Atomic ordering and magnetic properties in Ni2Mn(GaxAl1−x) Heusler alloys

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Acta Materialia 56 (2008) 4789–4797 www.elsevier.com/locate/actamat

Atomic ordering and magnetic properties in Ni2Mn(GaxAl1x) Heusler alloys H. Ishikawa a, R.Y. Umetsu b,*, K. Kobayashi a,1, A. Fujita a, R. Kainuma b, K. Ishida a a

Department of Materials Science, Graduate School of Engineering, Tohoku University, 2-2-06 Aoba-yama, Sendai 980-8579, Japan b Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan Received 7 November 2007; received in revised form 25 May 2008; accepted 26 May 2008 Available online 28 July 2008

Abstract The phase stability and magnetic properties of Ni2Mn(GaxAl1x) alloys were studied by differential scanning calorimetric and magnetometric measurements, and X-ray diffraction and transmission electronic microscopic observations. The order–disorder transition 1 temperature from the B2 to the L21 phase, T B2=L2 , linearly increases with increasing x and the magnetic properties depend on the annealt ing conditions. Especially in the Ni2Mn(Ga0.5Al0.5) alloy, the condition of the atomic order can be varied from a B2 to an L21 structure by the annealing temperature. The magnetic property of the fully ordered L21 phase is ferromagnetic with a Curie temperature TC of about 380 K, while that in the B2 phase is antiferromagnetic with the Ne´el temperature TN of about 300 K. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel alloys; Heusler phases; Order–disorder phenomena; Magnetic properties; Microstructure

1. Introduction Ferromagnetic shape memory alloys (FSMAs) have attracted considerable interest as a new type of applicable materials for actuators and sensors which can be controlled by external magnetic fields. Among the various FSMAs, the largest magnetic field-induced strain (MFIS), i.e. up to about 10%, has been reported in off-stoichiometric Ni2MnGa single crystals [1,2]. The magnetic shape memory effect is caused by the magnetic field-induced rearrangement of the twin variants, and the origin of this behavior comes from the high magnetocrystalline anisotropy energy [3,4]. Moreover, recent studies have revealed that the Ni2MnGa alloys exhibit other attractive properties, such as large magnetoresistance and magnetocaloric effects, besides the MFIS phenomenon [5–8]. Ni2+xMn1xGa *

Corresponding author. Tel.: +81 22 217 5816; fax: +81 22 217 5828. E-mail address: [email protected] (R.Y. Umetsu). 1 Present address: Technical Division, Department of Instrumental Analysis, School of Engineering, Tohoku University, 6-6-11 Aoba, Sendai 980-8579, Japan.

alloys have also shown interesting changes in structural, magnetic and electronic properties as a function of composition [9–13]. Because of this, a large number of investigations into Ni–Mn–Ga alloys have been carried out. For practical applications, Ni2MnGa alloy does, however, have some drawbacks, such as high cost due to the expensive Ga element component and poor workability, as exhibited by its low ductility. The present authors’ group has recently found that the ferromagnetic parent phase with an L21-type structure in Ni–Mn–Al alloys transforms to the martensite phase with a long period stacking order structure [14–17] and that a polycrystalline specimen of Ni53Mn25Al22 alloy exhibits MFIS behavior with a maximum value of about 100 ppm just above the martensite finish temperature Mf [17]. It is known that the magnetic property of the B2 phase in the Ni2MnAl alloy, obtained by quenching from high temperatures, is antiferromagnetic with a conical antiferromagnetic structure, the Ne´el temperature TN being about 300 K [18]. On the other hand, it has been suggested from theoretical calculations that the magnetic moment and the Curie temperature TC of the L21 phase in the

1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.05.034

H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797

2. Experimental procedures Several kinds of alloys were prepared from high-purity Ni (99.9%), Mn (99.7%), Ga (99.99%) and Al (99.7%) by induction furnace melting under an argon gas atmosphere. Small specimens cut from the ingots were sealed in quartz tubes after being wrapped in molybdenum foil to prevent reaction with the quartz tubes. They were annealed at 1273 K for 3 days as a solution heat treatment and subsequently quenched in ice water. Additional annealing of the specimens at various temperatures was also performed. The order–disorder transition temperature from the B2 B2=L21 to the L21 phase T t and the magnetic transition temperatures (the Curie temperature TC or the Ne´el temperature TN) were determined by differential scanning calorimetric (DSC) and magnetic measurements, the heating and cooling rates of DSC was 5 K/min. Magnetic measurements with a superconducting quantum interference device magnetometer were also carried out. Identifications of the crystal structure and the microstructures of the specimens were achieved by electron diffraction, X-ray powder diffraction (XRD) and transmission electron microscopic (TEM) observations. 3. Results 3.1. Order–disorder transition temperature and magnetic transition temperature of Ni2Mn(GaxAl1x) alloys Fig. 1(a) shows the DSC heating curves of Ni2Mn(GaxAl1x) alloys for x = 0.50, 0.68, 0.84 and 1.00 obtained by quenching from 1273 K. In the figure, anoma-

a

quenched from 1273 K

x = 1.00 DSC, Exothermic

Ni2MnAl and Ni2MnGa alloys are comparable to each other [19–21]. However, the magnetic properties of the L21 phase in the Ni2MnAl alloys are not in accord with the theoretical results, whereas the experimental magnetic properties in the Ni2MnGa alloy agree well with them [22]. Recently, based on experimental studies, Acet et al. [23] and Man˜osa et al. [24] reported that an Ni2MnAl specimen annealed at low-temperature seemed to be a mixed L21 and B2 phase, and that its magnetic properties could be characterized as incorporating both the ferromagnetic and antiferromagnetic components. This mixed phase has been explained as resulting from the significantly lower order–disorder transition temperature from the B2 to the B2=L21 L21 phase T t compared with that of the Ni2MnGa alloy [25]. The phase condition and the magnetic properties of the Ni2MnAl alloy should be further clarified in order to facilitate its use in applications. In the present study, we investigated the phase stability, crystal structures and magnetic properties of Ni2Mn(Gax Al1x) (0 6 x 6 1) alloys in order to clarify the difference in the magnetic properties between the Ni2MnAl and Ni2MnGa alloys. In particular, correlations between the degree of long-range order and the magnetic properties of the Ni2Mn(Ga0.5Al0.5) alloy were investigated.

0.84

TtB2/L21 0.68 0.50

900

950

1000

1050

1100

Heating temperature (K)

b

1300

TtB2/L21 (quenched from 1273 K) Sutou et al. Overholser et al.

1200

Temperature (K)

4790

1100

B2 (para)

1000 900

L21 (para)

800 700

0

0.2

0.4

0.6

0.8

Ni2MnAl

1.0

Ni2MnGa

Ga composition, x Fig. 1. (a) DSC heating curves of Ni2Mn(GaxAl1x) alloys quenched from 1273 K for x = 0.50, 0.68, 0.84 and 1.00. The arrows in the figure indicate the order–disorder transition temperature from the B2 to the L21 phase 1 1 T B2=L2 . (b) Concentration dependence of the T B2=L2 of the Ni2Mn(Gax t t Al1x) alloys, together with the reported data [14,25].

lies associated with the order–disorder transition from the B2 to the L21 phase are observed, as indicated by solid B2=L21 arrows. The transition temperature T t increases with increasing x, suggesting that the L21 phase in the Ni2Mn(GaxAl1x) alloys is stabilized by the substitution B2=L21 of the Ga element. The T t determined by the DSC measurements in Fig. 1(a) for the Ni2Mn(GaxAl1x) alloys are listed in Table 1. Concentration dependence of the B2=L21 Tt is plotted in Fig. 1(b), together with the experimental data reported by Sutou et al. for the Ni2MnAl alloy [14] and Overholser et al. for the Ni2MnGa alloy [25]. It is seen that the present result for x = 1.00 (Ni2MnGa) is in good agreement with that of the literature [25] and that the B2=L21 Tt linearly increases with increasing Ga content. Fig. 2 indicates thermomagnetization curves measured under a magnetic field of 500 Oe for the Ni2Mn(GaxAl1x) alloys with x = 0.0, 0.50, 0.68 and 1.00 annealed at 823,

H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797 Table 1 1 Order–disorder transition temperature from B2 to L21 phase T B2=L2 (K) of t Ni2Mn(GaxAl1x) alloys determined from DSC heating curves, together with the reported experimental data [14,25] x

0.0

Present study Ref.

775 [14]

0.50

0.68

0.84

1.00

931

989

1033

1069 1071 [25]

973, 1013 and 1093 K, respectively, for 1 day and then quenched in ice water, where the annealing temperatures B2=L21 were selected as being about 20 K higher than the T t B2=L21 ðT t þ 20 KÞ for each alloy as determined by the DSC curves in Fig. 1(a). The magnetic properties of the alloys of x = 0.0 and 0.50, as indicated in the inset, are antiferromagnetic, with almost the same value of the Ne´el temperature TN of about 300 K. On the other hand, the alloys of x = 0.68 and 1.00 show ferromagnetic behavior, with the Curie temperatures TC of about 351 and 361 K, respectively. Although the TN of x = 0.0 (Ni2MnAl) is in good agreement with the reported data [18], the TC of x = 1.00 (Ni2MnGa) is slightly lower than that for the reported ones [9,12,22]. A kink observed around 160 K in the thermomagnetization curve for x = 1.00 corresponds to the martensitic transformation, where TAs and TAf mean the martensitic reverse transformation starting and finishing temperatures, respectively. Such a martensitic transformation is not observed in the other specimens. It is known that the magnetic properties of the Ni2MnAl alloy depend strongly on the degree of long-range order, that is, the B2 phase shows antiferromagnetic properties and the L21 phase shows ferromagnetic properties [18,23,24]. These

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facts suggest that the appearance of the ferromagnetism of x = 0.68 and 1.00 is induced by the stabilization of the L21 phase due to the increase in Ga content. The selected area diffraction (SAD) patterns tilted to the ½01 1B2 or L21 matrix zone axis for the specimens of x = 0.50 annealed at 973 K (a) and x = 0.68 annealed at 1013 K (b) are shown in Fig. 3(a) and (b), respectively. Here, the SAD pattern for x = 0.50 is indexed as the B2-type structure, in contrast to that for x = 0.68, which is indexed as the L21-type structure because {111}L21 superlattice reflections are clearly observed, as shown in Fig. 3(b). These results are consistent with the magnetic data in Fig. 2, and it is expected that the magnetic properties of the Ni2Mn(GaxAl1x) alloys can be controlled by the degree of long-range order changed by the heat treatment. Fig. 4(a) shows the thermomagnetization heating curves measured in a magnetic field of 500 Oe of Ni2Mn(Gax Al1x) alloys for x = 0.0, 0.50, 0.68, 0.84 and 1.00 annealed at 673 K for 1 day in order to progress the degree of longrange order. In the figure, the TC is indicated by solid arrows. It is seen that the annealing at 673 K induces ferromagnetism in all the alloys, although the TC of x = 0.00 is lower than that of other alloys. On the other hand, a kink associated to the martensitic reverse transformation is observed in the curves for x = 1.00 and 0.84. In addition, as shown in Fig. 4(b), where some curves in Fig. 4(a) are enlarged, a faint dip can also be seen around 250, 220

(a) x = 0.50 (B2)

200 100

annealed at TtB2/L21 + 20 K 0.2

500 Oe

000

TN

M (emu/g)

Magnetization (emu/g)

15 0.1

TC

x = 0.00 (823 K)

10 0.0 0

011

x = 0.50 (973 K)

[011]B2

100 200 300 400

(b) x = 0.68 (L21)

T (K) x = 1.00 (1093 K) TAf

5

400 0 0

TAs

100

x = 0.68 (1013 K)

200

200 300

111

400

Temperature (K) Fig. 2. Thermomagnetization curves measured in a magnetic field of 500 Oe for Ni2Mn(GaxAl1x) alloys with x = 0.0, 0.50, 0.68 and 1.00 annealed at 823, 973, 1013 and 1093 K for 1 day, respectively, and then quenched in ice water. The annealing temperatures were selected to be B2=L21 B2=L21 about 20 K higher than the T t ðT t þ 20 KÞ for each alloy. In the curve for the x = 1.00, TAs and TAf are the martensitic reverse transformation temperatures starting and finishing temperatures, respectively. The arrows indicate the Curie temperature TC and the Ne´el temperature TN.

000

022

[011]L21 Fig. 3. Selected area diffraction patterns of Ni2Mn(GaxAl1x) alloys tilted to the ½011B2 or L21 matrix zone axis for the alloys of x = 0.50 (a) and 0.68 (b) annealed at 973 and 1013 K for 1 day, respectively.

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H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797 annealed at 673 K

30

x = 1.00

Magnetization (emu/g)

TAf

TI

20 TI

0.84

TAf TI

10

0.68

TAs

300

200

0.50 100

TAs 0.00 0

0

100

200

300

400

Temperature (K) x = 1.00

25.0 24.5 24.0

TC (annealed at 673 K) TC (annealed at TtB2/L21 + 20 K) TN Vasil'ev et al. Albertini et al. Webster et al. TI TAf TAs

0.0 0.2 Ni2MnAl

(annealed at 673 K)

0.4

0.6

0.8

Ga composition, x

1.0 Ni2MnGa

Fig. 5. Concentration dependence of the magnetic transition temperatures of Ni2Mn(GaxAl1x) alloys, together with the reported data [9,12,22]. The open triangles indicate the TC for the specimens annealed at 673 K for 1 day. The closed triangles and squares are the TC and TN for the specimens B2=L21 B2=L21 annealed at temperatures 20 K higher than T t ðT t þ 20 KÞ for 1 day, respectively. The transformation temperature from the parent to the intermediate phase TI, and the martensitic reverse transformation starting and finishing temperatures TAs and TAf are also indicated.

b Magnetization (emu/g)

400

TC

500 Oe

TC, TN, TI, TAf, TAs (K)

a

TI

14.5 14.0 x = 0.84

13.5 8.5 8.0

x = 0.68

7.5 0

100

200

300

400

Temperature (K) Fig. 4. (a) Thermomagnetization curves measured in a magnetic field of 500 Oe of Ni2Mn(GaxAl1x) alloys for x = 0.0, 0.50, 0.68, 0.84 and 1.00 annealed at 673 K for 1 day. TAs and TAf are the martensitic reverse transformation starting and finishing temperatures, respectively. The arrows indicate the Curie temperature TC. (b) Expanded scale of the thermomagnetization curves for x = 0.68, 0.84 and 1.00. The dip, which may be related to the intermediate phase transformation, is indicated by arrows.

and 80 K for x = 1.00, 0.84 and 0.68, respectively. It has been reported in the Ni2MnGa alloy that a transformation from the parent to an intermediate phase exists at around 240 K [26,27] and that in relation to this transformation an anomaly appears in an AC thermomagnetization curve [26]. This suggests that the dips detected for x = 1.00, 0.84 and 0.68 correspond to the reverse transformation temperature TI from the intermediate to the parent phase. The TC and TN obtained in Figs. 2 and 4 in the Ni2Mn(GaxAl1x) alloys are plotted in Fig. 5, together with some reported experimental data [9,12,22], and these numerical values are listed in Table 2. Here, open triangles indicate the TC for the specimens annealed at 673 K for 1 day, and closed triangles and squares show the TC and TN for the specimens annealed for 1 day at the temperatures 20 K higher B2=L21 B2=L21 than T t ðT t þ 20 KÞ, respectively. As can be seen

from Fig. 5, the TC for the alloys of x P 0.5 annealed at 673 K (M) is almost constant, at about 380 K, and the TN of x = 0.0 and 0.5 for the B2 phase (j) is also the same, at about 300 K. The martensitic reverse transformation starting and finishing temperatures, TAs and TAf, and the TI are also plotted in Fig. 5 and listed in Table 2, where the TAs and TAf are defined using the low- and high-temperature intersections of the base lines and the tangent line with the largest slope of the kink in the thermomagnetization curves, as shown in Fig. 4(a), and the TI is as the temperature with a minimum point in the faint dip, as shown by arrows in Fig. 4(b). In both cases, the martensitic transformation temperatures decrease monotonically with decreasing Ga composition. In addition, it is noteworthy that the martensitic transformation temperature depends on the annealing temperature. That is, the TAs and TAf of the specimen annealed at 673 K for x = 1.00 (Ni2MnGa) are 188 and 194 K, respectively, whereas those of the specB2=L21 imen annealed at 1093 K ðT t þ 20 KÞ are 137 and 159 K, respectively. It is said that the Ni2MnGa alloy with a higher-ordered L21 structure exhibits a higher martensitic transformation temperature. It is concluded that the B2/L21 order–disorder transformation can be suppressed by quenching from the B2 phase region only in the Al-rich alloys of x = 0.0 and 0.50, but not in the Ga-rich alloys. This difference, which is dependent on the alloy composition, can be explained by the difB2=L21 ference in atomic diffusivity at around the T t of the B2=L21 alloys; that is, in the Al-rich alloys with a low T t , the atomic diffusivity in the ordered phase region is low. It is seen that the degree of long-range order can be varied across the widest range in the alloy with x = 0.50.

H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797

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Table 2 The Curie temperature TC (K) and the Ne´el temperature TN (K) for the specimens annealed at 673 K for 1 day and at the temperatures 20 K higher than 1 1 the order–disorder phase transition temperature T B2=L2 ðT B2=L2 þ 20 KÞ for 1 day in the Ni2Mn(GaxAl1x) alloys, together with the reported values [18,22] t t X

TC (K) annealed at 673 K

0.0

357

0.50 0.68 0.84 1.00

381 380 380 379

TC (K) B2=L21 Tt þ 20 K

TN (K) B2=L21 Tt þ 20 K

Ref.

301

295 [18]a* 300 [18]b*

TAs (K) annealed at 673 K

TAf (K) annealed at 673 K

TI (K) annealed at 673 K

97 188

102 194

77 220 252

299 351 360 361

375 [22]**

The martensitic reverse transformation starting and finishing temperature TAs and TAf and the intermediate reverse transformation temperature TI are for the specimens annealed at 673 K. * a and b were obtained by quenching and slow cooling from 1073 K, respectively. ** Annealed at 1073 K and quenched from that temperature.

Therefore, in a further examination, we selected an alloy with x = 0.50 to investigate the correlation between the magnetic properties and the degree of long-range order of the L21 phase. 3.2. Effect of annealing temperature for Ni2Mn(Ga0.5Al0.5) alloy

fied as the ordered L21 phase by comparison with the calculated patterns. It is difficult to quantitatively evaluate the difference in the degree of long-range order for the specNi2Mn(Ga0.5Al0.5)

a 4.2 K

100

873 K

673 K

Magnetization (emu/g)

673 K

80

773 K

60

873 K

40

20 973 K

0

0

10

20

30

40

50

Magnetic field (kOe)

b

Ni2Mn(Ga0.5Al0.5)

30

1.0

500 Oe

873 K

TC

673 K

0.8

20 0.6

873 K 773 K

0.4

10 673 K TN

0.2

Magnetization (emu/g)

Magnetization (emu/g)

Fig. 6(a) and (b) shows the magnetization curves measured at 4.2 K and the thermomagnetization curves under a magnetic field of 500 Oe for the Ni2Mn(Ga0.5Al0.5) specimens annealed at 673, 773, 873 and 973 K, respectively, for 1 day where the thermomagnetization curves of 673 and 973 K in Fig. 6(b) are the same as those presented in Figs. 2 and 4. In Fig. 6(a) and (b), the results for the specimen annealed at 673 K for 1 day subsequent to annealing at 873 K for 1 day (873 K ? 673 K) are also presented. From the magnetization and thermomagnetization curves, it is evident that the specimen annealed at 973 K exhibits an antiferromagnetic property with a TN of about 300 K. In other specimens, except that of 973 K, the magnetic properties exhibit ferromagnetism and the saturation magnetization Ms at 4.2 K seems to increase with decreasing annealing temperature. In addition, as seen in Fig. 6(b), the TC also increases with decreasing annealing temperature. It is interesting to note in Fig. 6(a) that saturation of the magnetization behavior gradually becomes harder with decreasing annealing temperature, that of the two-step annealed specimen of 873 K ? 673 K being easier than that of 673 K, while the TC is almost the same as that for annealing at 673 K. Fig. 7(a) shows the room temperature XRD patterns using Co Ka radiation for the Ni2Mn(Ga0.5Al0.5) alloys annealed at 673, 773 and 973 K for 1 day, together with the patterns calculated for the fully ordered L21-type structure. The powdered samples were prepared by annealing at 873 K in order to remove the strain and finally annealed at the each temperature. It is seen that the XRD pattern for the specimen annealed at 973 K has no 111 peak, which corresponds to the ordering between the Mn and (Ga,Al) sublattices. On the other hand, the specimens annealed at 673 and 773 K, showing a 111 peak at 2h  31°, are identi-

973 K

0 0

100

200

300

0.0 400

Temperature (K) Fig. 6. Magnetization curves measured at 4.2 K (a) and thermomagnetization curves measured in a magnetic field of 500 Oe (b) for the Ni2Mn(Ga0.5Al0.5) specimens annealed at 673, 773, 873 and 973 K for 1 day.

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H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797

curve in the L21 ordered phase region, while changing to a straight line in the B2 phase region. The parabolic-like behavior in the L21 phase region may be brought about by the change in the degree of long-range order. In the B2 phase region, it is deduced that the room temperature lattice parameters of the as-quenched specimens would exhibit constant or down side behavior due to the effect of the thermal vacancies. The origin of the increasing behavior of the lattice parameter in the present result is not clear, but it would be due to the effect of the shortrange order. The magnetic transition temperature, TC (N) or TN (j), and saturation magnetization Ms at 4.2 K as functions of the annealing temperature are shown in Fig. 8(a) and (b), respectively, where the value obtained from the specimen of 873 K ? 673 K is used as the data for 673 K. The TC (Fig. 8(a)) and Ms (Fig. 8(b)) decrease parabolically with B2=L21 increasing annealing temperature up to T t ¼ 931 K.

a

Intensity (arb. units)

973 K (B2)

773 K (L21)

111

220

200

673 K (L21)

Calculation (L21)

30

40

50

Diffraction angle (Deg.) 0.5832

B2 L21

0.5830

a

450

TC (L21) 0.5828

TN (B2)

TtB2/L21 = 931 K

400

0.5826

TC, TN (K)

Lattice parameter (nm)

b

0.5824 0.5822

350

TtB2/L21 = 931 K

0.5820

300 600

800

1000

1200

Table 3 Room temperature lattice parameter determined by XRD for the Ni2Mn(Ga0.5Al0.5) alloy annealed at various temperatures 673 0.5820

773 0.5821

873 0.5824

973 0.5828

1073 0.5830

imens annealed at 673 and 773 K because the peak intensity of the 111 superlattice peaks are significantly weak. The room temperature lattice parameters obtained from the XRD patterns for the Ni2Mn(Ga0.5Al0.5) alloy as a function of the annealing temperature are listed in Table 3 and shown in Fig. 7(b). The lattice parameters for the specimens annealed at 973 and 1073 K with the B2-type structure are doubled to enable comparison with those of the L21-type structure. The lattice parameter basically increases with increasing annealing temperature, and its annealing temperature dependence exhibits a parabolic-like

250

600

800

1000

Annealing temperature (K)

b

120

Saturation magnetization (emu/g)

Fig. 7. (a) Room temperature X-ray powder diffraction patterns using Co Ka radiation for the Ni2Mn(Ga0.5Al0.5) alloys annealed at 673, 773 and 973 K for 1 day, together with the calculated pattern as a fully ordered L21 phase. (b) The room temperature lattice parameter for the Ni2Mn(Ga0.5Al0.5) alloys as a function of the annealing temperature.

Annealing temperature (K) Lattice parameter (nm)

antiferro

ferro

Annealing temperature (K)

antiferro

ferro 100 80 60 40 20 0 600

800

1000

Annealing temperature (K) Fig. 8. (a) The magnetic transition temperatures of TC (N) or TN (j) as a function of the annealing temperature for the Ni2Mn(Ga0.5Al0.5) alloys. (b) The saturation magnetization Ms measured at 4.2 K for the Ni2Mn(Ga0.5Al0.5) alloys as a function of the annealing temperature.

H. Ishikawa et al. / Acta Materialia 56 (2008) 4789–4797

From these figures, it can be concluded that both the Ms and the TC are significantly sensitive to the annealing temperature, that is, the magnetic properties of the Ni2Mn(Ga0.5Al0.5) alloy are easily controlled by the annealing conditions. 4. Discussion 4.1. Phase stability of L21 phase in Ni2Mn(GaxAl1x) alloys As shown in Fig. 1(b), a concentration dependence of B2=L21 the order–disorder transition temperature T t for the Ni2Mn(GaxAl1x) alloys exhibits a linear increase with increasing Ga content. According to the Bragg–Williams– Gorsky (BWG) approximation [28,29], there is a proporB2=L21 tional relation between the value of T t and the interchange energy of the Y–Z bonds of X2YZ Heusler alloys under the assumption that the degree of order of the B2=L21 X element is perfect. In this case, the T t is simply given by X ð2Þ

B2=L21

Tt

¼

3W YZ 2k B

ð1Þ

X ð2Þ

where W YZ is the interchange energy between the Y and Z atoms in the second nearest neighbor surrounded by X atoms in the first nearest neighbor and kB, the Boltzmann constant [28,29]. Eq. (1) means that there is a linear relation X ð2Þ B2=L21 B2=L21 between T t and W YZ , and that T t is only a function X ð2Þ of W YZ , independent of the other pairwise interactions. B2=L21 Since T t of the Ni2MnGa alloy is about 300 K higher than that of the Ni2MnAl alloy, as shown in Fig. 1(b), Nið2Þ Nið2Þ W MnGa is larger than W MnAl , where X, Y and Z correspond to Ni, Mn and Ga or Al, respectively. It can be seen that B2=L21 Tt for the Ni2MnAl alloy extrapolated with a straight line from the data of the Ga-rich alloys is in good agreement with the reported experimental value shown in Fig. 1(b) [14]. Nið2Þ This means that the effective interchange energy W MnðGa;AlÞ between the Mn and (Ga,Al) sites in the substituted alloys is simply given by the weighted mean values between Nið2Þ Nið2Þ B2=L21 W MnGa and W MnAl . Such a linear relation of T t in the substituted Heusler alloys has been reported in the (Fe,Co, Ni,Cu)2TiAl [30] and Ni2(Ti,V,Cr,Mn)Al [31] alloys. 4.2. Effects of long-range order on the magnetic properties of Ni2Mn(GaxAl1x) alloys As shown in Figs. 2 and 5, the magnetic properties for Ni2Mn(GaxAl1x) alloys are significantly sensitive to the annealing temperature. It is known that the magnetic properties of the Ni2MnAl alloy depend strongly on the degree of the long-range order, that is, the B2 phase in the alloy exhibits antiferromagnetic properties with the conical antiferromagnetic structure, while the L21 phase exhibits ferromagnetic properties [18,22]. In the present Ni2Mn(GaxAl1x) alloys, antiferromagnetic or ferromagnetic properties were also observed in the specimens with

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x = 0.0 and 0.50, depending on the annealing temperature. On the other hand, in the concentration region over x = 0.50, an apparent change in the TC appears due to the increase in the degree of long-range order induced by low-temperature annealing, although the ordering from the B2 to the L21 phase cannot be suppressed by quenching because of the high stability of the L21 phase. The reported values of TC for the Ni2MnGa alloy are slightly different between the different researchers. This discrepancy could be a result of the difference in the degree of long-range order caused by the different heat treatments. Very recently, Sanchez-Alarcis et al. [32] determined the degree of long-range order in the Ni49.5Mn28.5Ga22 alloy using neutron diffractions (ND) and confirmed that the degree of long-range order between the Mn and Ga sites affects the TC and the martensitic transformation temperatures. By linear extrapolation from the TC determined in the present Ni2Mn(GaxAl1x) alloys, the TC for the fully ordered L21-type structure in the Ni2MnAl alloy is evaluated to be about 380 K, which is slightly higher than that of the Ni2MnGa alloy. This is in accordance with the theoretical results estimated from the spin stiffness constant based on the calculated total energies [20]. On the other hand, it is also clear that, if possessing the B2-type structure, the Ni2MnGa alloy becomes an antiferromagnetic phase with the TN at about 300 K. As shown in Fig. 6(a) and (b), it is evident that the saturation magnetization Ms and the TC of the alloy decrease with increasing annealing temperature. According to the ND investigations for Ni2MnGa [32], the degree of longrange order between the Mn and Ga sites, which differs between the B2 and L21 structures, drastically changes in B2=L21 the temperature range from 773 to 1053 K (= T t ) and reaches an almost perfect degree of long-range order B2=L21 due to annealing at temperatures below T ¼ 0:75T t . If this condition is applied the present Ni2Mn(Ga0.5Al0.5) B2=L21 alloy with T t at 931 K, the maximum temperature to effectively obtain a high degree of long-range order is estimated to be about 700 K (=931 K  0.75). From this, it can be concluded that the drastic changes of the lattice parameter, the Curie temperature and saturation magnetization, which depend on the annealing temperature in the range of 673–930 K, as shown in Figs. 7 and 8, result from the change in the degree of long-range order between the Mn and (Ga,Al) sites. These results suggest that in the Ni2Mn(GaxAl1x) alloys, including Ni2MnAl and Ni2MnGa, the degree of long-range order is one of the most important factors controlling the TC and Ms. The reason why the atomic ordering in the Ni2Mn(GaxAl1x) alloys strongly affects the magnetic properties has not been clarified. However, from the theoretical calculations, it has been suggested that since the magnetic moment of Ni in the Ni2MnAl alloy varies depending on its symmetry and its coordination around the Ni atoms, the change in the circumstances induced by the change in the degree of long-range order would influence the Ms and TC [20].

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4.3. Effects of APD structure on magnetic properties of the Ni2Mn(Ga0.5Al0.5) alloy It is seen in Fig. 6(b) that the TC of the Ni2Mn(Ga0.5Al0.5) alloy specimen annealed at 673 K is comparable to that of the specimen annealed at 873 K ? 673 K. The coincidence of the TC originates with the same degree of long-range order induced by the same final annealing temperature as discussed above. The magnetization curve for the 673 K specimen does not saturate even in the higher magnetic field, although the Ms of the 673 K specimen seems to reach a comparable value of 873 K ? 673 K. Such a difference in the magnetization curves can be discussed from the standpoint of the microstructures. TEM dark-field images using the (111)L21-ordered reflections taken from the specimens annealed at 673 and 773 K for 1 day and at 873 K for 1 day followed by annealing at 673 K (873 K ? 673 K) are shown in Fig. 9(a)–(c), respectively. It can be seen that all the specimens have an L21-type single phase with anti-phase domains (APDs),

a

673 K

50 nm

b

773 K

the size of which depends on the annealing temperature. Here, while the mean size of the APDs for the 673 K specimen is very small, the specimen annealed at 873 K ? 673 K shows APDs with a large mean size, which arises during the first-step annealing process at 873 K. The difference in the magnetization behavior between the 673 K and 873 K ? 673 K specimens is brought about by such a difference in the microstructure of the APDs. Anti-phase boundaries (APBs) formed during the ordering from the B2 to the L21 phase is a type of structural defect and has a finite thickness of nanometer order as well as a magnetic wall. Since the crystals located in the APBs lost the L21-type ordered configuration, the magnetic properties in the APBs, as well as those in the B2 phase, are expected to be antiferromagnetic. In this case, the APBs may act like an impurity phase and become a pinning site for magnetic wall displacement. It has been reported in TEM studies using Lorentz microscopy in Ni2MnGa and Ni2Mn(Ga,Al) alloys that the APBs behave as a strong pinning site for domain wall displacement and that most of the magnetic walls are of 180°-type [33–36]. The difference in the behavior in the magnetization process between the specimens annealed at different temperatures can clearly be explained by the difference in the pinning effect that depends on the APD size. Details on the correlation between the magnetization behavior and microstructure will be reported in another paper [37]. It is known that the Ni2MnAl alloy annealed at 673 K shows lower TC and Ms and that saturation of its magnetization curve is more difficult to achieve than that of the Ni2MnGa alloy [23]. In the present study, it was clarified that these negative characteristic features of the Ni2MnAl alloy are not essential for a fully ordered L21 alloy, as indicated by theoretical study. In order to achieve better ferromagnetic properties of the Ni2MnAl alloy suitable for FSMAs, both the degree of long-range order and the size of the APDs should be controlled by step annealing or very slow cooling, as demonstrated in the 873 K ? 673 K specimen. 5. Summary B2=L2

50 nm

c

873 K → 673 K

1 The order–disorder transition temperature T t from the B2 to the L21-type phase and magnetic transition temperatures (the Curie temperature TC or the Ne´el temperature TN) of Ni2Mn(GaxAl1x) alloys were investigated over the entire concentration range of x. Furthermore, magnetic measurements and microstructures were examined for the Ni2Mn(Ga0.5Al0.5) alloy with various heattreatment temperatures. The obtained results are summarized as follows:

B2=L2

50 nm Fig. 9. TEM dark-field images using the (111)L21 ordered reflection taken from the Ni2Mn(Ga0.5Al0.5) alloys annealed at 673 K (a) and 773 K (b) for 1 day, and 973 K ? 673 K (c).

1 (1) The T t of Ni2Mn(GaxAl1x) alloys increases linearly with increasing Ga content, and the value of B2=L21 Tt for the Ni2Mn(Al0.5Ga0.5) alloy is about 150 K higher than that of the Ni2MnAl alloy. The addition of Ga brings about a stabilization of the L21 phase.

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(2) The TC of the L21 phase in Ni2Mn(GaxAl1x) alloys of x P 0.5 and the TN of the B2 phase of x 6 0.5 are insensitive to Ga content, suggesting that the magnetic transition temperatures of the Ni2MnAl alloy are comparable with those of the Ni2MnGa alloy if the degree of long-range order is the same. (3) The room temperature lattice parameter of the Ni2Mn(Ga0.5Al0.5) alloy quenched from the temperature in the L21 phase region increases parabolically with increasing annealing temperature, being associated with a decreasing of the degree of long-range order. (4) The saturation magnetization Ms and the TC of the Ni2Mn(Ga0.5Al0.5) alloy increases with decreasing annealing temperature. It can be concluded that these magnetic properties are brought about by the degree of long-range order for the specimens.

Acknowledgements The present work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan and Core Research for Evolutional Science and Technology (CREST) from the Japan Science and Technology Agency (JST), and by Grant-in-Aid for Scientific Research (S) No. 18106012 from the Japan Society for the Promotion of Science (JSPS). The authors are very grateful to Associate Professors K. Oikawa and Y. Murakami of Tohoku University for many helpful discussions during this work. References [1] Ullakko K, Huang JK, Kanter C, Kokorin VV, O’Handley RC. Appl Phys Lett 1996;69:1966. [2] Chernenko VA, Kokorin VV, Babii OM, Zasimchuk IK. Intermetallics 1998;6:29. [3] O’Handley RC. J Appl Phys 1998;83:3263. [4] Sozinov A, Likhachev AA, Ullakko K. IEEE Trans Magn 2002;38:2814. [5] Biswas C, Rawat R, Barman SR. Appl Phys Lett 2005;86:202508. [6] Aliev A, Batdalov A, Bosko S, Buchelnikov V, Dikshtein I, Khovailo V, et al. J Magn Magn Mater 2004;272–276:2040. [7] Albertini F, Canepa F, Cirafici S, Franceschi EA, Napoletano M, Paoluzi A, et al. J Magn Magn Mater 2004;272–276:2111. [8] Zhou X, Li W, Kunkel HP, Williams G. J Phys Condens Matter 2004;16:L39.

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