metals

Article Magnetostriction of Ni2Mn1−xCrxGa Heusler Alloys

Takuo Sakon 1,*, Naoki Fujimoto 1, Takeshi Kanomata 2 and Yoshiya Adachi 3

1 Department of Mechanical and System Engineering, Faculty of Science and Technology, Ryukoku University, Otsu 520-2194, Shiga, Japan; [email protected] 2 Research Institute for Engineering and Technology, Tohoku Gakuin University, Tagajo 985-8537, Miyagi, Japan; [email protected] 3 Graduate School of Science and Engineering, Yamagata University, Yonezawa 992-8510, Yamagata, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-77-543-7443

Received: 12 August 2017; Accepted: 28 September 2017; Published: 1 October 2017

Abstract: Among the functionalities of magnetic Heusler alloys, magnetostriction is attracting considerable attention. The alloy Ni2MnGa has a premartensite phase, which is a precursor state to the martensitic transition. Some researchers have observed magnetostriction in this alloy in the premartensite phase. We performed magnetostriction studies on the premartensite phase of related Cr-substituted Ni2Mn1−xCrxGa alloys and measured the thermal strain, permeability, magnetisation, and magnetostriction of polycrystals. Our thermal expansion measurements show an anomaly that indicates the occurrence of lattice deformation below the premartensitic transition temperature TP. Our permeability measurements also showed an anomaly at the premartensitic transition. From our magnetisation results, we obtained the magnetic-anisotropy constant K1. In the martensite phase, we found that the magnetic-anisotropy constant of the x = 0.00 alloy is larger than that of the x = 0.15 alloy. At 0.24 MA/m, we obtained a magnetostriction of −120 ppm for the x = 0.15 alloy. Magnetostriction in the premartensite phase is larger than that in the austenite and martensite phases at low magnetic-field strength, thus indicating that it is related to lattice softening in the premartensite phase. The e/a is proportional to the magnetostriction and TP, which indicates that the electron energy, the magnetostriction, and the Tp are correlative each other.

Keywords: shape-memory alloys; premartensitic transition; thermal expansion; magnetostriction

1. Introduction

1.1. Magnetostriction and -Induced Strain of Ferroagnetic Shape Memory Alloys Recently, ferromagnetic shape-memory alloys (FSMAs) have been studied extensively as candidates for highly functional magnetostriction materials for use as actuators, tremblers, and magnetic . Among FSMAs, the alloy Ni2MnGa is the most well-known [1]. It has a cubic L21 type Heusler structure (space group Fm3m) and a ferromagnetic transition that occurs at the Curie temperature TC = 365 K [2,3]. During cooling from ambient temperature, a martensitic transition occurs at the martensite transition temperature TM = 200 K. Below TM, a superstructure state develops as a result of lattice modulation [4,5]. Conventional magnetostriction is the distortion of crystal lattice caused by the rotation of the magnetic moment. FSMAs can induce large strain through martensitic transition or rearrangements of variants induced by external magnetic fields. This is called “twinning magnetostriction”, which was discovered by Ullakko and colleagues [1,6]. They discovered 1.5 × 103 ppm magnetostriction for a of Ni-Mn-Ga. This value is comparable to the magnetostriction of 3d/rare-earth intermetallic compounds TbFe2, DyFe2 [7] and Tb0.3Dy0.7Fe2 (terfenol-D) [8]. The reverse transition from martensite phase to parent phase in magnetic fields—which

Metals 2017, 7, 410; doi:10.3390/met7100410 www.mdpi.com/journal/metals Metals 2017, 7, 410 2 of 13 is called magnetic-field-induced strain (MFIS)—can be observed for FSMAs. The large MFIS was mainly caused by the reorientation of variants and was highly sensitive to the temperature. The MFIS of a single crystal of Ni52Mn23Ga25 exhibited a martensitic transition at room temperature [9]. A large MFIS of −2700 ppm was obtained at 303 K and under atmospheric pressure. A net MFIS of 5400 ppm was induced when a 0.8 MA/m applied field was rotated from the [100] to the [001] directions of the sample. Furthermore, MFISs of 6–10 × 103 ppm have been reported in single crystals of Ni2MnGa near or below room temperature [10]. Some studies have also been conducted on the influence of Fe addition into Ni-Mn-Ga alloys around room temperature [11,12]. A 5.5 × 104 ppm MFIS of single-crystal Ni49.9Mn28.3Ga20.1Fe1.7 appeared at 293 K [11]. The MFIS of Ni52Mn16Fe8Ga24 single-crystal was 1.15 × 104 ppm at 293 K [12]. These MFIS were observed in the martensite phase. The magnetostriction in polycrystalline Ni50Mn23.1Ga24.6 was studied, which shows a martensitic transition at the martensite starting temperature TMs = 250 K [13]. The number of valence electrons per atom, e/a, for this alloy is 7.57, which is higher than that for Ni2MnGa (e/a = 7.50). A 540 ppm magnetostriction was observed at TMs. Near TM, lattice softening was observed. Therefore, the physical relation between the magnetostriction and the lattice softening around TM is interesting. The elastic constants of a Ni0.50Mn0.284Ga0.216 single crystal were studied by using the ultrasonic continuous-wave method [14]. They investigated the C11,C33,C66, and C44 modes, and found that every mode exhibited abrupt softening around TM. This lattice softening appears to be affected by the abrupt expansion that occurs just above TM when cooling from the austenite phase.

1.2. Magnetostriction in Premartensite Phase The temperature of the martensitic transition is very sensitive to the ratio of constitutive elements for ordered compounds close to stoichiometry, Ni2MnGa. Between a martensitic transition from a cubic phase (austenite) to a low symmetry phase (martensite), an intermediate phase appears. This intermediate phase is preceded by a so-called “premartensite phase”. The premartensitic transition between austenite phase and premartensite phase is weakly first-order and originates from softening of the shear elastic coefficient C’ = (C11 − C12)/2 [15–17] corresponding to a minimum on the slowest transversal phonon branch [3,18,19]. Lattice softening is the physical reason for the large variation observed at the martensitic transformation temperature [20]. At the transition, the material exhibits some kind of anomaly in the elastic [16,21], thermal [15], electric [22], and magnetic properties [20,23]. As for Ni2+xMn1−xGa polycrystal, the resistivity demonstrates either a peak (x = 0.00−0.04 samples) or a two-step-like behaviour (x = 0.06−0.08 samples) at the premartensitic transition temperature, TP [22]. The permeability demonstrates a dip at TP [23]. Singh et al. [24] have suggested that a 3M-like incommensurate premartensite phase exists in Ni2MnGa. The feature of the premartensite phase is that magnetostriction occurs. Clear magnetostrictions were observed around Tp in Ni2MnGa alloys. A minimum was found in both the magnetostriction and the elastic modulus at Tp and at the martensitic transition temperature TM in single crystalline Ni2MnGa [17,25]. Matsui et al. [26] investigated magnetostriction in polycrystalline Ni-Mn-Ga alloys and found a magnetostriction of −190 ppm in the premartensite phase—more than three times the amount in the austenite phase. Magnetostriction measurements were performed on polycrystalline Ni2MnGa [20]. It was found that the magnetostriction was negative, took on moderate values of approximately −100 ppm, and increased greatly in absolute value at both the premartensitic and martensitic transition temperatures, which arise from lattice softening at the transitions. In this study, we performed the measurements of the thermal strain, permeability, magnetisation, and magnetostriction of Cr-substituted Ni2Mn1−xCrxGa alloys.

1.3. Purpose of This Study

We chose Ni2Mn1−xCrxGa because the physical properties of Ni2MnGa undergo sudden changes with heat treatment. Therefore, we studied the physical properties of doped systems that could predict Metals 2017, 7, 410 3 of 13

high thermal stability. The values of TC and TM for the Ni2MnGa alloys change drastically when they are doped by replacing Mn with a fourth element, such as Fe, Co, Ni, or Cu [27–30]. For example, replacing Mn by Co, Ni, or Cu increases TM, but the value of TM for Ni2Mn1−xFexGa decreases with increasing Fe concentration x. Several authors have shown that the number of e/a is closely related to the value of TM for Ni-Mn-based FSMAs: a large e/a value indicates a high TM [31–33]. However, a larger e/a corresponds to a lower TM for Ni2Mn1−xFexGa as mentioned above. For Ni2Mn1−xCrxGa alloys, e/a decreases with Cr concentration x (7.50 for x = 0.00 and 7.46 for x = 0.15). Therefore, it would be interesting to know whether the relationship between Tp or magnetostriction and e/a applies 5 2 5 to Ni2Mn1−xCrxGa. The e/a becomes smaller when Mn (3d 4s ) is replaced by Cr (3d 4s). We are interested to investigate a correlation of magnetostriction and e/a which is larger and smaller than 7.50 with a result of the magnetostriction measurements of other Ni-Mn-Ga alloys. Now we will discuss the physical properties of Ni2Mn1−xCrxGa alloys. As for x ≤ 0.25, two anomalies were observed on the ρ-T curves for each sample, corresponding to the magnetic and structural phase transitions at the Curie temperature TC and the martensitic transition temperature TM [34]. Kinks corresponding to the premartensitic transition at the critical temperature TP also appeared. A clear variation was observed below the premartensitic transition temperature TP, thus indicating that lattice deformation occurs below TP. The martensite-austenite phase transition was investigated for a series of 0 ≤ x ≤ 0.7 Heusler alloys by using X-ray diffraction, DC magnetisation, and electrical resistivity measurements [35]. For x < 0.20, a ferromagnetic premartensite state appeared below TP. As the Cr concentration x increased, the martensitic phase transition shifted to higher temperatures, whereas the ferromagnetic transition shifted to lower temperatures. For x < 0.5, the martensitic transition occurred in a ferromagnetic state; however, for x > 0.5, the transition occurred in a paramagnetic state. Doping with Cr results in a rearrangement of the electronic structure, particularly near the Fermi level. This phenomenon is clearly shown by the resistivity data, where a systematic jump-like anomaly was observed in the vicinity of the martensite–austenite phase transition. The purpose of this study is to investigate the magnetic properties of Ni2Mn1−xCrxGa alloys more deeply than former studies. From the permeability and magnetization results, the magnetic-anisotropy constants in the three phases (austenite, premartensite, martensite) were obtained. The magnetostriction of the polycrystals of Ni2MnGa (x = 0.00) and Ni2Mn0.85Cr0.15Ga (x = 0.15)—both of which have austenite, premartensite, and martensite phases—were performed. We compared them with each other and with Ni2Mn0.75Cr0.25Ga (x = 0.25), which also has austenite and martensite phases. The relation between the and the magnetostriction was investigated. The relations between the e/a and magnetostriction and Tp were also investigated, and proportional relations were obtained.

2. Materials and Methods

We prepared polycrystalline Ni2Mn1−xCrxGa alloys by the repeated arc-melting of appropriate quantities of the constituent elements—namely, 3N Ni, 4N Mn, 4N Cr and 6N Ga—in an argon atmosphere. The reaction products were sealed in evacuated silica tubes, heated at 1073 K for three days and at 773 K for two more days, and then quenched in water. We employed strain gauges (KFL-02-120-C1-16, size: grid 0.2 mm length × 1.0 mm width, film base 2.5 mm length × 2.2 mm width. Kyowa Dengyo Co. Ltd., Yamagata, Japan) to measure the thermal strain and magnetostriction of bulk samples with sizes of 3.0 mm × 3.0 mm × 4.0 mm. The zero point of the linear thermal strain ∆L/L was set at 273.15 K, and the rate of temperature change rate was 2 K/min. For the magnetostriction measurements, we applied magnetic fields by using a water-cooled . We employed two gauges, and we applied the magnetic field parallel to (strain λ//) and, separately, perpendicular to (strain λ⊥) the gauges. The magnetic-field change rate was 8.8 kA/(ms). We calculated the magnetostriction λ from the equation λ = 2(λ// − λ⊥)/3 (see [36]). Magnetostriction measurements were also performed during cooling. We performed the permeability measurements in alternating magnetic fields with a frequency of 73 Hz and a maximum field of ±0.8 kA/m (±10 Oe), which we Metals 2017, 7, 410 4 of 13 verified using an magnetometer. We also employed a 3611 filter amp (NF Co. Ltd., Yokohama, Japan) and a 2000/J digital voltmeter (Keithley Co. Ltd, Salem, OR, USA). The measured temperature ranged betweenMetals 150 2017 K, 7 and, 410 400 K. The rate of temperature change was 2 K/min, the same as we used4 of for 12 the linear-strain measurements. We performed the magnetisation measurements by using a pulsed-field magnetas withwe used the for time the constant linear‐strain of 6.3 measurements. ms. The absolute We performed value was the calibrated magnetisation against measurements a sample of pure by Ni. The bulkusing samples a pulsed used‐field in magnet other measurementswith the time constant were also of used6.3 ms. to The compare absolute the value results was with calibrated each other. against a sample of pure Ni. The bulk samples used in other measurements were also used to compare 3. Resultsthe results and Discussionwith each other.

Figure3. Results1 shows and Discussion the temperature dependence of the linear strain ∆L/L in the (a) x = 0.00 alloy; (b) x = 0.15 alloy in zero field during cooling and heating. A jump is clearly seen between 195 K and Figure 1 shows the temperature dependence of the linear strain ∆L/L in the (a) x = 0.00 alloy; (b) 175 Kx in =x 0.15= 0.00 alloy alloy, in zero and field between during 205 cooling K and and 195 heating. K in x = A 0.15 jump alloy, is clearly because seen of between the martensitic 195 K and transition 175 duringK in cooling x = 0.00 and alloy, the and reverse-martensitic between 205 K and 195 transition K in x = 0.15 during alloy, heating. because of In the each martensitic alloy, approximately transition 1000 ppmduring shrinkage cooling and was the observed reverse‐martensitic during the transition martensitic during transition heating. In in each the coolingalloy, approximately process. Linear strain1000 measurements ppm shrinkage of singlewas observed crystalline during Ni the2MnGa martensitic [1] and transition polycrystalline in the cooling Ni49.6 process.Mn27.3 GaLinear23.1 [37] were performed.strain measurements The strain of single values crystalline were practically Ni2MnGa [1] the and same polycrystalline as our result. Ni49.6 ThoseMn27.3Ga results23.1 [37] were were less sensitiveperformed. than our The measurement. strain values were Therefore, practically our the measurements same as our result. are ofThose higher results resolution. were less Oursensitive result is than our measurement. Therefore, our measurements are of higher resolution. Our result is comparable to the thermal strain observed by Albertini et al. [38] in polycrystalline Ni2MnGa. comparable to the thermal strain observed by Albertini et al. [38] in polycrystalline Ni2MnGa. is clearly seen between the martensitic and reverse-martensitic transitions, thus Hysteresis is clearly seen between the martensitic and reverse‐martensitic transitions, thus indicating that the martensitic transition is a first-order phase transition. Identical TP values were indicating that the martensitic transition is a first‐order phase transition. Identical TP values were obtainedobtained for the for coolingthe cooling and and heating heating processes; processes; thethe difference was was at at most most 0.2 0.2 K. K.Singh Singh et al. et [24] al. [24] suggestedsuggested from from their their high-resolution high‐resolution X-ray X‐ray spectroscopy spectroscopy of single single-crystal‐crystal Ni Ni2MnGa2MnGa that that a 3M a‐ 3M-likelike structurestructure develops develops in the in the premartensite premartensite phase. phase. Considering Considering this this X X-ray‐ray spectroscopy spectroscopy result, result, the linear the linear thermalthermal expansion expansion results results of polycrystallineof polycrystalline sample sample inin this study study indicate indicate that that lattice lattice deformation deformation occurredoccurred below belowTP. TP.

0 0 TP Ni Mn Cr Ga TP Ni2MnGa 2 0.85 0.15 T T Rf T Ms Ms

TRf -1000 -1000 (ppm) (ppm) L/L L/L L/L

 

-2000 T Rs -2000 TRs T Mf Martensite Premartensite Austenite Martensite Premartensite Austenite

150 200 250 200 250 T (K) T (K) (a) (b)

Figure 1. Temperature dependence of the linear strain ∆L/L in the (a) x = 0.00 alloy; and (b) x = 0.15 Figure 1. Temperature dependence of the linear strain ∆L/L in the (a) x = 0.00 alloy; and (b) x = 0.15 alloy. The quantity TRs is the temperature where the reverse‐martensitic transition starts; TRf is the alloy. The quantity TRs is the temperature where the reverse-martensitic transition starts; TRf is the temperature where the reverse‐martensitic transition ends; TMs is the temperature where the temperature where the reverse-martensitic transition ends; T is the temperature where the martensitic martensitic transition starts; and TMf is the temperature whereMs the martensitic transition ends. The transitiondotted starts; lines andare intendedTMf is the to temperatureguide the eye. where the martensitic transition ends. The dotted lines are intended to guide the eye. Figure 2 shows the permeability μ of the (a) x = 0.00 alloy; and (b) x = 0.15 alloy during heating Figureand cooling2 shows in zero the magnetic permeability fields. Forµ xof = 0.00, the (a)the anomaliesx = 0.00 alloy;or jumps and appeared (b) x =at 0.15the martensitic alloy during transition at approximately 195 K, the premartensitic transition at approximately 255 K (at which the heating and cooling in zero magnetic fields. For x = 0.00, the anomalies or jumps appeared at temperature shows a dip, which was as same as single crystal [23]), and the ferromagnetic transition the martensitic transition at approximately 195 K, the premartensitic transition at approximately at approximately TC = 375 K. When cooling from 400 K through the austenite paramagnetic phase, 255 Kthe (at value which of μ theincreases temperature at approximately shows a dip, 375 whichK, thus wasindicating as same a ferromagnetic as single crystal transition [23]), in andthe the ferromagneticaustenite transitionphase. The at μ approximatelyvalue dips slightlyTC =below 375 K. 255 When K and cooling decreases from strongly 400 K throughbelow 195 the K. austenite The paramagneticpermeability phase, curve the indicates value of thatµ increasesthe magnetic at approximatelyanisotropy is small 375 in K, the thus ferromagnetic indicating austenite a ferromagnetic and transitionpremartensite in the austenite phases. phase. By contrast, The µ valuethe value dips of slightly the permeability below 255 Kdecreased and decreases drastically strongly at the below 195 K.martensite The permeability phase transition. curve indicates This result that indicates the magnetic that the anisotropy magnetic isanisotropy small in is the large ferromagnetic in the martensite phase. Considering that the thermal strain (as shown in Figure 1) decreases steeply with

Metals 2017, 7, 410 5 of 13 austenite and premartensite phases. By contrast, the value of the permeability decreased drastically at the martensite phase transition. This result indicates that the magnetic anisotropy is large in the martensiteMetals 2017 phase., 7, 410 Considering that the thermal strain (as shown in Figure1) decreases steeply5 of 12 with coolingcooling between between 260 260 K and K and 240 240 K K and and that that the the permeabilitypermeability shows shows a adip dip in inthis this temperature temperature range, range, we concludewe conclude that that lattice lattice deformation deformation occurred occurred becausebecause of of the the premartensitic premartensitic transition. transition. As a As result, a result, latticelattice deformation deformation increases increases magnetic magnetic anisotropy. anisotropy.

5 3

Ni2MnGa Ni2Mn0.85Cr0.15Ga T 4 P

TP 2 3 (arb. unit) (arb. unit)

2     1 Pre- 1 martensite Austenite Martensite Premartensite Austenite Martensite 0 0 150 200 250 300 350 400 150 200 250 300 350 400 T (K) T (K) (a) (b)

Figure 2. The permeability of the (a) x = 0.00 alloy; and (b) x = 0.15 alloy during heating and cooling Figure 2. The permeability of the (a) x = 0.00 alloy; and (b) x = 0.15 alloy during heating and cooling in in zero magnetic fields. The quantity TP is the premartensitic transition temperature. zero magnetic fields. The quantity TP is the premartensitic transition temperature. As for x = 0.15, the anomalies (jumps) are due to the martensitic transition at approximately 200 AsK, the for premartensiticx = 0.15, the anomaliestransition at (jumps) approximately are due Tp to = the225 martensiticK, and the ferromagnetic transition at transition approximately at 200 K,approximately the premartensitic TC = 340 transition K. The μ value at approximately dips slightly belowTp = 225 225 K,K and and decreases the ferromagnetic strongly below transition 200 at K. The magnetisation displays ferromagnetic properties at 5 K, with values of 83 Am2/kg for the x = approximately TC = 340 K. The µ value dips slightly below 225 K and decreases strongly below 200 K. The magnetisation0.15 alloy at 4 MA/m displays [35]. ferromagnetic Therefore, the martensite properties phase at 5 K, is witha ferromagnetic values of 83phase. Am The2/kg permeability for the x = 0.15 decrease in the ferromagnetic phase below 225 K is believed to be due to magnetic anisotropy. The alloy at 4 MA/m [35]. Therefore, the martensite phase is a ferromagnetic phase. The permeability permeability of Ni50.9Mn24.6Ga24.5 exhibited a dip around Tp, whereas Ni48.3Mn24.6Ga24.5Co2.6 showed a decrease in the ferromagnetic phase below 225 K is believed to be due to magnetic anisotropy. gradual decrease below Tp. Ni50.9Mn24.6Ga24.5 and Ni48.3Mn24.6Ga24.5Co2.6 have the same properties at x = The permeability0.00 and x = 0.15, of Nirespectively50.9Mn24.6 [39].Ga24.5 Theexhibited hysteresis a (difference dip around in coolingTp, whereas and heating Ni48.3 process)Mn24.6 Gaof μ 24.5ofCo 2.6 showedx = a0.15 gradual in the premartensite decrease below phaseTp .is Ni presumed50.9Mn24.6 toGa be24.5 dueand to the Ni 48.3differenceMn24.6 Gaof the24.5 Conucleation2.6 have in the the same propertiespremartensite at x = 0.00 phase and inx =cooling 0.15, respectivelyand heating [process.39]. The The hysteresis permeability (difference of No. in3 cooling(Ni51.7Mn and24.3Ga heating24.0 process)polycrystal, of µ of TxMs= = 0.15 265 K, in T theRf = 273 premartensite K, Tp = 285 K) phase shows isclear presumed hysteresis to in be the due premartensite to the difference phase [40]. of the nucleationThe difference in the premartensite between TMs and phase Tp, ∆T in = T coolingp − TMs = and20 K. heating This is smaller process. than The ∆T = permeability 63 K for x = 0.00 of in No. 3 this work. As for x = 0.15, ∆T = 25 K. Therefore, it is supposed that the hysteresis of the permeability (Ni51.7Mn24.3Ga24.0 polycrystal, TMs = 265 K, TRf = 273 K, Tp = 285 K) shows clear hysteresis in the appears when ∆T is small. premartensite phase [40]. The difference between TMs and Tp, ∆T = Tp − TMs = 20 K. This is smaller When the magnetic anisotropy is small, the magnetic moments are easily directed along the than ∆T = 63 K for x = 0.00 in this work. As for x = 0.15, ∆T = 25 K. Therefore, it is supposed that the applied alternative magnetic fields in permeability measurements. By contrast, large magnetic hysteresisanisotropies of the permeabilitymean that the magnetic appears moments when ∆T areis small.less easily directed along the applied AC magnetic Whenfields. In the the magnetic ferromagnetic anisotropy martensite is phase small, (tetragonal the magnetic symmetry), moments the magnetic are easily anisotropy directed is larger along the appliedthan alternative in the austenite magnetic phase fields(cubic insymmetry), permeability thus indicating measurements. that the permeability By contrast, is large small magnetic[41]. anisotropiesTaken together, mean that the thepermeability magnetic decreased moments below are less 225 easilyK as shown directed in Figure along 2b the and applied the linear AC‐strain magnetic fields.anomaly In the ferromagnetic below TP shown martensite in Figure phase1b imply (tetragonal that lattice symmetry), deformation the and magnetic the change anisotropy of magnetic is larger thananisotropy in the austenite have occurred phase (cubicbecause symmetry), of the premartensitic thus indicating transition. that The the TC permeability values for cooling is small and [41]. Takenheating together, are almost the permeability the same, consistent decreased with below the linear 225‐strain K as shown results. inThe Figure TP values2b and found the for linear-strain cooling and heating are also the same. Soto et al. [42] studied Fe‐doped NiMnGa (Ni52.5−xMn23Ga24.5Fex) alloys, anomaly below TP shown in Figure1b imply that lattice deformation and the change of magnetic finding that the premartensitic transition temperature was 186 K for the x = 4.4 alloy. No significant anisotropy have occurred because of the premartensitic transition. The T values for cooling and thermal hysteresis was detected at the premartensitic transition, and no appreciableC features were heatingobserved are almost in the the calorimetric same, consistent curves at with the thepremartensitic linear-strain transition. results. TheBy contrast,TP values our found permeability for cooling and heatingmeasurements are also showed the same. a small Soto dip et at al. the [42 ]premartensitic studied Fe-doped transition, NiMnGa and the (Ni 52.5linear−x Mnstrain23Ga and24.5 Fex) alloys,permeability finding that exhibited the premartensitic clear variations transitionfor the x = temperature0.15 alloy. Uijttewaal was 186 et Kal. for[43] the statex that= 4.4 the alloy. No significantcontributions thermal of both hysteresis magnons and was phonons detected to at the the free premartensitic energy of premartensite transition, and and austenite no appreciable only features“slightly were differ” observed and that in the the existence calorimetric of the premartensitic curves at the transition premartensitic results from transition. a delicate interplay By contrast, our permeabilitybetween the vibrational measurements and magnetic showed excitation a small mechanisms. dip at the premartensitic We considered transition,that the clear and variation the linear

Metals 2017, 7, 410 6 of 13 strain and permeability exhibited clear variations for the x = 0.15 alloy. Uijttewaal et al. [43] state that the contributions of both magnons and phonons to the free energy of premartensite and austenite only “slightly differ” and that the existence of the premartensitic transition results from a delicate interplay betweenMetals the 2017 vibrational, 7, 410 and magnetic excitation mechanisms. We considered that the clear6 variation of 12 in the linear strain indicates lattice deformation and a softening of the lattice. Therefore, changes in the magneticin the state linear are strain ultimately indicates reflected lattice deformation in the permeability and a softening changes. of the lattice. Therefore, changes in Figurethe magnetic3 shows state the are magnetisation ultimately reflected curve in for the the permeability (a) x = 0.00 changes. alloy and (b) x = 0.15 alloy measured Figure 3 shows the magnetisation curve for the (a) x = 0.00 alloy and (b) x = 0.15 alloy measured during cooling process. As for x = 0.00, the magnetisation becomes almost saturated around 0.24 MA/m during cooling process. As for x = 0.00, the magnetisation becomes almost saturated around 0.24 above 220 K, thus indicating that the magnetic anisotropy is small. At 200 K, which is slightly higher MA/m above 220 K, thus indicating that the magnetic anisotropy is small. At 200 K, which is slightly than T , the magnetisation increases steeply from 0 MA/m. This value is comparable to the results for higherMs than TMs, the magnetisation increases steeply from 0 MA/m. This value is comparable to the the permeabilityresults for the at permeability 200 K because at 200 the K gradient because ofthe the gradient magnetisation of the magnetisation is proportional is proportional to the permeability. to the In thepermeability. martensite phase In the atmartensite 150 K, the phase magnetisation at 150 K, the increasesmagnetisation gradually increases with gradually increasing with magnetic-field increasing strengthmagnetic because‐field of strength large magnetic because of anisotropy. large magnetic The anisotropy. properties The of magnetisation properties of magnetisation curves for x curves= 0.15 are almostfor the x = same 0.15 are as almost those for the thesamex =as 0.00 those alloy. for the x = 0.00 alloy.

150 K 150 K 80 80 220 K 210 K

60 60 293 K /kg) /kg) 2 2 293 K (Am 40 (Am 40 M M

20 20 Ni2Mn0.85Cr0.15Ga Ni2MnGa

0 0 0 1 2 0 1 2 Applied Field H (MA/m) Applied Field H (MA/m) (a) (b)

Figure 3. The magnetisation M of the (a) x = 0.00 alloy; and (b) x = 0.15 alloy. Blue: martensite phase, Figure 3. The magnetisation M of the (a) x = 0.00 alloy; and (b) x = 0.15 alloy. Blue: martensite phase, Green: premartensite phase, Red: austenite phase. Green: premartensite phase, Red: austenite phase. To determine the amount of magnetic anisotropy, we determined the magnetic‐anisotropy field ToHA determine from the magnetisation the amount results. of magnetic This quantity anisotropy, was obtained we determined by the peak the of magnetic-anisotropythe twice‐differentiated field 2 2 HA frommagnetisation the magnetisation curve, d M results./d (μ0H This) , by quantity means of was the derivation obtained bymethod the peak of H ofA by the the twice-differentiated analysis of the magnetization of Ni22MnGa by Chu2 et al. [44]. The magnetic‐anisotropy constant K1 is then provided magnetisation curve, d M/d (µ0H) , by means of the derivation method of HA by the analysis of the by the equation K1 = μ0MSHA/2 [38,44], where MS is the saturation value of the magnetisation. This magnetization of Ni2MnGa by Chu et al. [44]. The magnetic-anisotropy constant K1 is then provided approach is not the actual way to properly determine the magnetic anisotropy, and might be an by the equation K1 = µ0MSHA/2 [38,44], where MS is the saturation value of the magnetisation. approximation. Therefore, error bars are indicated in Figure 4a,b. The resulting values of HA and K1 This approach is not the actual way to properly determine the magnetic anisotropy, and might be an are shown in Figure 4a,b, respectively. From the saturated magnetisation Ms obtained from the approximation.magnetisation Therefore, curves in errorFigure bars 3 and are from indicated these values in Figure of HA,4 wea,b. found The resultingthe value of values K1 at 150 of KH inA and K1 arethe shown martensite in Figure phase4 a,b,to be respectively. K1 = 4.0 × 106 Fromerg/cm the3 in saturatedcgs‐emu unit. magnetisation This value is comparableMs obtained to other from the magnetisationresults for curvesK1 [38,44]. in The Figure values3 and of K from1 at 220 these K in the values premartensite of HA, we phase found and the at 293 value K in of theK austenite1 at 150 K in 6 63 3 6 3 the martensitephase are phasesimilarly to befoundK1 =to 4.0 be× K110 = 0.34erg/cm × 10 erg/cmin cgs-emu and unit.K1 = 0.30 This × value 10 erg/cm is comparable, respectively, to other approximately one‐tenth of the value at 150 K. Albertini [38] also suggested that the value of K1 above results for K1 [38,44]. The values of K1 at 220 K in the premartensite phase and at 293 K in the austenite the martensitic transition temperature is smaller6 than that3 in the martensite phase.6 3 phase are similarly found to be K1 = 0.34 × 10 erg/cm and K1 = 0.30 × 10 erg/cm , respectively, As for x = 0.15, the HA at 150 K in the martensite phase is smaller than that for the x = 0.00 alloy approximately one-tenth of the value at 150 K. Albertini [38] also suggested that the value of K1 above at 150 K. Above TMs, the HA is considerably smaller than at 150 K in the martensite phase. Conversely, the martensitic transition temperature is smaller than that in the martensite phase. the values of HA in the premartensite and austenite phases are larger than those for the x = 0.00 alloy. As for x = 0.15, the H at 150 K in the martensite phase is smaller than that for the x = 0.00 alloy at The resulting value ofA K1 at 150 K in the martensite phase is K1 = 3.1 × 106 erg/cm3, whereas the values 150 K.at Above 210 K inT Msthe, thepremartensiteHA is considerably phase and at smaller 293 K in than the ataustenite 150 K inphase the are martensite K1 = 1.0 × phase.106 erg/cm Conversely,3 and the valuesK1 = 0.58 of H× A10in6 erg/cm the premartensite3, respectively. andSimilar austenite to the case phases for the are x = larger 0.00 alloy, than the those permeability for the x exhibits= 0.00 alloy. 6 3 The resultinga small dip value around of K1 Tatp. 150By contrast, K in the we martensite found a large phase decrease is K1 = 3.1below× 10 Tp forerg/cm the x =, whereas0.15 alloy. the This values 6 3 at 210result K in indicates the premartensite that both the phase magnetic and anisotropy at 293 K in and the the austenite value of K phase1 in the are premartensiteK1 = 1.0 × phase10 erg/cm for x = 0.15 are larger6 than those3 for x = 0.00. and K1 = 0.58 × 10 erg/cm , respectively. Similar to the case for the x = 0.00 alloy, the permeability exhibits a small dip around Tp. By contrast, we found a large decrease below Tp for the x = 0.15 alloy.

Metals 2017, 7, 410 7 of 13

This result indicates that both the magnetic anisotropy and the value of K1 in the premartensite phase for x = 0.15Metals are 2017 larger, 7, 410 than those for x = 0.00. 7 of 12

6 1.0 5.0x10

Ni MnGa 0.8 Ni2MnGa 4.0 2 Ni2Mn0.85Cr0.15Ga Ni2Mn0.85Cr0.15Ga ) 0.6 3 3.0 Metals 2017, 7, 410 7 of 12 (MA/m) (erg/cm A 1

H 0.4 2.0 K 6 1.0 5.0x10

0.2 1.0 Ni MnGa 0.8 Ni2MnGa 4.0 2 Ni2Mn0.85Cr0.15Ga Ni2Mn0.85Cr0.15Ga 0 0 ) 0.6150 200 250 300 3 3.0 150 200 250 300 T (K) T (K) (MA/m) (erg/cm A 1

H 0.4 2.0 (a) K (b)

A Figure0.2 4. (a) The temperature dependence of the magnetic1.0 ‐anisotropy field H ; (b) The temperature Figure 4. (a) The temperature dependence of the magnetic-anisotropy field HA;(b) The temperature dependence of the magnetic‐anisotropy energy K1. The error bars were indicated. dependence of the magnetic-anisotropy energy K . The error bars were indicated. 0 1 0 150 200 250 300 150 200 250 300 We measured the magnetostrictionT (K) by using the two‐gauge methodT (K) described in Section 2. WeFigure measured 5 shows the the magnetostriction magnetostriction(a) for by the using(a) x = 0.00 the alloy; two-gauge and (b) x method =( b0.15) alloy. described As for x in= 0.00, Section 2. the magnetostriction saturated above 0.08 MA/m in the austenite and premartensite phases. This Figure5 showsFigure the 4. magnetostriction(a) The temperature dependence for the of (a) the magneticx = 0.00‐anisotropy alloy; field and HA; ( (b)b) Thex temperature= 0.15 alloy. As for finding is consistent with the value of the magnetic‐anisotropy field HA = 0.083 MA/m at 220 K x = 0.00,(premartensite). the magnetostrictiondependence By of thecontrast, magnetic saturated at‐ anisotropy162 K above in theenergy 0.08martensite K1. MA/mThe error phase, bars in the werethe austenitemagnetostriction indicated. and premartensite increased with phases. This findingincreasing is consistent field strength, with although the value it showed of the indications magnetic-anisotropy of saturation at field 1.27H MA/m.A = 0.083 In other MA/m words, at 220 K We measured the magnetostriction by using the two‐gauge method described in Section 2. in order to generate a high driving force for the magnetic domains variants, highly anisotropic and (premartensite).Figure 5 shows By contrast, the magnetostriction at 162 K in for the the martensite (a) x = 0.00 alloy; phase, and the (b) magnetostrictionx = 0.15 alloy. As for x increased = 0.00, with increasinghighlythe field magnetostriction saturated strength, magnetisation although saturated itvalues above showed are0.08 needed indicationsMA/m [9]. in theIn the ofaustenite saturationaustenite and and premartensite at premartensite 1.27 MA/m. phases. phases, In otherThis the words, magnetic anisotropy was small; therefore, the motive force acts only below 0.083 MA/m. However, in order tofinding generate is consistent a high with driving the value force of for the the magnetic magnetic‐anisotropy domains field variants, HA = 0.083 highly MA/m anisotropicat 220 K and in the martensite phase, the anisotropy field and the magnetic‐anisotropy constant K1 were large (as highly saturated(premartensite). magnetisation By contrast, values at 162 K are in the needed martensite [9]. phase, In the the austenite magnetostriction and premartensite increased with phases, mentionedincreasing above, field strength, the value although of K1 in it the showed martensite indications phase of was saturation more than at 1.27 10 timesMA/m. larger In other than words, that in the magnetic anisotropy was small; therefore, the motive force acts only below 0.083 MA/m. However, thein premartensiteorder to generate phase). a high Therefore, driving force under for weak the magnetic magnetic domains fields, the variants, variants highly cannot anisotropic move because and in the martensiteofhighly the highsaturated phase, magnetic magnetisation the anisotropy. anisotropy values The fieldare neededmotive and [9]. theforce In magnetic-anisotropy thethen austenite acts untiland premartensite 1.27 constantMA/m, phases, andK 1 largethewere large (as mentionedmagnetostrictionmagnetic above, anisotropy the was value observed.was ofsmall;K1 Regarding intherefore, the martensite thex = 0.15,motive a phasemagnetostriction force acts was only more below of than −120 0.083 10 ppm timesMA/m. was larger observedHowever, than in that in the premartensitethein premartensitethe martensite phase). phase.phase, Therefore, theIn the anisotropy austenite under field weak and and premartensite magnetic the magnetic fields, phases,‐anisotropy the the variants magnetostrictionconstant cannot K1 were move largesaturated (as because of the highabove magneticmentioned 0.24 MA/m, anisotropy. above, whichthe value The corresponds of motive K1 in the forceto martensite the then anisotropic phase acts until was field more 1.27 HA =than MA/m, 0.21 10 MA/m times and largerobtained large than magnetostriction from that inthe magnetisationthe premartensite curves phase). at 210 Therefore, K. The magnetostriction under weak magnetic in the fields, martensite the variants phase cannot (181 Kmove in Figure because 5b) was observed. Regarding x = 0.15, a magnetostriction of −120 ppm was observed in the premartensite saturatedof the highat 0.95 magnetic MA/m, whichanisotropy. is comparable The motive to the force value then of H Aacts = 0.75 until MA/m 1.27 at MA/m, 150 K. Consideringand large phase. Inthemagnetostriction the permeability austenite shown and was premartensiteobserved. in Figure Regarding 2b and phases, the x = magnetisation 0.15, the a magnetostriction magnetostriction plotted in of Figure −120 saturated ppm 3b, wewas aboveconclude observed 0.24 thatin MA/m, which correspondsthisthe result premartensite is due to the to thephase. anisotropic large In magneticthe austenite field anisotropyH andA = premartensite 0.21 in MA/mthe martensite phases, obtained phase. the magnetostriction from the magnetisation saturated curves at 210 K. Theabove magnetostriction 0.24 MA/m, which incorresponds the martensite to the anisotropic phase (181 field K H inA Figure= 0.21 MA/m5b) saturated obtained from at 0.95 the MA/m, magnetisation0 curves at 210 K. The magnetostriction in 0the martensite phase (181 K in Figure 5b) which is comparable to the value of HA = 0.75281 MA/m K at 150 K. Considering the permeability 290 K shown in A saturated-50 at 0.95 MA/m, which is comparable to the value of H = 0.75 MA/m at 150 K. Considering Figure2b and the magnetisation plotted in Figure3b, we conclude that this result is due181 toK the large the permeability shown in Figure 2b and 262the K magnetisation plotted in Figure 3b, we conclude that -100 magneticthis anisotropy result is due in theto the martensite large magnetic phase. anisotropy244 K in the martensite phase. 243 K -50 -150 0 (ppm) 0 (ppm) 

  -200 251281 K K 290 K -50 181 K 262 K Ni2Mn0.85Cr0.15Ga -250 Ni2MnGa -100 -100 244 K 243 K -300 162 K -50 217 K -150 (ppm) (ppm) 0 0.5 1.0  0 0.5 1.0   -200 251 K Applied Field H (MA/m) Applies Field H (MA/m)

-250 Ni2Mn0.85Cr0.15Ga (a) Ni2MnGa (b) -100 Figure-300 5. The magnetostriction λ for the (162a) K x = 0.00 alloy; and (b) x = 0.15 alloy, measured during217 K

cooling.0 The horizontal0.5 axis shows the1.0 applied magnetic field0 H. 0.5 1.0 Applied Field H (MA/m) Applies Field H (MA/m) (a) (b)

Figure 5. The magnetostriction λ for the (a) x = 0.00 alloy; and (b) x = 0.15 alloy, measured during λ Figure 5. cooling.The magnetostriction The horizontal axis showsfor the the applied (a) x = magnetic 0.00 alloy; field andH. (b) x = 0.15 alloy, measured during cooling. The horizontal axis shows the applied magnetic field H.

Metals 2017, 7, 410 8 of 12 Metals 2017, 7, 410 8 of 13

Figure 6 shows the temperature dependence of the magnetostriction values for the (a) x = 0.00 alloyFigure and (b)6 shows x = 0.15 the alloy. temperature As for x dependence = 0.00, in the of austenite the magnetostriction phase, the magnetostriction values for the (a) valuex = 0.00 was alloyapproximately and (b) x −=60 0.15 ppm alloy. at 290 As K, for andx =the 0.00, absolute in the magnetostriction austenite phase, value the magnetostriction increased slightly value with wascooling. approximately In the premartensite−60 ppm at phase, 290 K, the and absolute the absolute magnetostriction magnetostriction value value increased increased drastically, slightly withreaching cooling. a magnetostriction In the premartensite value of phase, −180 theppm absolute at 250 K. magnetostriction The sudden decrease value between increased 260 drastically, K and 240 reachingK in Figure a magnetostriction 6a corresponds to value the temperature of −180 ppm range at 250 in K.which The the sudden dip in decrease permeability between is seen 260 (Figure K and 2402a). K Singh in Figure et al.6a [24] corresponds suggested to that the temperaturea 3M premartensite range in phase which appears the dip inbelow permeability TP; therefore, is seen the (Figuremagnetostriction2a). Singh etis al. correlated [ 24] suggested with thatlattice a 3M deformation premartensite and phase magnetic appears anisotropy. below TP ;Ultrasonic therefore, themeasurements magnetostriction indicate is that correlated the shear with elastic lattice C’ coefficient, deformation C’ and= (C11 magnetic − C12)/2, decreases anisotropy. around Ultrasonic TP [17], measurementsindicating that indicatelattice softening that the occurred shear elastic aroundC’ coefficient, TP. The magnetostrictionC’ = (C11 − C12 at)/2, 1.27 decreases MA/m increased around TdrasticallyP [17], indicating around that the lattice martensitic softening transition occurred aroundtemperatureTP. The TM magnetostriction. At 162 K, we at 1.27observed MA/m a increasedmagnetostriction drastically of − around330 ppm. the This martensitic temperature transition dependence temperature of the TmagnetostrictionM. At 162 K, we has observed the same a magnetostrictionshape as the magnetostrain of −330 ppm. of Ni This2MnGa temperature single crystals dependence measured of the at magnetostriction 0.4 MA/m [25]. Figure has the 6a same also shapeshows as the the temperature magnetostrain dependence of Ni2MnGa of singlethe magnetostriction crystals measured at 0.080 at 0.4 MA/m, MA/m as [25 indicated]. Figure6 aby also the showstriangle the symbols. temperature The dependencevalue of the of magnetic the magnetostriction‐anisotropy field at 0.080 HA MA/m,in the austenite as indicated and by premartensite the triangle symbols.phases is The approximately value of the 0.083 magnetic-anisotropy MA/m; we also show field HtheA inmagnetostriction the austenite and values premartensite at 0.080 MA/m phases near is approximatelyHA in Figure 6a. 0.083 A sharp MA/m; peak we can also be showobserved the magnetostrictionjust below the premartensitic values at 0.080 transition MA/m temperature near HA in FigureTp (which6a. A was sharp defined peak can by the be observed thermal strain just below measurement the premartensitic in Figure transition 1a). In the temperature martensite Tphase,p (which the wasmagnetic defined anisotropy by the thermal is larger strain than measurement in the premartensite in Figure phase,1a). Inthus the indicating martensite that phase, the variants the magnetic cannot anisotropymove in low is larger magnetic than in fields. the premartensite As for x = phase,0.15, the thus temperature indicating that dependence the variants of cannot the saturated move in lowmagnetostriction magnetic fields. values As for atx =0.24 0.15, MA/m the temperature is equal to dependence the anisotropic of the saturatedfield in the magnetostriction austenite and valuespremartensite at 0.24 MA/mphases. isThe equal full towidth the anisotropicat half maximum field in (FWHM) the austenite of the and peak premartensite in the premartensite phases. Thephase full is width 20 K. atBy half contrast, maximum the FWHM (FWHM) for of the the x peak= 0.00 in alloy the premartensite (Figure 6a) is phaseonly 10 is K, 20 thus K. By indicating contrast, thethat FWHM the anomaly for the (dip)x = 0.00 in the alloy permeability (Figure6a) isof only the x 10 = 0.15 K, thus alloy indicating is larger thatthan the that anomaly of the x (dip) = 0.00 in alloy. the permeabilityIn the martensite of the x = phase, 0.15 alloy the is magnetostriction larger than that offor the thex x= = 0.00 0.15 alloy. alloy at 1.27 MA/m and 180 K (−35 ppm)In was the noticeably martensite smaller phase, thethan magnetostriction that of the x = 0.00 for alloy the xat= 1.27 0.15 MA/m alloy atand 1.27 163 MA/m K (−330 and ppm); 180 the K (−temperature35 ppm) was was noticeably approximately smaller than35 K that lower of the thanx = T 0.00Ms. alloyThis finding at 1.27 MA/m suggests and that 163 Kthe (− amount330 ppm); of themagnetostriction temperature was decreased approximately with 35 increasing K lower than CrT Msconcentration.. This finding suggestsWe also that measured the amount the of magnetostrictionmagnetostriction decreased for an x with= 0.25 increasing alloy, which Cr concentration. had a martensitic We also transition measured starting the magnetostriction temperature forTMs an = 214x = 0.25K. alloy, which had a martensitic transition starting temperature TMs = 214 K.

0 0 -50 Pre- -100 martensite -150 Martensite -200 Austenite -50 -250 -300 -350 Austenite

(ppm) Martensite (ppm)  -400  -450 Ni2MnGa -100 -500 0.080 MA/m Ni2Mn0.85Cr0.15Ga -550 Premartensite 1.27 MA/m 0.24 MA/m -600 1.27 MA/m -650 -700 -150 200 250 200 250 T (K) T (K) (a) (b)

FigureFigure 6. Temperature 6. Temperature dependence dependence of the ofmagnetostriction the magnetostriction λ for theλ (afor) x = the 0.00 ( aalloy;) x = and 0.00 (b alloy;) x = 0.15 and alloy. (b) x = 0.15 alloy. Figure 7 shows the temperature dependence of the magnetostriction for the x = 0.25 alloy at 1.27 MA/m, which peaks around TMs. This property is the same as for the Ni52.3Mn23.1Ga24.6 and Ni2MnGa Figure7 shows the temperature dependence of the magnetostriction for the x = 0.25 alloy at alloys [13,26]. The magnetostriction of the x = 0.25 alloy at 1.27 MA/m in the martensite phase is 1.27 MA/m, which peaks around T . This property is the same as for the Ni Mn Ga and between −30 ppm and −35 ppm, whichMs is equal to that of the x = 0.15 alloy. These52.3 results23.1 confirm24.6 that Ni MnGa alloys [13,26]. The magnetostriction of the x = 0.25 alloy at 1.27 MA/m in the martensite the2 magnetostriction decreases with increasing Cr concentration. For the x = 0.00 alloy, the magnetic‐ phase is between −30 ppm and −35 ppm, which is equal to that of the x = 0.15 alloy. These results anisotropy constant (K1 = 4.0 × 106 erg/cm3) was larger than that for the x = 0.15 alloy (K1 = 3.1 × 106 confirm that the magnetostriction decreases with increasing Cr concentration. For the x = 0.00 alloy, erg/cm3). The magnetisation value for the x = 0.00 alloy was also larger than that for x = 0.15. We the magnetic-anisotropy constant (K = 4.0 × 106 erg/cm3) was larger than that for the x = 0.15 conclude that larger magnetic anisotropy1 and larger magnetisation generate larger magnetostriction.

Metals 2017, 7, 410 9 of 13

6 3 alloyMetals ( 2017K1 =, 7 3.1, 410× 10 erg/cm ). The magnetisation value for the x = 0.00 alloy was also larger than9 of 12 that for x = 0.15. We conclude that larger magnetic anisotropy and larger magnetisation generate largerHowever, magnetostriction. the change in However,the amount the of changemagnetostriction in the amount is considerably of magnetostriction larger than is the considerably changes in largermagnetisation than the or changes magnetic in magnetisationanisotropy. Matsui or magnetic et al. [40] anisotropy. measured the Matsui magnetostriction et al. [40] measured of a Si‐doped the magnetostrictionNi2MnGa polycrystal of a Si-doped and found Ni2 thatMnGa the polycrystal amount of and magnetostriction found that the in amount the martensite of magnetostriction phase was inconsiderably the martensite smaller phase than was that considerably of a Ni2MnGa smaller polycrystal. than that ofConversely, a Ni2MnGa the polycrystal. MFIS for an Conversely, Fe‐doped 3 3 theNi52 MFISMn16 forFe8Ga an24 Fe-doped single crystal Ni52Mn is 7.516Fe × 810Ga ppm,24 single which crystal is twice is 7.5 as× large10 ppm, as that which of a Ni is twice52Mn24 asGa large24 single as 3 3 thatcrystal of a (3.5 Ni52 ×Mn 1024 ppm)Ga24 single[12]. They crystal mentioned (3.5 × 10 thatppm) Fe substitution [12]. They mentioned for Mn improves that Fe substitutionthe temperature for Mndependence improves of the MFIS. temperature dependence of MFIS.

0

Martensite Austenite

-20

-40 (ppm)  -60

Ni2Mn0.75Cr0.25Ga -80 1.27 MA/m

-100 200 250 T (K) FigureFigure 7. 7.Temperature Temperature dependence dependence of of the the magnetostriction magnetostrictionλ λ forfor the thex x= = 0.25 0.25 alloy. alloy.

In order to investigate the relation between valence electron e/a and the magnetostriction value In order to investigate the relation between valence electron e/a and the magnetostriction around the premartensitic transition, Figure 8 (a) demonstrates the relationship between e/a and the value around the premartensitic transition, Figure8 (a) demonstrates the relationship between e/a magnetostriction value around TP. Figure 8 (b) demonstrates the e/a dependence of the TP. Table 1 and the magnetostriction value around TP. Figure8 (b) demonstrates the e/a dependence of the shows the valence electron e/a, the premartensite temperature TP, and peak value of the TP. Table1 shows the valence electron e/a, the premartensite temperature TP, and peak value of magnetostriction around the TP for each composition. Three Ni‐Mn‐Ga polycrystals [26,40], two the magnetostriction around the TP for each composition. Three Ni-Mn-Ga polycrystals [26,40], Ni2MnGa single crystals [17,26], x =0.00, and x = 0.15 were used for this figure. To compare between two Ni2MnGa single crystals [17,26], x =0.00, and x = 0.15 were used for this figure. To compare the polycrystal and single crystal, the magnetostriction λ of the single crystal was calculated as λ ≈ between the polycrystal and single crystal, the magnetostriction λ of the single crystal was calculated 2λ100/3, where λ100 is the magnetostriction parallel to the [100] axis. The magnetostriction is almost as λ ≈ 2λ100/3, where λ100 is the magnetostriction parallel to the [100] axis. The magnetostriction is proportional to the e/a. As shown in Figure 8b, the Tp is also almost proportional to the e/a. It was almost proportional to the e/a. As shown in Figure8b, the Tp is also almost proportional to the e/a. reported earlier that Tp is proportional to the e/a [45]. From these results, it is considered that the It was reported earlier that Tp is proportional to the e/a [45]. From these results, it is considered that electron energy, the magnetostriction, and the Tp are correlated each other. In doped Ni2MnGa alloys, the electron energy, the magnetostriction, and the Tp are correlated each other. In doped Ni2MnGa the e/a values change; therefore, it is considered that the itinerant electric and magnetic states also alloys, the e/a values change; therefore, it is considered that the itinerant electric and magnetic states vary. As a result, the magneto‐structural strain (magnetostriction or MFIS) can be changed. also vary. As a result, the magneto-structural strain (magnetostriction or MFIS) can be changed.

Table 1. The valence electron e/a, the premartensite temperature TP, and peak value of the

Tablemagnetostriction 1. The valence around electron the TP fore/ aeach, the composition. premartensite PC: temperature polycrystal; SC:TP, single and peakcrystal. value of the magnetostriction around the TP for each composition. PC: polycrystal; SC: single crystal. Composition e/a TP (K) λ (ppm) References

Ni51.7MnComposition24.3Ga24.0 7.59e /a285 TP (K) −λ (ppm)550 ReferencesPC Matsui [26,40] Ni49.9Mn26.2Ga23.9 7.54 259 −360 PC Matsui [26,40] Ni51.7Mn24.3Ga24.0 7.59 285 −550 PC Matsui [26,40] NiNi2MnGa49.9Mn 26.2Ga23.9 7.507.54 259 259 −−360227 PC MatsuiSC [Seiner26,40] [17] Ni2MnGaNi2MnGa 7.50 7.50 258 259 −−227180 SC SeinerPC This [17] work Ni MnGa 7.50 258 −180 PC This work Ni49.2Mn26.5Ga2 24.3 7.50 248 −182 SC Matsui [40] Ni49.2Mn26.5Ga24.3 7.50 248 −182 SC Matsui [40] Ni47.9Mn28.0Ga24.1 7.47 225 −180 PC Matsui [26,40] Ni47.9Mn28.0Ga24.1 7.47 225 −180 PC Matsui [26,40] 2 0.85 0.15 Ni MnNi2MnCr 0.85GaCr 0.15Ga7.46 7.46 225 225 −−120120 PC ThisPC work This work

Further research is needed both for the kinetic physics and for the itinerant magnetism for Further research is needed both for the kinetic physics and for the itinerant magnetism for Ni2MnGa‐related alloys. The martensitic transformation in stoichiometric Ni2MnGa alloys is Ni MnGa-related alloys. The martensitic transformation in stoichiometric Ni MnGa alloys is preceded preceded2 by a weakly first‐order transformation from a high‐temperature cubic2 phase to a near‐cubic, modulated, intermediate (premartensite) phase related to the presence of a soft phonon mode [46]. The appearance of this transformation has been proposed as a consequence of magneto‐elastic coupling. An inelastic neutron‐scattering experiment performed in an external magnetic field also

Metals 2017, 7, 410 10 of 13 by a weakly first-order transformation from a high-temperature cubic phase to a near-cubic, modulated, intermediate (premartensite) phase related to the presence of a soft phonon mode [46]. The appearance ofMetals this 2017 transformation, 7, 410 has been proposed as a consequence of magneto-elastic coupling. An inelastic10 of 12 neutron-scattering experiment performed in an external magnetic field also indicated a strong magneto-elasticindicated a strong interaction magneto at‐elastic the premartensitic interaction at transition. the premartensitic We conclude transition. that the large We conclude magnetostriction that the oflarge the magnetostrictionx = 0.15 alloy is related of the tox = lattice 0.15 alloy softening is related in the to premartensite lattice softening phase, in the similar premartensite to that with phase, the xsimilar= 0.00 alloy.to that We with expect the that x = magnetostriction 0.00 alloy. We expect can be observedthat magnetostriction in the premartensite can be phaseobserved because in the of thepremartensite softening caused phase bybecause a perturbing of the softening magnetic caused field. Further by a perturbing studies (acoustic magnetic measurements, field. Further etc.) studies are needed(acoustic to measurements, clarify these issues. etc.) are needed to clarify these issues.

0 300 Polycrystal this work Matsui Single Crystal Matsui Seiner -200 (ppm) (K) p T max  250 -400 Polycrystal this work Matsui Single Crystal Matsui Seiner -600 7.46 7.48 7.50 7.52 7.54 7.56 7.58 7.60 7.46 7.48 7.50 7.52 7.54 7.56 7.58 7.60 Valence electron concentration e/a Valence electron concentration e/a (a) (b)

FigureFigure 8.8. ((aa)) TheThe valencevalence electronelectrone e//a dependence of peak valuevalue ofof thethe magnetostrictionmagnetostriction aroundaround thethe premartensite temperature TP; (b) The valence electron e/a dependence of the TP. Filled circles: this premartensite temperature TP;(b) The valence electron e/a dependence of the TP. Filled circles: this work.work. FilledFilled triangles:triangles: polycrystal, Matsui etet al.al. [[26,40].26,40]. Cross: single, Matsui et al. [[40].40]. Filled square: single,single, SeinerSeiner etet al.al. [[17].17]. DottedDotted lineslines areare fittingfitting lines.lines. TheThe errorerror barsbars inin thisthis workwork werewere indicated.indicated.

4. Conclusions 4. Conclusions We have measured the thermal strain, permeability, magnetisation, and magnetostriction of We have measured the thermal strain, permeability, magnetisation, and magnetostriction of novel magnetic Heusler Ni2Mn1 − xCrxGa polycrystals. The thermal expansion measurements show an novel magnetic Heusler Ni2Mn1 − xCrxGa polycrystals. The thermal expansion measurements show anomaly, thus indicating that lattice deformation occurs below the premartensitic transition an anomaly, thus indicating that lattice deformation occurs below the premartensitic transition temperature TP. The permeability measurements also show an anomaly at the premartensitic temperature TP. The permeability measurements also show an anomaly at the premartensitic transition. transition. From the magnetisation results, we obtained the magnetic‐anisotropy constant K1. In the From the magnetisation results, we obtained the magnetic-anisotropy constant K1. In the martensite 6 martensite phase, we found the magnetic‐anisotropy constant for the x = 0.00 alloy6 (K1 = 4.03 × 10 phase, we found the magnetic-anisotropy constant for the x = 0.00 alloy (K1 = 4.0 × 10 erg/cm ) to be 3 6 3 erg/cm ) to be larger than that for the x = 0.15 alloy6 (K1 = 3.13 × 10 erg/cm ). Magnetostriction in the larger than that for the x = 0.15 alloy (K1 = 3.1 × 10 erg/cm ). Magnetostriction in the premartensite premartensite phase is larger than that in the austenite and martensite phases at low magnetic fields, phase is larger than that in the austenite and martensite phases at low magnetic fields, thus indicating thus indicating that they are related to lattice softening in the premartensite phase. The that they are related to lattice softening in the premartensite phase. The magnetostriction and TP are magnetostriction and TP are proportional to the e/a, which indicates that the electron energy, the proportional to the e/a, which indicates that the electron energy, the magnetostriction, and the Tp are magnetostriction, and the Tp are correlated each other. correlated each other.

Acknowledgments:Acknowledgments: TheThe authorsauthors wouldwould likelike toto expressexpress ourour sinceresincere thanksthanks toto ToetsuToetsu ShishidoShishido andand KazuoKazuo ObaraObara inin InstituteInstitute forfor MaterialsMaterials Research,Research, Tohoku University,University, andand RyujiRyuji KoutaKouta inin FacutyFacuty ofof Engineering,Engineering, YamagataYamagata UniversityUniversity forfor theirtheir helphelp onon thethe samplesample preparation.preparation. The authors also thankthank toto MitsuoMitsuo OkamotoOkamoto inin RyukokuRyukoku UniversityUniversity forfor helpinghelping toto makemake thethe apparatus.apparatus. This project is partly supported by the Ryukoku Extension CenterCenter (REC) at Ryukoku University. (REC) at Ryukoku University. Author Contributions: Yoshiya Adachi prepared the samples; Takuo Sakon and Takeshi Kanomata conceived andAuthor designed Contributions: the experiments; Yoshiya Naoki Adachi Fujimoto prepared and the Takuo samples; Sakon performedTakuo Sakon the and experiments; Takeshi Kanomata Naoki Fujimoto conceived and Takuoand designed Sakon analysed the experiments; the data; TakuoNaoki SakonFujimoto and and Takeshi Takuo Kanomata Sakon performed wrote the the paper. experiments; Naoki Fujimoto and Takuo Sakon analysed the data; Takuo Sakon and Takeshi Kanomata wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

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