Cite this Article
Wang Li-Ying, Dai Xue-Fang, Wang Xiao-Tian, Lin Ting-Ting, Chen Lei, Liu Ran, Cui Yu-Ting, Liu Guo-Dong†. Electronic structures and magnetisms of the Co2TiSb1− xSn x ( x = 0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior . Chinese Physics B, 24(12): 126201  
Permissions
Electronic structures and magnetisms of the Co2TiSb1− xSn x ( x = 0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior
Wang Li-Yinga),b), Dai Xue-Fangb), Wang Xiao-Tianb), Lin Ting-Tinga), Chen Leia), Liu Rana), Cui Yu-Tinga), Liu Guo-Dong†a),b)
School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400044, China
School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China

†Corresponding author. E-mail: gdliu1978@126.com

*Project supported by the Chongqing City Funds for Distinguished Young Scientists, China (Grant No. cstc2014jcyjjq50003), the Basic and Frontier Research Project of Chongqing City, China (Grant No. cstc2013jjB50001), the Project of Chongqing Normal University, China (Grant No. 13XLB030), and the Project of Scientific Research for High Level Talent in Colleges and Universities of Hebei Province, China (Grant No. GCC2014042).

Abstract

The total energy, electronic structures, and magnetisms of the AlCu2Mn-type Co2TiSb1− xSn x ( x = 0, 0.25, 0.5) with the different lattice parameter ratios of c/ a are studied by using the first-principles calculations. It is found that the phase transformation from the cubic to the tetragonal structure lowers the total energy, indicating that the martensitic phase is more stable and that a phase transition from austenite to martensite may happen at a lower temperature. Thus, a ferromagnetic shape memory effect can be expected to occur in these alloys. The AlCu2Mn-type Co2TiSb1− xSn x ( x = 0, 0.25, 0.5) alloys are weak ferrimagnets in the austenitic phase and martensitic phase.

PACS: 62.20.fg; 63.20.dk; 31.10.+z
Keyword: Heusler alloy; martensitic transformation; ferromagnetic shape memory alloy
1. Introduction

The ferromagnetic shape memory effect was first discovered in Ni2MnGa alloy in 1984.[1] At that time, the investigation on the related physical effect mainly focused on the large magnetic-field-induced strain.[1– 3] Over the past 30 years, in succession, several material systems with Heusler structure, such as Ni– Fe– Ga, [4] Co– Ni– Ga(Al), [5– 7] Mn– Ni– Ga(Al, In), [8– 10] Ni– Mn– In (Sn or Sb), [11– 13] and Mn2PtIn, [14] have been found to be ferromagnetic shape memory alloys (FSMAs).[15– 20] Accompanied by more and more FSMAs, more physical effects, such as magnetic-field-induced shape memory effect, [12] large magnetoresistance, [21, 22] large magnetocaloric effect, [23] and exchange bias[24] were also developed in FSMAs. The various physical effects of FSMAs have received much attention and made them a promising candidate for the future technological applications in many fields. Therefore, efforts to explore new FSMAs and to improve their properties are in progress.

Co-based Heusler alloy is one of the important systems among the FSMAs family. The Co– Ni– Ga[5] and Co– Ni– Al[25] have been reported to be FSMAs. However, the relevant investigations on the ferromagnetic shape memory effect in CoTi-based alloys were rarely carried out. Up to now, although Co2TiZ (Z = Al, Ga, Si, Ge, Sn, Sb)[26– 28] have been investigated widely in theory and experiment, most of the investigations focus on their half-metallic properties. Especially, Co2TiSb alloy is almost forgotten for it cannot crystallize into a pure AlCu2Mn-type structure.[27] In this paper, we will focus on Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys. We will investigate the martensitic transformation and the magnetism in the alloys by using the first-principles calculations.

2. Computational methods

The electronic structures were calculated by using the pseudopotential method with a plane-wave basis set based on density-functional theory.[29, 30] The interactions between the atomic core and the valence electrons are described by the ultrasoft pseudopotential.[31] The electronic exchange– correlation energy has been treated under the generalized gradient approximation (GGA). For all cases, a plane-wave basis set cut-off of 400 eV was used and 182 k points were employed in the irreducible Brillouin zone. The convergence tolerance in the calculations was selected to 1 × 10− 6 eV/atom.

3. Results and discussion
3.1. Structure and geometry optimization

Heusler alloy with chemical composition X2YZ, consists of four interleaving f.c.c. sublattices along a body diagonal with one formula unit per unit cell.[32] It contains 8X atoms, 4Y atoms, and 4Z atoms per unit cell. The AlCu2Mn-type crystallizes into the L21 structure (space group ) and CuHg2Ti-type (space group ) structures that are two different atom arrangement forms in Heusler alloys.[32] For AlCu2Mn-type Co2TiSb1− xSnx alloy, two Co atoms occupy 8c (1/4, 1/4, 1/4) and (3/4, 3/4, 3/4) Wyckoff positions and the Ti atom enters 4a (0, 0, 0), leaving 4b (1/2, 1/2, 1/2) to Sb and Sn atoms, and the structure model is shown in Fig. 1(a). For the CuHg2Ti-type structure, two Co atoms occupy 4a (0, 0, 0) and 4c (1/4, 1/4, 1/4) Wyckoff positions, Ti and Sb or Sn atoms are located at 4b (1/2, 1/2, 1/2) and 4d (3/4, 3/4, 3/4) positions, respectively, as shown in Fig. 1(b). To determine the equilibrium lattice parameter and test the site preference in Co2TiSb1− xSnx (x = 0, 0.25, 0.5), we perform the total energy (Et) calculations on Co2TiSb1− xSnx with the AlCu2Mn-type and CuHg2Ti-type structure in non-magnetic (NM) and ferromagnetic (FM) state, respectively.

Fig. 1. Unit cell configurations for (a) AlCu2Mn-type structure and (b) CuHg2Ti-type structure Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys.

The curves of total energy versus the lattice parameters are shown in Fig. 2. It can be seen that the FM state is lower in the total energy for both AlCu2Mn-type and CuHg2Ti-type structures. The total energy of AlCu2Mn-type structure is lower than that of CuHg2Ti-type structure, which indicates that Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys prefer to crystallize into AlCu2Mn-type structure. The atom arrangement forms in Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys are consistent with the site preference rule proposed in Ref. [24] where they showed that the site preference of 3d elements is determined by the number of the valence electrons and the elements with less d electrons prefer to occupy the B sites, whereas elements with more electrons prefer to occupy the (A, C) sites.[25] The achieved equilibrium lattice parameters are 6.08 Å , 6.04 Å , and 6.02 Å for AlCu2Mn-type Co2TiSb1− xSnx (x = 0, 0.25, 0.5). The data are also collected in Table 1.

Fig. 2. Variations of total energy with lattice parameter for cubic AlCu2Mn-type and CuHg2Ti-type (a) Co2TiSb, (b) Co2TiSb0.75Sn0.25, and (c) Co2TiSb0.5Sn0.5 in the non-magnetic (PM) and ferromagnetic (FM) states.

Table 1. Calculated structural, energy, and magnetic properties of Co2TiSb, Co2TiSb0.75Sn0.25, and Co2TiSb0.5Sn0.5 alloys corresponding to the ground state. Δ Et and Δ M are the energy difference and magnetic moment difference between the martensitic phase (c/a > 1) and the cubic phase (c/a = 1).
3.2. Martensitic transformation in Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys

The first-principles calculations are used for analyzing and predicting the phase stability and potential martensitic transformations by calculating the total energy and electronic structures of the target system.[8, 9, 33– 35] Next, the tetragonal distortion is investigated as the potential pathway to martensitic transformations. That is, we simulate the martensitic transformation by changing the axis ratio (c/a) from the cubic phase to the non-modulated tetragonal phase. In the calculations, the volume of the unit cell remains constant.

The Et– c/a curves are shown in Fig. 3 for AlCu2Mn-type Co2TiSb1− xSnx alloys. From Fig. 3, it can be seen that the global minimum of the total energy is at c/a = 1.16 where the lattice parameters are a = b = 5.787 Å and c = 6.539 Å , and a local energy minimmum occurs at c/a = 0.94 for the Co2TiSb alloy. The phenomenon of two minima of the total energy is also observed in the well-known FSMA Ni2MnGa.[36] At a local energy minimum of c/a = 0.94, the system may undergo a shuffling transformation, and at a global energy minimum of c/a = 1.16, the tetragonal martensite is more stable for Co2TiSb alloy. At c/a = 1.16, the driving force (the total energy difference between the tetragonal martensite phase and the cubic austenite phase) is as large as – 108 meV/f.u. which is far higher than the previously reported driving forces, i.e., – 7.08 meV for FSMAs Ni2MnGa, [37] – 30.10 meV for Ni2FeGa, [37] and – 9.29 meV for Mn2NiGa.[38] Furthermore, the degree of distortion of c/a = 1.16 is smaller than those of Ni2MnGa (c/a = 1.22), [37] Ni2FeGa (c/a = 1.33)[37] and Mn2NiGa (c/a = 1.23).[38] A smaller degree of distortion implies that the martensitic transformation in the system needs a smaller driving force. So the results indicate that the AlCu2Mn-type Co2TiSb alloy has a sufficient thermodynamic driving force to overcome the resistance of the phase transformation. That is, AlCu2Mn-type Co2TiSb alloy is a potential FSMA.

Fig. 3. Variations of total energy difference (Δ Et) between cubic (c/a = 1) and tetragonally-distorted phase with c/a ratio in the constant volume for the Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys.

From Fig. 3, we can also see that the cases of alloys Co2TiSb0.75Sn0.25 and Co2TiSb0.5Sn0.5 are quite similar to a scenario of Co2TiSb alloy in the shape of the Et– c/a curve. Two minima of total energy are also observed for Co2TiSb0.75Sn0.25 and Co2TiSb0.5Sn0.5 alloys. The main difference is that the degrees of distortion at two minima of total energy and the driving force decrease with the increase of Sn content. The local minimum occurs at c/a = 0.98 and 1.0 for Co2TiSb0.75Sn0.25 and Co2TiSb0.5Sn0.5 alloys, respectively. Especially, we should notice that the local minimum occurs at c/a = 1.0 for Co2TiSb0.5Sn0.5 alloys, which implies that the cubic structure (austenite) is at the local minimum and the shuffling transformation can be ruled out in this alloy. The global minima are at c/a = 1.13 and 1.10 respectively, and the driving forces are – 67 meV/f.u. and – 14 meV/f.u. for Co2TiSb0.75Sn0.25 and Co2TiSb0.5Sn0.5 alloys, respectively. Although the driving force decreases with the increase of Sn content, Co2TiSb0.75Sn0.25 and Co2TiSb0.5Sn0.5 alloys still have the driving forces about equal to or higher than those of FSMAs reported previously. In addition, the c/a values of 1.13 and 1.10 are also smaller. The energy differences between the cubic and the tetragonal phases are also listed in Table 1. All these results illustrated above indicate that AlCu2Mn-type Co2TiSb1− xSnx alloys are a series of new materials with martensitic transformation.

Figure 4(a) shows the density of state (DOS) patterns of the cubic AlCu2Mn-type Co2TiSb alloy. We mainly focus on the DOS near the Fermi level, for only the DOS is closely related to the structure stability. The Fermi level is located at a pseudogap in the spin-up channel. However, in the spin-down channel, the Fermi level is located at a high DOS peak, which indicates a high N(Ef) (the density of states at the Fermi level). It has been reported that high N(Ef) reduces the structure stability while low N(Ef) has the opposite effect.[39, 40] Figure 4(a) shows the total and partial DOS of the tetragonal AlCu2Mn-type Co2TiSb. It is seen that the tetragonal distortion does not affect the general configuration of the total DOS. A main difference from the cubic AlCu2Mn-type Co2TiSb is that the sharp peak at the Fermi level in the spin-down channel is split into two relative weak peaks when the c/a ratio is 0.94. More obviously, the sharp peak is deeply split into two parts and a pseudogap occurs at the Fermi level at the c/a = 1.16. The occurrence of the pseudogap indicates that the hybridization between Co and Ti is strengthened. The strong d– d hybridization helps to stabilize the martensitic phase.[41] Similar results have been observed in Ni2MnGa alloy and are known as the John– Teller effect, in which the density of state peak at the Fermi level in the cubic phase is divided into two peaks below and above the Fermi level with tetragonal distortion, resulting in a lower total energy and causing martensitic transformation.[42]

Fig. 4. Spin-polarized total and atom-projected densities of states for (a) Co2TiSb, (b) Co2TiSb0.75Sn0.25, and (c) Co2TiSb0.5Sn0.5, calculated at the cubic phase, the local minimum of total energy and the global minimum of total energy. The Fermi energy is considered to be zero.

For the cubic and tetragonal AlCu2Mn-type alloys Co2TiSb1− xSnx (x = 0.25, 0.5), we show the DOS and the PDOS in Figs. 4(b) and 4(c). It is found that the Fermi level shifts to the low energy in both spin-up and spin-down channels when Sn is partly substituted for Sb in cubic Co2TiSb1− xSnx, which is obviously attributed to the less valence electrons of Sn atom than those of Sb atom to fill in the states. So, the Fermi level shifts from the high DOS peak toward a gap in the spin-down channel. The N(Ef) decreases with increasing Sn content, which indicates that the doping Sn makes the cubic AlCu2Mn-type structure more stable for the Co2TiSb1− xSnx system. For the Co2TiSb1− xSnx (x = 0.25, 0.5) alloys, the change of DOS induced by the transformation from cubic to tetragonal structure is similar to the undoped AlCu2Mn-type Co2TiSb alloy.

3.3. The magnetic properties of the AlCu2Mn-type Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys

The total and atomic magnetic moments are indicated in Table 1 for the cubic and various tetragonal Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys. Generally, the Co atoms each have a large magnetic moment and are the main contributors to the magnetization for the AlCu2Mn-type Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys. The Ti atoms each show a smaller and negative magnetic moment. So, the AlCu2Mn-type Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys are weak ferrimagnets. From the DOS patterns of cubic AlCu2Mn-type Co2TiSb1− xSnx (x = 0, 0.25, 0.5) alloys (c/a = 1), it can be seen that the spin splitting has little change and it mainly is that the Fermi level equally shifts down in spin-up and spin-down channels to neutralize the decrease of the valence electrons caused by the doping Sn. Because the Fermi level is located in a pseudogap in the spin-up channel and a high peak in the spin-down channel, the states pushed above the Fermi level are more in the spin-down channel than in the spin-up channel when the Fermi level equally shifts down in two spin channels. So, the total and Co atomic magnetic moment increase with the increasing Sn content.

For the tetragonal Co2TiSb1− xSnx (x = 0, 0.25) alloys at the local minimum, the total and atomic magnetic moments only have a small change with the Sn content due to the small degree of distortion. At the global minimum, the magnetization differences between the cubic and tetragonal structures are − 0.33 μ B, − 0.27 μ B, and − 0.27 μ B for Co2TiSb1− xSnx (x = 0, 0.25, 0.5), respectively. A large magnetization difference between cubic and tetragonal structures implies a strong effect of the external magnetic field on the martensitic transformation from the cubic to tetragonal structure.

4. Conclusions

The electronic structure and magnetic properties of the Heusler alloys Co2TiSb1− xSnx (x = 0, 0.25, 0.5) are studied by the first-principles calculations. It is found that the cubic AlCu2Mn-type Co2TiSb1− xSnx alloys are unstable in total energy and electronic structure. It is possible that a martensitic transformation from cubic to tetragonal structure occurs in AlCu2Mn-type Co2TiSb1− xSnx alloys. The Co2TiSb1− xSnx alloys are weak ferrimagnets. We predict that the AlCu2Mn-type Co2TiSb1− xSnx alloys are the new members of FSMAs’ family.

Reference
1 Webster P J, Ziebeck K R A, Town S L and Peak M S 1984 Philos. Mag. B 49 295 DOI:10.1080/13642817408246515 [Cited within:2]
2 Ullakko K, Huang J K, Kantner C, O’Hand ley R C and Kokorin V V 1996 Appl. Phys. Lett. 69 1966 DOI:10.1063/1.117637 [Cited within:1]
3 Wu G H, Yu C H, Meng L Q, Chen J L, Yang F M, Qi S R, Zhan W S, Wang Z, Zheng Y F and Zhao L C 1999 Appl. Phys. Lett. 75 2990 DOI:10.1063/1.125211 [Cited within:1]
4 Liu Z H, Zhang M, Cui Y T, Zhou Y Q, Wang W H, Wu G H and Zhang X X 2003 Appl. Phys. Lett. 82 424 DOI:10.1063/1.1534612 [Cited within:1]
5 Wuttig M, Li J and Craciunescu C 2001 Scr. Mater. 44 2393 DOI:10.1016/S1359-6462(01)00939-3 [Cited within:2]
6 Morito H, Fujita A, Kainuma R and Ishida K 2002 Appl. Phys. Lett. 81 1657 DOI:10.1063/1.1503851 [Cited within:1]
7 Karaca H E, Karaman I, Lagoudas D C, Maier H J and Chumlyakov Y I 2003 Scr. Mater. 49 831 DOI:10.1016/S1359-6462(03)00470-6 [Cited within:1]
8 Liu G D, Chen J L, Liu Z H, Dai X F, Wu G H, Zhang B and Zhang X X 2005 Appl. Phys. Lett. 87 262504 DOI:10.1063/1.2158507 [Cited within:2]
9 Sánchez Llamazares J L, Sanchez T, Santos J D, Pérez M J, Sanchez M L, Hernand o B, Escoda L L, Suñol J J and Varga R 2008 Appl. Phys. Lett. 92 012513 DOI:10.1063/1.2827179 [Cited within:1]
10 Feng L, Ma L, Liu E K, Wu G H, Wang W H and Zhang W X 2012 Appl. Phys. Lett. 100 152401 DOI:10.1063/1.3701136 [Cited within:1]
11 Sutou Y, Imano Y, Koeda N, Omori T, Kainuma R, Ishid K and Oikawa K 2004 Appl. Phys. Lett. 85 4358 DOI:10.1063/1.1808879 [Cited within:1]
12 Kainuma R, Imano Y, Ito W, Sutou Y, Morito H, Okamoto S, Kitakami O, Oikawa K, Fujita A, Kanomata T and Ishida K 2006 Nature 439 957 DOI:10.1038/nature04493 [Cited within:1]
13 Zhang Y Z, Cao J M, Tan C L, Cao Y J and Cai W 2014 Chin. Phys. B 23 037504 DOI:10.1088/1674-1056/23/3/037504 [Cited within:1]
14 Luo H Z, Jia P Z, Liu G D, Meng F B, Liu H Y, Liu E K, Wang W H and Wu G H 2013 Solid State Commun. 170 44 DOI:10.1016/j.ssc.2013.07.020 [Cited within:1]
15 Ullakko K, Huang J K, Kantner C, O’Hand ley R C and Kokorin V V 1996 Appl. Phys. Lett. 69 1966 DOI:10.1063/1.117637 [Cited within:1]
16 James R D and Wuttig M 1998 Phil. Mag. A 77 1273 DOI:10.1080/01418619808214252 [Cited within:1]
17 Wu G H, Yu C H, Meng L Q, Chen J L, Yang F M, Qi S R, Zhan W S, Wang Z, Zheng Y F and Zhao L C 1999 Appl. Phys. Lett. 75 2990 DOI:10.1063/1.125211 [Cited within:1]
18 Fujita A, Fukamichi K, Gejima F, Kainuma R and Ishida K 2000 Appl. Phys. Lett. 77 3054 DOI:10.1063/1.1323552 [Cited within:1]
19 Oikawa K, Ota T, Ohmori T, Tanaka Y, Morito H, Fujita A, Kainuma R, Fukamichi K and Ishida K 2002 Appl. Phys. Lett. 81 5201 DOI:10.1063/1.1532105 [Cited within:1]
20 Kakeshita T, Takeuchi T, Fukuda T, Tsujiguchi M, Saburi T, Oshima R and Muto S 2000 Appl. Phys. Lett. 77 1502 DOI:10.1063/1.1290694 [Cited within:1]
21 Yu S Y, Liu Z H, Liu G D, Chen J L, Cao Z X, Wu G H, Zhang B and Zhang X X 2006 Appl. Phys. Lett. 89 162503 DOI:10.1063/1.2362581 [Cited within:1]
22 Barand iarán J M, Chernenko V A, Lázpita P, Gutiérrez J and Feuchtwanger J 2009 Phys. Rev. B 80 104404 DOI:10.1103/PhysRevB.80.104404 [Cited within:1]
23 Krenke T, Duman E, Acet M, Wassermann E F, Moya X, Manosa L and Planes A 2005 Nat. Mater. 4 450 DOI:10.1038/nmat1395 [Cited within:1]
24 Ma L, Wang W H, Lu J B, Li J Q, Zhen C M, Hou D L and Wu G H 2011 Appl. Phys. Lett. 99 182507 DOI:10.1063/1.3651767 [Cited within:2]
25 Oikawa K, Wulff L, Iijima T, Gejima F, Ohmori T, Fujita A, Fukamichi K, Kainuma R and Ishida K 2001 Appl. Phys. Lett. 79 3290 DOI:10.1063/1.1418259 [Cited within:2]
26 Webster P J and Ziebeck K R A 1973 J. Phys. Chem. Solids 34 1647 DOI:10.1016/S0022-3697(73)80130-1 [Cited within:1]
27 Lee S C, Lee T D, Blaha P and Schwarz K 2005 J. Appl. Phys. 97 10C307 DOI:10.1063/1.1853899g [Cited within:1]
28 Rai D P and Thapa R K 2013 Chin. J. Phys. 51 812 DOI:10.6122/CJP.51.812 [Cited within:1]
29 Payne M C, Teter M P, Allan D C, Arias T A and Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045 DOI:10.1103/RevModPhys.64.1045 [Cited within:1]
30 Segall M D, Lindan P L D, Probert M J, Pickard C J, Hasnip P J, Clark S J and Payne M C 2002 J. Phys. : Condens. Matter 14 2717 DOI:10.1088/0953-8984/14/11/301 [Cited within:1]
31 Vand erbilt D 1990 Phys. Rev. B 41 78 DOI:10.1103/PhysRevA.41.78 [Cited within:1]
32 Webster P 1969 Contemp. Phys. 10 559 DOI:10.1080/00107516908204800 [Cited within:2]
33 Kand pal H C, Fecher G H and Felser C 2007 J. Phys. D: Appl. Phys. 40 1507 DOI:10.1088/0022-3727/40/6/S01 [Cited within:1]
34 Liu G D, Dai X F, Yu S Y, Zhu Z Y, Chen J L, Wu G H, Zhu H and Xiao J Q 2006 Phys. Rev. B 74 054435 DOI:10.1103/PhysRevB.74.054435 [Cited within:1]
35 Luo H Z, Meng F B, Feng Z Q, Li Y X, Zhu W, Wu G H, Zhu X X, Jiang C B and Xu H B 2010 J. Appl. Phys. 107 013905 DOI:10.1063/1.3269722 [Cited within:1]
36 Entel P, Dannenberg A, Siewert M, Herper H C, Gruner M E, Comtesse D, Elmers H J and Kallmayer M 2012 Metall. Mater. Trans. A 43A 2891 DOI:10.1007/s11661-011-0832-7 [Cited within:1]
37 Sahariah M B, Ghosh S, Singh C S, Gowtham S and Pand ey R 2013 J. Phys. : Condens. Matter 25 025502 DOI:10.1088/0953-8984/25/2/025502 [Cited within:4]
38 Felser C, Alijani V, Winterlik J, Chadov S and Nayak A K 2013 IEEE Trans. Magn. 49 682 DOI:10.1109/TMAG.2012.2223661 [Cited within:2]
39 Xu J H, Oguchi T and Freeman A J 1987 Phys. Rev. B 36 4186 DOI:10.1103/PhysRevB.36.4186 [Cited within:1]
40 Tobola J and Pierre J 2000 J. Alloys Compd. 296 243 DOI:10.1016/S0925-8388(99)00549-6 [Cited within:1]
41 Ye M, Kimura A, Miura Y, Shirai M, Cui Y T, Shimada K, Namatame H, Taniguchi M, Ueda S, Kobayashi K, Kainuma R, Shishido T, Fukushima K and Kanomata T 2010 Phys. Rev. Lett. 104 176401 DOI:10.1103/PhysRevLett.104.176401 [Cited within:1]
42 Fujii S, Ishida S and Asano S 1989 J. Phys. Soc. Jpn. 58 3657 DOI:10.1143/JPSJ.58.3657 [Cited within:1]