Ferromagnetic exchange interaction between Co

JOURNAL OF APPLIED PHYSICS 107, 013913 共2010兲

Ferromagnetic exchange interaction between Co and Mn in the Heusler alloy CuCoMnAl L. Feng,1 L. Ma,1 Z. Y. Zhu,1 W. Zhu,1 E. K. Liu,1 J. L. Chen,1 G. H. Wu,1,a兲 F. B. Meng,2 H. Y. Liu,2 H. Z. Luo,2 and Y. X. Li2 1

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China 2 School of Material Science and Engineering, Hebei University of Technology, Tianjin, 300130, People’s Republic of China

共Received 24 September 2009; accepted 19 November 2009; published online 12 January 2010兲 The ferromagnetic exchange interaction between Co and Mn in Heusler alloys has been phenomenologically investigated by analyzing the composition dependence of the magnetic moment and the Curie temperature in a series of quaternary CuCoMnAl alloys. The curves of the composition dependence of the magnetic moment show an interesting valleylike profile and their minima are positioned at different Co contents for different Mn concentrations. The ferromagnetic Co–Mn exchange interaction is a short-range effect which is only effective at the nearest-neighbor distance. At this distance, the exchange interaction can be further enhanced by a Mn-rich composition, but it might be destroyed by the lattice distortion due to the martensitic transformation. © 2010 American Institute of Physics. 关doi:10.1063/1.3275859兴 I. INTRODUCTION

Ferromagnetic shape-memory Heusler alloys such as NiCoMnIn, NiCoMnSn, NiCoMnGa, and NiCoMnSb alloys have attracted great interest as new actuator materials because the martensitic transformation can be induced by a magnetic field.1–4 They usually are synthesized by adding Co at Mn-rich compositions. Adding Co has become a very effective method to improve the magnetic properties of these materials because the antiferromagnetic Mn–Mn coupling is changed to ferromagnetic coupling in the parent phase, achieving a high magnetization. Very strangely, however, this effect disappears in the martensite phase. At the transformation from the parent phase to the martensite phase, the ferromagnetic Mn–Mn coupling becomes antiferromagnetic, showing a low magnetization. Thus, as desired, a large magnetization difference, ⌬M, between these two phases can be achieved. A large ⌬M is a necessary condition to realize the magnetic field-induced martensitic transformation in these materials. So far, however, it is still not clear why the Co atom affects the magnetic structures of the two phases in such opposite ways. It seems that the strong exchange interaction between Co and Mn in Heusler alloys is a known phenomenon but it has not been investigated in detail. Attempting to address this question, the Heusler alloys Cu2MnAl and Co2MnAl and a series of intermediate CuCoMnAl alloys have been selected as study subjects in the present work. Cu2MnAl is an ideal system for clearly revealing the magnetic structure because the Mn atom is the only origin of magnetization. Co2MnAl is a typical system to reflect the exchange interaction when Co is involved because it has a similar composition as Cu2MnAl. Besides using the disordered B2 structure of Co2MnAl,5 also the Mn-rich coma兲

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positions have been utilized to create more serious disorder of the Mn atoms. This composition strategy establishes an environment very similar to the one in the above ferromagnetic shape-memory alloys with Mn-rich composition.1–4 The exchange interaction has been investigated phenomenologically based on the composition and structure dependence of the magnetic moments and the Curie temperature. It has been found that the strong ferromagnetic Co–Mn exchange interaction in Heusler alloys is a short-range effect and that it is further enhanced in Mn-rich compositions. The disappearance of this strong exchange interaction in the martensitic structure is also discussed. II. EXPERIMENTAL

All alloys were prepared by arc melting high-purity metals in argon atmosphere. The CuMnAl series of alloys was annealed at 900 ° C for 20 h and quenched in ice water.6 For obtaining homogeneous alloys and high atomic order, the CoMnAl series of alloys was annealed at 800 ° C for 3 days.7 X-ray diffraction 共XRD兲 was employed to characterize the crystal structure of the alloys. The magnetization of the samples was measured in a superconducting quantum interference device at 5 K in magnetic fields up to 5 T and the Curie temperature was measured in a vibrating sample magnetometer 共VSM兲 with a high-temperature facility. III. RESULTS AND DISCUSSION

Figure 1 shows the L21 crystal structure of the Heusler alloy Cu2MnAl. In some magnetic Heusler alloys containing Mn, the Mn atom may possess a quite large magnetic moment of about 3.0– 4.0 ␮B. In the L21 structure, ferromagnetic coupling between two Mn moments is only achieved when the atoms occupy the B sites 共denoted as MnB兲 with high atomic order. However, antiferromagnetic coupling will occur if Mn atoms occupy a wrong site 共usually at the D site

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© 2010 American Institute of Physics

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magnetic moment (µB/f.u.)

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160 140

(a)

120 100 80 60 40

Co50Mn25+xAl25-x Cu50Mn25+xAl25-x

20 0 -20 700

(b)

650 600

TC (K)

FIG. 1. L21 structure of the Heusler alloy Cu2MnAl.

Co50Mn25+xAl25-x Cu50Mn25+xAl25-x

550

(422)

Co2MnAl

(422)

(400) (400)

(111) (200)

(220)

Cu2MnAl

(200)

Cu50Mn35Al15 (220)

intensity (a.u)

(220)

denoted as MnD兲 in an atomically disordered case or in a material which has been purposely synthesized with a Mnrich 共 ⬎ 25 at. %兲 off-stoichiometrical composition.8 On the other hand, the structures of some Heusler alloys with Co are different. For example, Co2MnAl orders in the B2 structure, in which the Co atoms occupying the A and C sites have high atomic order, while due to the presence of Co, Mn and Al atoms randomly occupy the B and D sites.5 Even though independent of the degree of atomic order, the MnB and MnD moments always couple ferromagnetically. Based on this fact, a strong ferromagnetic exchange interaction between Co and Mn atoms has been speculated.8 Figure 2 shows a series of XRD patterns of CuMnAl and CoMnAl alloys. Indexing the characteristic reflections, we find that the stoichiometric Heusler alloys Cu2MnAl and Co2MnAl are both pure bcc phase and their superlattice reflections indicate that Cu2MnAl has the L21 structure and Co2MnAl has the disordered B2 structure. On the other hand, a fcc phase 共␥ phase兲 marked by the arrows appears in the Mn-rich alloys, for example, in Cu50Mn35Al15 sample, as shown in Fig. 2. In order to avoid the ␥ phase, the alloys with 35 at. % Mn or more have been prepared by the meltspinning method. As seen in Fig. 2, the ␥ phase is effectively eliminated in the ribbon samples. In both the CuMnAl and

(400)

(111) (200)

30

(422)

Cu50Mn35Al15ribbon

40

50

60

2θ

70

80

90

FIG. 2. XRD patterns of alloys of the CuMnAl and CoMnAl series prepared by arc melting and melt spinning.

500 450 -4 -2

0

2

4

x

6

8 10 12 14 16

FIG. 3. Dependence of the moment per formula unit and TC on the Mn content of off-stoichiometric Mn-rich alloys. A formula unit with 100 atoms is used in the present work.

the CoMnAl systems, the lattice parameters show very little change upon increasing the Mn content, so that it can be deduced that Cu and Co determine the lattice frame. Substituting Co for Cu, a series of Cu50−xCoxMnAl 共x = 0 – 50兲 alloys has been synthesized to determine the dependence of the lattice parameter on the Co content. It is found that the lattice parameter linearly decreases when the alloy composition is gradually changed from CuMnAl to CoMnAl. Typically, for the off-stoichiometric series of Cu50−xCoxMn33Al17 alloys, the lattice parameter changes from 5.942 Å for Cu50Mn33Al17 to 5.743 Å for Co50Mn33Al17 with an average ratio of 0.004 Å per Co atom. This is because the atomic diameter of Co is smaller than that of Cu. It suggests that, upon changing the composition, the magnetic properties should change monotonically, if the lattice parameter, and thus the distance, is the determining factor. Figure 3共a兲 shows the dependence of the magnetic moment on the Mn concentration for the two Heusler alloys Cu50Mn25+xAl25−x and Co50Mn25+xAl25−x. The moments have been derived from the saturation magnetization at 5 K. For the CuMnAl alloys, the moment decreases monotonically with increasing Mn content. This should be attributed to the antiferromagnetic coupling between the excess MnD moments with the MnB moments.8 This magnetic-moment dependence also reflects the distance dependence of Mn–Mn coupling in Heusler alloys without Co. The distance between two MnB sites is 4.207 Å at which they have ferromagnetic exchange interaction, while the distance between MnB and MnD is only 2.975 Å at which antiferromagnetic coupling occurs. The moment values for the x = 25, 30, and 33 samples show a linear relationship with a slope of 4.4 ␮B / Mn atom


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magnetic moment (µB/f.u.)

which is a little larger than 4.12 ␮B of MnB.8 The values for the x = 35, 37, and 40 samples 共ribbon samples兲 show a somewhat anomalous decrease, reaching an almost zero value of the moment for x = 40. This is because the melt-spin method usually causes serious atomic disorder, making more Mn atoms occupy the D sites due to the very fast solidifying rate.6 The results in Fig. 3共a兲 indicate that, in CuMnAl alloys, antiferromagnetic coupling will occur and that the magnetization will decrease, if a Mn atom occupies the D site. However, this is not the case in the Heusler alloy Co2MnAl. The results in literature5 indicate that Co2MnAl usually solidifies in a quite disordered B2 structure in which Mn and Al atoms randomly occupy the B and D sites. Furthermore, more Mn atoms will occupy the D site if the CoMnAl composition is Mn rich. Figure 3共a兲 also shows the dependence of the moment per formula unit of Co50Mn25+xAl25−x alloys on the Mn content. In contrast to the CuMnAl alloys, the moment monotonically increases in CoMnAl alloys when Mn atoms are increasingly added. This observation strongly suggests that the Co moments realize a very strong exchange interaction by which the moments of Mn atoms can be aligned ferromagnetically, other than antiferromagnetically as happened in the CuMnAl alloys. By Mössbauer spectroscopy, it has earlier been found that the MnD moment 共MnZ in the reference兲 has a strong negative hyperfine field in compounds containing Co, which implies a strong ferromagnetic exchange interaction between Co and MnD.8 By linearly fitting the experimental data for the CoMnAl alloys, we find that the moment increases with about 4.06 ␮B / Mn atom. It should be noted that this value is too large to be consistent with the results reported in previous reports,7,9 in which the total moment is in the range 4.06– 4.16␮B for stoichiometric Co2MnAl. Subtracting the moment of 0.6␮B of Co, the moment of a Mn atom is only around 3.0␮B. The excess moment of about 1.0␮B deserves some attention. By Korringa-Kohn-Rostocker coherentpotential and local density approximation 共KKR-CPA-LDA兲 calculations, we find that this excess moment is due to an increase in the moment of Co, while the moment of Mn even decreases a little when Mn is added. In detail, the moment of Co increases by about 0.02␮B if one Mn atom is added. Figure 3共b兲 shows the composition dependence of TC for both series of alloys. In CuMnAl alloys, the Curie temperature TC decreases with increasing Mn content. Apparently, the antiferromagnetic coupling between MnB and MnD weakens the overall ferromagnetic exchange interaction in the system. Turning to CoMnAl alloys, however, TC increases with increasing Mn content, showing an enhancement of the exchange interaction. Taking into account the increase in the Co moment mentioned above, it is reasonable to believe that although the exchange interaction of Co–Mn in the stoichiometric Co2MnAl alloy is very strong, it can be further enhanced by adding Mn atoms. Figure 4共a兲 shows the magnetic moments per formula unit of three series of CuCoMnAl alloys with fixed Mn content. In these alloys, Cu is gradually substituted by Co and finally, the CuMnAl alloys become CoMnAl ones. From literature8 and above discussion, we know that the Co atoms

(a) Cu50-xCoxMn25Al25 Cu50-xCoxMn30Al20

120 100

Cu50-xCoxMn33Al17

80 60 40

20 700

(b)

650

Cu50-xCoxMn30Al20 Cu50-xCoxMn33Al17

600

Tc(K)

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550 500 450 400 0

10

20

30

Co content x

40

50

FIG. 4. Dependence of the moment per formula unit and TC on the Co content of three series CuCoMnAl alloys with fixed Mn content and varying Cu:Co ratio. A formula unit with 100 atoms is used in the present work.

can switch antiferromagnetic Mn moments to ferromagnetic ones and increase the magnetization. Based on this and the fact that the nonmagnetic Cu is replaced by magnetic Co, one would expect the moment of all alloys to increase monotonically with increasing Co content. Very interestingly, however, it is found that all curves of the magnetic moments show a valleylike profile with their respective minima. In all curves, the moment first decreases with increasing Co content and then dramatically increases after passing through a minimum which is located at a different Co content for each series. The higher the Mn content, the lower the Co content at which the minimum is found. This behavior cannot be explained in terms of changes in the lattice parameter because this parameter changes monotonically. From the above discussion, we know that both the existence of Co atoms and the Mn-rich composition give rise to many MnD atoms in CuMnAl and CoMnAl alloys. In CuMnAl, these MnD moments should be antiferromagnetic. On the other hand, in CoMnAl, the ferromagnetic Co–Mn exchange interaction may make the MnD moments couple ferromagnetically with MnB moments. These two opposite effects play a role in the magnetization of the quaternary CuCoMnAl alloys. It is likely that the competition between these two effects results in the interesting profile of the curves. The decreasing moment at the low-Co side originates from the domination of the antiferromagnetic coupling, whereas the increase results from the domination of the ferromagnetic coupling. The question arises why these two effects dominate at different Co contents. Figure 5 shows the atomic configuration surrounding the Co atom added in Cu2MnAl. A MnB atom is located at the


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FIG. 5. Atomic configuration surrounding the Co atom substituting for a Cu atom in Cu2MnAl. The MnB atom is surrounded by an Al octahedron.

center of an octahedron composed of six Al atoms at a nextnearest-neighbor distance of 2.975 Å. Thus, there are six possible D sites for MnB disorder. Among these six positions, three of them 共open circles in Fig. 5兲 are at a nearestneighbor distance of 2.576 Å to the added Co atom. If a MnB occupies one of these three positions, it will couple ferromagnetically with other Mn atoms in a CoMnAl environment. In this case, compared with the magnetization without Co substitution, the magnetization almost does not change. However, the other three positions 共half-solid circles in Fig. 5兲 are at a distance quite far from the Co. If a MnB occupies one of these three positions, it will couple antiferromagnetically with other Mn atoms in a CuMnAl environment 共assuming the added Co is the first one to represent the low Co content兲. In this case, the total moment of the system without Co is reduced by the moment of two ferromagnetic Mn atoms, resulting in a decreasing magnetization. As the Co content increases, the CuMnAl region will decrease and the CoMnAl one will increase. Thus, sooner or later the positive magnetic effect will dominate and make the magnetic moments increase. It results in the valleylike curves and the minimum reflects the balance between these two effects. This observation clearly indicates that the ferromagnetic exchange interaction between Co and Mn in Heusler alloys is only effective at a very short distance, in the nearestneighbor range. For the other two systems with 30 and 33 at. % Mn, the atoms surrounding MnB are not only Al but also excess MnD. This will increase the number of MnD atoms at the nearest-neighbor distance to the added Co atom and decrease the probability of Mn changing from ferromagnetic to antiferromagnetic in the system. These two factors benefit to the positive magnetic effect and thus shift the minima of Mn-rich samples to lower Co contents. Figure 4共b兲 compares the composition dependence of TC of two samples with different Mn-rich levels. The similar valley profile and the shift of the minimum indicate the competition between the positive and negative effects on the exchange interaction. Observing the curves carefully, one may note that the curve for the alloy with richer Mn composition has a relative small slope at the low-Co side. This indicates that the negative effect on the exchange interaction is rela-

tively weak in the alloys with higher Mn content. This observation evidently confirms again the point we concluded above: the Mn atoms have a further enhancing effect on the ferromagnetic Co–Mn exchange interaction in Heusler alloys. Now, based on the present results, we may answer the question why the magnetization can be effectively increased in the parent phase of ferromagnetic shape-memory alloys. The strong exchange interaction between Co and the nearestneighbor Mn aligns the moments ferromagnetically. The Mnrich composition has two contributions to the magnetic structure, providing more magnetic moments and also enhancing the exchange interaction. This is why the magnetic fieldinduced martensitic transformation usually occurs in Mn-rich materials. Since we have found that the ferromagnetic exchange interaction in Heusler alloys is a short-range effect effective at nearest-neighbor distance, one may expect to consider its sensitivity to the distance between Co and Mn atoms. A good material to study this is the Heusler alloy Mn2CoZ 共Z = Al, Ga, Sn and Sb兲 with the Hg2CuTi structure.10 There are two kinds of neighborships between Mn and Co atoms in these systems, nearest and next-nearest neighbors. For example, in Mn2CoAl, the Co moment couples ferromagnetically with the nearest Mn moment and antiferromagnetically with the next-nearest Mn moment, so that the system shows a quite low magnetization. Calculating the difference between the nearest- and the next-nearest-neighbor distances in Mn2CoAl, a quite small value of 0.391 Å, which is about 6.7% of the lattice parameter, is obtained. This shows that a very small distance change will destroy the short-range ferromagnetic exchange interaction between Co and Mn. For the ferromagnetic shape-memory alloy of NiMnGa, structural distortions are in the range 0.382–0.795 Å depending on the category of the martensite phase.11,12 This value is quite comparable to the above distance difference between the nearest- and the next-nearest-neighbor sites. Thus, it is reasonable to speculate that the short-range ferromagnetic exchange interaction is destroyed by the lattice distortion at martensitic transformation and that the magnetization of martensite cannot be increased by adding Co.

IV. CONCLUSION

In order to investigate the ferromagnetic exchange interaction between Co and Mn in Heusler alloys, Cu50Mn25+xAl25−x and Co50Mn25+xAl25−x, and a series of intermediate quaternary CuCoMnAl alloys have been synthesized to study the composition dependence of the magnetic moment and TC. In order to highlight the ferromagnetic exchange interaction between Co and Mn, the fact that Co causes atomic disorder of the Mn atoms has been synthesized and Mn-rich alloys have been used to generate a more seriously Mn-disordered environment 共containing more MnD兲. An interesting valleylike composition dependence of the magnetization has been observed. The experimental results prove that the ferromagnetic Co–Mn exchange interaction in Heusler alloys is a short-range effect which is only effective at the nearest-neighbor distance. At this distance, the ex-


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change interaction can be further enhanced by a Mn-rich composition, but it is likely to be destroyed by the lattice distortion at the martensitic transformation. ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China, Grant Nos. 10774178 and 50771103, and specific funding of the Discipline and Graduate Education Project of Beijing Municipal Commission of Education. 1

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