- Email: [email protected]
First principles study of 3d transition metal doped Cu3N
Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
Contents lists available at SciVerse ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
First principles study of 3d transition metal doped Cu3 N X.Y. Cui a,b,n, A. Soon a,c, A.E. Phillips a, R.K. Zheng b, Z.W. Liu b, B. Delley d, S.P. Ringer b, C. Stampfl a a
School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia Australian Centre for Microscopy & Microanalysis, University of Sydney, Sydney, New South Wales 2006, Australia Department of Materials Science and Engineering, Yonsei University, Seoul, Republic of Korea d Paul Scherrer Institut, WHGA/123 CH-5232 Villigen PSI, Switzerland b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 March 2012 Received in revised form 8 May 2012 Available online 23 May 2012
Interstitially doped Cu3 N represents a model system to study ‘‘enclosed atoms’’ in a cuboctahedral environment. Based on density functional theory calculations using the generalized gradient approximation, we report a systematic study of 3d-transition metals (TM), as well as Li-, H-, and Pd-doped Cu3 N, whose stabilities and magnetic properties are investigated. The interposition of 3d-TM atoms leads to mechanically stable yet brittle structures, with Sc, Mn, Ni, Cu, Zn possessing relatively small positive (endothermic) formation energies ð0:12 0:54 eV=TMÞ, suggesting it may be easier to realize them experimentally than other 3d-TM elements. Li-, H-, Pd-doping in Cu3 N are exothermic, while Ti, V, Cr, Fe, and Co have higher formation energy (0.93 1.39 eV/TM) at a doping concentration 3.7 %. The fully 3d-TM doped Cu3 N systems exhibit a wide spectrum of magnetic properties, ranging from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviour. In particular, Ti : Cu3 N exhibits weak itinerant magnetic properties with a large positive magnetovolume effect. All the 3d-TM atom intercalations into cubic Cu3 N lead to a semiconductor-to-metal transition for both 100% and 3.7% doping, with the exception of Ni : Cu3 N exhibiting a weak metallic or narrow semiconducting behaviour depending on the doping concentration. & 2012 Elsevier B.V. All rights reserved.
Keywords: Density functional theory Formation energy Magnetism
1. Introduction Transition metal nitrides show a wide variety of properties and applications. Among them, copper nitrides have attracted considerable attention. Owing to its low decomposition temperature and discriminating resistivity and optical properties [1–3], the semiconductor Cu3 N is used for optical storage devices [1,3] and spintronics [4]. It can be also used as a barrier in low resistance magnetic tunnel junctions [5] and as a candidate electrode material for rechargeable Li-ion batteries [6]. Very recently, copper nitride nanocubes, which are promising for cathodic electrocatalysts in alkaline fuel cells, are synthesized using a facile one-phase process [7]. Pure Cu3 N has a rather open anti-Re3 O crystal structure [8,9], in which the copper atoms occupy the center of the cubic edges forming collinear bonds with the two nearest neighbor nitrogen atoms instead of occupying the face-centered cubic close-packed sites (see Fig. 1(a)). Naively, such a structure is expected to be suitable for the interposition of other elements. Indeed, Pd [10], Cu [11,2], Li [13] and Zn [14]
n Corresponding author at: School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia. E-mail address: [email protected] (X.Y. Cui).
0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.05.021
atoms can be inserted into the body centered position of the cubic unit cell, inducing significant changes in the optical and electronic properties. This opens a route for significant potential applications [15]. On the other hand, the dopant ions locate in an octahedral environment, with each face equivalently representing a ligand (see Fig. 1(b)). Thus, the doped Cu3 N presents an interesting model structure to study ‘‘enclosed atoms’’. For a free atom, as a consequence of Hund’s rule, electrons occupy the energy levels on an atom in a manner favoring spin-polarized configurations, and therefore usually carry a finite spin moment. These exchange split spinpolarized configurations survive in a solid only when the energy levels broaden to form non-overlapping or partially over-lapping bands. In the doped Cu3 N systems, the ‘‘enclosed dopant atoms’’ bridge the free and condensed atom situations. One would then envisage some interesting magnetic properties in doped Cu3 N. In this regard, 3d transition metal (TM) atoms present the most promising candidates. Moreover, compared to conventional 3d-TM substitutionally doped magnetic semiconductors, interstitially doping TM atoms in semiconductors presents a possible route to resolve the clustering problem of magnetic elements [16], and may open another avenue for producing potentially useful extended magnetic semiconductors. Thus, the realisation of possible magnetism, particularly ferromagnetism in Cu3 N may expand the application of this material in the field of spintronics.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
3139
Fig. 1. Structures of (a) pure, (b) doped unit cell, and (c) doped large 3 3 3 supercell, (d) supercell containing pair TM atoms for the calculation of ferromagnetic and antiferromagnetic orderings of Cu3 N. Copper and nitrogen atoms are shown as large and small (green) spheres, respectively, and the dopant atoms as large (red) spheres. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Previous first principles studies on TM:Cu3 N (TM¼Ni, Cu, Zn, Pd, Ag, Cd, Rh, and Ru) revealed that the addition of such metal atoms modify the electronic properties of Cu3 N and turns all copper nitrides into displaying metallic behaviour [17–21]. In particular, Rh : Cu3 N was predicted to be a good candidate for exhibiting either quantum critical behaviour or itinerant electron meta-magnetism [20]. Hou [21] studied the structural stability of Cu, N and Li doped Cu3 N, and showed that while both Cu4 N and Li : Cu3 N can be stabilized thermodynamically and mechanically, cubic Cu3 N2 could not be mechanically stable. To our knowledge, a systematic study of the stability of 3d-TM doped Cu3 N is yet to be performed and the associated rich magnetic properties are largely unexplored. These forge the key motivations for this work.
2. Computational details We perform all-electron spin-polarized density functional theory (DFT) calculations using the generalized gradient approximation (GGA) [22] for the exchange correlation functional as 3 implemented in the DMol [23] code. Some results are also 3 checked using the WIEN2k code [24]. For the DMol calculations, the wave functions are expanded in terms of a double-numerical quality localized basis set with a real-space cutoff of ‘‘medium’’, namely 9:8211:5 bohr for TM atoms and 7.4 bohr for N atoms. Using the WIEN2k code, the wave functions in the interstitial region are expanded in plane waves with a cutoff of Kmax ¼9/Rmt. The charge density is Fourier expanded up to Gmax ¼17 a.u. We use muffin-tin radii of 1.7 a.u. for Cu, 1.5 a.u. for N, and 1.8 a.u. for TM atoms. Angular momenta up to l ¼10 are included. For both methods, we use 56 k-points in the irreducible part of the Brillouin zone. The equilibrium lattice constants are obtained by calculating the total energy at various volumes and then fitting the obtained curve to the Murnaghan equation of state [25]. The elastic constants cij are derived by applying a set of homogeneous deformations and calculating the second derivative of the total energy as a function of volume tetragonal and trigonal lattice distortions around the 3 equilibrium structures, as implemented in the DMol code. For a structure with cubic symmetry, there are only three unique stiffness constants: c11 ð ¼ c22 ¼ c33 ), c12 ð ¼ c13 ¼ c23 Þ, and c44 ð ¼ c55 ¼ c66 Þ. The shear modulus can be given by G ¼ 15ðc11 c12 þ 3c44 Þ:
ð1Þ
For cubic systems, the isotropic bulk modulus, B, which quantifies a material’s resistance to volume compression, is B ¼ 13ðc11 þ2c12 Þ:
ð2Þ
Using these quantities, we can then determine the isotropic Young’s modulus E¼
9BG , 3B þ G
ð3Þ
which encapsulates a material’s resistance to linear compression, and the isotropic Poisson’s ratio
n¼
3B2G : 2ð3B þ GÞ
ð4Þ
3. Results For undoped Cu3 N, the calculated equilibrium lattice constant ˚ is 3.849 A, compared with the experimental values of 3.812 A˚ [13], and 3.819 A˚ [9], and is in agreement with previous first principles calculations [17–21]. Pure Cu3 N is a semiconduc3 tor with an indirect bandgap of 0.29 eV ðDMol Þ and 0.25 eV (WIEN2k), in good agreement with other DFT studies [18,17]. These calculated bandgap values are significantly lower than the experimental ones, which range from 0.8 up to 1.9 eV, depending on the substrate and growth conditions [5]. The calculated heat 3 of formation of undoped Cu3 N is 1.30 eV ðDMol Þ and 1.23 eV (WIEN2k), which compares well to the value of 1.18 eV [21] obtained using DFT-GGA in the framework of the plane wave pseudopotential method. These values exhibit the typical overbinding characteristic of DFT-GGA, when compared to the experimental value of 0.868 eV [26]. Using the structure shown in Fig. 1(b), i.e., doping into a single unit cell of Cu3 N, the calculated lattice constants, elastic properties, and formation energies for pure and TM-doped Cu3 N are given in 3 Table 1, as calculated using the DMol code. For comparison, results of H- [27], Li- and Pd-doped Cu3 N are also listed. Interestingly, both codes consistently predict that the inclusion of a Ni atom leads to a marginal lattice compression, changing the cubic lattice constant from 3.849 A˚ to 3.839 A˚ (WIEN2k), rather than an expansion as found for all the other doped atoms, including H. Doping with Sc, the largest dopant atom studied here, leads to the ˚ most significant lattice expansion; from 3.849 A˚ to 4.077 A. With regard to the elastic constants and the shear, bulk and Young’s modulus, for the pure and Cu-doped Cu3 N, the only ones for which calculated data are available, our results are in good agreement with those reported in Ref. [21]. Elastic constants can be employed to evaluate the mechanical stability, which according to Ref. [28], should obey c11 4B 4c12 , c11 40, c44 4 0, and (c11 þ 2c12 Þ 4 0, where B is the bulk modulus. We find all the systems studied obey these requirements simultaneously, indicating all the systems should be mechanically stable. It is known that the bulk modulus does not correlate with hardness for some ionic and covalent materials and the shear modulus is a more reliable indicator of hardness [29,30]. Our data seems to support
3140
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
Table 1 Lattice constant, a0, elastic constants, shear modulus, G, bulk modulus, B, Young’s modulus, E, and formation energy, Ef of pure and, H and 3d-transition metal doped Cu3 N using the unit cell. Ef333 is the formation energy using the large 3 3 3 supercell. System
˚ a0 ðAÞ
c11
c12
c44
G (GPa)
B (GPa)
E (GPa)
B/G
Ef (eV)
Ef333 (eV)
Pure ScTiVCrMnFeCoNiCuZnHLiPd-
3.849 4.077 3.983 3.964 3.966 3.949 3.887 3.855 3.838 3.888 3.967 3.853 3.926 3.902
227.3 130.6 156.5 170.1 161.6 151.8 170.4 245.7 272.0 226.8 173.5 214.8 190.7 253.4
50.0 103.6 107.5 92.3 89.1 92.7 104.8 87.7 91.3 85.1 87.3 67.6 56.1 101.5
16.7 29.8 34.0 37.4 34.8 30.3 18.7 44.2 39.1 33.4 26.4 11.2 29.7 45.2
45.4 23.3 30.2 38.0 35.4 30.0 24.3 58.1 59.6 48.4 33.1 36.1 44.7 57.5
109.1 112.6 123.9 118.2 113.3 112.4 126.6 140.4 151.5 132.4 116.0 116.7 101.0 152.1
119.7 65.4 83.8 103.0 96.2 82.7 68.6 153.2 158.1 129.4 90.6 98.3 116.9 153.2
2.40 4.83 4.11 3.11 3.20 3.75 5.21 2.41 2.54 2.73 3.51 3.22 2.26 2.64
0.21 1.21 1.67 1.32 0.82 1.37 1.32 0.44 0.21 0.15 0.42 0.54 0.77
0.22 1.16 1.39 0.93 0.54 0.98 0.93 0.52 0.16 0.20 0.38 0.51 0.72
Table 2 Electron density of states at the Fermi energy, NðEF Þ, magnetic moments (MM) at the doped atoms using the unit cells and the large 3 3 3 supercell, energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) states, DEFMAFM , and the ground magnetic states of H and 3d-TM doped Cu3 N systems.
NðEF Þ (states/eV) MM ðmB Þ MM333 ðmB Þ DEAFMFM (eV) Ground state
H-
Sc-
Ti-
V-
Cr-
Mn-
Fe-
Co-
Ni-
Cu-
Zn-
1.46 0.38 0.32 0.018 AFM
5.16 0.0013 0 0.001 AFM
3.73 0.43 0.38 0.098 AFM
4.69 3.23 3.41 0.44 AFM
2.62 4.42 4.52 0.18 AFM
3.70 4.19 4.12 0.16 FM
5.11 2.92 2.78 0.19 FM
3.72 1.56 1.52 0.051 FM
0.82 – – – –
1.96 – – – –
2.39 – – – –
such a conclusion as these two modulus quantities show a different variation behaviour: only Co-, Ni-, Cu-, and Pd-doped Cu3 N possess larger values for both bulk modulus and shear modulus than those of pure Cu3 N, and only Li:Cu3 N has a smaller values for both quantities. All the other systems exhibit a smaller shear modulus and a larger bulk modulus compared to the pure Cu3 N. The value of B/G ratio for cubic Cu3 N is 2.40, which can be compared to 2.458 as obtained in Ref. [21] by the pseudopotential plane wave method. Except for the Li-doped case, the inclusion of dopants in Cu3 N leads to larger B/G values than pure Cu3 N. All the B=G values are larger than the critical value (1.75) separating ductile and brittle materials [31], indicating that pure and 3d-TM doped Cu3 N can be categorised as being brittle materials. We assume metal-rich growth conditions; i.e., the atom added to the host Cu3 N comes from the corresponding bulk reservoir; thus the formation energies of TM : Cu3 N systems are calculated TM:Cu3 N Cu3 N TM:Cu3 N Cu3 N as Ef ¼ Etot Etot ETM , Etot and ETM tot are the tot , where Etot total energies of TM : Cu3 N, Cu3 N and the ground state of the bulk TM metal, respectively. Our calculated formation energies for Cu- and Li-doped Cu3 N are 0.21 eV and 0.54 eV, respectively, which can be compared to 0.33 eV and 0.51 eV as obtained in Ref. [21]. Negative formation energies are obtained for Li- ( 0.54 eV), Pd- ( 0.77 eV) and H-doped (0.42 eV) Cu3 N, indicating it is thermodynamically favourable for the doped compounds to form, as have been realised in experiments for Pd [10], H [12] and Li [13]. Small positive (endothemic) formation energies are predicted for Sc- (0.21 eV), Ni- (0.44 eV) and Cu- (0.21 eV), and Zn- (0.15 eV), indicating it should be relatively easier for these materials to be synthesized experimentally compared to the other 3d-TM doped cases. Indeed, the interposition of Cu atoms in Cu3 N has been reported in experiments [2,11], and recently, Zn atoms have been doped into the centres of Cu3 N cells, resulting in a stoichiometry of Cu3 NZn0:231 [14,15]. By contrast, doping Ti atoms in Cu3 N by cylindrical magnetron sputtering method did not result in insertion
into the body centred position of the lattice [32], but rather segregated to the grain boundaries [33,34]. The large formation energy, 1.21 eV per Ti atom, explains such a challenge. Our results further indicate that in order to insert 3d-TM atoms such as Ti, V, Cr, Fe, Co atoms into the body-center-position of Cu3 N, delicate nonequilibrium growth methods will be required. Spin-polarised calculations show that H-, V-, Cr-, Mn-, Fe- and Co-doped Cu3 N are magnetic; and that Ni-, Cu- and Zn-doped Cu3 N are non-magnetic (see Table 2). For the Sc-doped case, it is predicted to be virtually non-magnetic using unit cell, with the atomic moment being 0:0013mB and the total moment 0:011mB (by WIEN2k), and being non-magnetic using the large 3 3 3 supercell. For magnetic systems, in order to study the magnetic stability, we have performed fixed spin moment calculations, namely calculation of the total energy as a function of the total magnetic moment per cell at the equilibrium lattice constants, as [20]. The results for selected systems are shown in Fig. 2, where H-, and Co-doped Cu3 N are typical magnetic systems, with a moment of 1:0mB and 1:28mB per formula cell, respectively. Ni : Cu3 N exhibits typical non-magnetic behaviour. These results are also confirmed using the 3 3 3 supercell. The most interesting system is Ti : Cu3 N, which is predicted to be magnetic with a total moment 0:52mB per cell, with 0:43mB residing at the Ti atom at the equilibrium structure. The very flat total energy variation with total magnetic moment shows a typical weak itinerant magnetic behaviour, as found in RhCu3 N [20]. Also interestingly, still for Ti : Cu3 N, it exhibits a strong large magnetovolume effect (MVE), in which the magnetic moment sensitively responds to the volume change around the vicinity of the equilibrium geometry, as shown in Fig. 3. This behaviour implies that the magnetic properties of Ti : Cu3 N might also sensitively respond to temperature and pressure. For Fe : Cu3 N, it can be seen from Fig. 3, that it shows a typical MVE, while for Ni : Cu3 N, the non-magnetism is robust against volume change.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
300
Energy (meV)
250 200 150 100 CoHNiTi-
50 0 -50 0
0.5
1
1.5
2
2.5
Total Magnetic Moment (µB)
Total magnetic moment (µB)
Fig. 2. Fixed spin moment calculations of the total energy for H-, Co-, Ni- and Ti-doped Cu3 N. For each case, the energies are given relative to the ground state. Co- and H-doped systems show a typical magnetic behaviour. Ni : Cu3 N is a nonmagnetic system. Ti : Cu3 N is predicted to be a weak itinerant magnetic system.
4 3 FeNiTi-
2 1 0 -1
3.6
3.8 4 Lattice constants (Å)
4.2
Fig. 3. Dependence of the total magnetic moment on the lattice constants for Ni-, Fe- and Ti-doped Cu3 N. Ti : Cu3 N exhibits a strong magnetovolume effect. The arrows indicate the equilibrium volumes.
To investigate a lower doping concentration, and to simulate the isolated ‘‘enclosed atoms’’, a supercell of 108 atom (3a0 3a0 3a0) is employed, where a0 is the lattice constant of the host Cu3 N, see Fig. 1(c). We allow full atomic relaxation. The calculated formation energy values are compared with those obtained using the small unit cell. While the general conclusion regarding the systems will small formation values are consistent, the variation of these two sets of values are clearly system-dependent; with the largest derivation being for Fe- and Co-doped Cu3 N. These results strongly indicate that there are appreciable, and for some systems, strong interaction between the neighbouring dopants in the unit cell. The sizably smaller values of formation energy in larger supercell (i.e., lower doping concentration) also indicate the repulsive interaction between the dopants. Indeed, adding two Fe atom in the ˚ and a 3 3 3 supercell, with a ‘‘near’’ (Fe–Fe distance of 3.854 A) ˚ configurations, the non-spin-polarised calculations ‘‘far’’ (6.675 A) (spin-polarised calculations encountered convergence difficulty) show that the ‘‘far’’ structure is energetically more favourable, by 0.113 eV. These results suggest that some 3d-TM interstitial doped Cu3 N systems are expected to fundamentally overcome the clustering problem. To investigate the magnetic interaction between the neighbouring dopants, i.e., ferromagnetic versus antiferromagnetic couplings, we used a model whose lattice vectors are (0, a, a), (a, 0, a), and (a, a, 0), where a is the optimized TM:Cu3 N lattice constants, as shown in Fig. 1(d). The main magnetic results are tabulated in Table 2. It can be seen that the 3d-TM doped Cu3 N
3141
systems exhibit a wide spectrum of magnetic properties, changing from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviours. Such interesting magnetic properties result from the manifestation of the enclosed dopant atoms and their interaction with the host Cu3 N. Mulliken population analysis (not shown) reveals the clear occurrence of charge transfer within the TM atom, and between the TM atom and the Cu3 N host. Within the 3d-TM dopants, from Sc to Ni, electrons transfer from 4s to 3d; for Cu and Zn, from 4s to 4p. Specifically, for Ni : Cu3 N, charge transfer leads to a fully occupied Ni-3d10 orbital, preventing net spin moment from leading to magnetism. This behaviour is robust against volume change. Similarly, the full 3d orbital occupation in Cu and Zn atoms explains the non-magnetism in Cu- and Zn-doped Cu3 N. By contrast, for Ti : Cu3 N, the spin-resolved 3d occupation changes evidently responding to the volume variation. For the electron transfer between TM atom and Cu3 N host, the charge redistribution occurs via orbital hybridization between TM-3d with Cu-3d and 4p, and N-2p. This can be seen from the total and TM partial density of states (DOS) as shown in Fig. 4. The 3d electrons in TM atoms play a dominant role for the metallicity as well as the magnetic properties. For all the 3d-doped Cu3 N systems, using the unit cell, the total DOS show metallic behaviour, indicating that 3d-TM atom intercalations into cubic Cu3 N all lead to a semiconductor-to-metal transition, with Ni : Cu3 N being predicted to be of weak conductivity (0.85 states/eV, see Table 2). The lower concentration Ni doped Cu3 N in the large 3 3 3 supercell actually shows a semiconducting behaviour, i.e., with a narrow band gap of 0.16 eV. For other 3d TM doped systems, the metallic behaviour is predicted to be robust to doping concentration. Experimentally, the implantation of hydrogen [12] and zinc [14] (here increasing the zinc concentration from 0 to 5.44 at.%) leads the electrical conductivity to be increased by more than two and three orders of magnitude at room temperature, compared well with our findings. Based on a band coupling model [35], for a given doped system, the magnetic ordering is determined by the p–d coupling and the d–d coupling. The dopant ions locate in an octahedral environment (with each face equivalently representing a ligand) (see Fig. 1(b)). The octahedral crystal field of the surrounding TM ligands splits the fivefold degenerate d states of the free TM ion into three low-lying t2g (dxy, dyz and dzx) and two high-lying eg (dz2 and dx2 y2 ) subsets. The final electronic configuration, a manifestation of DOS, is a delicate competition between crystal field splitting energy Dex and the exchange splitting energy DCF between the majority and minority electrons on the TM atoms. Increasing the 3d atomic number from Sc to Zn results in the Fermi level shifting higher in energy. From Sr to Cr, the increase of the occupation number will enhance the d–d super-exchange interactions, which leads to stronger antiferromagnetic ordering. For Fe (d8) and Co (d9) ions, there are two and one hole, respectively. The so-called ‘‘p–d hopping interaction’’ model [36], can stabilize ferromagetnic states, with the case of Fe : Cu3 N being stronger.
4. Summary Based on DFT calculations, we have systematically studied the equilibrium lattice constants, elastic constants, mechanical properties, formation energies, and magnetic properties of all the 3d-TM doped Cu3 N systems at doping concentrations of 100% and 3.7%. The interposition of a 3d-TM atom lead to a mechanically stable, yet brittle structure. For H-, Li- and Pd-doped, the calculated formation energies are negative; Sc-, Mn-, Ni-, Cu- and Zn- doped Cu3 N possess relatively small positive (endothermic) formation
3142
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
Sc
2
Ti
10 0 -10 10
0
0
-2
-10
TM−PDOS
DoS [1/eV]
2 1 0 -1 -2
DOS
DoS [1/eV]
DoS [1/eV]
DoS [1/eV]
TM−PDOS
10
Fe 10
5 0
0
-5
-10 Co
10 5 0 -5 -10
Ni
10 5 0 -5 -10
5 0
6 4 2 0 -2
8 Mn 6 4 2 0 -2 -4 -10 -5
10 5 0 -5 -10
Cr
10 0 -10 5 EF Energy [eV]
-10
-5
5 EF Energy [eV]
0 -5
10
DoS [1/eV]
DoS [1/eV]
-2
5
-10
DoS [1/eV]
0
DoS [1/eV]
10 5 0 -5 -10
V
DoS [1/eV]
DoS [1/eV]
-5 2
DOS
20 10 0 -10 -20
20 10 0 -10 -20
Cu
0
-10
Zn
20 0 -20 -5
EF 5 Energy [eV]
-10
-5
EF 5 Energy [eV]
Fig. 4. Partial density of states (PDOS) of TM atoms and total density of states for 3d-TM doped Cu3 N. In the TM-PDOS, blue represents the s orbital, green the p orbital, and grey the d orbital. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
energies. Introducing Ti, V, Cr, Fe and Co is predicted to be nontrivial due to their large positive formation energies, and would require careful nonequilibrium growth methods. Quite unexpectedly, inserting Ni to Cu3 N, which is non-magnetic, results in a decrease of the lattice constant. The 3d-TM doped Cu3 N systems exhibit a wide spectrum of magnetic properties, changing from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviours. In particular, Ti : Cu3 N exhibits weak itinerant magnetic properties with a large positive magnetovolume effect. All the 3d-TM atom intercalations into cubic Cu3 N lead to a semiconductor-to-metal transition for both 100% and 3.7% doping, with the exception of Ni : Cu3 N exhibiting a weak metallic or narrow semiconducting behaviour depending on the doping concentration.
Acknowledgements We acknowledge the computing resources provided by the National Computational Infrastructure (Australia) and support from the Australian Research Council. References [1] M. Asano, K. Umeda, A. Tasaki, Japanese Journal of Applied Physics 29 (1990) 1985. [2] T. Maruyama, T. Morishita, Journal of Applied Physics 78 (1995) 4104.
[3] T. Maruyama, T. Morishita, Applied Physics Letters 69 (1996) 890. [4] C. Navio, J. Alvarez, M.J. Capitan, J. Camarero, R. Miranda, Applied Physics Letters 94 (2009) 263112. [5] D.M. Borsa, S. Grachev, C. Presura, D.O. Boerma, Applied Physics Letters 80 (2002) 1823. [6] N. Pereira, L. Dupont, J.M. Tarascon, L.C. Klein, G.G. Amatucci, Journal of Electrochemical Society 150 (2003) A1273. [7] H. Wu, W. Chen, Journal of the American Chemical Society 133 (2011) 15236. ¨ Anorganische und Allgemeine Chemie 241 [8] R. Juza, H. Hahn, Zeitschrift fur (1939) 172. [9] U. Zachwieja, H. Jacobs, Journal of Less-Common Metals 161 (1990) 175. [10] U. Zachwieja, H. Jacobs, Journal of Less-Common Metals 170 (1991) 185. [11] J. Blucher, K. Bang, B.C. Giessen, Materials Science and Engineering A 117 (1989) L1. [12] Y. Hayashi, T. Ishikawa, D. Shimokawa, Journal of Alloys Compounds 330–332 (2002) 348. [13] F. Gulo, A. Simon, J. Kohler, R.K. Kremer, Angewandte Chemie International Edition 43 (2004) 2032. [14] L. Gao, A.L. Ji, W.B. Zhang, Z.X. Cao, Journal of Crystal Growth 321 (2011) 157. [15] A. Ji, D. Yun, L. Gao, Z.X. Cao, Physica Status Solidi A 207 (2010) 2769. [16] X.Y. Cui, J. Medvedeva, A.J. Freeman, B. Delley, N. Newman, C. Stampfl, Physical Review Letters 95 (2005) 256404. [17] U. Hahn, W. Weber, Physical Review B 53 (1996) 12684. [18] M.G. Moreno-Armenta, A. Martynez-Ruiz, N. Takeuchi, Solid State Science 6 (2004). [19] M.G. Moreno-Armenta, W.L. Peorez, N. Takeuchi, Solid State Science 9 (2007) 166. [20] M. Sieberer, S. Khmelevskyi, P. Mohn, Physical Review B 74 (2006) 014416. [21] Z.F. Hou, Solid State Science 10 (2008) 1651. [22] J.P. Perdew, K. Burke, M. Ernzerhof, Physical Review Letters 77 (1996) 3865. [23] B. Delley, Journal of Chemical Physics 113 (2000) 7756; B. Delley, Journal of Chemical Physics 92 (1990) 508. [24] K. Schwarz, P. Blaha, Computational Materials Science 28 (2003) 259. [25] F.D. Murnaghan, Proceedings of National Academy of Science USA 30 (1944) 244.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
[26] CRC Handbook of Chemistry and Physics, 85th ed., CRC Press, Cleveland, Ohio, 2004. [27] In this study, for the purpose of comparison, we only consider the dopants residing at the center location. For H : Cu3 N, however, we note that this is not the energetically favorable configuration. [28] G. Grimvall, Thermophysical Properties of Materials, Elsevier/North-Holland, Amsterdam, 1999. [29] J.M. Leger, P. Djemia, F. Ganot, J. Haines, A.S. Pereira, J.A.H. da Jomada, Applied Physics Letters 79 (2001) 2169. [30] D.M. Teter, MRS Bulletin 23 (1998) 22. [31] S.F. Pugh, Philosophical Magazine 45 (1954) 823.
3143
[32] A. Rahmati, H. Bidadi, K. Ahmadi, F. Hadian, Journal of Coatings Technology and Research 8 (2010) 289. [33] X.Y. Fan, Z.G. Wu, G.A. Zhang, C. Li, B.S. Geng, H.J. Li, P.X. Yan, Journal of Alloys and Compounds 440 (2007) 254. [34] X.Y. Fan, Z.G. Wu, H.J. Li, B.S. Geng, C. Li, P.X. Yan, Journal of Physics D: Applied Physics 40 (2007) 3430. [35] G.M. Dalpian, S.H. Wei, X.G. Gong, A.J.R. Da Silva, A. Fazzio, Solid State Communications 138 (2006) 353. [36] D.D. Sarma, P. Mahadevan, T. Saha-Dasgupta, S. Ray, A. Kumar, Physical Review Letters 85 (2000) 2549.
Contents lists available at SciVerse ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
First principles study of 3d transition metal doped Cu3 N X.Y. Cui a,b,n, A. Soon a,c, A.E. Phillips a, R.K. Zheng b, Z.W. Liu b, B. Delley d, S.P. Ringer b, C. Stampfl a a
School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia Australian Centre for Microscopy & Microanalysis, University of Sydney, Sydney, New South Wales 2006, Australia Department of Materials Science and Engineering, Yonsei University, Seoul, Republic of Korea d Paul Scherrer Institut, WHGA/123 CH-5232 Villigen PSI, Switzerland b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 March 2012 Received in revised form 8 May 2012 Available online 23 May 2012
Interstitially doped Cu3 N represents a model system to study ‘‘enclosed atoms’’ in a cuboctahedral environment. Based on density functional theory calculations using the generalized gradient approximation, we report a systematic study of 3d-transition metals (TM), as well as Li-, H-, and Pd-doped Cu3 N, whose stabilities and magnetic properties are investigated. The interposition of 3d-TM atoms leads to mechanically stable yet brittle structures, with Sc, Mn, Ni, Cu, Zn possessing relatively small positive (endothermic) formation energies ð0:12 0:54 eV=TMÞ, suggesting it may be easier to realize them experimentally than other 3d-TM elements. Li-, H-, Pd-doping in Cu3 N are exothermic, while Ti, V, Cr, Fe, and Co have higher formation energy (0.93 1.39 eV/TM) at a doping concentration 3.7 %. The fully 3d-TM doped Cu3 N systems exhibit a wide spectrum of magnetic properties, ranging from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviour. In particular, Ti : Cu3 N exhibits weak itinerant magnetic properties with a large positive magnetovolume effect. All the 3d-TM atom intercalations into cubic Cu3 N lead to a semiconductor-to-metal transition for both 100% and 3.7% doping, with the exception of Ni : Cu3 N exhibiting a weak metallic or narrow semiconducting behaviour depending on the doping concentration. & 2012 Elsevier B.V. All rights reserved.
Keywords: Density functional theory Formation energy Magnetism
1. Introduction Transition metal nitrides show a wide variety of properties and applications. Among them, copper nitrides have attracted considerable attention. Owing to its low decomposition temperature and discriminating resistivity and optical properties [1–3], the semiconductor Cu3 N is used for optical storage devices [1,3] and spintronics [4]. It can be also used as a barrier in low resistance magnetic tunnel junctions [5] and as a candidate electrode material for rechargeable Li-ion batteries [6]. Very recently, copper nitride nanocubes, which are promising for cathodic electrocatalysts in alkaline fuel cells, are synthesized using a facile one-phase process [7]. Pure Cu3 N has a rather open anti-Re3 O crystal structure [8,9], in which the copper atoms occupy the center of the cubic edges forming collinear bonds with the two nearest neighbor nitrogen atoms instead of occupying the face-centered cubic close-packed sites (see Fig. 1(a)). Naively, such a structure is expected to be suitable for the interposition of other elements. Indeed, Pd [10], Cu [11,2], Li [13] and Zn [14]
n Corresponding author at: School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia. E-mail address: [email protected] (X.Y. Cui).
0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.05.021
atoms can be inserted into the body centered position of the cubic unit cell, inducing significant changes in the optical and electronic properties. This opens a route for significant potential applications [15]. On the other hand, the dopant ions locate in an octahedral environment, with each face equivalently representing a ligand (see Fig. 1(b)). Thus, the doped Cu3 N presents an interesting model structure to study ‘‘enclosed atoms’’. For a free atom, as a consequence of Hund’s rule, electrons occupy the energy levels on an atom in a manner favoring spin-polarized configurations, and therefore usually carry a finite spin moment. These exchange split spinpolarized configurations survive in a solid only when the energy levels broaden to form non-overlapping or partially over-lapping bands. In the doped Cu3 N systems, the ‘‘enclosed dopant atoms’’ bridge the free and condensed atom situations. One would then envisage some interesting magnetic properties in doped Cu3 N. In this regard, 3d transition metal (TM) atoms present the most promising candidates. Moreover, compared to conventional 3d-TM substitutionally doped magnetic semiconductors, interstitially doping TM atoms in semiconductors presents a possible route to resolve the clustering problem of magnetic elements [16], and may open another avenue for producing potentially useful extended magnetic semiconductors. Thus, the realisation of possible magnetism, particularly ferromagnetism in Cu3 N may expand the application of this material in the field of spintronics.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
3139
Fig. 1. Structures of (a) pure, (b) doped unit cell, and (c) doped large 3 3 3 supercell, (d) supercell containing pair TM atoms for the calculation of ferromagnetic and antiferromagnetic orderings of Cu3 N. Copper and nitrogen atoms are shown as large and small (green) spheres, respectively, and the dopant atoms as large (red) spheres. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
Previous first principles studies on TM:Cu3 N (TM¼Ni, Cu, Zn, Pd, Ag, Cd, Rh, and Ru) revealed that the addition of such metal atoms modify the electronic properties of Cu3 N and turns all copper nitrides into displaying metallic behaviour [17–21]. In particular, Rh : Cu3 N was predicted to be a good candidate for exhibiting either quantum critical behaviour or itinerant electron meta-magnetism [20]. Hou [21] studied the structural stability of Cu, N and Li doped Cu3 N, and showed that while both Cu4 N and Li : Cu3 N can be stabilized thermodynamically and mechanically, cubic Cu3 N2 could not be mechanically stable. To our knowledge, a systematic study of the stability of 3d-TM doped Cu3 N is yet to be performed and the associated rich magnetic properties are largely unexplored. These forge the key motivations for this work.
2. Computational details We perform all-electron spin-polarized density functional theory (DFT) calculations using the generalized gradient approximation (GGA) [22] for the exchange correlation functional as 3 implemented in the DMol [23] code. Some results are also 3 checked using the WIEN2k code [24]. For the DMol calculations, the wave functions are expanded in terms of a double-numerical quality localized basis set with a real-space cutoff of ‘‘medium’’, namely 9:8211:5 bohr for TM atoms and 7.4 bohr for N atoms. Using the WIEN2k code, the wave functions in the interstitial region are expanded in plane waves with a cutoff of Kmax ¼9/Rmt. The charge density is Fourier expanded up to Gmax ¼17 a.u. We use muffin-tin radii of 1.7 a.u. for Cu, 1.5 a.u. for N, and 1.8 a.u. for TM atoms. Angular momenta up to l ¼10 are included. For both methods, we use 56 k-points in the irreducible part of the Brillouin zone. The equilibrium lattice constants are obtained by calculating the total energy at various volumes and then fitting the obtained curve to the Murnaghan equation of state [25]. The elastic constants cij are derived by applying a set of homogeneous deformations and calculating the second derivative of the total energy as a function of volume tetragonal and trigonal lattice distortions around the 3 equilibrium structures, as implemented in the DMol code. For a structure with cubic symmetry, there are only three unique stiffness constants: c11 ð ¼ c22 ¼ c33 ), c12 ð ¼ c13 ¼ c23 Þ, and c44 ð ¼ c55 ¼ c66 Þ. The shear modulus can be given by G ¼ 15ðc11 c12 þ 3c44 Þ:
ð1Þ
For cubic systems, the isotropic bulk modulus, B, which quantifies a material’s resistance to volume compression, is B ¼ 13ðc11 þ2c12 Þ:
ð2Þ
Using these quantities, we can then determine the isotropic Young’s modulus E¼
9BG , 3B þ G
ð3Þ
which encapsulates a material’s resistance to linear compression, and the isotropic Poisson’s ratio
n¼
3B2G : 2ð3B þ GÞ
ð4Þ
3. Results For undoped Cu3 N, the calculated equilibrium lattice constant ˚ is 3.849 A, compared with the experimental values of 3.812 A˚ [13], and 3.819 A˚ [9], and is in agreement with previous first principles calculations [17–21]. Pure Cu3 N is a semiconduc3 tor with an indirect bandgap of 0.29 eV ðDMol Þ and 0.25 eV (WIEN2k), in good agreement with other DFT studies [18,17]. These calculated bandgap values are significantly lower than the experimental ones, which range from 0.8 up to 1.9 eV, depending on the substrate and growth conditions [5]. The calculated heat 3 of formation of undoped Cu3 N is 1.30 eV ðDMol Þ and 1.23 eV (WIEN2k), which compares well to the value of 1.18 eV [21] obtained using DFT-GGA in the framework of the plane wave pseudopotential method. These values exhibit the typical overbinding characteristic of DFT-GGA, when compared to the experimental value of 0.868 eV [26]. Using the structure shown in Fig. 1(b), i.e., doping into a single unit cell of Cu3 N, the calculated lattice constants, elastic properties, and formation energies for pure and TM-doped Cu3 N are given in 3 Table 1, as calculated using the DMol code. For comparison, results of H- [27], Li- and Pd-doped Cu3 N are also listed. Interestingly, both codes consistently predict that the inclusion of a Ni atom leads to a marginal lattice compression, changing the cubic lattice constant from 3.849 A˚ to 3.839 A˚ (WIEN2k), rather than an expansion as found for all the other doped atoms, including H. Doping with Sc, the largest dopant atom studied here, leads to the ˚ most significant lattice expansion; from 3.849 A˚ to 4.077 A. With regard to the elastic constants and the shear, bulk and Young’s modulus, for the pure and Cu-doped Cu3 N, the only ones for which calculated data are available, our results are in good agreement with those reported in Ref. [21]. Elastic constants can be employed to evaluate the mechanical stability, which according to Ref. [28], should obey c11 4B 4c12 , c11 40, c44 4 0, and (c11 þ 2c12 Þ 4 0, where B is the bulk modulus. We find all the systems studied obey these requirements simultaneously, indicating all the systems should be mechanically stable. It is known that the bulk modulus does not correlate with hardness for some ionic and covalent materials and the shear modulus is a more reliable indicator of hardness [29,30]. Our data seems to support
3140
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
Table 1 Lattice constant, a0, elastic constants, shear modulus, G, bulk modulus, B, Young’s modulus, E, and formation energy, Ef of pure and, H and 3d-transition metal doped Cu3 N using the unit cell. Ef333 is the formation energy using the large 3 3 3 supercell. System
˚ a0 ðAÞ
c11
c12
c44
G (GPa)
B (GPa)
E (GPa)
B/G
Ef (eV)
Ef333 (eV)
Pure ScTiVCrMnFeCoNiCuZnHLiPd-
3.849 4.077 3.983 3.964 3.966 3.949 3.887 3.855 3.838 3.888 3.967 3.853 3.926 3.902
227.3 130.6 156.5 170.1 161.6 151.8 170.4 245.7 272.0 226.8 173.5 214.8 190.7 253.4
50.0 103.6 107.5 92.3 89.1 92.7 104.8 87.7 91.3 85.1 87.3 67.6 56.1 101.5
16.7 29.8 34.0 37.4 34.8 30.3 18.7 44.2 39.1 33.4 26.4 11.2 29.7 45.2
45.4 23.3 30.2 38.0 35.4 30.0 24.3 58.1 59.6 48.4 33.1 36.1 44.7 57.5
109.1 112.6 123.9 118.2 113.3 112.4 126.6 140.4 151.5 132.4 116.0 116.7 101.0 152.1
119.7 65.4 83.8 103.0 96.2 82.7 68.6 153.2 158.1 129.4 90.6 98.3 116.9 153.2
2.40 4.83 4.11 3.11 3.20 3.75 5.21 2.41 2.54 2.73 3.51 3.22 2.26 2.64
0.21 1.21 1.67 1.32 0.82 1.37 1.32 0.44 0.21 0.15 0.42 0.54 0.77
0.22 1.16 1.39 0.93 0.54 0.98 0.93 0.52 0.16 0.20 0.38 0.51 0.72
Table 2 Electron density of states at the Fermi energy, NðEF Þ, magnetic moments (MM) at the doped atoms using the unit cells and the large 3 3 3 supercell, energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) states, DEFMAFM , and the ground magnetic states of H and 3d-TM doped Cu3 N systems.
NðEF Þ (states/eV) MM ðmB Þ MM333 ðmB Þ DEAFMFM (eV) Ground state
H-
Sc-
Ti-
V-
Cr-
Mn-
Fe-
Co-
Ni-
Cu-
Zn-
1.46 0.38 0.32 0.018 AFM
5.16 0.0013 0 0.001 AFM
3.73 0.43 0.38 0.098 AFM
4.69 3.23 3.41 0.44 AFM
2.62 4.42 4.52 0.18 AFM
3.70 4.19 4.12 0.16 FM
5.11 2.92 2.78 0.19 FM
3.72 1.56 1.52 0.051 FM
0.82 – – – –
1.96 – – – –
2.39 – – – –
such a conclusion as these two modulus quantities show a different variation behaviour: only Co-, Ni-, Cu-, and Pd-doped Cu3 N possess larger values for both bulk modulus and shear modulus than those of pure Cu3 N, and only Li:Cu3 N has a smaller values for both quantities. All the other systems exhibit a smaller shear modulus and a larger bulk modulus compared to the pure Cu3 N. The value of B/G ratio for cubic Cu3 N is 2.40, which can be compared to 2.458 as obtained in Ref. [21] by the pseudopotential plane wave method. Except for the Li-doped case, the inclusion of dopants in Cu3 N leads to larger B/G values than pure Cu3 N. All the B=G values are larger than the critical value (1.75) separating ductile and brittle materials [31], indicating that pure and 3d-TM doped Cu3 N can be categorised as being brittle materials. We assume metal-rich growth conditions; i.e., the atom added to the host Cu3 N comes from the corresponding bulk reservoir; thus the formation energies of TM : Cu3 N systems are calculated TM:Cu3 N Cu3 N TM:Cu3 N Cu3 N as Ef ¼ Etot Etot ETM , Etot and ETM tot are the tot , where Etot total energies of TM : Cu3 N, Cu3 N and the ground state of the bulk TM metal, respectively. Our calculated formation energies for Cu- and Li-doped Cu3 N are 0.21 eV and 0.54 eV, respectively, which can be compared to 0.33 eV and 0.51 eV as obtained in Ref. [21]. Negative formation energies are obtained for Li- ( 0.54 eV), Pd- ( 0.77 eV) and H-doped (0.42 eV) Cu3 N, indicating it is thermodynamically favourable for the doped compounds to form, as have been realised in experiments for Pd [10], H [12] and Li [13]. Small positive (endothemic) formation energies are predicted for Sc- (0.21 eV), Ni- (0.44 eV) and Cu- (0.21 eV), and Zn- (0.15 eV), indicating it should be relatively easier for these materials to be synthesized experimentally compared to the other 3d-TM doped cases. Indeed, the interposition of Cu atoms in Cu3 N has been reported in experiments [2,11], and recently, Zn atoms have been doped into the centres of Cu3 N cells, resulting in a stoichiometry of Cu3 NZn0:231 [14,15]. By contrast, doping Ti atoms in Cu3 N by cylindrical magnetron sputtering method did not result in insertion
into the body centred position of the lattice [32], but rather segregated to the grain boundaries [33,34]. The large formation energy, 1.21 eV per Ti atom, explains such a challenge. Our results further indicate that in order to insert 3d-TM atoms such as Ti, V, Cr, Fe, Co atoms into the body-center-position of Cu3 N, delicate nonequilibrium growth methods will be required. Spin-polarised calculations show that H-, V-, Cr-, Mn-, Fe- and Co-doped Cu3 N are magnetic; and that Ni-, Cu- and Zn-doped Cu3 N are non-magnetic (see Table 2). For the Sc-doped case, it is predicted to be virtually non-magnetic using unit cell, with the atomic moment being 0:0013mB and the total moment 0:011mB (by WIEN2k), and being non-magnetic using the large 3 3 3 supercell. For magnetic systems, in order to study the magnetic stability, we have performed fixed spin moment calculations, namely calculation of the total energy as a function of the total magnetic moment per cell at the equilibrium lattice constants, as [20]. The results for selected systems are shown in Fig. 2, where H-, and Co-doped Cu3 N are typical magnetic systems, with a moment of 1:0mB and 1:28mB per formula cell, respectively. Ni : Cu3 N exhibits typical non-magnetic behaviour. These results are also confirmed using the 3 3 3 supercell. The most interesting system is Ti : Cu3 N, which is predicted to be magnetic with a total moment 0:52mB per cell, with 0:43mB residing at the Ti atom at the equilibrium structure. The very flat total energy variation with total magnetic moment shows a typical weak itinerant magnetic behaviour, as found in RhCu3 N [20]. Also interestingly, still for Ti : Cu3 N, it exhibits a strong large magnetovolume effect (MVE), in which the magnetic moment sensitively responds to the volume change around the vicinity of the equilibrium geometry, as shown in Fig. 3. This behaviour implies that the magnetic properties of Ti : Cu3 N might also sensitively respond to temperature and pressure. For Fe : Cu3 N, it can be seen from Fig. 3, that it shows a typical MVE, while for Ni : Cu3 N, the non-magnetism is robust against volume change.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
300
Energy (meV)
250 200 150 100 CoHNiTi-
50 0 -50 0
0.5
1
1.5
2
2.5
Total Magnetic Moment (µB)
Total magnetic moment (µB)
Fig. 2. Fixed spin moment calculations of the total energy for H-, Co-, Ni- and Ti-doped Cu3 N. For each case, the energies are given relative to the ground state. Co- and H-doped systems show a typical magnetic behaviour. Ni : Cu3 N is a nonmagnetic system. Ti : Cu3 N is predicted to be a weak itinerant magnetic system.
4 3 FeNiTi-
2 1 0 -1
3.6
3.8 4 Lattice constants (Å)
4.2
Fig. 3. Dependence of the total magnetic moment on the lattice constants for Ni-, Fe- and Ti-doped Cu3 N. Ti : Cu3 N exhibits a strong magnetovolume effect. The arrows indicate the equilibrium volumes.
To investigate a lower doping concentration, and to simulate the isolated ‘‘enclosed atoms’’, a supercell of 108 atom (3a0 3a0 3a0) is employed, where a0 is the lattice constant of the host Cu3 N, see Fig. 1(c). We allow full atomic relaxation. The calculated formation energy values are compared with those obtained using the small unit cell. While the general conclusion regarding the systems will small formation values are consistent, the variation of these two sets of values are clearly system-dependent; with the largest derivation being for Fe- and Co-doped Cu3 N. These results strongly indicate that there are appreciable, and for some systems, strong interaction between the neighbouring dopants in the unit cell. The sizably smaller values of formation energy in larger supercell (i.e., lower doping concentration) also indicate the repulsive interaction between the dopants. Indeed, adding two Fe atom in the ˚ and a 3 3 3 supercell, with a ‘‘near’’ (Fe–Fe distance of 3.854 A) ˚ configurations, the non-spin-polarised calculations ‘‘far’’ (6.675 A) (spin-polarised calculations encountered convergence difficulty) show that the ‘‘far’’ structure is energetically more favourable, by 0.113 eV. These results suggest that some 3d-TM interstitial doped Cu3 N systems are expected to fundamentally overcome the clustering problem. To investigate the magnetic interaction between the neighbouring dopants, i.e., ferromagnetic versus antiferromagnetic couplings, we used a model whose lattice vectors are (0, a, a), (a, 0, a), and (a, a, 0), where a is the optimized TM:Cu3 N lattice constants, as shown in Fig. 1(d). The main magnetic results are tabulated in Table 2. It can be seen that the 3d-TM doped Cu3 N
3141
systems exhibit a wide spectrum of magnetic properties, changing from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviours. Such interesting magnetic properties result from the manifestation of the enclosed dopant atoms and their interaction with the host Cu3 N. Mulliken population analysis (not shown) reveals the clear occurrence of charge transfer within the TM atom, and between the TM atom and the Cu3 N host. Within the 3d-TM dopants, from Sc to Ni, electrons transfer from 4s to 3d; for Cu and Zn, from 4s to 4p. Specifically, for Ni : Cu3 N, charge transfer leads to a fully occupied Ni-3d10 orbital, preventing net spin moment from leading to magnetism. This behaviour is robust against volume change. Similarly, the full 3d orbital occupation in Cu and Zn atoms explains the non-magnetism in Cu- and Zn-doped Cu3 N. By contrast, for Ti : Cu3 N, the spin-resolved 3d occupation changes evidently responding to the volume variation. For the electron transfer between TM atom and Cu3 N host, the charge redistribution occurs via orbital hybridization between TM-3d with Cu-3d and 4p, and N-2p. This can be seen from the total and TM partial density of states (DOS) as shown in Fig. 4. The 3d electrons in TM atoms play a dominant role for the metallicity as well as the magnetic properties. For all the 3d-doped Cu3 N systems, using the unit cell, the total DOS show metallic behaviour, indicating that 3d-TM atom intercalations into cubic Cu3 N all lead to a semiconductor-to-metal transition, with Ni : Cu3 N being predicted to be of weak conductivity (0.85 states/eV, see Table 2). The lower concentration Ni doped Cu3 N in the large 3 3 3 supercell actually shows a semiconducting behaviour, i.e., with a narrow band gap of 0.16 eV. For other 3d TM doped systems, the metallic behaviour is predicted to be robust to doping concentration. Experimentally, the implantation of hydrogen [12] and zinc [14] (here increasing the zinc concentration from 0 to 5.44 at.%) leads the electrical conductivity to be increased by more than two and three orders of magnitude at room temperature, compared well with our findings. Based on a band coupling model [35], for a given doped system, the magnetic ordering is determined by the p–d coupling and the d–d coupling. The dopant ions locate in an octahedral environment (with each face equivalently representing a ligand) (see Fig. 1(b)). The octahedral crystal field of the surrounding TM ligands splits the fivefold degenerate d states of the free TM ion into three low-lying t2g (dxy, dyz and dzx) and two high-lying eg (dz2 and dx2 y2 ) subsets. The final electronic configuration, a manifestation of DOS, is a delicate competition between crystal field splitting energy Dex and the exchange splitting energy DCF between the majority and minority electrons on the TM atoms. Increasing the 3d atomic number from Sc to Zn results in the Fermi level shifting higher in energy. From Sr to Cr, the increase of the occupation number will enhance the d–d super-exchange interactions, which leads to stronger antiferromagnetic ordering. For Fe (d8) and Co (d9) ions, there are two and one hole, respectively. The so-called ‘‘p–d hopping interaction’’ model [36], can stabilize ferromagetnic states, with the case of Fe : Cu3 N being stronger.
4. Summary Based on DFT calculations, we have systematically studied the equilibrium lattice constants, elastic constants, mechanical properties, formation energies, and magnetic properties of all the 3d-TM doped Cu3 N systems at doping concentrations of 100% and 3.7%. The interposition of a 3d-TM atom lead to a mechanically stable, yet brittle structure. For H-, Li- and Pd-doped, the calculated formation energies are negative; Sc-, Mn-, Ni-, Cu- and Zn- doped Cu3 N possess relatively small positive (endothermic) formation
3142
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
Sc
2
Ti
10 0 -10 10
0
0
-2
-10
TM−PDOS
DoS [1/eV]
2 1 0 -1 -2
DOS
DoS [1/eV]
DoS [1/eV]
DoS [1/eV]
TM−PDOS
10
Fe 10
5 0
0
-5
-10 Co
10 5 0 -5 -10
Ni
10 5 0 -5 -10
5 0
6 4 2 0 -2
8 Mn 6 4 2 0 -2 -4 -10 -5
10 5 0 -5 -10
Cr
10 0 -10 5 EF Energy [eV]
-10
-5
5 EF Energy [eV]
0 -5
10
DoS [1/eV]
DoS [1/eV]
-2
5
-10
DoS [1/eV]
0
DoS [1/eV]
10 5 0 -5 -10
V
DoS [1/eV]
DoS [1/eV]
-5 2
DOS
20 10 0 -10 -20
20 10 0 -10 -20
Cu
0
-10
Zn
20 0 -20 -5
EF 5 Energy [eV]
-10
-5
EF 5 Energy [eV]
Fig. 4. Partial density of states (PDOS) of TM atoms and total density of states for 3d-TM doped Cu3 N. In the TM-PDOS, blue represents the s orbital, green the p orbital, and grey the d orbital. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
energies. Introducing Ti, V, Cr, Fe and Co is predicted to be nontrivial due to their large positive formation energies, and would require careful nonequilibrium growth methods. Quite unexpectedly, inserting Ni to Cu3 N, which is non-magnetic, results in a decrease of the lattice constant. The 3d-TM doped Cu3 N systems exhibit a wide spectrum of magnetic properties, changing from weak antiferromagnetic (Sc-), antiferromagnetic (Ti-, V-, Cr-) to ferromagnetic (Mn-, Fe-, Co-) and non-magnetic (Ni-, Cu-, Zn-) behaviours. In particular, Ti : Cu3 N exhibits weak itinerant magnetic properties with a large positive magnetovolume effect. All the 3d-TM atom intercalations into cubic Cu3 N lead to a semiconductor-to-metal transition for both 100% and 3.7% doping, with the exception of Ni : Cu3 N exhibiting a weak metallic or narrow semiconducting behaviour depending on the doping concentration.
Acknowledgements We acknowledge the computing resources provided by the National Computational Infrastructure (Australia) and support from the Australian Research Council. References [1] M. Asano, K. Umeda, A. Tasaki, Japanese Journal of Applied Physics 29 (1990) 1985. [2] T. Maruyama, T. Morishita, Journal of Applied Physics 78 (1995) 4104.
[3] T. Maruyama, T. Morishita, Applied Physics Letters 69 (1996) 890. [4] C. Navio, J. Alvarez, M.J. Capitan, J. Camarero, R. Miranda, Applied Physics Letters 94 (2009) 263112. [5] D.M. Borsa, S. Grachev, C. Presura, D.O. Boerma, Applied Physics Letters 80 (2002) 1823. [6] N. Pereira, L. Dupont, J.M. Tarascon, L.C. Klein, G.G. Amatucci, Journal of Electrochemical Society 150 (2003) A1273. [7] H. Wu, W. Chen, Journal of the American Chemical Society 133 (2011) 15236. ¨ Anorganische und Allgemeine Chemie 241 [8] R. Juza, H. Hahn, Zeitschrift fur (1939) 172. [9] U. Zachwieja, H. Jacobs, Journal of Less-Common Metals 161 (1990) 175. [10] U. Zachwieja, H. Jacobs, Journal of Less-Common Metals 170 (1991) 185. [11] J. Blucher, K. Bang, B.C. Giessen, Materials Science and Engineering A 117 (1989) L1. [12] Y. Hayashi, T. Ishikawa, D. Shimokawa, Journal of Alloys Compounds 330–332 (2002) 348. [13] F. Gulo, A. Simon, J. Kohler, R.K. Kremer, Angewandte Chemie International Edition 43 (2004) 2032. [14] L. Gao, A.L. Ji, W.B. Zhang, Z.X. Cao, Journal of Crystal Growth 321 (2011) 157. [15] A. Ji, D. Yun, L. Gao, Z.X. Cao, Physica Status Solidi A 207 (2010) 2769. [16] X.Y. Cui, J. Medvedeva, A.J. Freeman, B. Delley, N. Newman, C. Stampfl, Physical Review Letters 95 (2005) 256404. [17] U. Hahn, W. Weber, Physical Review B 53 (1996) 12684. [18] M.G. Moreno-Armenta, A. Martynez-Ruiz, N. Takeuchi, Solid State Science 6 (2004). [19] M.G. Moreno-Armenta, W.L. Peorez, N. Takeuchi, Solid State Science 9 (2007) 166. [20] M. Sieberer, S. Khmelevskyi, P. Mohn, Physical Review B 74 (2006) 014416. [21] Z.F. Hou, Solid State Science 10 (2008) 1651. [22] J.P. Perdew, K. Burke, M. Ernzerhof, Physical Review Letters 77 (1996) 3865. [23] B. Delley, Journal of Chemical Physics 113 (2000) 7756; B. Delley, Journal of Chemical Physics 92 (1990) 508. [24] K. Schwarz, P. Blaha, Computational Materials Science 28 (2003) 259. [25] F.D. Murnaghan, Proceedings of National Academy of Science USA 30 (1944) 244.
X.Y. Cui et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3138–3143
[26] CRC Handbook of Chemistry and Physics, 85th ed., CRC Press, Cleveland, Ohio, 2004. [27] In this study, for the purpose of comparison, we only consider the dopants residing at the center location. For H : Cu3 N, however, we note that this is not the energetically favorable configuration. [28] G. Grimvall, Thermophysical Properties of Materials, Elsevier/North-Holland, Amsterdam, 1999. [29] J.M. Leger, P. Djemia, F. Ganot, J. Haines, A.S. Pereira, J.A.H. da Jomada, Applied Physics Letters 79 (2001) 2169. [30] D.M. Teter, MRS Bulletin 23 (1998) 22. [31] S.F. Pugh, Philosophical Magazine 45 (1954) 823.
3143
[32] A. Rahmati, H. Bidadi, K. Ahmadi, F. Hadian, Journal of Coatings Technology and Research 8 (2010) 289. [33] X.Y. Fan, Z.G. Wu, G.A. Zhang, C. Li, B.S. Geng, H.J. Li, P.X. Yan, Journal of Alloys and Compounds 440 (2007) 254. [34] X.Y. Fan, Z.G. Wu, H.J. Li, B.S. Geng, C. Li, P.X. Yan, Journal of Physics D: Applied Physics 40 (2007) 3430. [35] G.M. Dalpian, S.H. Wei, X.G. Gong, A.J.R. Da Silva, A. Fazzio, Solid State Communications 138 (2006) 353. [36] D.D. Sarma, P. Mahadevan, T. Saha-Dasgupta, S. Ray, A. Kumar, Physical Review Letters 85 (2000) 2549.