- Email: [email protected]
Structure and magnetic properties of Fe2CoGe synthesized by ball-milling
ARTICLE IN PRESS Physica B 405 (2010) 2840–2843
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Structure and magnetic properties of Fe2CoGe synthesized by ball-milling Z. Ren a, S.T. Li a,n, H.Z. Luo b a b
School of Mathematics and Physics, North China Electric Power University, Baoding 071003, PR China School of Material Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 January 2010 Received in revised form 3 April 2010 Accepted 6 April 2010
A Heusler alloy Fe2CoGe has been synthesized by the ball-milling method. Its structure and magnetic properties have been studied. The results suggest that ball-milling can be a possible way to produce new Heusler alloys. Both X-ray diffraction and DTA measurement evidenced the formation of a partly amorphous phase after milling for 25 h. It is found that highly ordered Fe2CoGe can be obtained by annealing the as-milled powder at 1073 K, while a disordered A2 phase is resulted by annealing at 773 K. The magnetic properties of Fe2CoGe are not very sensitive to the atomic disorder. Electronic structure calculation suggests a ferromagnetic ground state in highly ordered Fe2CoGe and the total spin moment is 5.03mB/f.u., which agrees well with the experimental value of 5.06mB for the sample annealed at 1073 K. It is also found that the atomic disorder does not strongly change the ferromagnetic coupling between Fe and Co moments and also the general structure of the DOS. So the total spin moment only slightly increases when atomic disorder occurs. & 2010 Elsevier B.V. All rights reserved.
Keywords: Heusler alloys Band structure Magnetic properties Ball-milling
1. Introduction Study of the Heusler alloys has increased obviously in recent years due to new phenomenon, such as half-metallicity and shape memory effect, in this alloy family [1–4]. The Heusler alloy crystallizes in an ordered body-centered-cubic (bcc) structure and has a stoichiometric composition of X2YZ, where X and Y are transition metal elements, and Z is a main group element. Generally the Heusler structure can be looked on as four interpenetrating face-centered-cubic (fcc) lattices, in which the X and Y atoms occupy the A (0, 0,0), B 14 , 14 , 14 and C 12 , 12 , 12 sites, 3 3 3 and Z atom occupies the D 4 , 4 , 4 site in the Wyckoff coordinates. In the study of the Heusler alloys, melt-spinning technique has been widely used, which is a non-equilibrium process and can retain the meta-stable phase to room temperature [5,6]. So it is a promising way to investigate new functional materials in the Heusler alloys. Here, ball-milling is another non-equilibrium way to synthesize new meta-stable materials; however, there are only few reports on its application in the Heusler alloys. Robinson et al. reported that Cu2MnAl can be prepared via a combination of mechanical alloying and heat treatment [7]. Later, Zhang synthesized a DO3 type Fe2MnGe phase by annealing the as-milled amorphous powder at 673 K [8]. A typical shape memory alloy Ni–Mn–Ga was also synthesized and interesting magnetic properties change has been found in it [9]. Till now, the Heusler alloys synthesized by ball-milling are mainly Mn-based.
n
Corresponding author. Tel.: + 86 312 7525086; fax: +86 312 7525081. E-mail address: [email protected] (S.T. Li).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.04.008
When some antisite disorder was introduced to the lattice by ball-milling, the Mn moments in different sites may form an antiparallel coupling which will decrease the total moment and influence other magnetic properties. So it is interesting to study the effect of ball-milling in Mn-free Heusler alloy Fe2CoGe. In this paper, we report the structure and magnetic properties of a new Heusler alloy Fe2CoGe prepared by ball-milling. Since Co2FeSi was predicted as a half-metallic ferromagnet (HMF) by Wurmehl et al. [10], the work on Fe2CoGe which has similar composition with Co2FeSi can also be helpful in searching for new HMFs.
2. Experimental details and computational method Fe2CoGe sample was prepared by ball-milling in a planetary ball mill from high purity powder components (99.9% or higher). The mass of the loaded initial powder is 8 g. The mixture was sealed in steel vial with balls of different diameters made of hardened steel under argon atmosphere in a glove box. The ball to powder weight ratio is 10:1. The milling time is 25 h, which is sufficient for the formation of the compound. The samples were pressed into discs and sealed in a quartz tube filled with high purity argon and then annealed at 773 and 1073 K, respectively. X-ray powder diffraction (XRD) with Cu Ka radiation was used to check the crystal structure and to determine the lattice constants. The magnetization curves were measured by a Quantum Design MPMS-7 superconducting quantum interference device (SQUID) magnetometer with applied field up to 5 T. The Curie temperature
ARTICLE IN PRESS Z. Ren et al. / Physica B 405 (2010) 2840–2843
Fe2CoGe milling for 25h
DTA T
was measured by an AC susceptometer with an AC magnetic field of amplitude 5 Oe. We carried out the electronic structure calculation using the density functional theory (DFT) plane-wave pseudopotential method [11,12]. The exchange-correlation function was based on the Perdew–Burke–Ernzerhof generalized-gradient approximation (GGA) potential [13]. The interactions between the valence electrons and ion cores were described as ultrasoft pseudopotentials, first introduced by Vanderbilt [14]. The cut off energy for plane waves is 500 eV for all the cases to ensure good convergence of the total energy. The self-consistent calculations employed a grid of 182k points from a 15 15 15 mesh in the irreducible Brillouin zone. The convergence tolerance was set to 5 10 6 eV/atom.
2841
300
3. Results and discussion
350
400
450
500
550
T (°C)
Fe (100)
Ge (111)
Fe2CoGe
Intensity (arb. units)
Co
1h Ge Co
Ge
Fe
Fe
Ge
5h
25h
30
40
50 60 2θ (degree)
70
80
Fig. 1. XRD patterns of the Fe2CoGe powder milled for different times.
90
723K
(220)
annealed at
30
(111)
(400)
25
(200)
Fe2CoGe annealed at
(422)
(220)
Fig. 2. Continuous-heating DTA curve at 20 1C/min of the as-milled powder of Fe2CoGe.
Intensity (arb. units)
1073K
20
30
40
50 60 2θ (degree)
(422)
(400)
(311)
(200)
25
(111)
The XRD pattern of the samples milled for different times is shown in Fig. 1. It is clear that the XRD patterns change obviously with prolonged milling time. When milling for 1 h, the starting elemental powder is simply crushed together. The XRD pattern shows only the elemental peaks, which are somewhat broadened by the stress and reduction of the grain size. After 5 h, only the iron diffraction peaks are identified and other elemental peaks vanish. It is also found that the iron peaks have a broad shoulder and moves to the low angle end. This may indicate the formation of a bcc Fe–(Co, Ge) solid solution. When the milling time reaches 25 h, a broad high peak at about 441 and two small peaks at 651 and 821 are observed. These diffraction peaks indicate that a disorder bcc A2 phase is formed after 25 h ball-milling. The triangular shape of the main peak may be attributed to the formation of some amorphous phase in the A2 phase [8,15], as has been confirmed by subsequent DTA measurement. Another possibility for the broad peak is the stress introduced by ball-milling, which may lead to the distortion of the lattice. The DTA curve of the Fe2CoGe powder milled for 25 h is shown in Fig. 2. The heating rate is 20 1C/min. The huge exothermic peak around 450 1C corresponds to the crystallization of the amorphous phase in the as-milled Fe2CoGe powder. This confirms the conclusion in preceding discussions. In order to investigate the crystal structure after crystallization and the influence of different annealing temperatures, we tried annealing the as-milled powder at 773 and 1073 K, respectively. The former is close to the crystallization temperature and the latter is much higher above it. It may be expected that they will
70
80
30
90
Fig. 3. XRD patterns of the Fe2CoGe powder annealed at 773 and 1073 K, respectively.
have different influence on the crystal structure as well as the magnetic properties. Fig. 3 gives the XRD patterns of Fe2CoGe powder annealed at 773 and 1073 K, respectively. It is clear that different annealing temperatures have no obvious influence on the basic structure. After annealing, the full width at half maximum (FWHM) decreases and the diffraction peaks become sharper compared with which of the as-milled powder. This is due to the increase of grain size and the elimination of the stress. In both cases, a bcc structure is retained. However, the annealing temperatures influence the atomic order in Fe2CoGe strongly. For the sample annealed at 773 K, only three diffraction peaks: (2 2 0), (4 0 0), (4 2 2) are observed, indicating that a disordered A2 phase are formed. But for the sample annealed at 1073 K, superlattice diffraction peaks (1 1 1) and (2 0 0) are identified together with the main peaks. Since the (2 2 0) peak is too strong in the pattern, we show the detail in the insets of Fig. 3. It is known that the ordered Heusler structure is represented by the existence of the superlattice reflections (1 1 1) and (2 0 0). Usually the (1 1 1) diffraction represents the order between the B and D sites, and (2 0 0) diffraction is corresponding to the order between the (A, C) atoms and B sites. So our results prove that an
ARTICLE IN PRESS 2842
Z. Ren et al. / Physica B 405 (2010) 2840–2843
ordered structure can be obtained in Fe2CoGe after annealing at 1073 K and also that ball-milling is a possible way to synthesize new Heusler alloys. The derived lattice constant for ordered Fe2CoGe is 5.764 A˚ at room temperature. The temperature dependence of the AC susceptibility for the Fe2CoGe samples annealed at different temperatures is presented in Fig. 4(a). It can be seen that the Curie temperature TC of the disorder A2 phase is about 50 K lower than that of the ordered one. But both of them are higher than 900 K. This decrease may be attributed to the weakening of the exchange interaction in the disordered structure. Similar results are also found in Ni2MnAl, in which the atomic disorder affects its TC strongly [16]. Fig. 4(b) gives the magnetization curves of Fe2CoGe samples measured at 5 K. The derived saturation magnetic moments are 5.25mB and 5.06mB for the alloy annealed at 773 and 1073 K, respectively. This difference is due to the atomic disorder in Fe2CoGe alloy. However, we can see the influence of atomic disorder on the spin moment is quite small in Fe2CoGe. This may be attributed to the strong ferromagnetic coupling between the Fe and Co atoms in both order and disorder structure, as will be discussed in the next section.
Recently, Co2FeSi is predicted as a new half-metallic ferromagnet [10]. Here, Fe2CoGe has similar composition with it and also has a high Curie temperature. So it is meaningful to study the electronic structure of Fe2CoGe. The effect of atomic disorder on the electronic structure and magnetic moments is also investigated. Fig. 5 gives the calculated total and partial DOS for Fe2CoGe. In the total DOS, we can find a clear exchange splitting between the minority and majority spin states. The Fermi level lies in the lowdensity part in both spin directions and separates the bonding and antibonding peaks in the minority spin. It has been reported that the separation of bonding and antibonding states by a low-density region, in which the Fermi level is located, can stabilize the ferromagnetic state [17,18]. So the electronic structure calculation indicates the ferromagnetic state is the stable ground state, which agrees with the experimental results well. It can be seen that there exists strong hybridization between the d electrons of the transition metal atoms, which results in the formation of a pseudo-gap in the minority-spin band around the Fermi level [19]. However, EF locates at the shoulder of the DOS peak, thus Fe2CoGe does not show half-metallic character. This is different
χ (arb. units)
Fe2CoGe
annealed at 1073K annealed at 723K
300
400
500
600
700
800
900
1000
T (K) 140 Fe2CoGe 120
M (emu / g)
100 80 60
annealed at 1073K annealed at 723K
40 20 0 0
10000
20000 30000 Field (Oe)
40000
50000
Fig. 4. Temperature dependence of the AC susceptibility (a) and magnetization curves (b) for Fe2CoGe samples annealed at different temperatures.
ARTICLE IN PRESS
DOS (electrons / eV)
Z. Ren et al. / Physica B 405 (2010) 2840–2843
10 5 0 -5 4 2 0 -2 4 2 0 -2 6 3 0 -3 2 0 -2
electronic structure of Fe2CoGe with a degree of atomic disorder by the super cell approach. Here, we assume that there are two types of atomic site disorder, i.e. Fe (B)–Co and Fe (B)–Ge type, in the Fe2CoGe alloy, which are the most common cases in Heusler alloys. The calculated total DOS together with spin moments are presented in Fig. 6. It is clear that the random occupation of the Fe (B)–Co or Fe (B)–Ge atoms leads to a small increase of the spin moment. This coincides with the experimental results quite well. It can also be seen that the atomic disorder does not change the general structure of the DOS. The Fe and Co moments are always in parallel coupling, which leads to the stability of the total moments.
up Total
down
Fe (A)
Co (C)
Fe (B)
4. Conclusions
Ge -2 Energy (eV)
-4
0
2
Fig. 5. Calculated spin-projected total and partial DOS plots for Fe2CoGe.
18
up
5.19μB
12 6
DOS (electrons / eV)
0 -6 -12
2843
Fe-Co disorder
down
A new Heusler alloy Fe2CoGe has been synthesized by the ball-milling technique. The as-milled powder is partly amorphous and a crystallization exothermic peak is observed in the DTA curve. The ordered Heusler structure can be obtained by ballmilling and subsequent annealing at 1073 K. But when annealing at 773 K, only a disordered A2 phase is observed. The Curie temperature of the disordered phase is about 50 K lower than that of the ordered one. The electronic structure calculation suggests a ferromagnetic ground state in Fe2CoGe and the total spin moment is 5.03mB/f.u., which is close to the experimental value of 5.06mB. It is also found that in Fe2CoGe, the saturation magnetic moment is not very sensitive to the atomic disorder, which is confirmed by electronic structure calculations.
-18 18
5.10μB
12
Acknowledgements
6 0 -6
Fe-Ge disorder
-12 -18 -6
-4
-2
0
2
This work has been supported by the Fundamental Research Funds for the Central Universities (No. 09ML56) and the Science Foundation of North China Electric Power University (No. 200912005).
Energy (eV) Fig. 6. Total DOS of Fe2CoGe with Fe–Co or Fe–Ge type of disorder.
from Co2FeSi, in which the Fermi level moves to the bottom of the energy gap and results in a 100% spin polarization [20]. It is known that Fe has fewer valence electrons than Co does, which leads to the shift of the minority DOS of Fe2CoGe. Meanwhile, the states at EF are also low in the majority spin band, which makes the spin polarization of Fe2CoGe sensitive to the small change of the minority band and leads to the loss of half-metallicity. In the partial DOS of Fig. 5, the states of Fe (B) show a two-peak structure (bonding and anti-bonding peak) separated by a dip in DOS, due to the bcc crystal field effect. It can be seen that in majority spin states, both the two peaks are below the Fermi level and occupied, but in minority spin the exchange splitting moves the anti-bonding peak high above the Fermi level, which results in a large magnetic moment at Fe (B) site. The calculated spin moment of Fe (B) is 2.74mB, which agrees well with previous studies in other Fe-based Heusler alloys [21]. The partial moments of Fe (A) and Co are 1.38mB and 0.94mB, respectively. The Ge atom only has a small moment of 0.06mB and has almost no contribution to the total spin moment. The calculated total spin moment is 5.03mB/f.u., which fits the saturation moments at 5 K quite well. In the preceding section, we found that the saturation moment of Fe2CoGe is insensitive to the atomic disorder. To get a better understanding on the effect of disorder, we calculated the
References [1] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [2] H.C. Kandpal, G.H. Fecher, C. Felser, J. Phys. D: Appl. Phys. 40 (2007) 1507. [3] R.C. O’Handley, J. Appl. Phys. 83 (1998) 3263. [4] G.H. Wu, C.H. Yu, L.Q. Meng, J.L. Chen, F.M. Yang, S.R. Qi, Appl. Phys. Lett. 75 (1999) 2990. [5] H.Z. Luo, Z.Y. Zhu, L. Ma, S.F. Xu, H.Y. Liu, Y.X. Li, G.H. Wu, J. Phys. D: Appl. Phys. 40 (2007) 7127. [6] Z.H. Liu, H.N. Hu, G.D. Liu, Y.T. Cui, M. Zhang, J.L. Chen, G.H. Wu, Phys. Rev. B. 69 (2006) 134415. [7] J.S. Robinson, P.G. McCormick, R. Street, J. Phys.: Condens. Matter 7 (1995) 4259. ¨ [8] L. Zhang, E. Bruck, O. Tegus, K.H.J. Buschow, F.R. de Boer, Physica B 328 (2003) 295. [9] T.D. Hatchard, J.S. Thorne, S.P. Farrell, R.A. Dunlap, J. Phys.: Condens. Matter 20 (2008) 445205. [10] S. Wurmehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, Appl. Phys. Lett. 88 (2006) 032503. [11] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [12] W. Kohn, L.J. Sham, Phys. Rev. 140 (1964) A1133. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [15] C. Suryanarayana, Prog. Mater. Sci. 46 (2001) 1. [16] M. Acet, E. Duman, E.F. Wassermann, L. Manosa, A. Planes, J. Appl. Phys. 92 (2002) 3867. [17] J. Yamashita, S. Asano, S. Wakoh, Prog. Theor. Phys. 47 (1972) 774. [18] B.R.K. Nanda, I. Dasgupta, J. Phys.: Condens. Matter 15 (2003) 7307. [19] M. Zhang, Y.T. Cui, Z.H. Liu, G.D. Liu, J.L. Chen, G.H. Wu, Y. Sui, Y.Q. Liu, Z.N. ¨ Qian, E. Bruck, F.R. de Boer, Phys. Status Solidi (a) 201 (2004) 1570. [20] S. Wurmehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, H.J. Lin, J. Morais, Phys. Rev. B 72 (2005) 184434. [21] A. Bansil, S. Kaprzyk, E.P. Mijnarends, J. Tobola, Phys. Rev. B 60 (1999) 13396.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Structure and magnetic properties of Fe2CoGe synthesized by ball-milling Z. Ren a, S.T. Li a,n, H.Z. Luo b a b
School of Mathematics and Physics, North China Electric Power University, Baoding 071003, PR China School of Material Science and Engineering, Hebei University of Technology, Tianjin 300130, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 January 2010 Received in revised form 3 April 2010 Accepted 6 April 2010
A Heusler alloy Fe2CoGe has been synthesized by the ball-milling method. Its structure and magnetic properties have been studied. The results suggest that ball-milling can be a possible way to produce new Heusler alloys. Both X-ray diffraction and DTA measurement evidenced the formation of a partly amorphous phase after milling for 25 h. It is found that highly ordered Fe2CoGe can be obtained by annealing the as-milled powder at 1073 K, while a disordered A2 phase is resulted by annealing at 773 K. The magnetic properties of Fe2CoGe are not very sensitive to the atomic disorder. Electronic structure calculation suggests a ferromagnetic ground state in highly ordered Fe2CoGe and the total spin moment is 5.03mB/f.u., which agrees well with the experimental value of 5.06mB for the sample annealed at 1073 K. It is also found that the atomic disorder does not strongly change the ferromagnetic coupling between Fe and Co moments and also the general structure of the DOS. So the total spin moment only slightly increases when atomic disorder occurs. & 2010 Elsevier B.V. All rights reserved.
Keywords: Heusler alloys Band structure Magnetic properties Ball-milling
1. Introduction Study of the Heusler alloys has increased obviously in recent years due to new phenomenon, such as half-metallicity and shape memory effect, in this alloy family [1–4]. The Heusler alloy crystallizes in an ordered body-centered-cubic (bcc) structure and has a stoichiometric composition of X2YZ, where X and Y are transition metal elements, and Z is a main group element. Generally the Heusler structure can be looked on as four interpenetrating face-centered-cubic (fcc) lattices, in which the X and Y atoms occupy the A (0, 0,0), B 14 , 14 , 14 and C 12 , 12 , 12 sites, 3 3 3 and Z atom occupies the D 4 , 4 , 4 site in the Wyckoff coordinates. In the study of the Heusler alloys, melt-spinning technique has been widely used, which is a non-equilibrium process and can retain the meta-stable phase to room temperature [5,6]. So it is a promising way to investigate new functional materials in the Heusler alloys. Here, ball-milling is another non-equilibrium way to synthesize new meta-stable materials; however, there are only few reports on its application in the Heusler alloys. Robinson et al. reported that Cu2MnAl can be prepared via a combination of mechanical alloying and heat treatment [7]. Later, Zhang synthesized a DO3 type Fe2MnGe phase by annealing the as-milled amorphous powder at 673 K [8]. A typical shape memory alloy Ni–Mn–Ga was also synthesized and interesting magnetic properties change has been found in it [9]. Till now, the Heusler alloys synthesized by ball-milling are mainly Mn-based.
n
Corresponding author. Tel.: + 86 312 7525086; fax: +86 312 7525081. E-mail address: [email protected] (S.T. Li).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.04.008
When some antisite disorder was introduced to the lattice by ball-milling, the Mn moments in different sites may form an antiparallel coupling which will decrease the total moment and influence other magnetic properties. So it is interesting to study the effect of ball-milling in Mn-free Heusler alloy Fe2CoGe. In this paper, we report the structure and magnetic properties of a new Heusler alloy Fe2CoGe prepared by ball-milling. Since Co2FeSi was predicted as a half-metallic ferromagnet (HMF) by Wurmehl et al. [10], the work on Fe2CoGe which has similar composition with Co2FeSi can also be helpful in searching for new HMFs.
2. Experimental details and computational method Fe2CoGe sample was prepared by ball-milling in a planetary ball mill from high purity powder components (99.9% or higher). The mass of the loaded initial powder is 8 g. The mixture was sealed in steel vial with balls of different diameters made of hardened steel under argon atmosphere in a glove box. The ball to powder weight ratio is 10:1. The milling time is 25 h, which is sufficient for the formation of the compound. The samples were pressed into discs and sealed in a quartz tube filled with high purity argon and then annealed at 773 and 1073 K, respectively. X-ray powder diffraction (XRD) with Cu Ka radiation was used to check the crystal structure and to determine the lattice constants. The magnetization curves were measured by a Quantum Design MPMS-7 superconducting quantum interference device (SQUID) magnetometer with applied field up to 5 T. The Curie temperature
ARTICLE IN PRESS Z. Ren et al. / Physica B 405 (2010) 2840–2843
Fe2CoGe milling for 25h
DTA T
was measured by an AC susceptometer with an AC magnetic field of amplitude 5 Oe. We carried out the electronic structure calculation using the density functional theory (DFT) plane-wave pseudopotential method [11,12]. The exchange-correlation function was based on the Perdew–Burke–Ernzerhof generalized-gradient approximation (GGA) potential [13]. The interactions between the valence electrons and ion cores were described as ultrasoft pseudopotentials, first introduced by Vanderbilt [14]. The cut off energy for plane waves is 500 eV for all the cases to ensure good convergence of the total energy. The self-consistent calculations employed a grid of 182k points from a 15 15 15 mesh in the irreducible Brillouin zone. The convergence tolerance was set to 5 10 6 eV/atom.
2841
300
3. Results and discussion
350
400
450
500
550
T (°C)
Fe (100)
Ge (111)
Fe2CoGe
Intensity (arb. units)
Co
1h Ge Co
Ge
Fe
Fe
Ge
5h
25h
30
40
50 60 2θ (degree)
70
80
Fig. 1. XRD patterns of the Fe2CoGe powder milled for different times.
90
723K
(220)
annealed at
30
(111)
(400)
25
(200)
Fe2CoGe annealed at
(422)
(220)
Fig. 2. Continuous-heating DTA curve at 20 1C/min of the as-milled powder of Fe2CoGe.
Intensity (arb. units)
1073K
20
30
40
50 60 2θ (degree)
(422)
(400)
(311)
(200)
25
(111)
The XRD pattern of the samples milled for different times is shown in Fig. 1. It is clear that the XRD patterns change obviously with prolonged milling time. When milling for 1 h, the starting elemental powder is simply crushed together. The XRD pattern shows only the elemental peaks, which are somewhat broadened by the stress and reduction of the grain size. After 5 h, only the iron diffraction peaks are identified and other elemental peaks vanish. It is also found that the iron peaks have a broad shoulder and moves to the low angle end. This may indicate the formation of a bcc Fe–(Co, Ge) solid solution. When the milling time reaches 25 h, a broad high peak at about 441 and two small peaks at 651 and 821 are observed. These diffraction peaks indicate that a disorder bcc A2 phase is formed after 25 h ball-milling. The triangular shape of the main peak may be attributed to the formation of some amorphous phase in the A2 phase [8,15], as has been confirmed by subsequent DTA measurement. Another possibility for the broad peak is the stress introduced by ball-milling, which may lead to the distortion of the lattice. The DTA curve of the Fe2CoGe powder milled for 25 h is shown in Fig. 2. The heating rate is 20 1C/min. The huge exothermic peak around 450 1C corresponds to the crystallization of the amorphous phase in the as-milled Fe2CoGe powder. This confirms the conclusion in preceding discussions. In order to investigate the crystal structure after crystallization and the influence of different annealing temperatures, we tried annealing the as-milled powder at 773 and 1073 K, respectively. The former is close to the crystallization temperature and the latter is much higher above it. It may be expected that they will
70
80
30
90
Fig. 3. XRD patterns of the Fe2CoGe powder annealed at 773 and 1073 K, respectively.
have different influence on the crystal structure as well as the magnetic properties. Fig. 3 gives the XRD patterns of Fe2CoGe powder annealed at 773 and 1073 K, respectively. It is clear that different annealing temperatures have no obvious influence on the basic structure. After annealing, the full width at half maximum (FWHM) decreases and the diffraction peaks become sharper compared with which of the as-milled powder. This is due to the increase of grain size and the elimination of the stress. In both cases, a bcc structure is retained. However, the annealing temperatures influence the atomic order in Fe2CoGe strongly. For the sample annealed at 773 K, only three diffraction peaks: (2 2 0), (4 0 0), (4 2 2) are observed, indicating that a disordered A2 phase are formed. But for the sample annealed at 1073 K, superlattice diffraction peaks (1 1 1) and (2 0 0) are identified together with the main peaks. Since the (2 2 0) peak is too strong in the pattern, we show the detail in the insets of Fig. 3. It is known that the ordered Heusler structure is represented by the existence of the superlattice reflections (1 1 1) and (2 0 0). Usually the (1 1 1) diffraction represents the order between the B and D sites, and (2 0 0) diffraction is corresponding to the order between the (A, C) atoms and B sites. So our results prove that an
ARTICLE IN PRESS 2842
Z. Ren et al. / Physica B 405 (2010) 2840–2843
ordered structure can be obtained in Fe2CoGe after annealing at 1073 K and also that ball-milling is a possible way to synthesize new Heusler alloys. The derived lattice constant for ordered Fe2CoGe is 5.764 A˚ at room temperature. The temperature dependence of the AC susceptibility for the Fe2CoGe samples annealed at different temperatures is presented in Fig. 4(a). It can be seen that the Curie temperature TC of the disorder A2 phase is about 50 K lower than that of the ordered one. But both of them are higher than 900 K. This decrease may be attributed to the weakening of the exchange interaction in the disordered structure. Similar results are also found in Ni2MnAl, in which the atomic disorder affects its TC strongly [16]. Fig. 4(b) gives the magnetization curves of Fe2CoGe samples measured at 5 K. The derived saturation magnetic moments are 5.25mB and 5.06mB for the alloy annealed at 773 and 1073 K, respectively. This difference is due to the atomic disorder in Fe2CoGe alloy. However, we can see the influence of atomic disorder on the spin moment is quite small in Fe2CoGe. This may be attributed to the strong ferromagnetic coupling between the Fe and Co atoms in both order and disorder structure, as will be discussed in the next section.
Recently, Co2FeSi is predicted as a new half-metallic ferromagnet [10]. Here, Fe2CoGe has similar composition with it and also has a high Curie temperature. So it is meaningful to study the electronic structure of Fe2CoGe. The effect of atomic disorder on the electronic structure and magnetic moments is also investigated. Fig. 5 gives the calculated total and partial DOS for Fe2CoGe. In the total DOS, we can find a clear exchange splitting between the minority and majority spin states. The Fermi level lies in the lowdensity part in both spin directions and separates the bonding and antibonding peaks in the minority spin. It has been reported that the separation of bonding and antibonding states by a low-density region, in which the Fermi level is located, can stabilize the ferromagnetic state [17,18]. So the electronic structure calculation indicates the ferromagnetic state is the stable ground state, which agrees with the experimental results well. It can be seen that there exists strong hybridization between the d electrons of the transition metal atoms, which results in the formation of a pseudo-gap in the minority-spin band around the Fermi level [19]. However, EF locates at the shoulder of the DOS peak, thus Fe2CoGe does not show half-metallic character. This is different
χ (arb. units)
Fe2CoGe
annealed at 1073K annealed at 723K
300
400
500
600
700
800
900
1000
T (K) 140 Fe2CoGe 120
M (emu / g)
100 80 60
annealed at 1073K annealed at 723K
40 20 0 0
10000
20000 30000 Field (Oe)
40000
50000
Fig. 4. Temperature dependence of the AC susceptibility (a) and magnetization curves (b) for Fe2CoGe samples annealed at different temperatures.
ARTICLE IN PRESS
DOS (electrons / eV)
Z. Ren et al. / Physica B 405 (2010) 2840–2843
10 5 0 -5 4 2 0 -2 4 2 0 -2 6 3 0 -3 2 0 -2
electronic structure of Fe2CoGe with a degree of atomic disorder by the super cell approach. Here, we assume that there are two types of atomic site disorder, i.e. Fe (B)–Co and Fe (B)–Ge type, in the Fe2CoGe alloy, which are the most common cases in Heusler alloys. The calculated total DOS together with spin moments are presented in Fig. 6. It is clear that the random occupation of the Fe (B)–Co or Fe (B)–Ge atoms leads to a small increase of the spin moment. This coincides with the experimental results quite well. It can also be seen that the atomic disorder does not change the general structure of the DOS. The Fe and Co moments are always in parallel coupling, which leads to the stability of the total moments.
up Total
down
Fe (A)
Co (C)
Fe (B)
4. Conclusions
Ge -2 Energy (eV)
-4
0
2
Fig. 5. Calculated spin-projected total and partial DOS plots for Fe2CoGe.
18
up
5.19μB
12 6
DOS (electrons / eV)
0 -6 -12
2843
Fe-Co disorder
down
A new Heusler alloy Fe2CoGe has been synthesized by the ball-milling technique. The as-milled powder is partly amorphous and a crystallization exothermic peak is observed in the DTA curve. The ordered Heusler structure can be obtained by ballmilling and subsequent annealing at 1073 K. But when annealing at 773 K, only a disordered A2 phase is observed. The Curie temperature of the disordered phase is about 50 K lower than that of the ordered one. The electronic structure calculation suggests a ferromagnetic ground state in Fe2CoGe and the total spin moment is 5.03mB/f.u., which is close to the experimental value of 5.06mB. It is also found that in Fe2CoGe, the saturation magnetic moment is not very sensitive to the atomic disorder, which is confirmed by electronic structure calculations.
-18 18
5.10μB
12
Acknowledgements
6 0 -6
Fe-Ge disorder
-12 -18 -6
-4
-2
0
2
This work has been supported by the Fundamental Research Funds for the Central Universities (No. 09ML56) and the Science Foundation of North China Electric Power University (No. 200912005).
Energy (eV) Fig. 6. Total DOS of Fe2CoGe with Fe–Co or Fe–Ge type of disorder.
from Co2FeSi, in which the Fermi level moves to the bottom of the energy gap and results in a 100% spin polarization [20]. It is known that Fe has fewer valence electrons than Co does, which leads to the shift of the minority DOS of Fe2CoGe. Meanwhile, the states at EF are also low in the majority spin band, which makes the spin polarization of Fe2CoGe sensitive to the small change of the minority band and leads to the loss of half-metallicity. In the partial DOS of Fig. 5, the states of Fe (B) show a two-peak structure (bonding and anti-bonding peak) separated by a dip in DOS, due to the bcc crystal field effect. It can be seen that in majority spin states, both the two peaks are below the Fermi level and occupied, but in minority spin the exchange splitting moves the anti-bonding peak high above the Fermi level, which results in a large magnetic moment at Fe (B) site. The calculated spin moment of Fe (B) is 2.74mB, which agrees well with previous studies in other Fe-based Heusler alloys [21]. The partial moments of Fe (A) and Co are 1.38mB and 0.94mB, respectively. The Ge atom only has a small moment of 0.06mB and has almost no contribution to the total spin moment. The calculated total spin moment is 5.03mB/f.u., which fits the saturation moments at 5 K quite well. In the preceding section, we found that the saturation moment of Fe2CoGe is insensitive to the atomic disorder. To get a better understanding on the effect of disorder, we calculated the
References [1] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [2] H.C. Kandpal, G.H. Fecher, C. Felser, J. Phys. D: Appl. Phys. 40 (2007) 1507. [3] R.C. O’Handley, J. Appl. Phys. 83 (1998) 3263. [4] G.H. Wu, C.H. Yu, L.Q. Meng, J.L. Chen, F.M. Yang, S.R. Qi, Appl. Phys. Lett. 75 (1999) 2990. [5] H.Z. Luo, Z.Y. Zhu, L. Ma, S.F. Xu, H.Y. Liu, Y.X. Li, G.H. Wu, J. Phys. D: Appl. Phys. 40 (2007) 7127. [6] Z.H. Liu, H.N. Hu, G.D. Liu, Y.T. Cui, M. Zhang, J.L. Chen, G.H. Wu, Phys. Rev. B. 69 (2006) 134415. [7] J.S. Robinson, P.G. McCormick, R. Street, J. Phys.: Condens. Matter 7 (1995) 4259. ¨ [8] L. Zhang, E. Bruck, O. Tegus, K.H.J. Buschow, F.R. de Boer, Physica B 328 (2003) 295. [9] T.D. Hatchard, J.S. Thorne, S.P. Farrell, R.A. Dunlap, J. Phys.: Condens. Matter 20 (2008) 445205. [10] S. Wurmehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, Appl. Phys. Lett. 88 (2006) 032503. [11] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [12] W. Kohn, L.J. Sham, Phys. Rev. 140 (1964) A1133. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [15] C. Suryanarayana, Prog. Mater. Sci. 46 (2001) 1. [16] M. Acet, E. Duman, E.F. Wassermann, L. Manosa, A. Planes, J. Appl. Phys. 92 (2002) 3867. [17] J. Yamashita, S. Asano, S. Wakoh, Prog. Theor. Phys. 47 (1972) 774. [18] B.R.K. Nanda, I. Dasgupta, J. Phys.: Condens. Matter 15 (2003) 7307. [19] M. Zhang, Y.T. Cui, Z.H. Liu, G.D. Liu, J.L. Chen, G.H. Wu, Y. Sui, Y.Q. Liu, Z.N. ¨ Qian, E. Bruck, F.R. de Boer, Phys. Status Solidi (a) 201 (2004) 1570. [20] S. Wurmehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, H.J. Lin, J. Morais, Phys. Rev. B 72 (2005) 184434. [21] A. Bansil, S. Kaprzyk, E.P. Mijnarends, J. Tobola, Phys. Rev. B 60 (1999) 13396.