CHAPTER 4. ELECTRONIC AND MAGNETIC PROPERTIES OF MX 2 (M = V, Nb; X = Al, Ga, In, Cl, Br AND I) COMPOUNDS IN CdI 2 -TYPE STRUCTURE

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1 84 CHAPTER 4 ELECTRONIC AND MAGNETIC PROPERTIES OF MX 2 (M = V, Nb; X = Al, Ga, In, Cl, Br AND I) COMPOUNDS IN CdI 2 -TYPE STRUCTURE 4.1 INTRODUCTION As ideal materials for use in spintronic devices, the half-metallic ferromagnets are attracting more and more attention. So far, a number of halfmetallic ferromagnets have been identified. Several layered binary transition metal compounds have interesting magnetic properties (Benedek and Frey 1980). The CdI 2 -type VX 2 (X = Cl, Br and I) compounds belongs to the layered crystals (Wyckoff 1972) and have been investigated experimentally (Niel et al 1977). The magnetic properties of CdI 2 -type VX 2 compounds (X = Cl, Br and I) have been studied extensively. These compounds show an antiferromagnetic behaviour in their ground-state phase. These compounds have attracted much attention from the aspect of the effect of the frustration in the triangular anti-ferromagnets (van Erk and Haas 1975, Friedt et al 1976, Hirakawa et al 1983a, 1983b, Yamada et al 1984, Itoh et al 1984, Takeda et al 1984, Kadowaki et al 1985, Tabek et al 1993, Wosnitza et al 1994). The anti-ferromagnetic materials are supposed to be more advantageous than half-metallic ferromagnets because of the following reasons: (i) high magnetic transition temperature is obtained and (ii) easy to

2 85 inject spin due to their small shape magnetic anisotropy. However, these materials cannot fulfill the requirements of being half-metallic because due to their spin-rotational symmetry. The possibility of half-metalic antiferromagnetic materials (i.e. compensated ferrimagnets) was first proposed by van Leuken and de Groot in Based on first-principles calculations they proposed CrMnSb and V 7 MnFe 8 Sb 7 In as candidates for HM-AFM s. Many other systems have been suggested to have HM-AFM s, including double perovskites, thiospinels and a vacancy induced NiO system. Despite several experimental challenges, no actual HM-AFM s, have been reported yet (Masao 2006, Long et al 2009). To the best of our knowledge, until now, there is no experimental or theoretical studies on the titled compounds except VX 2 (X = Cl, Br and I) compounds. The motivation of the present work is to investigate the halfmetallic ferromagnetism in the titled compounds by performing first principles electronic structure calculations by means of TBLMTO method within the density functional formalism. The results of these calculations are compared with other transition metal based half-metallic ferromagnets (Akinaga et al 2000, Sanvito and Hill 2000, Shirai 2003, Galanakis and Mavropoulos 2003, Xie et al 2003a, 2003b, Miao and Walter 2005a, 2005b). 4.2 PRESENT WORK In this work, the electronic band structure calculations for the VX 2 (X = Cl, Br and I) in their ground-state CdI 2 -type structure also VAl 2, VGa 2, VIn 2 and NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds in the hypothetical CdI 2 -type structure have been systematically studied. For this purpose, both spin-polarization and non-spin-polarization calculations are carried out for each compound. It has been done in order to obtain the electronic and magnetic properties of these compounds by computing the band structure and density of states. The half-metallic property and ferromagnetism in these

3 86 compounds is predicted for the first time. In addition, the band structures and density of states for titled compounds were plotted Crystal Structure and Method of Calculation Within the framework of DFT (Hohenberg and Kohn 1964, Kohn and Sham 1965), the electronic structure calculations are performed using the TB-LMTO method. This method has been described well in the literature (Andersen and Jepsen 1984, Andersen et al 1986). The exchange-correlation potential within the local density approximation is calculated using the parameterization scheme of von Barth and Hedin scheme (1972). Atomic sphere approximation (ASA) has been used. For the calculations the scalar relativistic approach has been used that includes the mass velocity and Darwin corrections, but neglect the spin-orbit couplings. All k-space integrations are performed with tetrahedron method (Jepsen and Ansersen 1971) and the self-consistency is obtained with 162 irreducible k-points. E and k convergence are also checked carefully. The Wigner-Seitz sphere is chosen in such a way that the potential discontinuity at the sphere boundary is minimum and the charge flow between the atoms is in accordance with the electro-negativity criteria. The following basis sets are used for the calculations: V : 4s 2 4p 0 3d 3, Nb: 5s 2 5p 0 4d 3 Al: 3s 2 3p 1 3d 0, Ga: 4s 2 4p 1 4d 0 In: 5s 2 5p 1 5d 0 Cl: 3s 2 3p 5 3d 0, Br: 4s 2 4p 5 4d 0 I: 5s 2 5p 5 5d 0 The CdI 2 -type structure is given in Figure 4.1. In the CdI 2 -type structure (space group: P-3m1, No.: 164), the M and X atoms occupy the (0, 0, 0) and (0.33, 0.66, z) positions. For VX 2 (X = Cl, Br and I) compounds, the z-parameter values are taken from experimental results of Wyckoff 1972

4 87 and Hirakawa et al 1983a, 1983b. The LMTO method gives accurate results only for close packed structures. Hence, an empty sphere is placed at the appropriate position, E: (0, 0, 0.82). For VAl 2, VGa 2, VIn 2 and NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds, the cell parameter values are optimized using the experimental cell parameter values of VX 2 (X = Cl, Br and I) compounds. Figure 4.1 CdI 2 -type structure 4.3 TOTAL ENERGY CALCULATION AND RELATED PROPERTIES Both spin-polarization and non-spin-polarization calculations were carried out for the titled compounds in the CdI 2 -type structure in a manner similar to our earlier work. The total energy as a function of molecular volume is calculated for these compounds and are shown in Figures 4.2 and 4.3. From the total energy calculations, it is observed that VX 2 (X = Al, Ga, In, Cl, Br and I) compounds have lower energies in ferromagnetic phase compared with non-magnetic phase whereas NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds are energetically stable in non-magnetic phase at their equilibrium volume.

5 88 Figure 4.2 Calculated total energy per formula unit vs. Volume (Å 3 ) of MX 2 (M = V, Nb; X = Al, Ga and In) compounds

6 89 Figure 4.3 Calculated total energy per formula unit vs. Volume (Å 3 ) of MX 2 (M = V, Nb; X = Cl, Br and I) compounds

7 90 The calculated equilibrium lattice parameters and bulk modulus of these compounds were estimated by fitting the total energies to the Birch equation of state (Birch 1978). The calculated values are listed in Table 4.1 and are compared with the available experimental results in the literature. The calculated bulk modulus decreases from VAl 2 to NbI 2, suggesting that the compressibility increases from VAl 2 to NbI 2. The formation energy or heat of formation is also calculated in order to study the stability of phase. For each of the compounds, MX 2 (M= V, Nb; X = Al, Ga, In, Cl, Br and I), the heat of formation (H) is calculated using equation (3.2) and it is given in Table ELECTRONIC BAND STRUCTURE CALCULATIONS AND DENSITY OF STATES The self-consistent relativistic spin-dependent electronic band structure and density of states for titled compounds are obtained using spinpolarized and non-spin-polarized calculations within the LDA along the highsymmetry directions. The spin-polarization calculations show that VX 2 (X = Al, Ga, In, Cl, Br and I) compounds are ferromagnets whereas NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds are non-magnets because no effective polarization of the energy states occurs at their equilibrium volume. Figure 4.4 shows spin-dependent electronic band structures for ferromagnetic CdI 2 -type VX 2 (X = Cl, Br and I) compound at their equilibrium volume. It is observed that, the majority-spin channel is metallic whereas in the minority-spin channel there is an energy gap around the Fermi level. Therefore, VX 2 (X = Cl, Br and I) compounds are half-metallic ferromagnets. This result is similar to other half-metals like transition metal based pnictides and chalcogenides. The bands lying around -15 ev are due to anion s-like states, and the band above this value are due to anion p-like states, followed by cation d- and s-like states. The bands that are very close to the Fermi level are due to the cation d-like states and anion p-like states.

8 Table 4.1 Calculated equilibrium lattice constants (a, c) in Å, bulk modulus (B 0 ) in GPa and heat of formation (H) in kj/mol. in ferromagnetic phase. The values in the parenthesis are for non-magnetic phase. Lattice constants Compounds Present Exp. a B 0 H a c a c VAl (3.332) (5.399) (508.25) ( ) VGa (3.442) (5.587) (412.01) ( ) VIn (3.517) (5.707) (355.32) ( ) NbAl NbGa NbIn VCl (3.476) (5.634) (501.95) ( ) VBr (3.638) (5.966) (417.08) ( ) VI (3.937) (6.557) (367.65) ( ) NbCl NbBr NbI a Wyckoff 1972, Hirakawa et al 1983a, 1983b 91

9 Figure 4.4 Spin-dependent electronic band structures of VX 2 (X = Cl, Br and I) compounds at their equilibrium volume 92

10 93 In order to obtain a deeper insight into the changes in the electronic band compositions, the spin-dependent total and partial density of states for VX 2 (X = Cl, Br and I) compounds are shown in Figure 4.5. The density of states for these compounds lies mainly in four energy regions: (i) the lowest region streaming mainly from the anion s-like states, (ii) the low-energy p-d bonding region; it originating from the anion p- like states and partial amount of cation d-like states, (iii) the region around the E F ; the minority spin channel there is an energy gap while the minority spin channel cut the Fermi level, (iv) the energy region above E F dominates by unoccupied transition metal s-like states. In these compounds, the bond formation occurs from the cation s- like electrons and anion p-like electrons. However, the magnetism arises mainly due to the cation d- like electrons. It is clearly shown in Figure 4.5. The cation d-like states are strongly spin-split i.e. strongly spin polarized and is situated close to the Fermi level. The magnetic moments of these compounds originates mainly from the d-electrons of the cation. The calculated magnetic moments for these compounds is 3.00 µ B per formula unit as expected. An integer value of magnetic moment is a characteristic feature of HM ferromagnets. The calculated magnetic moments for these compounds are given in Table 4.2 along with partial magnetic moments at each atomic site. From the table, it can be seen that the main contribution to the magnetic moment of 3.00 µ B, comes from the cation d-electrons. From the table one can

11 94 Figure 4.5 Spin-dependent total (left panel) and partial (right panel) DOS s of VX 2 (X = Cl, Br and I) compounds at their equilibrium volume

12 95 observe easily that the X atom has an induced local magnetic moment opposite to the transition metal atom. It is due to the fact that the minority spin band is more located within the anion p-band; whereas the majority spin p-band is more hybridized with the low d-orbital and thus more shared with the d atoms. This is in agreement with previous results on binary transition metal based pnictides and chalcogenide compounds (Akinaga et al 2000, Sanvito and Hill 2000, Shirai 2003, Galanakis et al 2003, Xie et al 2003a, 2003b, Miao and Walter 2005a, 2005b). A very small contribution to the magnetic moment comes from the interstitial site. The calculated spin-dependent electronic band structures for VX 2 (X = Al, Ga and In) compounds at their equilibrium volume are shown in Figure 4.6 along the high-symmetry directions. These three compounds exhibit ferromagnetic property with small magnetic moment and both the spins have metallic nature. In these compounds, the bands which are lying around -10 ev are mainly due to the anion s-like states. The bands lying above this are mainly contributed by anion p-like states and cation s- and d-like states. The hybridized bands of anion p-like and cation d- and s-like states lie close to the Fermi level. The band structure profiles of majority spin and minority spin for these compounds are slightly different. The slight difference, which can be seen at the Г-point, is that the hybridized bands of anion p-like and cation d- like states shifts towards the Fermi level, which is not the case in minority spin. It is shown clearly in total and partial density of states histogram (Figure 4.7). This may be one of the reasons why there is small magnetic moment induced in the anion p-like states. The overall band structure profiles for these three compounds are similar.

13 96 Figure 4.6 Spin-dependent electronic band structures of VX 2 (X = Al, Ga and In) compounds at their equilibrium volume

14 97 Figure 4.7 Spin-dependent total (left panel) and partial (right panel) DOS s of VX 2 (X = Al, Ga and In) compounds at their equilibrium volume

15 98 The calculated total magnetic moments for these compounds are given in Table 4.2 along with partial magnetic moments at each atomic site. From the table, it can be observed that the main contribution to the magnetic moment comes from the transition metal atom. Their magnetic moments are very small around the equilibrium volumes compared with VCl 2, VBr 2 and VI 2. Table 4.2 Calculated total and partial magnetic moments (µ) in µ B, minority spin-bandgap (E g ) in ev and spin-flip-gap (E sfg ) in ev Magnetic moments Cation Anion Empty Total E g E sfg VAl VGa VIn VCl VBr VI Figures 4.8 (a) and (b) show the variation of lattice constant with magnetic moments for VX 2 (X = Al, Ga, In, Cl, Br and I) compounds. From the Figure 4.8(a), it can be seen that the calculated magnetic moment of 3.00 m B per formula unit remains constant for VCl 2, VBr 2 and VI 2 compounds. However, on still reducing the cell volumes, the magnetic moment starts decreasing monotonically and becomes non-magnetic. From the Figure 4.8(b), it can be seen that the magnetic moment for VAl 2, VGa 2 and VIn 2 compounds is slowly decreasing with reducing the cell volumes, finally it becomes non-magnetic.

16 99 (a) (b) Figure 4.8 Volume vs. magnetic moment of (a) VX 2 (X = Cl, Br and I) and (b) VX 2 (X = Al, Ga and In) compounds Figures 4.9 and 4.10 show the spin-dependent electronic band structures and total density of states of CdI 2 -type NbX 2 (X = Cl, Br and I) at their equilibrium volume. The overall electronic band structure profiles for these compounds are similar to majority spin band of VX 2 (X = Cl, Br and I). These compounds exhibit non-magnetic behaviour. In these compounds, both the spin bands are metallic. However, the cation d-electrons transfer from minority spin band to majority spin band with increasing volume, so that their minority spin states are pushed to higher energy and the p-d hybridization gap become wide, and the true half-metallic ferromagnetism with 3.00 µ B appears when their volumes becomes large enough. It can be seen in Figure The total and partial density of states histograms (Figure 4.12) show that cation d-like states are hybridized with anion p-like states. For these compounds, half-metallic lattice constants, total and partial magnetic moments, spin-flipgap and minority spin-bandgap are listed in Table 4.3.

17 Figure 4.9 Spin-dependent electronic band structures of NbX 2 (X = Cl, Br and I) compounds at their equilibrium volume 100

18 101 Figure 4.10 Spin-dependent total DOS s of NbX 2 (X = Cl, Br and I) compounds at their equilibrium volume

19 Figure 4.11 Spin-dependent electronic band structures of NbX 2 (X = Cl, Br and I) compounds at their half-metallic volume 102

20 Figure 4.12 Spin-dependent total and partial DOS s of NbX 2 (X = Cl, Br and I) compounds at their half-metallic volume 103

21 104 Table 4.3 Calculated half-metallic lattice constants (a hm, c hm ) in Å, total and partial magnetic moments (µ) in µ B, minority spinbandgap (E g ) in ev, spin-flip-gap (E sfg ) in ev for NbX 2 (X = Cl, Br and I) compounds Magnetic moments a hm c hm Cation Anion Empty Total E g E sfg NbCl NbBr NbI The spin-dependent electronic band structures and total density of states for NbAl 2, NbGa 2 and NbIn 2 compounds are given in Figures 4.13 and These compounds exhibit non-magnetic behaviour at their equilibrium volume. The overall electronic band structure profiles for these compounds are similar to majority spin band of VX 2 (X = Al, Ga and In) compounds. For expanded volume, these compounds exhibit ferromagnetic property with small magnetic moment. Both spins have metallic character and is given in Figure The spin-dependent electronic band structure profile for these compounds are similar and is in agreement with VAl 2, VGa 2 and VIn 2 compounds. The difference between majority spin and minority spin states is that, along the Г-direction, the hybridized band of anion p-like and cation d-like states shifts towards the lower energy and lies below the Fermi level in the spin up states. With increasing volume, the cation d-electrons transfer from minority spin to majority spin. The spin-dependent total and partial density of states for these compounds are given in Figure The critical lattice constants, total and partial magnetic moments, spin-flip-gap, minority spin-bandgap for these compounds are given in Table 4.4.

22 Figure 4.13 Spin-dependent electronic band structures of NbX 2 (X = Al, Ga and In) compounds at their equilibrium volume 105

23 106 Figure 4.14 Spin-dependent total DOS s of NbX 2 (X = Al, Ga and In) compounds at their equilibrium volume

24 Figure 4.15 Spin-dependent electronic band structures of NbX 2 (X = Al, Ga and In) compounds at their expanded volume 107

25 108 Figure 4.16 Spin-dependent total and partial DOS s of NbX 2 (X = Al, Ga and In) at their expanded volume

26 109 Table 4.4 Calculated critical lattice constants (a cri, c cri ) in Å, total and partial magnetic moments (µ) in µ B for NbX 2 (X = Al, Ga and In) compounds a cri c cri Magnetic moments Cation Anion Empty Total NbAl NbGa NbIn SUMMARY To summarize, the electronic band structure calculations have been carried out for MX 2 (M = V, Nb; X = Al, Ga, In, Cl, Br and I) compounds in CdI 2 -type structure in order to find half-metallic ferromagnetism. From the total energy calculations, one can observe easily that VX 2 (X = Al, Ga, In, Cl, Br and I) compounds have lower energies in ferromagnetic phase compared with nonmagnetic phase whereas NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds are nonmagnets at their equilibrium volume. The spinpolarization calculation shows that VCl 2, VBr 2 and VI 2 compounds are halfmetallic ferromagnets with the magnetic moments of 3.00 m B per formula unit as expected at their equilibrium volume. The magnetism arises mainly from the cation d-like states. As well as, VAl 2, VGa 2 and VIn 2 compounds exhibit ferromagnetic property with small magnetic moment. NbX 2 (X = Al, Ga, In, Cl, Br and I) compounds are non-magnetic and metallic at their equilibrium volume. However, these compounds exhibit ferromagnetism under large volume expansion and also NbX 2 (X = Cl, Br and I) compounds show halfmetallic behaviour. In these compounds, unit cell volume plays an important role in exhibiting half-metallicity. This result is similar to other transition metal based group V compounds.