Journal of Magnetism and Magnetic Materials 324 (2012) 729–734

Contents lists available at SciVerse ScienceDirect

Journal of Magnetism and Magnetic Materials

0304-88

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jmmm

The magnetic properties across the martensitic transitionin the Co38Ni34Al28 alloy

Ashish Khandelwal n, V.K. Sharma, L.S. Sharath Chandra, Parul Arora, M.K. Chattopadhyay, S.B. Roy

Magnetic & Superconducting Materials Section, Raja Ramanna Centre for Advanced Technology, Indore 452 013, India

a r t i c l e i n f o

Article history:

Received 28 January 2011

Received in revised form

30 August 2011Available online 19 September 2011

Keywords:

Martensitic transition

Ferromagnetic

Spin wave

Magnetic anisotropy

53/$ - see front matter & 2011 Elsevier B.V. A

016/j.jmmm.2011.09.006

esponding author. Tel.: þ91 731 248 8305; fa

ail address: ashishkhandelwal@rrcat.gov.in (A

a b s t r a c t

The magnetic properties of the Co38Ni34Al28 alloy have been studied. The alloy exhibits a first order

austenite–martensite phase transition in the temperature region between 155 and 247 K. A strain of

0.07% is produced across this phase transition. The Arrott plots obtained from the isothermal magnetic

field dependence of magnetization indicate the presence of spontaneous magnetization both in the

austenite and martensite phases, confirming the ferromagnetic character of the alloy up to room

temperature. The temperature dependence of the high field magnetization indicates the presence of

spin wave excitations, spin wave excitation gap and spin wave–spin wave interactions in the

martensite phase. The magnetic anisotropy energy constant for the Co38Ni34Al28 alloy is estimated

both with the help of the standard law of approach to saturation of magnetization, and also from the

field dependence of magnetization using the field for technical saturation of magnetization. The

temperature dependences of these energy terms are compared. The estimated values of the magnetic

anisotropy constant seem to be in agreement with the magnitude of the spin wave excitation gap

estimated from the temperature dependence of high field magnetization.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

The recent interest in research on the off-stoichiometricNi–Co–Al based alloys is because of their potential as ferromag-netic shape memory materials [1–5]. Earlier, the NiAl basedsystems came into focus with the discovery of shape memoryeffect in the paramagnetic NiAl–b phase by Enami and Nenno [6].With the addition of Co in the NiAl alloys, a new class of alloysemerged in which the b phase martensitically transforms into ab0(L10) structure. Depending on the concentration of Ni and Coand varying annealing conditions, a g (A1 structure) or g0 (Ni3Al,L12 structure) phase having different mechanical properties canbe precipitated in the alloys [7]. The introduction of g-phaseincorporates ductility in the otherwise brittle b-phase Co–Ni–Alalloy, making the alloy more machinable. Oikawa et al. [1] havereported the composition dependence of the Curie temperature(Tc), and the martensite start and austenite finish temperatures inthe Ni71�xCoxAl29 alloy. With a slight change in Co concentration,the magnetic state of the high temperature austenite phase andthe low temperature martensite phase can be chosen to be eitherparamagnetic or ferromagnetic in character. Chatterjee et al. havestudied the temperature dependent magnetic and structural

ll rights reserved.

x: þ91 731 248 8300.

. Khandelwal).

properties for different Co–Ni–Al alloys across the martensitictransition [8]. Apart from the dependence on composition, themartensite start and austenite finish transition temperatures alsodepend strongly on the annealing conditions [9,10]. Tanaka et al.[9] extensively studied the dependence of the martensitic andmagnetic phase transitions on the annealing conditions. The Curietemperature and the martensite start temperature increases withincreasing annealing temperature for the Co38Ni34Al28 alloy dueto the variation of chemical composition of the b and g phases.However, to the best of our knowledge, a detailed understandingof the magnetic properties of the Co38Ni34Al28 alloy across themartensitic transition has not yet evolved.

In the present work, we have studied in detail the magneticproperties across the martensitic transition in the Co38Ni34Al28

alloy. This particular composition was chosen because as per thecompositional phase diagram of the Ni–Co–Al alloys reported byOikawa et al. [1] this composition is expected to be a ferromag-netic shape memory alloy with ferromagnetic austenite andmartensite phases. We have found that a strain of 0.07% isproduced across this phase transition. The magnetization resultsconfirm the ferromagnetic character of the alloy up to roomtemperature. The nature of the magnetic excitations in themartensite phase and the magnetic anisotropy in the martensiteand austenite phases of the alloy is studied, which revealsinteresting features that could be useful the for future applicationof this alloy system.

0.96

1.00

1.04

1.08

100 150 200 250 300

-0.15

-0.10

-0.05

0.00

T (K)

ρ/ρ 3

00K

ΔL/L

293

(%)

Fig. 1. (a) Normalized electrical resistivity and (b) strain as a function of

temperature of the Co38Ni34Al28 alloy.

A. Khandelwal et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 729–734730

2. Experimental details

A polycrystalline sample with the nominal composition Co38

Ni34Al28 was prepared using high purity elements in an arc meltingfurnace in an inert argon atmosphere. The sample was flipped andre-melted several times to ensure the homogeneity. The sample wasthen sealed in a quartz ampoule in argon atmosphere, and wasannealed at 1275 1C for 24 h followed by quenching in ice water tointroduce the g phase in the otherwise brittle b phase [9]. Structuralcharacterization of the alloy was done with the help of X-raydiffraction (XRD) study performed in a PANalitical X‘Pert PROMRD machine, using Cu Ka radiation (l¼1.54056 A). The XRDresults indicate the presence of both b (approximately 40%) and g(approximately 60%) phases in the sample. The b phase has a bcc(B2) structure with a lattice parameter of 2.86 A, and the g phasehas an FCC (A1) structure with a lattice parameter of 3.575 A. Onlythe b-phase undergoes a transition from the cubic austenite phaseto the tetragonal martensite b0-phase, whereas g phase remainsunchanged and does not play any role in the martensitic transition.There was no indication of the martensite b0(L10) phase from theXRD pattern at room temperature. The electrical resistivity of thesample as a function of temperature was measured between 350 Kand 77 K, using the standard four probe technique in a homemadeliquid nitrogen cryostat. DC magnetization (M) as a function oftemperature (T) and applied magnetic field (H) was measured usinga SQUID magnetometer (MPMS-XL, Quantum design) and a vibrat-ing sample magnetometer (VSM, Quantum Design). Strain measure-ment as a function of temperature was performed between 350 Kand 77 K using the strain gage technique [11]. In this measurementthe relative change in length DL/L was measured using a differentialmethod, keeping copper as the reference material, and the length at293 K as the reference length. The temperature dependence of strainis thus expressed in terms of DL/L293 where L293 is the length of thesample at 293 K.

3. Results and discussion

Fig. 1(a) shows the temperature dependence of the normalizedelectrical resistivity of the Co38Ni34Al28 alloy as a function oftemperature. While cooling down the sample from room tem-perature, resistivity first decreases nearly linearly as is normallyexpected in a metal. But below 210 K, it increases sharply beforeexhibiting the near-linear temperature dependence again below150 K. While warming up, the sample exhibits a similar tempera-ture dependence of electrical resistivity along with a distinctthermal hysteresis associated with the sharp drop in the magni-tude of resistivity. Thermal hysteresis in an experimental obser-vable is a signature of a first order phase transition [12]. TheCo–Ni–Al alloy system is known to exhibit a first order austenite–martensite phase transition with varying temperature [13]. The largechange in resistivity along with the associated thermal hysteresisobserved in Fig. 1(a) is therefore attributed to the first orderaustenite–martensite phase transition in the present Co38Ni34Al28

alloy. The martensite start and the austenite start temperature arelocated from the change in the curvature of the resistivity vs.temperature curves using the first order derivatives of these curves.The martensite start and the austenite start temperature are found tobe 224 and 171 K, respectively. The martensite finish temperatureis defined as the point of convergence of the heating and coolingcurves on low temperature side (the limit of supercooling [12] ofthe austenite phase). This temperature is found to be 155 K. Theresistivity vs. temperature curves for heating and cooling for thepresent Co38Ni34Al28 alloy do not converge on the high temperatureside making the austenite finish temperature difficult to determine.This non-convergence is related to the fact that the resistivity of the

alloy keeps increasing every time it is taken through a heating-and-cooling cycle across the martensitic transition. However, as anapproximation the austenite finish temperature is taken as thetemperature from where the heating and the cooling curves becomesparallel and this comes out to be 247 K.

Fig. 1(b) shows the temperature dependence of the strain(DL/L293) in the Co38Ni34Al28 alloy. Starting from well inside theaustenite phase, the strain decreases with the decrease in tem-perature, shows a sharp step-like feature starting at 203 K andthen decreases continuously with further decrease in tempera-ture. Similar behavior is also observed in the warming-up cycle,along with a thermal hysteresis associated with the step-likefeature mentioned above. The step in the warming-up cycle isbroader and less sharp as compared with the cooling down cycle.The step-like feature in the temperature dependence of strain andthe associated thermal hysteresis is attributed to the austenite–martensite phase transition in the alloy. The characteristic tem-peratures for this phase transition obtained from the temperaturedependence of strain by following a similar procedure as done forresistivity are: martensite start temperature¼210 K; martensitefinish temperature¼170 K; austenite start temperature¼177 Kand austenite finish temperature¼240 K. These temperaturesmatch reasonably well with those obtained from the resistivitymeasurements. A change of strain of about 0.07% is observedacross the austenite–martensite phase transition. However, thischange of strain is less than that observed by Wang et al. whomeasured a strain of 0.15% across this phase transition in Co39

Ni33Al28 ribbons [14].Fig. 2 shows the dc-magnetization of the Co38Ni34Al28 sample

as a function of temperature in zero-field cooling (ZFC), fieldcooled cooling (FCC) and field cooled warming (FCW) protocols inthe presence of 100 Oe and 50 kOe applied magnetic fields. In theZFC protocol the sample is cooled down to 5 K in zero magneticfield and then the measurement is performed in the desired field

3

4

5

6

7

8

50 100 150 200 250 30036

40

44

48

52

T (K)

M (e

mu/

g)

100 Oe

ZFCFCCFCW

M (e

mu/

g)

50 kOe

Fig. 2. Magnetization as a function of temperature for Co38Ni34Al28 alloy for the

applied magnetic fields of 100 Oe and 50 kOe measured in the zero field cooling,

field cooled cooling and field cooled warming protocols.

0 10 20 30 40 50 60 700

10

20

30

40

50

-5 -4 -3 -2 -1 0 1 2 3 4 5

-40

-20

0

20

40

175K200K225K250K275K300K

H (kOe)

5K25K50K75K100K150K

H (kOe)

M (e

mu/

g)

MH_5KHc=260 Oe

M (e

mu/

g)

Fig. 3. (a) Magnetization as a function of applied magnetic field at 5 K, and (b)

magnetization vs. applied field curves at different temperatures.

A. Khandelwal et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 729–734 731

of measurement while warming up the sample. In the FCCprotocol the desired field is applied above 300 K and the mea-surement is performed while cooling down the sample to 5 K.Measurement of magnetization with increasing temperature afterreaching 5 K in the FCC mode is termed as the FCW protocol. Athermal hysteresis is observed between FCC and FCW magnetiza-tion curves obtained in 100 Oe applied field. This hysteresis isattributed to the first order austenite–martensite phase transitionin the alloy. Interestingly, the width of the thermal hysteresisappears to decrease with increasing magnetic field (see Fig. 2(b)).

Fig. 3(a) shows the magnetization as a function of appliedmagnetic field at 5 K, which shows a coercivity of about 260 Oe.Magnetization behavior as a function of applied magnetic field upto 70 kOe is shown at different temperatures in Fig. 3(b).Figs. 2 and 3(b) show that the magnetization is higher in themartensite phase as compared with the austenite phase in theCo38Ni34Al28 alloy. The value of saturation magnetization at 5 K is54.3 emu/g, which decreases to 38.6 emu/g at 300 K.

The presence of magnetic saturation in the Co38Ni34Al28 alloyin the entire temperature range of measurement indicates thatthe alloy is ferromagnetic both in the austenite and martensitephases. The confirmation of this ferromagnetic nature is obtainedfrom the so-called Arrott plots or the M2 vs. H/M plots [15] shownin Fig. 4(a). The linear high-field (60–70 kOe) region of the Arrottplots was extrapolated to obtain the value of spontaneousmagnetization of the Co38Ni34Al28 alloy at different temperatures.Fig. 4(b) shows the temperature dependence of spontaneousmagnetization of the Co38Ni34Al28 alloy. The value of spontaneousmagnetization changes slowly from 32.66 to 53.74 emu/g as the

temperature is reduced from 300 to 5 K, confirming the ferro-magnetic character of both the austenite and martensite phases.

Fig. 5 shows the temperature dependence of the reducedmagnetization in the ferromagnetic martensite phase in thepresence of an applied magnetic field of 50 kOe. The applied fieldis well above the field required for technical saturation as can beseen from Fig. 3(b). The low temperature magnetic excitationspresent in the Co38Ni34Al28 alloy were analyzed with the help offollowing equation:

M Tð Þ�Mð0Þ

Mð0Þ¼ a1T3=2 expð�Tg=TÞþa2T5=2

þa3T2ð1Þ

Here, M(0) is the saturation magnetization at T¼0. The T3/2 termarises from the long wavelength spin wave excitation, and theexponential factor accounts for the intrinsic energy gap in thespin-wave excitation spectrum arising because of magnetic ani-sotropy [16,17]. Here, Tg is the temperature equivalent to the gapin the energy spectrum. The T5/2 term in Eq. (1) arises from spinwave–spin wave interaction while the T2 dependence is due toStoner band excitations [16,18]. In the case of an isotropic ferro-magnet, there will be no gap in the magnon spectrum andtherefore the exponential factor will not appear in Eq. (1)[16,17]. However, for the present sample the inclusion of theexponential factor in Eq. (1) gave a better fit (lower w2 value) tothe experimental M vs. T curve obtained in 50 kOe magnetic field.The solid line in Fig. 5 represents this best fit curve and it fits theexperimental curve up to 26 K. The constants a1, a2, a3 and Tg inEq. (1) were obtained as the fitting parameters. The values of

0 400 800 1200 16000

800

1600

2400

3200

0 100 200 30030

35

40

45

50

55

300K275K250K230K220K200K

175K150K100K50K25K5K

M2

(em

u2 g-2

)

H /M

T (K)

Msp

onta

neou

s (e

mu

/g)

Fig. 4. (a) Arrott plots obtained from the isothermal field dependence of

magnetization of Co38Ni34Al28 alloy and (b) variation of spontaneous magnetiza-

tion as a function of temperature obtained from the extrapolation of the linear

high field region between 60 and 70 kOe of the Arrott plots.

Fig. 5. Reduced magnetization vs. temperature plot for Co38Ni34Al28 in the

martensite phase for an applied magnetic field of 50 kOe. The solid line represents

the fitted curve using the first two terms of Eq. 1.

A. Khandelwal et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 729–734732

M(0), ‘a1’ and ‘a2’ come out to be 54.045 emu/g, 4.2�10–4 K�3/2

and 5.4�10�6 K�5/2, respectively. The parameter a3 is found tobe zero, and the absence of this T2 term in the best-fit curveindicates the localized moment character of the alloy. On theother hand, the value of the gap temperature Tg comes out to be8.9 K. This value may be compared with those for Fe and Ni,which are reported to be 53.5 K and 5.8 K, respectively [17].

In the absence of a gap (and the exponential factor) the spin-wave stiffness constant ‘D’ can be calculated using the value offitting parameter ‘a1’ in the following equation [16,19]:

D¼ ð2:612Þ2=3 gmB

a1Mð0Þ

� �2=3 kB

4p ð2Þ

Here, g is the Lande splitting factor, mB is the Bohr magneton andkB is the Boltzmann constant. However, it may be noted in Eq. (1)that the constant ‘a1’ is the coefficient to both the T3/2 and theexp(�Tg/T) terms, and thus may be related to both spin wavestiffness and anisotropy. This might introduce an error in thevalue of ‘D’ that can be estimated using the value of fittingparameter ‘a1’ in Eq. (2). On the other hand, the martensite phasein the present Co38Ni34Al28 alloy has a tetragonal structure (lowersymmetry), and in fact, the b0 martensitic phase in the singlecrystals of Co37Ni34Al29 and Co41Ni32Al27 alloy samples has beenreported to exhibit magnetic anisotropy [2,4]. Therefore someeffect of magnetic anisotropy is expected in the temperaturedependence of high field magnetization of the present Co38

Ni34Al28 alloy as well. Moreover, Eq. (1) (or equivalent) has earlierbeen used to analyze the high field M vs. T curves for Fe, Ni, Co,etc. [16,17,20,21]. We have therefore estimated the value of ‘D’using the values of ‘a1’ obtained by fitting Eq. (1) to the experi-mental data, and it comes out to be 30.69 meV A2. This value islower than the 74 meV A2 value obtained by Liu et al. for theCo39Ni33Al28 ribbon samples [22] and 116 meV A2 obtained byChatterjee et al. for Co37Ni34Al29 [23]. This indicates that the lowtemperature magnetic excitations are affected significantly by asmall change in the composition. The values of Tg and ‘D’ for thepresent Co38Ni34Al28 alloy are quite comparable with that for theNi49.1Mn29.4Ga21.5 alloy, which are reported to be 2.2 K and198 meV A2, respectively. These values for the Ni49.1Mn29.4Ga21.5

alloy were estimated from neutron spectroscopy experiments[24]. We will also see here that the value of Tg obtained fromthe high field M vs. T curve is consistent with the anisotropyenergy estimated from the M vs. H curves.

In order to shed more light on the ferromagnetic character andthe magneto-crystalline anisotropy of the Co38Ni34Al28 alloy inthe martensite and austenite phases, the M vs. H data at aparticular temperature are analyzed using the law of approachto saturation magnetization [25,26 and references therein], whichis given by

M¼MS 1�b

H2

� �þcH1=2

ð3Þ

Here Ms is the saturation magnetization and ‘b’ and ‘c’ are theconstants. The coefficient ‘b’ is a measure of magnetic anisotropyenergy and last term represents the paraprocess. The coefficient‘c’ is independent of metallurgical treatment. Eq. (3) is fitted tothe M vs. H curves of the Co38Ni34Al28 alloy above 20 kOemagnetic field, and the constants Ms, ‘b’ and ‘c’ are obtained asthe fitting parameters, and these are then plotted as functions oftemperature in Fig. 6(a), (b) and (c), respectively. Saturationmagnetization of the specimen decreases with the increase oftemperature. It is found to be higher for the martensite phase ascompared to the austenite phase. The temperature dependence ofthe fitting coefficient ‘b’ is shown in Fig. 6(b), which is a functionof the anisotropy energy. For a polycrystalline sample with cubic

0 100 200 3000

1

2

3

4

0 100 200 3000.8

1.2

1.6

2.0

0 100 200 300

30

40

50

0 100 200 3002.0

2.4

2.8

3.2

3.6

c (1

0-2 e

mug

-1 O

e-1/2

)

T (K)

b (1

07 O

e2 )

T (K)

Ms

(em

u/g)

T (K)

T (K)

K (1

06 er

g/c

c)

Fig. 6. Results of analysis of the high field portions of the isothermal magnetiza-

tion vs. applied field curves using the law of approach to saturation of magnetiza-

tion (Eq. (3)): (a) Temperature dependence of the saturation magnetization Ms.

(b, c) The temperature dependence of the fitting coefficients ‘b’ and ‘c’.

(d) Temperature dependence of the anisotropy energy constant obtained using

Eqs. (4) and (5) for the cubic austenite phase (solid triangles) and the tetragonal

martensite phase (open squares) of the Co38Ni34Al28 alloy, respectively.

3.2

3.6

4.0

4.4

0 100 200 300

3.2

4.8

6.4

T (K)

K1

(106

erg

/cc)

K1

(106

erg

/cc)

Fig. 7. Temperature dependence of the anisotropy energy constant ‘K1’ calculated:

(a) using Eq. 4 considering the cubic structure for both the martensite and

austenite phases and (b) using anisotropy field (discussed in text).

A. Khandelwal et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 729–734 733

structure, ‘b’ is related to the anisotropy energy constant ‘K1’as [25]

b¼8

105

K21

M2s

ð4Þ

However, for a polycrystalline sample with tetragonal struc-ture, ‘b’ is related to the effective anisotropy energy constant ‘Keff’as [27]

b¼4

15

K2ef f

M2s

ð5Þ

where Keff is related to the anisotropy constants K1, K2 and K3 for atetragonal system as

K2ef f ¼ K2

1þ167 ðK1þ

23 K2ÞK2þ

16021 K2

3 ð6Þ

It is observed from the X-ray diffraction studies that the roomtemperature austenite phase for the present alloy has a cubiccrystal structure. On the other hand it is reported in literature thatthe low temperature martensite phase of the alloy is tetragonal(L10) [2,7]. Therefore the anisotropy constant has been calculatedfor the high temperature cubic phase and the low temperaturetetragonal phase using Eqs. (4) and (5), respectively. These valuesare plotted as a function of temperature in Fig. 6(d). Theanisotropy constant has not been calculated across themartensite–austenite transition region (200–250 K) because ofthe uncertainty in the crystal structure across this transition. Theanisotropy energy for the martensite phase is found to be smallerthan that for the austenite phase of the Co38Ni34Al28 alloy. This

observation is contrary to what is expected in a potentialferromagnetic shape memory alloy [28]. It is known that theCo38Ni34Al28 alloy goes to a multi-variant state in the martensitephase, and this leads to errors in the estimation of the magneto-crystalline anisotropy energy [2]. In some of the earlier reports,the anisotropy energy constant has been calculated using Eq. (4)for both the martensite and austenite phases [26]. Following asimilar approach, the anisotropy constant has been calculated forthe present alloy as well. This is shown as a function oftemperature on Fig. 7(a). In this method the value of anisotropyenergy constant comes out to be larger in the martensite phase ascompared to the austenite phase. The value of anisotropy constantin martensite phase using Eq. (5) at 10 K is 2.249 �106 erg/cc(multiplying the fitted value with calculated density for compositionCo38Ni34Al28¼7.164 g/cc). This value is comparable with thosereported for the b0 martensitic phase in the single crystals ofCo41Ni32Al27 (3.2�106 erg/cc) [4] and Co37Ni34Al29 (3.9�106 erg/cc) alloys [2]. For a complete comparison of the values of themagneto-crystalline anisotropy constants obtained in differentmethods, we have also calculated the same using the relationHA¼2 K1/MS. Here MS is the saturation magnetization and HA isthe anisotropy field, which is equal to the field for technicalsaturation. The temperature variation of the anisotropy constantcalculated using the above relation is shown in Fig. 7(b). The value ofanisotropy energy constant calculated in this manner is higher inthe martensite phase and then decreases while approaching theaustenite phase. However the value of the anisotropy constant of themartensite phase is higher than that obtained using the law ofapproach to saturation. Here it may be recalled that the XRD resultsindicate that the present sample consists of 40% b phase and 60% gphase, where the b phase has a bcc (B2) structure and the g phasehas an fcc (A1) structure. According to the literature it is only the bphase that undergoes a transformation to a tetragonal structure

A. Khandelwal et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 729–734734

through a martensitic phase transition. The g phase remainsuntransformed with varying temperature [7,9]. This, along withthe multi-variant configuration of the b0 phase at low temperaturescould probably lead to uncertainties in the values of the anisotropyenergy constant estimated through any of the methods describedabove.

The anisotropy energy estimated above may be compared withthe Tg (¼Eg/kB) determined from the high field M vs. T curve. Theenergy gap appearing in the spin wave spectrum is related to theanisotropy through the following relation [16]:

Eg ¼ gmB HþHAþ43pMð0Þ

� �ð7Þ

In Eq. (7), HA is the anisotropy field incorporated to account forthe anisotropy energy for each magnetic excitation that is created.Here, the demagnetization field is considered negligible so thatthe applied magnetic field of 50 kOe is taken to be the totalinternal magnetic field (H). M(0) is the saturation magnetizationat T¼0 K obtained using Eq. (1). To find the correct value of Tg, anaccurate estimation of HA is crucial. It is obtained using therelation HA¼2K1/MS. Here anisotropy energy constant K1 for cubicmartensite structure is obtained from the M vs. H curve at 10 Kusing Eq. (4), and MS is obtained from the same curve using Eq. (3).Substituting these values in Eq. (7) the gap temperature comes outto be 9.9 K. This is quite close to the value of gap temperatureobtained by fitting Eq. (1) to the high field M vs. T curve. If the sameestimation is done for the tetragonal martensite structure at 10 K,then the gap temperature comes out to be 8.3 K, which is slightlylower than the above value.

4. Summary and conclusion

The magnetic properties of a polycrystalline Co38Ni34Al28 alloyhave been studied both in the high temperature austenite phaseand the lower temperature martensite phase. The alloy exhibits athermal hysteresis across this austenite–martensite phase transi-tion that can be observed in the temperature dependence ofelectrical resistivity, strain and magnetization in the temperatureregion between 155 and 247 K in zero and low (100 Oe) magneticfields. This hysteresis effect is attributed to the first order natureof the austenite–martensite phase transition. The hysteresis,however, appears to diminish in high magnetic field (50 kOe).A strain of 0.07% is produced across the austenite–martensitephase transition in the alloy. The Arrott plots obtained from themagnetic field dependence of magnetization indicate the pre-sence of spontaneous magnetization both in the austenite andmartensite phases, confirming the ferromagnetic character of thealloy up to room temperature. A coercivity of about 260 Oe isobserved at 5 K, but it is negligible at room temperature Themeasured magnetization values and the spontaneous magnetiza-tion obtained from the Arrott plots are found to be significantlyhigher in the martensite phase. The temperature dependence ofthe high field magnetization indicates the presence of spin waveexcitations and spin wave–spin wave interactions in the marten-site phase. The value of spin wave stiffness constant D in themartensite phase of the Co38Ni34Al28 alloy comes out to be30.69 meV A2, which is lower than the 74 meV A2 and 116 meV A2

values obtained for the Co39Ni33Al28 and Co37Ni34Al29 alloys,respectively. The present study thus indicates that the lowtemperature magnetic excitations are influenced significantly bya small change in the composition. The temperature dependenceof the high field magnetization also indicates the presence of an

excitation gap in the spin wave spectrum. The magnetic aniso-tropy energy constant for the Co38Ni34Al28 alloy is estimatedusing the standard law of approach to saturation of magnetiza-tion, taking into consideration the cubic and tetragonal crystalstructures of the austenite and martensite phases of the alloy,respectively. A direct estimation of the magnetic anisotropyenergy constant using the field for technical saturation of mag-netization is also performed and the temperature dependence ofthese anisotropy energy constants is compared. The values of themagnetic anisotropy energy constant obtained using the law ofapproach to saturation magnetization seems to be in agreementwith the value of the excitation gap in the spin wave spectrumestimated from the temperature dependence of the high fieldmagnetization.

Acknowledgment

The authors thank Mr. R.K. Meena for his help in samplepreparation, and Dr. Tapas Ganguli for doing XRD measurements.Ashish Khandelwal and L.S. Sharath Chandra would like to thankBRNS, DAE, India for the financial assistance in the form of(K.S. Krishnan Research Associateship).

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