

ments of the ferromagnetic shape memory alloy Ni52Mn25Ga23 were performed across the martensite

transition temperature TM and reverse martensite transition temperature TR at atmospheric pressure.

When cooling from the austenite phase, thermal strain steeply decreases because of martensite

transition. Permeability suddenly increases at the Curie temperature TC¼358 K, indicating ferromag-

netism, and suddenly decreases to around TM¼328 K. This indicates that the lattice transformation and

magnetic phase transition correspond to each other. The percentage of contraction by martensite

transition at TM and in a magnetic field is twice that in zero fields. Considering with other Ni–Mn–Ga

alloys, it is supposed that the magnetic field influences the orientation of the easy c-axis along the

magnetic field, and then the variant rearrangement occurs, and consequently, the variation in the strain

between zero fields and non-zero field is observed. The measurement results indicate that the regions

above and below TM or TR are the ferromagnetic-austenite (Ferro-A) and ferromagnetic-martensite

(Ferro-M) phases, respectively. Magnetic phase diagrams were constructed from the results of the

temperature dependence of thermal strain. TM and TR increase gradually with magnetic field. TM shift in

magnetic fields (B) around zero magnetic field was estimated as dTM/dB¼0.46 K/T, indicating that

magnetization influences martensite transition and the dTM/dB value is the same as that of

Ni52Mn12.5Fe12.5Ga23, thereby suggesting the Ferro-M to Ferro-A transition.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Ferromagnetic shape memory alloys (FSMAs) have been exten-sively studied as potential candidates for smart materials. AmongFSMAs, Ni2MnGa is the most familiar alloy [1]. It has a cubic L21

Heusler structure (space group Fm3 m) with the lattice parametera¼5.825 A at room temperature, and it orders ferromagneticallyat the Curie temperature TCE365 K [2,3]. Upon cooling fromroom temperature, a martensite transition occurs at the marten-site transition temperature TME200 K. Below TM, a superstruc-ture forms because of lattice modulation [4,5]. For the Ni–Mn–Ga

ll rights reserved.

cal and Systems Engineering,

rsity, Otsu 520-2194, Japan.

n).

Heusler alloys, TM varies from 200 to 330 K by nonstoichiome-trically changing the concentration of composite elements.

Several studies on Ni–Mn–Ga alloys address the martensitetransition and correlation between magnetism and crystallo-graphic structures [6–18]. Ma et al. studied the crystallographyof Ni50þxMn25Ga25�x alloys (x¼2–11) by powder X-ray diffrac-tion and optical microspectroscopy [7]. In the martensite phase,typical microstructures were observed for xo7. The martensitevariants exhibit configurations typical of self-accommodationarrangements. The TEM image of Ni54Mn25Ga21 indicates thatthe typical width of a variant is about 1 mm. The interactionbetween the magnetism and crystallographic rearrangementswas discussed in Refs. [1,8,17,18]. The memory strain wasobserved in single crystal Ni2MnGa and polycrystallineNi53.6Mn27.1Ga19.3 [10]. As for the magnetism, the magneticanisotropy constant KU in martensite phase is 1.17�105 J/m3,which is four times higher than that in the austenite phase

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165 159

(0.27�105 J/m3) [1]. Manosa et al. suggested that the martensitictransition takes place in the ferromagnetic phase, and thedecrease in magnetization observed at intermediate fields(0oBo1 T) is due to the strong magnetic anisotropy of themartensite phase in association with the multi-domain structureof the martensite state [8]. Likhachev and Ullakko. stated that themagnetic driving force responsible for twin boundary motion ispractically equal to the magnetic anisotropy constant KU [17].The magnetization results indicate that the martensite Ni–Mn–Gaalloys have higher magnetocrystalline anisotropy. Furthermore,the magnetization results indicate that the coercivity and satura-tion field at martensite phase are higher than those of the cubicaustenite phase [11–15]. Zhu et al. investigated the lattice con-stant change Dc/c of �4.8% by means of X-ray diffraction studyaround martensite transition temperature [11]. Chernenko et al.also studied about the magnetization and the X-ray powderdiffractions, and clear changes were found at martensite tem-perature for both measurements [12]. Murray et al. studied thepolycrystalline Ni–Mn–Ga alloys [18]. The magnetization step atTM is also observed and this is a reflection of the magneticanisotropy in the tetragonal martensite phase. In the martensitephase, strong magnetic anisotropy exists. Then the magnetizationthat reflects the percentage of magnetic moments parallel to themagnetic field is smaller than that in the austenite phase wherethe magnetic anisotropy is not strong in the weak magnetic field.Therefore the magnetization step is observed at TM. NMR experi-ments indicate Mn–Mn indirect exchange via the faults in Mn–Galayers interchange caused by excessive Ga [13]. This resultindicates that the exchange interaction between Mn–Mn mag-netic moments is sensitive with the lattice transformation.Then the magnetism changes from soft magnet in the austenitephase to hard magnet in the martensite phase, which is due tohigher magnetic anisotropy.

To use Ni–Mn–Ga alloys as advanced materials for actuators,polycrystalline materials, etc. are useful because of their robust-ness. Moreover, in daily use, magnetic actuators should be usedaround room temperature (300 K). Therefore, we selected theNi52Mn25Ga23 alloy, which shows ferromagnetic transition at theCurie temperature TC, about 360 K, and the martensite transfor-mation occurs around 330 K.

The purpose of this study is to investigate the correlationbetween magnetism and crystallographic structures as it relatesto the martensite transition of Ni52Mn25Ga23, which undergoesthe martensite transition below TC [6,7]. Especially, we focused onthe physical properties in magnetic fields. We performed in thisstudy that by using the polycrystalline samples, it is possible toprovide information on the easy axis of magnetization in themartensite structure with temperature dependent strain mea-surements under constant magnetic fields. In this paper, thermalstrain, permeability, and magnetization measurements wereperformed for polycrystalline Ni52Mn25Ga23 in magnetic fields(B), and magnetic phase diagrams (B–T phase diagram) wereconstructed. The results of thermal strain in a magnetic fieldand magnetic-field-induced strain yield information about thetwin boundary motion in the fields. From the permeability andmagnetization measurements, the magnetic anisotropy constantKU can be calculated. The experimental results were comparedwith those of other Ni–Mn–Ga single crystalline or polycrystallinealloys, and correlations between magnetism and martensitetransition were found.

2. Experimental

The Ni52Mn25Ga23 alloy was prepared by arc melting 99.99%pure Ni, 99.99% pure Mn, and 99.9999% pure Ga in an argon

atmosphere. To obtain a homogenized sample, the reaction productwas sealed in double-evacuated silica tubes, and then annealed at1123 K for 3 days and quenched in cold water. The obtained samplewas polycrystalline. From X-ray powder diffraction, the 14M (P2/m)martensite structure and the D022 tetragonal structure were mixedat 298 K. The lattice parameters of the 14M structure werea¼4.2634 A, b¼5.5048 A, c¼29.5044 A, and b¼85.8631, and thoseof the D022 structure were a¼3.8925 A, and c¼6.5117 A. The size ofthe sample was 2.0 mm�2.0 mm�4.0 mm.

The measurements in this study were performed at atmo-spheric pressure, P¼0.10 MPa. Thermal strain measurementswere performed using strain gauges (Kyowa Dengyo Co., Ltd.,Chofu, Japan). Electrical resistivity of the strain gauges wasmeasured by the four-probe method. The relationship betweenstrain, e, and deviation of electrical resistivity, DR, is given by

e¼ 1

KS

DR

R0¼

1

KS

ðR�R0Þ

R0, ð1Þ

where KS is the gauge factor (KS¼1.98) and R0 is the electricalresistivity above TR. The strain gauge was fixed parallel to thelongitudinal axis of the sample.

Thermal strain measurements were performed using a 10 Thelium-free cryocooled superconducting magnet at the High FieldLaboratory for Superconducting Materials, Institute for MaterialsResearch, Tohoku University. In each field, the beginning tem-perature is 370 K and one thermal cycle, 370 K-310 K-370 K(370 K-320 K-370 K for 3 T and 5 T) was performed. Themagnetic field was applied along the longitudinal axis of thesample. The thermal strain is denoted by the reference strain at350 K.

Magnetization measurements were performed using a Bitter-type water-cooled pulsed magnet (inner bore: 26 mm; totallength: 200 mm) at Akita University. The magnetic field wasapplied along the longitudinal axis of the sample. The values ofmagnetization were corrected using the values of spontaneousmagnetization for 99.99% pure Ni. The magnetic permeabilitymeasurements were performed in AC fields with the frequencyf¼73 Hz and the maximum field Bmax¼0.0050 T using an ACwave generator WF 1945B (NF Co., Ltd., Yokohama, Japan) and anaudio amp PM17 (Marantz Co. Ltd., Kawasaki, Japan) at AkitaUniversity with the same magnet that we used for the magneti-zation measurement, having the compensating high homogeneitymagnetic field. AC fields were applied along the longitudinal axisof the sample.

3. Results and discussions

Fig. 1 shows the temperature dependence of permeability.When heating from 300 K, permeability increases gradually. Asshown in Fig. 1, permeability increases above 330 K and suddenlydecreases around 360 K. When cooling from a high temperature,permeability shows a sudden increase at about 356 K anddecreases at 325 K. The sudden changes in permeability indicatethat the ferrromagnetic transition occurs around 358 K.The temperature dependence of permeability for Ni52Mn25Ga23

is similar to that for Ni52Mn12.5Fe12.5Ga23, which shows a transi-tion of a ferromagnetic-martensite (Ferro-M) phase to aferromagnetic-austenite (Ferro-A) phase [19]. The step around330 K (heating process) and 325 K (cooling process) reflectsstronger magnetic anisotropy in the tetragonal martensite phase[8,18]. Polycrystalline Ni49.5Mn28.5Ga22, Ni50Mn28Ga22 andNi52Mn12.5Fe12.5Ga23 alloys also indicate the magnetization (orpermeability) step at TM [9,18,20] below the field of 10 mT.

Fig. 2(a) shows the linear thermal strain of Ni52Mn25Ga23.Solid lines are the experimental data and dotted lines are the

Fig. 1. Temperature dependence of the magnetic permeability m of Ni52Mn25Ga23

in AC fields with f¼73 Hz and Bmax¼0.0050 T. The origin of the vertical axis is the

reference point when the sample is empty in the pickup coil of the magnetic

permeability measurement system.

-4x10-3

-3

-2

-1

0

Rel

ativ

e th

erm

al s

train

360350340330320

O T

1 T

3 T

5 T

10 T

8x10-4

7

6

5

4

3

Stra

in

1086420Magnetic Field (T)

T (K)

Ni52Mn25Ga23

Fig. 2. (a). Temperature dependence of the linear thermal strain of Ni52Mn25Ga23

in static magnetic fields. The dotted lines are the extrapolated lines of the thermal

strain. (b). Magnetic field dependence of the strain at the martensite transition

temperature obtained from the thermal strain in (a).

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165160

extrapolated lines. At zero magnetic fields, the memory strain wasobserved, as polycrystalline Ni53.6Mn27.1Ga19.3 [10]. When heatingfrom 300 K, slight strain is observed first at zero magnetic fields.Around 334 K, a sharp strain is observed. The results of previousstudies [6,7] suggest that this is because of the reverse martensitetransition TR¼334 K, which is defined as the midpoint tempera-ture of the transition. When cooling from 370 K, a suddendecrease is observed at 328 K. Therefore the martensite transitiontemperature TM is 328 K. The permeability at the Ferro-M phase isvery low compared with that at the Ferro-A phase. The results ofpermeability and linear strain measurements indicate that theregion above TM is a Ferro-A phase and that below TM is a Ferro-Mphase. The permeability measurement results indicate that theferromagnetic transition from the paramagnetic-austenite (Para-A) phase to the Ferro-A phase occurs around 358 K (see Fig. 1). Onthe other hand, the linear strain does not show a noticeableanomaly at the ferromagnetic transition around 358 K.

When cooling from 370 K, the thermal strain shows a peak at329 K. This may be attributed to the intermingling of the L21

austenite lattices and the M14 martensite lattices at the marten-site transition. The sequential phenomenon is observed in singlecrystalline Ni2.19Mn0.81Ga [22]. Zhu et al. suggests that the smallsatellite peaks in the heat flow plot, which flanks the central peak,indicates the structural transition taking place in multiple steps[11]. The contraction at TM under zero fields is about 0.5�10�3

(0.05%). As for other Heusler alloys, Ni52Mn12.5Fe12.5Ga23 andNi2Mn0.75Cu0.25Ga, the contraction occurs at martensite tempera-ture [20]. The strain at TM of polycrystalline Ni52Mn12.5Fe12.5Ga23

was estimated as 0.14% contraction. This value is larger than thatof Ni52Mn25Ga23. After zero field measurements of the linearstrain, measurements in magnetic fields from 1 T to 10 T wereperformed. The strain at TM under the magnetic field of 1 T wasestimated as 0.10% contraction, which is twice to that under zeromagnetic field (0.05%). These results indicate that the magneticfields influence the structural phase transition. After these ther-mal cycles in magnetic fields, the thermal strain in zero fields was0.05% contraction, which is as same as the first cycle in zero fields.Around 358 K, which is the ferromagnetic transition temperature,no anomaly was observed in the magnetic fields. Fig. 2(b) showsthe magnetic field dependence of the strain at TM. At zero field,the strain is 3.6�10�4. On the other hand, the strain in amagnetic field is about 7.1�10�4, which is almost twice to thatin zero field. Ullakko et al. measured the magnetic-field-induced

strain of a Ni2MnGa single crystal [1]. The strain at TM in zero fieldwas 2�10�4. This is only a small fraction compared with thelattice constant change for c-axis from the austenite to martensitephases, which was Dc/c¼6.56%. It is proposed that the strainaccommodation is occurred by different twin variant orientations.As shown in Fig. 2(b), the thermal strain under the magnetic field

Fig. 3. Magnetostriction of Ni52Mn25Ga23 at 300 K in a static magnetic field

up to 10 T.

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165 161

of 1 T was 7.2�10�4, indicating that the field aligned some of thetwin variants.

In the martensite phase, the magnetic moment in the magneticeasy direction was coupled with the strain along the short c-axisof the martensite variant structure. As a result, under the appliedmagnetic field, the variant rearrangement occurs with the assis-tance of twin boundary motion, such that the magnetic easy axisis parallel to the applied field. Therefore, the total magnetic freeenergy is minimal. The variant rearrangement results in fieldinfluence on the thermal expansion as shown in Fig. 2(b).

Variation in the strain between zero field and non-zero field wasobserved for Ni2.19Mn0.81Ga and Ni2.20Mn0.80Ga polycrystallinesamples [21]. The change in the sample length by means of thethermal strain measurements at the martensite phase transition was0.04% for Ni2.19Mn0.81Ga and 0.12% for Ni2.20Mn0.80Ga. The thermalstrain for Ni2.19Mn0.81Ga in the presence of 1.4 T magnetic field wasincreased to 0.13%, which means 3.2 times increase of strain.The increase of strain was 2.6 times (0.31% strain) forNi2.20Mn0.80Ga. The variation in the strain between zero field andnon-zero field was also observed for Ni49.6Mn27.3Ga23.1 polycrystal-line samples [31]. With increasing measured magnetic fields, thedifference in the strain increased. Aksoy et al. proposed that thestrain increase is due to increase of the preferred alignment of theshort c-axis along the applied field, and, high twin boundarymobility in Ni–Mn–Ga is expected to be the main case of thealignment, although the martensite variant nucleation with pre-ferred c-axis orientation in the external field at the martensitetransition temperature is also the influence of the shrinkage [31].Further they mentioned that, when the sample was cooled from theaustenite down to the martensite phase in zero fields, no preferredorientation is given to the variant growth during nucleation,whether the easy axis is a long axis or a short axis. When a magneticfield is applied in the austenite phase and the sample is cooled downthrough TM in the constant field, a preferred growth direction isprovided to the variants. Consequently, the variants with easy axisalong the applied field direction nucleate more and more. If the easyaxis is a short axis, the sample length decreases. Then the contrac-tion at TM is observed in thermal strain measurements.

As for Ni2MnGa single crystal, in the zero-field cooling process,strains of nearly 0.02% have been observed at TM¼276 K [1].The strain at transformation in 1.0 T is 0.145%, indicating that thefield has aligned some of the twin variants. Now we compare thestrain and the magnetization results of Ni2þxMn1�xGa alloys [28].For the alloys which showed increase of strain for x¼0.18 and0.20, the TM and TC are identical temperatures. Consequently, themagnetization change is large. For alloys of these compositions,clear hysteresis in the magnetization was observed, which indi-cates first order magnetic transition. From these results, it issupposed that the magnetic field influences the orientation of theeasy c-axis along the magnetic field. As for Ni52Mn25Ga23, themagnetization change is large at TM, as shown in Fig. 8. Thepermeability in Fig. 1 shows clear change and hysteresis, whichindicates the first order transition. It is also supposed that themagnetic field influences the orientation of the easy c-axis alongthe magnetic field, and then the variant rearrangement occurs.Consequently, the variation in the strain between zero fields andnon-zero field was observed.

Fig. 3 shows the magnetic-field-induced strain at 300 K (Ferro-M phase) in a static magnetic field. When increasing the magneticfield from zero field, a sudden contraction occurs up to 1 T. Above1 T, a gradual contraction is observed. When decreasing themagnetic field from 10 T, a modicum of strain occurs. Below 1 T,a sudden strain is observed. The magnetic-field-induced strain at10 T is �100 ppm or �0.010%.

Now we compare the differences in the driving forces ofthe variant rearrangements in two cases. One is martensitic

transformation shown in Fig. 2(a), and the other is magnetic-field-induced strain shown in Fig. 3. For the former case, thedriving force is originated from phase transformation. Thereforethe magnitude is great and, as a consequence, the phase-inducedvariant rearrangements are easy and occur throughout the sam-ple. For the latter case, the magnetic-field-induced twin boundarymotion is driven by the limited magnetic anisotropy energy,which is lower than the martensitic phase transformation drivingforce. Consequently, the variant orientation is limited by themobile twin boundaries that are not pinned by any obstaclessuch as grain boundaries or defects. As a result, the variantrearrangement and the magnetostriction are limited. Thereforethe magnetic-field-induced strain is smaller than the strain at TM,in the linear strain measurements.

The magnetic-field-induced strain of the polycrystallineNi50Mn28Ga22 alloy was reported by Murray et al. [18]. Theymentioned that the strain in the martensite phase below TM is anorder of magnitude smaller than that of a single crystal ofstoichiometric compounds [1]. They attributed this to the poly-crystalline nature of the material or to the presence of impuritiesthat impede twin boundary motion. The field-induced strain ofNi50Mn28Ga22 increases on cooling from the austenite phase,leading to an abrupt increase with the appearance of twin variantbelow TM. On heating from the martensite phase, an abruptincrease occurs in the field-induced strain around TM. Theysuggest that this is caused by lattice softening near TM. As forthe thermal strain of Ni52Mn25Ga23, shown in Fig. 2(a), peaksappear for both TM and TR in zero field and all values of themagnetic field. The peak at TR, associated with heating, is largerthan that at TM, associated with cooling. These peaks indicate thatthe lattice expands abruptly. Dai et al. studied the elasticconstants of a Ni0.50Mn0.284Ga0.216 single crystal using the ultra-sonic continuous-wave method [22]. C11, C33, C66, and C44 modeswere investigated; every mode indicated abrupt softening aroundTM. This lattice softening appears to be affected by the abruptexpansion just above TM when cooling from the austenite phase.

Fig. 4 shows the magnetic phase diagram of Ni52Mn25Ga23.With increasing field, TM and TR gradually increase. The shifts in TM

and TR around zero magnetic field are estimated as dTM/dB¼0.46 K/T and dTR/dB¼0.43 K/T, respectively, which are similarto those of the Ni52Mn12.5Fe12.5Ga23 alloy (dTM/dB¼0.5 K/T) [20].

Fig. 5 shows magnetization curves of Ni52Mn25Ga23 in a pulsedmagnetic field up to 2.2 T. The unit of magnetization M is J/m0 kg Tin the SI unit system or emu/g in the CGS unit system

Fig. 4. Magnetic phase diagram of Ni52Mn25Ga23. Filled squares indicate the

martensite transition temperature TM. Filled triangles indicate reverse martensite

temperature TR.

Fig. 5. Magnetization of Ni52Mn25Ga23 in a pulsed magnetic field up to 2.2 T.

Fig. 6. Magnetization of Ni52Mn25Ga23 in a pulsed magnetic field up to 15 T.

Fig. 7. Arrott plot of magnetization of Ni52Mn25Ga23. Dotted straight lines are

extrapolated lines.

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165162

(both having identical numerical values). The M–B curves weremeasured from low temperature. The hysteresis of the M–B curveis considerably small. The magnetocaloric effects in other mag-netic materials were also reported; for example, Levitin et al.reported for Gd3Ga5O12 [23]. They performed magnetizationmeasurements at an initial temperature of 4.2 K, where themagnetic contribution to heat capacity is comparable to thelattice heat capacity. In our experiment, the temperature changeof the sample due to the magnetocaloric effect is considered to bewithin 1 K. This is because these experiments were performedaround room temperature, where the lattice heat capacity ismuch larger than the heating or cooling power by the magneto-caloric effect.

The M–B curves show ferromagnetic behavior below 356 K. Itis clear that the field dependence of magnetization at the Ferro-Aphase above TR¼334 K is different from that at the Ferro-M phasebelow TR. At the Ferro-M phase, magnetization increases withmagnetic fields. On the other hand, at the Ferro-A phase between334 and 356 K, a sudden increase in magnetization occursbetween 0 and 0.1 T.

Fig. 6 shows magnetization in a magnetic field up to 15 T. Inhigh magnetic fields, an almost linear increase can be seen foreach M–B curve. In particular, as for the M–B curve below 334 K,the high magnetic field susceptibility is quite small.

Fig. 7 shows the Arrott plot of Ni52Mn25Ga23. The spontaneousmagnetization at 294 K in a Ferro-M phase is 55.0 J/m0 kg T. TheCurie temperature of the austenite phase TCA determined byArrott plots in Fig. 7 is 358 K. This is consistent with the x–T

phase diagram of Ni50þxMn25Ga25�x [6,7]. In high magnetic fields,an almost linear increase can be seen for each M–B curve.Ni2Mn0.75Cu0.25Ga also shows the difference in magnetizationbetween 302 and 305 K, which is somewhat lower than TC¼307 Kor TM¼308 K [20]. Note that the Arrott plots of Ni52Mn25Ga23 lefta space between 333 and 335 K, and Ni2Mn0.75Cu0.25Ga left aspace between 302 and 303 K. The spontaneous magnetizationsof Ni52Mn25Ga23 are 42.2 J/m0 kg T at 333 K and 34.2 J/m0 kg T at335 K, which were obtained by the Arrott plot shown in Fig. 7. Asfor Ni2Mn0.75Cu0.25Ga, the spontaneous magnetizations are 40.0 J/m0 kg T at 302 K and 28.3 J/m0 kg T at 303 K.

Fig. 8 shows the temperature dependence of the magnetizationM–T at 0.1, 0.5, and 1 T, which was obtained by magnetizationmeasurements in pulsed magnetic fields. Open circles are thespontaneous magnetizations, which was obtained by the Arrottplot method. A sudden decrease is apparent between 333 and

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165 163

336 K for each field. This temperature region corresponds to thesharp increase in permeability when heating from low temperaturein Fig. 1, and just below TR, which was obtained by the linear strainmeasurement in Fig. 2(a).

The M–T curve in Fig. 8 can be seen as the combination of twosingle-phase M–T curves. One corresponds to the martensitephase, and the other corresponds to the austenite phase. Theobtained Curie temperatures in the martensite phase and theaustenite phase are TCM¼333.570.5 K and TCA¼358.070.5 K.This is due to the difference inferromagnetic interactions for bothstructural phases. These analyses of magnetic properties inNi51.9Mn23.2Ga24.9 were also reported in Ref. [11].

It is well known that the tetragonal martensite Ni–Mn–Ga hashigher magnetocrystalline anisotropy in association with themulti-dominant structure of the martensite phase. Consequently,lower initial permeability and higher coercivity than the cubicaustenite Ni–Mn–Ga alloys can occur [8,11–13,15]. The martensitetransition occurs in the ferromagnetic phase, and the decrease inmagnetization is observed at intermediate fields for 0oBo0.5 T,as shown in Fig. 8. This property is also shown by magnetization inmany Ni–Mn–Ga alloys (e.g., Ni49.5Mn25.4Ga25.1) and Ni–Mn–Snalloys (e.g., Ni50Mn35Sn15) [8,24,25]. Consequently, at low field,

Table 1Spontaneous magnetization and dTM/dB of Ni2þxMn1�xGa, Ni52Mn12.5Fe12.5Ga23, N

spontaneous magnetizations in martensite phase and austenite phase, respectively. Fe

Sample MM MA

Ni2MnGa 90 J/m0 kg T at 180 K (n1) 80 J/m0 kg T at 220

Ferro Ferro

Ni2.19Mn0.81Ga 2.0 (a.u.) (n4) at 300 K 0 (a.u.) (n4) at 350

Ferro Para

Ni52Mn12.5Fe12.5Ga23 63.1 J/m0 kg T at 250 K 52.7 J/m0 kg T at 3

Ferro Ferro

Ni2Mn0.75Cu0.25Ga 42.4 J/m0 kg T at 300 K 0 J/m0 kg T at 307

Ferro Para

Ni2MnGa0.88Cu0.12 37.3 J/m0 kg T at 330 K 0 J/m0 kg T at 340

Ferro Para

Ni52Mn25Ga23 42.2 J/m0 kg T at 333 K 34.2 J/m0 kg T at 3

Ferro Ferro

60

40

20

0

Mag

netiz

atio

n (J

/µ0k

gT)

370360350340330320310300

0.1 T

0.5 T

1 T

T (K)

TCM TCA

Ni52Mn25Ga23

Fig. 8. Temperature dependence of magnetization of Ni52Mn25Ga23. Open circles

are spontaneous magnetizations, which was obtained by the Arrott plot method.

Dotted lines are the extrapolated lines of spontaneous magnetization plots. TCM

and TCA indicate the martensite Curie temperature and the austenite Curie

temperature, respectively.

the austenitic Ni–Mn–Ga (with softer ferromagnetism) shows anabrupt increase in M, while the martensite Ni–Mn–Ga (withharder ferromagnetism) shows gradual increase in M with thefield. On the other hand, the martensite Ni–Mn–Ga (in low-temperature phase) has higher saturation magnetization (typi-cally, Ms increases with decreasing temperature) than the auste-nite Ni–Mn–Ga. As a result, at very high field or saturation field(41 T), magnetization of the martensite is higher than that of theaustenite, as shown in Figs. 6 and 8. As for other Ni–Mn–Ga alloys,Kim et al. reported magnetization in a Ni2.14Mn0.84Ga1.02 singlecrystal, which shows a transition from the Ferro-A phase toFerro-M phase with 14M structure [14]. The magnetization curvein Ni2.14Mn0.84Ga1.02 at 290 K, just below the martensite transitiontemperature, sharply bend at the critical field, BS¼0.6 T, and above0.6 T, the magnetization slightly increases with increasing fields. Onthe other hand, a bend in the magnetization is not clear. We definedthe critical field BS in Ni52Mn25Ga23 as the field where themagnetization Arrott plot was off from the extrapolated linear line,which is illustrated by the dotted line in Fig. 7, and obtained BS as0.84 T, which is of the same order as that in Ni2.14Mn0.84Ga1.02.The magnetization is the same as that in Ni52Mn25Ga23. The magneticanisotropy constant KU in a Ni2MnGa single crystal is 1.17�105 J/m3

(11.7�105 erg/cm3) in the martensite phase and 2.7�104 J/m3

(2.7�105 erg/cm3) in the austenite phase [1], indicating that themagnetic anisotropy is about four times larger in the martensitephase than that in the austenite phase. The Zeeman energy and/ormagnetocrystalline anisotropy energy that is sufficient to inducemotion of the twin boundary is denoted as MSBS/2¼KU [1].Kim et al. also mentioned that the magnetocrystalline anisotropyenergy is of the order of 105 J/m3 [14]. The spontaneous magnetiza-tion in Ni52Mn25Ga23 at 333 K, just below TR is 42.2 J/m0 kg T, whichwas obtained by the Arrott plot in Fig. 8. When using this value as MS,the magnetocrystalline anisotropy energy in the martensite phaseof Ni52Mn25Ga23 is MSBS/2¼KU¼1.04�105 J/m3, which is on thesame order as that in the martensite phase of Ni2MnGa. Thesemagnetic properties were also shown for Ni51.9Mn23.2Ga24.9 [11],Ni49.5Mn25.4Ga25.1 [12], and Ni54Mn21Ga25 [13].

The relationship between magnetism and TM in magnetic fieldsis discussed for Ni2MnGa-type Heusler alloys. Table 1 shows thespontaneous magnetizations and dTM/dB values of Ni2þxMn1�xGa,Ni52Mn12.5Fe12.5Ga23, Ni2Mn0.75Cu0.25Ga, Ni2MnGa0.88Cu0.12, andNi52Mn25Ga23. As for Ni2þxMn1�xGa alloys, shifts in TM in mag-netic fields were observed by magnetization measurements[2,26–28]. TM and TC of Ni2MnGa (x¼0) are 200 and 360 K,respectively. The region above TM is the Ferro-A phase. The samplewith x¼0 of Ni2þxMn1�xGa shows phase transition from theFerro-A to Ferro-M phases at TM. The sample with x¼0.19 shows

i2Mn0.75Cu0.25Ga, Ni2MnGa0.88Cu0.12, and Ni52Mn25Ga23. MM and MA indicate

rro and Para mean the ferromagnetic and the paramagnetic phases, respectively.

(MM�MA)/MM dTM/dB (K/T) Remarks

K (n1) 0.11 0.20 (n2) n1 Ref. [2]

0.4070.25 (n3) n2 Ref. [26]

n3 Ref. [27]

K 1.0 1.0 (n4) n4 Ref. [29]

00 K 0.16 0.5 Ref. [20]

K 1.0 1.2 Ref. [20]

K 1.0 1.3 Ref. [30]

35 K 0.19 0.43 This work

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165164

ferromagnetic transition and martensite transition at TM. For x¼0,the shift in TM is estimated as dTM/dB¼0.2 K/T [26] and forx¼0.19, dTM/dB¼1.0 K/T [27]. The shift in TM for x¼0.19 is higherthan that for x¼0. These results indicate that the shift in TM for thealloy that shows Para-A to Ferro-M phase transition is larger thanthat for the alloy that shows Ferro-A to Ferro-M phase transition.The values of dTM/dB are roughly proportional to the change inspontaneous magnetization, (MM�MA)/MM, as shown in Table 1.This indicates that the magnetic moments influence the marten-site transition; in other words, the structural transition and the TM

increase in accordance with the magnetic fields are proportionalto the difference between the magnetization of the austenitephase and that of the martensite phase. Therefore, it is consideredthat the alloys, in which TM and TC are close to each other, show alarger shift in TM in magnetic fields.

Khovailo et al. discussed the correlation between the shifts inTM for Ni2þxMn1�xGa (0rxr0.19) using theoretical calculationsaccording to the Clapeyron–Clausius formalism [28,29].The experimental values of this shift for Ni2þxMn1�xGa (0rxr0.19) are in good agreement with the theoretical calculationresults. In general, in a magnetic field, the Gibbs free energy islowered by the Zeeman energy �DMB that enhances the motiveforce of the martensite phase transition. Thus, TM of the ferro-magnetic Heusler alloys Ni52Mn12.5Fe12.5Ga23, Ni2Mn0.75Cu0.25Ga,and Ni2MnGa0.88Cu0.12 in recent studies [20,30] andNi52Mn25Ga23 in this study are considered to have shifted inaccordance with the magnetic fields because high magnetic fieldsare favorable for ferromagnetic-martensite phases.

Chernenko et al. studied the temperature dependence of boththe saturation magnetic field values and the x-ray powderdiffraction patterns of Ni–Mn–Ga alloys and analyzed with thetheoretical consideration [12]. The theory proposes that the freeenergy for ferromagnetic-martensite phase, exposed to an exter-nal magnetic field, is expressed as three terms. First term is themagnetic anisotropy energy. The second and third terms describethe magnetostatic and the Zeeman energy, respectively. The c/aratio is expressed as

c=a¼ 1�½ðHS=MÞþ9D1�D29�

12d, ð2Þ

where Hs indicates the saturation magnetic field. M denotes theabsolute value of the magnetization. D1 and D2 denote thediagonal matrix elements, and d is the dimensionless magnetoe-lastic parameter. The linear dependence of the magnetic aniso-tropy constant on the tetragonal distortion of the cubic crystallattice arises in the course of the martensite transition.

In order to apply this theory to our present work, it isconsidered that further theoretical consideration is needed toapply this theory for analyzing the influence between the mar-tensite variant structure and the magnetic field, which is reflectedby the Zeeman term.

4. Conclusions

Thermal strain, permeability, and magnetization measure-ments were performed on the Heusler alloy Ni52Mn25Ga23.

1.

Thermal strain: When cooling from the austenite phase, a steepdecrease in the thermal strain is obtained because of themartensite transition. TM and TR increase gradually withincreasing magnetic fields. The shifts in TM and TR in amagnetic field are estimated as dTM/dB¼0.46 K/T and dTR/dB¼0.43 K/T, respectively.

2.

Magnetization and permeability: Permeability abruptly changesaround TM and TR. Permeability below TM is about one-third to

that above TM. The temperature dependence of magnetizationalso shows a clear discontinuity around TM. The Arrott plot ofmagnetization indicates that TC is 358 K. The sudden decreasein magnetization at the temperature of martensite transitionand the M–B curve indicate the magnetism of the hard Ferro-Mphase and the soft Ferro-A phase.

3.

The dTM/dB values are roughly proportional to the change inspontaneous magnetization [(MM�MA)/MM] in Ni2MnGa-typeHeusler alloys. The TM of the ferromagnetic Heusler alloyNi52Mn25Ga23 in the magnetic field is shifted in accordancewith the magnetic fields and proportional to the difference inmagnetization between the austenite and martensite phases.

Acknowledgments

This study was supported by a Grant-in-Aid of the threeuniversities cooperation project in North Tohoku area in Japan,and Japan Science and Technology Project no. AS232Z02122B.This study was also partly supported by a Grant-in-Aid forScientific Research (C) (Grant no. 21560693) from the JapanSociety for the Promotion of Science (JSPS) of the Ministry ofEducation, Culture, Sports, Science and Technology, Japan.

This study was technically supported by the Center forIntegrated Nanotechnology Support, Tohoku University, and theHigh Field Laboratory for Superconducting Materials, Institute forMaterials Research, Tohoku University. One of the authors (H.N.)acknowledges the support by GCOE-material integration.

References

[1] K. Ullakko, J.K. Huang, C. Kantner, R.C. O’Handley, V.V. Kokorin, Appl. Phys.Lett. 69 (1996) 1966–1968.

[2] P.J. Webster, K.R.A. Ziebeck, S.L. Town, M.S. Peak, Philos. Mag. B 49 (1984)295–310.

[3] P.J. Brown, J. Crangle, T. Kanomata, M. Matsumoto, K.-U. Neumann,B. Ouladdiaf, K.R.A. Ziebeck, J. Phys.: Condens. Matter 14 (2002)10159–10172.

[4] J. Pons, R. Santamarta, V.A. Chernenko, E. Cesari, J. Appl. Phys. 97 (2005)083516–083522.

[5] R. Ranjan, S. Banik, S.R. Barman, U. Kumar, P.K. Mukhopadhyay, D. Pandey,Phys. Rev. B 74 (2006) 224443–224450.

[6] C. Jiang, G. Feng, S. Gong, H. Xu, Mater. Sci. Eng. A 342 (2003) 231.[7] Y. Ma, C. Jiang, Y. Li, H. Xu, C. Wang, X. Liu, Acta Mater. 55 (2007) 1533–1541.[8] L. Manosa, X. Moya, A. Planes, T. Krenke, M. Acet, E.F. Wassermann, Mater. Sci.

Eng. A 481–482 (2008) 49–56.[9] V. Sanchez-Ala’rcos, J.I. Perez-Landaza’bal, C. Go’mez-Polo, V. Recarte, J.

Magn. Magn. Mater. 320 (2008) e160–e163.[10] A. Rudajevov�a, J. Alloys Compd. 430 (2007) 153–157.[11] F.Q. Zhu, F.Y. Yang, C.L. Chien, L. Ritchie, G. Xiao, G.H. Wu, J. Magn. and Magn.

Mater. 288 (2005) 79–83.[12] V.A. Chernenko, V.A. L’vov, V.V. Khovailo, T. Takagi, T. Kanomata, T. Suzuki,

R. Kainuma, J. Phys.: Condens. Matter 16 (2004) 8345–8352.[13] V.O. Golub, A.Y. Vovk, C.J. O’Connor, V.V. Kotov, P.G. Yakovenko, K. Ullakko, J.

App. Phys. 93 (2003) 8504.[14] J. Kim, F. Inaba, T. Fukuda, T. Kakeshita, Acta Mater. 54 (2006) 493–499.[15] A. Gonzalez-Comas, E. Obrado, L. Mafiosa, A. Planes, A. Labarta, J. Magn.

Magn. Mater. 196–197 (1999) 637–638.[16] N. Lanska, O. So€derberg, A. Sozinov, Y. Ge, K. Ullakko, V.K. Lindroos, J. App.

Phys. 95 (2004) 8074.[17] A.A. Likhachev, K. Ullakko, Phy. Lett. A 275 (2000) 142–151.[18] S.J. Murray, M. Farinelli, C. Kantner, J.K. Huang, S.M. Allen, R.C. O’Handley, J.

App. Phys. 83 (1998) 7297–7299.[19] D. Kikuchi, T. Kanomata, Y. Yamaguchi, H. Nishihara, J. Alloys Compd. 426

(2006) 223–227.[20] T. Sakon, H. Nagashio, K. Sasaki, S. Susuga, K. Endo, H. Nojiri, T. Kanomata,

Mater. Trans. 52 (2011) 1142–1147.[21] A.N. Vasil’ev, E.I. Estrin, V.V. Khovailo, A.D. Bozhko, R.A. Ischuk,

M. Matsumoto, T. Takagi, J. Tani, Int. J. Appl. Electromagn. Mechan. 12(2000) 35–40.

[22] L. Dai, J. Cullen, M. Witting, J. Appl. Phys. 95 (2004) 6957–6959.[23] R.Z. Levitin, V.V. Snegirev, A.V. Kopylov, A.S. Lagutin, A. Gerber, J. Magn.

Magn. Mater. 170 (1997) 223–227.[24] J. Markos, A. Planes, L. Manosa, F. Casanova, X. Battle, A. Labarta, B. Martinez,

Phys. Rev. B 66 (2002) 224413.

T. Sakon et al. / Journal of Physics and Chemistry of Solids 74 (2013) 158–165 165

[25] T. Krenke, M. Acet, E.F. Wassermann, X. Moya, L. Manosa, A. Planes, Phys. Rev.B 72 (2005) 014412.

[26] A. Gonz�alez-Comas, E. Obrado, L. Manos, A. Planes, V.A. Chernenko,B.J. Hattink, A. Labarta, Phys. Rev. B 60 (1999) 7085–7090.

[27] D.A. Filippov, V.V. Khovailo, V.V. Koledov, E.P. Krasnoperov, R.Z. Levitin,V.G. Shavrov, T. Takagi, J. Magn. Magn. Mater. 258–259 (2003) 507–509.

[28] V.V. Khovailo, V. Novosad, T. Takagi, D.A. Filippov, R.Z. Levitin, A.N. Vasil’ev,Phys. Rev. B 70 (2004) 174413–174418.

[29] V.V. Khovailo, T. Takagi, T.J. Tani, R.Z. Levitin, A.A. Cherechukin,M. Matsumoto, R. Note, Phys. Rev. B 65 (2002) 092410–092413.

[30] T. Sakon, H. Nagashio, K. Sasaki, S. Susuga, D. Numakura, M. Abe, K. Endo,

H. Nojiri, T. Kanomata, Phys. Scr. 84 (2011) 045603. (6 pages).[31] S. Aksoy, T. Krenke, M. Acet, E.F. Wassermann, Appl. Phys. Lett. 91 (2007)

251915. (3 pages).