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Journal of Magnetism and Magnetic Materials 302 (2006) 34–39

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Intermartensitic phase transitions in Ni–Mn–Ga alloy,magnetic field effect

V.V. Kokorina,�, A.O. Perekosb, A.A. Tshcherbac, O.M. Babiya, T.V. Efimovab

aInstitute of Magnetism of NAS and Ministry of Education of Ukraine, 36 b Vernadsky street, 03142 Kiev-142, UkrainebInstitute of Metal Physics NAS of Ukraine, 36 Vernadsky street, 03142 Kiev-142, UkrainecInstitute of Electrodynamics NAS of Ukraine, 56 Pobedy street, 03680 Kiev-57, Ukraine

Received 11 April 2005; received in revised form 5 August 2005

Available online 6 September 2005

Abstract

The aim of the present study was to investigate the magnetic field influence on the intermartensitic transformations in

Ni–Mn–Ga alloy. The temperature dependencies of low field magnetic susceptibility, electrical resistivity (r) and

magnetization (I) were studied in magnetic fields. The measurements of rðTÞ and IðTÞ were performed in the fields up to

10 kOe. The intermartensitic start temperature M 0s depends on magnetic field (H), M 0

s is rising on DT ¼ 7� 1K for the

field H ¼ 10 kOe. The nature of field-dependent shift of M 0s was discussed.

r 2005 Elsevier B.V. All rights reserved.

PACS: 75.80.+q; 81.30.Kf

Keywords: Ni–Mn–Ga; Intermartensitic transformation; Magnetic field influence

1. Introduction

Ferromagnetic shape memory alloys have at-tracted attention due to the detection of significantstrains generated by the magnetic field [1] in themartensite phase of Ni–Mn–Ga alloys. Themagnetoplastic strain caused by a displacementof movable boundaries of the martensite twinshaving high magnetic crystal anisotropy (Keff �

$ - see front matter r 2005 Elsevier B.V. All rights reserve

/j.jmmm.2005.08.010

onding author. Tel.: +380 44 424 0131.

address: kokorin@im.imag.kiev.ua (V.V. Kokorin).

105 j=m3) in magnetic field HX3 kOe was observedin these alloys. The possibility of such a strain bytwinning owing to the external field was discussedbefore [2] in connection with interpretation of themagnetization curves for crystals of rare earthelement, Dy, in field HX100 kOe.The martensite crystal lattice is unstable in these

alloys and is capable demonstrating a successionof the martensitic transitions named as intermar-tensitic transformations both under the action ofmechanical stresses [3] and as a result of cooling[4]. The study of spontaneous intermartensitic

d.

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V.V. Kokorin et al. / Journal of Magnetism and Magnetic Materials 302 (2006) 34–39 35

transitions is interesting both from the generalpoint of view since changing of physical propertiesat these transitions is not adequately explored andin practical aspect (using of shape memory effectthat also takes place in this case [5]). In particular,it is important to study a magnetic field’s influenceon intermartensitic transitions taking into accountthat magnetic field-induced martensitic transitionscan be used for a generation of the strain inmagnetic field [6]. Meanwhile the field-inducedshift of intermartensitic transition characteristictemperatures may be significantly higher in com-parison with a case when the field affects the basictransition: high-temperature phase-martensite. So,the shift of an equilibrium temperature betweentwo ferromagnetic martensitic phases DT�HDM=DS [7], where DM and DS are differences ofmagnetic moments and entropies of these phases,and as is well known, latent heat of martensitictransformation L ¼ T0 DS, where T0 is transitiontemperature. In the case of intermartensitic transi-tions, L is approximately ten times less than heateffect of the basic transition [8]. According toabove-mentioned formula for DT , the decreasingof DS in case of the same value of DM can result inconsiderable increasing of DT for an intermarten-sitic transition. In this paper, we describe an effectof large displacement of intermartensitic starttemperature induced by magnetic field.

2. Experimental results and discussion

The alloy (at%): (Ni–52, Mn–24,4, Ga–23,6)was melted in the induction furnace in argonatmosphere. An ingot was again melted in thefurnace with electric resistivity heater. In thecourse of cooling, an ingot had been exposed for2 h at 1273K, and then it was slowly cooledtogether with furnace. The measurement of thetemperature dependencies of electrical resistivity(r) and magnetization (I) in different magneticfields has been carried out. The low-field magneticAC susceptibility (w) was measured with using analternating magnetic field (frequency n ¼ 1 kHz,amplitude HAC � 4Oe). The combination ofalternating and stationary bias fields HDCp1 kOewas also used. Field dependencies of the marten-

site phase magnetization were measured at roomtemperature. The samples were annealed in thevacuum furnace at 973K for 12 h. Electricalresistivity has been measured using the alternatingcurrent with frequency 1 kHz, an axis of thespecimen has been disposed in the electromagneticgap in parallel with field H. As shown before [3],the intermartensitic transitions give rise to thechanging of w. Electrical resistivity of the differentmartensitic phases is different too [9]. Character-istic temperatures of martensitic and intermarten-sitic transitions of Ni–Mn–Ga specimen weredetermined using wðTÞ dependencies (Fig. 1). Incase of quenched specimen (Fig. 1a,b) the marten-site transformation start temperature Ms � 300K,and intermartensitic transition M 0

s � 240K.Appreciable increasing of w at M 0

s correspondsto a transition of b2 phase, having a lattice withseven-layer modulation,to b3-phase having non-modulated crystal lattice, which is in accordancewith the results given in Refs. [9–11]. The phasewith five-layer modulation was also detectedbefore in the Ni–Mn–Ga system [5] (atMsp280K), which we will denote as b1. There isa reverse transformation b3! b2 accompanied bydecreasing of w in course of heating at A0s ¼ 262.The field HDC ¼ 600Oe, applied along the speci-men axis, changes the form of the curve wðTÞ,Fig. 1b. The temperature M 0

s is displaced towardsthe high temperatures on the value of 1K, and thetemperature A0s is not displaced. The susceptibilitymaximum was observed at the Curie temperature(T c). Applied stationary field at T � Tc generatessingle magnetic domain state, it gives an opportu-nity to see the susceptibility peak which is typicalfor second-order phase transition at T ¼ Tc. Incase of HDC ¼ 0, the contributions to w from themagnetic domain boundaries are masking thispeak.Annealing at 973K for 12 h changes a state of

austenitic phase of the specimen, it also changescharacteristic temperatures of martensitic trans-formation. As can be seen (Figs. 1c and 2a), theisothermal annealing gives rise to the increase ofMs up to 325K and M 0

s ¼ 273K, A0s ¼ 293K. Atemperature hysteresis of the basic transformationhas decreased essentially and amounted to 2–3K.The curves rðTÞ (Fig. 2) were used for increasing

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0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

M′s

T,K

M′s(H=10kOe)

ρ/ρ m

ax

200 220 240 260 280 300 320 340 360 380T,K

200 220 240 260 280 300 320 340 360 380

ρ/ρ m

ax

(a) (b)

Fig. 2. Temperature dependence of electrical resistivity (r) of Ni–Mn–Ga alloy annealed at 973K for 12 h: (a) HDC ¼ 0 (temperatures

M 0s and A0s correspond to an intersection of line segments depicted in the figure). (b) HDC ¼ 10 kOe.

0

1.0

0.5

0.0

0.2

0.4

0.6

0.8

1.0Ms

Ms

A′s

A′s

M′s

M′s

As

Tc

Tc

T,K150 250200 300 350 400

T,K150 250200 300 350 400

T,K150 250200 300 350 400 450

χ/χ m

ax

0.0

0.2

0.4

0.6

0.8

1.0

χ/χ m

ax

χ/χ m

ax

(a) (b)

(c)

Fig. 1. Temperature dependence of low-field magnetic susceptibility w/wmax (wmax –maximum value of w): (a) wðTÞ measured at

HDC ¼ 0Oe, temperature Ms corresponds to a start of direct (during the cooling) and As to reverse (during the heating) basic

martensitic transformation; temperatures M 0s and A0s correspond to a start of direct and reverse intermartensitic transformations; Tc is

Curie temperature of a high-temperature phase. (b) wðTÞ measured at HDC ¼ 600Oe. (c) wðTÞ, HDC ¼ 0, sample annealed at 973K for

12 h.

V.V. Kokorin et al. / Journal of Magnetism and Magnetic Materials 302 (2006) 34–3936

of an accuracy of characteristic temperaturemeasurements in magnetic field. Another impor-tant moment is the stability of rðTÞ curves as

to the different values of H. These curves donot change their view in the different fields (seeFig. 2). It permits to measure the characteristic

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225 250 275 300 325 350 375 400 4250

10

20

30

40

50

60

70

c)

b)

I, A

m2 /k

g

a)

T, K

Fig. 4. Temperature dependencies of magnetization at different

values of magnetic field H: (a) 500Oe, (b) 5 kOe, (c) 10 kOe.

V.V. Kokorin et al. / Journal of Magnetism and Magnetic Materials 302 (2006) 34–39 37

temperatures for the fields HDCX10 kOe. Mean-while, the magnetization difference between b2 andb3 phases becomes rather small at fields H45 kOe.

The dependence of rðTÞ (Fig. 2b) is shown forannealed specimen at field HDC ¼ 10 kOe. Themagnetic field does not have an influence oncharacteristic temperatures of the basic transfor-mation within limit of measurement error (1K), itagrees with the results [12], where displacement ofthe basic transformation temperatures does notexceed 1K also in the field HDC ¼ 10 kOe. Morenoticeable influence of the field was observed incase of intermartensitic transitions. So, M 0

s isdisplaced on DT ¼ 7� 1K, whereas HDC is risingup to 10 kOe (Figs. 2b and 3). It is substantial thatthe temperature A0s does not change due to thefield.

There is the narrowing of temperature hysteresisof intermartensitic transformation in the magneticfield (Fig. 3). It is evident that temperatures M 0

s

and A0s are approaching during field rising.Temperature dependencies IðTÞ depicted in Fig. 4

show that the magnetization of b2-martensite beingformed during austenite cooling at the fieldsHDCo10 kOe is noticeably less in comparison withb3-martensite existing at ToM 0

s. The magnetizationdifference for these phases is decreasing duringmagnetic field increasing. So, we have DI/I2 � 0:45,0.24, 0.05 for magnetic fields HDC ¼ 0:5, 1, 5 kOe,respectively. Here, DI ¼ I32I2 is the magnetizationdifference of b3 and b2 phases at T ¼ 298K.

0 10

240

260

280

300

M′f

M′s

A′s

T,K

H,kOe2 4 6 8

Fig. 3. Characteristic temperature dependencies of intermar-

tensitic transformation on field value, M 0f temperature (during

cooling) of intermartensitic transformation finish.

Depending on cooling mode, b2- or b3-phase canbe formed at room temperature. There is a P! b2transition (P-high-temperature phase) during cool-ing from austenitic state to room temperature,whereas the cooling to the temperature ToM 0

s

and subsequent heating to T ¼ 298K creates a b3-phase state. In accordance with Ref. [9], theaustenite transforms to martensite phase b2 withorthorhombic crystal lattice and seven-layer mod-ulation (7M) in Ni–Mn–Ga alloys havingMsX320K, b2 transforms to b3-martensite withtetragonal crystal lattice without modulation [4,11]in the course of further cooling.The shape of magnetization curves presented in

Fig. 5 points to the higher magnetocrystallineanisotropy of b2 phase in comparison with b3phase. Just a difference in effective anisotropyconstants of b2 and b3 phases determines the typeof curves IðTÞ (Fig. 4). A comparative study of themartensite phase magnetic anisotropies was car-ried out in Ref. [13] for Ni–Mn–Ga alloys of thedifferent compositions. In the present work, acomparison of magnetic properties of martensitephases having the same chemical composition canbe made. Judging roughly the curves in Fig. 5, thesaturation field is higher for b2-martensite. It ispossible to estimate approximately an effective

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0 100

10

20

30

40

50

60

ab

I,Am

2 /kg

H,kOe

T=291K

2 4 6 8

Fig. 5. Field dependencies of magnetization b2 (a) and b3 (b)

phases, field increasing.

V.V. Kokorin et al. / Journal of Magnetism and Magnetic Materials 302 (2006) 34–3938

anisotropy constant (Keff ) using the well-knownformula HA ¼ 2Keff /I s, where HA is the aniso-tropy field that is equal to the saturation field, Isthe saturation magnetization. The data (Fig. 5)were plotted to get the dependencies Ið1=HÞ. Itwas assumed that the saturation corresponds tothe field values when the curves Ið1=HÞ transformto the straight lines. We have got Keff (b2-phase)E2.6� 105 j/m3 and Keff (b3-martensite) E2.2�105 j/m3. The magnetization of both martensitephases is generally realized at the expense of therotation processes, it confirms by small values ofcoercive force (H � 0) and narrow loops of curvesIðHÞ. In accordance with Fig. 5, the differencebetween I s for b2 and b3-martensites does notexceed 1–2Am2/kg. Let us evaluate the transfor-mation enthalpy change L for intermartensitictransition using a value DIsffi2Am2/kg andformula [7,14]

DT=DH ¼ DI sT0=L.

We will get Lp0:1 j=g for DT/DH ¼ 7K/T. So,the measurement of the dependence of M 0

sðHÞ athigh fields permits to evaluate a rather small latentheat of intermartensitic transition if a value DI swas precisely measured. Strictly speaking, theabove-mentioned formula does not take intoaccount the magnetic anisotropy energy difference(DKeff ) of the martensitic phases. This circum-stance determines its applicability at HX100 kOe,where magnetic energy IH is considerably largerthan anisotropy energy [15]. In our case, we have

H ¼ 10 kOe and it is also enough probable thatDI s � 0. The difference (DKeff ) can be responsiblefor the shift of M 0

s in the magnetic field. Indeed, aphase with the high anisotropy energy (b2) will bereplaced by b3-phase in the vicinity of a phaseequilibrium temperature due to a field. It makesM 0

s to increase. A lack of the A0s displacement inthe magnetic field is probably connected with acloseness of A0s and Curie temperatures providingthe negligible values of both DI s and DKeff .

3. Conclusion

Our experiments show that one of the ways toestablish the magnetic field dependence of theintermartensitic transformation characteristic tem-peratures of Ni–Mn–Ga alloys is to measure theirtemperature dependencies of electrical resistivityin different magnetic fields. The intermartensiticstart temperature M 0

s increases on DT � 7K atH ¼ 10 kOe. The minor difference of the marten-sitic phases saturation magnetizations permits oneto suppose that magnetic field induced shift of M 0

s

can be explained by the magnetic anisotropyenergy difference of Ni–Mn–Ga martensites.

Acknowledgements

We acknowledge support from the Science andTechnology Center in Ukraine, project N 2346.

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