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Effects of S and N doping on the structural, magnetic and electronic properties of rutile CrO2
Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
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Effects of S and N doping on the structural, magnetic and electronic properties of rutile CrO2 You Xie a,b,n, An-Ning Zhou b, Kai-Gang Sun a, Ya-Ting Zhang b, Yi-Ping Huo c, Su-Fang Wang a, Jian-Min Zhang c a
College of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China College of Chemistry & Chemical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China c College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 11 April 2015 Received in revised form 2 November 2015 Accepted 21 December 2015 Available online 23 December 2015
Magnetic and electronic properties of S- and N-doped CrO2 are studied by using the first-principle projector augmented wave potential within the generalized gradient approximation. The optimized lattice constants for CrO2 agree well with the previous work. With increasing S doping (N doping), the lattice constants of CrO2 xSx (CrO2 xNx) (x ¼ 0.5, 1 and 1.5) all increase (decrease), While these compounds remain the tetragonal structure. CrO1.5S0.5, CrO1.5N0.5 and CrON compounds remain the halfmetallicity, while the band gap is determined by different factors. It is also found that the change of the total magnetic moment with equivalent atom S doping in CrO2 compound is small except for x ¼1. & 2015 Elsevier B.V. All rights reserved.
Keywords: CrO2 Half-metallic Magnetic properties First-principle
1. Introduction Increased interest in the field of magnetoelectronics or spin electronics during the last decade has intensified research on the so-called half-metallic ferromagnetic materials [1–6], a material that is a metal for one spin channel and an insulator for the other. Their characterization has attracted great attention, since a fully spin-polarized ferromagnetic material can be very useful for fabricating spin batteries and ideal magnetic tunnel junctions used in spintronics applications [7–9]. These offer opportunities for a new generation of devices combining standard microelectronic with spin-dependent effects such as nonvolatile magnetic random access memories and magnetic sensors [10]. This in turn has lead to the study of composites of ferromagnetic and ferroelectric materials, which can exhibit properties superior to a single-phase compound [11]. A potential candidate for spintronic applications is CrO2, which is a well established half-metallic ferromagnet (TC 400 K) [12– 15]. Since its early discovery, several works were devoted to its physical properties [16,17]. In pure CrO2, Cr atoms appear to have a single þ4 valence state and a magnetic moment of 2 μB. However, the electronic properties of CrO2 are still not fully understood. For instance, the resistivity between 10 and 300 K is usually described n
Corresponding author. Tel.: +86 29 85583136. E-mail address: [email protected] (Y. Xie).
http://dx.doi.org/10.1016/j.jmmm.2015.12.071 0304-8853/& 2015 Elsevier B.V. All rights reserved.
in terms of an excitation gap [18,19], while a clear connection with an electronic or spin gap excitation cannot be made. Also, different results have been reported with respect to the Hall effect. Recent theoretical works suggested that self-doping generates the maxed valence state of Cr atoms and oxygen-mediated the double exchange interaction [20,21]. Insight into the electronic properties can also be obtained though doping studies. Chetry et al. investigated the electronic and magnetic structure of CrO2–RuO2 interfaces [22]. The relatively good matching between the majority of the energy bands of CrO2 and both RuO2 channels in the (100), (110), and (001) directions was found. For (100) interfaces, they find a small induced Ru moment oriented opposite to that of the Cr moments. While the large negative moment that forms when a Ru ion substitutes for a Cr ion. Williams et al. also suggested that the Cr-doped rutile-phase material remained FM and half-metallic even for high concentrations in V1 xCrxO2 [23]. Recently, Ren et al. revealed the tuning of magnetic transition and associated reversible magnetocaloric effect in CrO2 xFx by manipulating the doping levels [24]. At x ¼0.12, the magnetic transition occurs at room temperature, with magnetic-entropy changes of around 4 J kg 1 K 1 and relative cooling power of 388 J kg 1 at magneticfield changes from 0 to 50 kOe. The reversibility was verified by negligible thermal and magnetic hysteresis, as well as the positive slope at Arrott plots. Up to now, the equivalent valence atom S doping in CrO2 compound has not been reported. So, it is interesting to investigate the effects of the S doping on magnetic and electronic properties of CrO2 compound.
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In this paper, we study systematically the effects of S- and Ndoped on the structural, magnetic and electronic properties of CrO2 by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). The paper is organized as follows. In Section 2, the computational method is described. In Section 3, the optimized lattice constants, formation energy, electric structure and magnetic properties are discussed. Finally in Section 4, we summarize our results and conclusions.
2. Computational method The calculations are performed using the Vienna ab initio simulation package (VASP) based on the density function theory (DFT) [25–28]. The electron–ionic core interaction is represented by the projector augmented wave (PAW) potentials [29] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew–Burke–Ernzerhof (PBE) [30] formulation of the generalized gradient approximation (GGA). A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 10 4 eV/ion and 0.01 eV/Å, respectively. The cutoff energy for the plane-waves is chosen to be 400 eV. A 5 5 9 Monkhorst–Pack grid for k-point sampling is adopted for Brillouin zone integration, together with a Gaussian smearing broadening of 0.2 eV.
3. Results and discussions See Fig. 1(a), CrO2 has a rutile structure (P42/mnm) with 2-formula-unit supercell (2 Cr atoms and 4 O atoms). With S (N) substituting O, CrO1.5S0.5 (CrO1.5N0.5), CrOS (CrON) and CrO0.5S1.5 (CrO0.5N1.5) compounds are got. As an example, here we only show the structures of CrO1.5S0.5, CrOS and CrO0.5S1.5 in Fig. 1 (b), (c) and (d), respectively. After completely relaxing, the structures of these compounds are optimized and the lattice constants are listed in Table 1. The optimized lattice constants of a ¼b¼4.454 Å and c ¼2.923 Å for CrO2 agree well with the previous work of a¼ b¼4.421 Å and c¼ 2.916 Å, respectively [31]. With increasing S-doped, the all of the lattice constants increase. The different case occurs in CrO2 compound with N-doped, the
lattice constants of c decrease with increasing N-doped, while the volume increases. The reason may be the atomic radius of 1.48 Å for S atom is slightly larger than that of 1.40 Å and 1.46 Å for O and N atoms, but the electronegativity of 2.58 for S is smaller than that of 3.44 and 3.04 for O and N atoms, respectively. We also calculate the distance lengths between Cr and O, Cr and S, as well as the distance lengths between Cr and N atoms. It can be seen that the Cr–O bonds (dCr1–O and dCr2–O) are obviously smaller than the Cr–S bonds (dCr1–S and dCr2–S) for the S-doped CrO2. But for N doping case, the Cr–O bonds (dCr1–O and dCr2–O) are equal to the Cr–N bonds (dCr1–N and dCr2–N) except for dCr2–N in CrO0.5N1.5 compound. With increasing both S- and N-doped, the compound maintains the tetragonal structure. The stability of the defective CrO2 compound is investigated, which can be deduced from the value of the formation energy. The defect formation energy Ef is calculated by
Ef = Edef − Eid −
∑ ni μ i
(1)
Where Edef and Eid represent the total energies of the compound with and without defect, respectively. The energy difference added or removed is represented by the last term ∑ ni μi . For the case of the substituting defect, ni is the number of atom transferred ( ni ¼ þ1 for the added atom and ni ¼ 1 for the removed atom) and μi is the chemical potential of these atoms in their stable solid or gas phase. As also listed in the last column of Table 1, we can see that with increasing S doping, the formation energy of the defective CrO2 decreases. That is to say, the impurity S facilitates stabilizing the structure. The formation energies of CrOS and CrO0.5S1.5 are negative values, suggesting the possibility of spontaneous formation of these kinds of the defective compounds. The same situations occur in CrO2 xNx (x¼ 0, 0.5, 1 and 1.5) compounds. While the positive value of the formation energy for CrO1.5S0.5 implies the formation processes of this defect is endothermic. Next, we further focus our attention on the electronic structure of CrO2 xSx and CrO2 xNx (x ¼0, 0.5, 1 and 1.5) compounds. Fig. 2 shows the total density of states (DOS) of CrO2 xSx with (a) x¼ 0, (b) x ¼0.5, (c) x¼ 1 and (d) x ¼1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. From Fig. 2(a), we can see that there is a positive spin-splitting between up-spin and down-spin channels around the Fermi level EF. Especially, the up-
Fig. 1. Crystal structures of CrO2 xSx (x ¼ 0, 0.5, 1, 1.5) compounds. (a), (b), (c) and (d) represent CrO2, CrO1.5S0.5, CrOS and CrO0.5S1.5, respectively.
Y. Xie et al. / Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
255
Table 1 The calculated Lattice constants (Å) and bond lengths (Å) of CrO2 xSx (CrO2 xNx) (x ¼0, 0.5, 1, 1.5) compounds, as well as the calculated formation energy Ef (eV) of CrO2 xSx (CrO2 xNx) (x¼ 0.5, 1, 1.5) compounds. Lattice constants (Å)
CrO2 CrO1.5S0.5 CrOS CrO0.5S1.5 CrO1.5N0.5 CrON CrO0.5N1.5
Bond lengths (Å)
Ef (eV)
a
b
c
dCr1 O
dCr1 S
dCr2 O
dCr2 S
4.454 4.752 5.095 5.286 4.461 4.585 4.595
4.454 4.752 5.095 5.286 4.461 4.585 4.595
2.923 3.031 3.051 3.296 2.850 2.791 2.644
1.91 1.91 1.92 2.02 1.89 1.74 1.85
2.33 2.29 2.28 1.89 1.86 1.87
1.91 1.94 1.95 1.86 1.91 1.74 2.03
2.24 2.36 2.30 1.87 1.86 1.86
spin channel crosses the Fermi level EF, while the down-spin channel forms a band gap of 1.046 eV around the Fermi level EF, which leads to a completely spin polarization (100%) at Fermi level EF and the realistic applications for spintronic devices [7–9]. It obviously can be found that the total DOS changes with increasing S-doped. For x ¼0.5, the compound remains the half-metallicity, while the gap width decreases and the Fermi level EF is close to the valence band maximum, as well as the total DOS contracts in the down-spin channel. However, for x ¼1 and 1.5, the half-metallic character disappears. Similar to the case of S doping, the halfmetallic character of CrO2 could be destroyed with increasing N-doped. In detail, the compound remains the half-metallicity until x ¼0.5, although the gap width of CrON compound is almost equal to zero (as shows in Fig. 3). It is interesting to note that the DOS of CrO0.5N1.5 compound are symmetrical, suggesting the compound is a nonmagnetic material. The partial DOSs (PDOSs) projected on atoms in S- and Ndoped CrO2 are shown in Figs. 4 and 5, respectively. From Fig. 4(a), it obviously can be seen that the band gap of CrO2 compound is determined by the valence band maximum of O atom and the conduction band minimum of Cr atom. It also can be seen that the
0.329 0.403 1.037 0.556 0.736 0.727
electronic structures for two Cr atoms are same, implying the same atomic environment, i.e., each Cr atom is surrounded by six O atoms. Although the half-metallicity disappears, the two Cr atoms in CrOS compound also have the similar feature of the electronic structures, except for some tiny difference (shown in Fig. 4(c)). The Cr1 atom has four nearest O atoms and two nextnearest S atoms, while Cr2 atom has two nearest O atoms and four next-nearest S atoms. We can see that the different atomic environments do not affect the electronic structure of Cr atom. This can be tentatively explained as follows: S atom substituting O atom doesn't destroy the symmetrical structure. For CrO1.5S0.5 compound, we can see that the band gap is determined by the valence band maximum of S atom and the conduction band minimum of Cr2 atom. Due to the asymmetrical structure, the electronic structures of Cr1 and Cr2 in CrO1.5S0.5 are different (shown in Fig. 4(b)). It is clearly seen in Fig. 4(d) that the similar electronic structure of Cr atom also can be observed in CrO0.5S1.5 compound. From Fig. 5, it is difference occurs in the case of S doping, the band gaps are still determined by the valence band maximum of O atom and the conduction band minimum of Cr atom in CrO1.5N0.5 and CrON compounds. We also can see that the
EF
EF
up-spin down-spin
4
DOS (states/eV)
0
-4
(a) CrO2
(b) CrO1.5S0.5
(c) CrOS
(d) CrO0.5S1.5
4
0
-4
-8
-6
-4
-2
0
2
4 -8 -6 Energy (eV)
-4
-2
0
2
4
Fig. 2. Calculated the total density of states of CrO2 xSx compounds with (a) x ¼0, (b) x¼ 0.5, (c) x ¼1 and (d) x¼ 1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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EF up-spin down-spin
3
DOS (states/eV)
0 -3 (a) CrO N 1.5 0.5
EF
3 0 -3
(c) CrO0.5N1.5
(b) CrON -8
-6
-4
-2
0
2
4 6 -8 -6 Energy (eV)
-4
-2
0
2
4
6
Fig. 3. Calculated the total density of states of CrO2 xNx compounds with (a) x ¼0.5, (b) x ¼1 and (c) x¼ 1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
PDOS for each atom are almost symmetrical and across the Fermi level EF for CrO0.5N1.5 compound, that because the too small spin splitting occurs and the magnetic moment can be neglect for each atom (as list in Table 2). As elucidated above, only CrO1.5S0.5, CrO1.5N0.5 and CrON compounds still remain the half-metallicity, but the band gaps form in different factors, as shown in Figs. 4 and 5. While with further increasing the amount of S atoms, the partial DOS of S shifts to
high energy region and crosses the Fermi level EF in down spin channel, as well as the half-metallicity disappears (shown in Fig. 4 (c) and (d)). Magnetic moments vary due to the lattice constants change with the S- and N-doped CrO2. Total magnetic moment of 2 μB per formula unit for CrO2 was first predicted by Schwarz [32]. Since then, the magnetic property has been confirmed by several previous experiments and theories [25,33–36]. As listed in the last
EF
EF
2 (a) CrO 2
(b) CrO 1.5S0.5
PDOS (states/eV)
0 O Cr2
-2
O1 O2 Cr1
Cr1
S Cr2
2 (c) CrOS
(d) CrO 0.5S1.5
0 O Cr1
-2 -8
-6
-4
O S1 Cr1
S Cr2 -2
0
2
4 -8
-6
-4
S2 Cr2 -2
0
2
4
Energy (eV) Fig. 4. Partial DOS projected on atoms in CrO2 xSx (x¼ 0, 0.5, 1 and 1.5) compounds. The positive and negative values denote the up-spin and down-spin channels. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Y. Xie et al. / Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
257
EF 1
(a) CrO1.5N0.5
PDOS (states/eV)
0 Cr1 O1 O2
-1
1
Cr2 N EF
(b) CrON
(c) CrO0.5N1.5
0 Cr1 O
-1 -8
-6
-4
Cr1 O N2
Cr2 N -2
0
2
4 6 -8 -6 Energy (eV)
-4
Cr2 N1 -2
0
2
4
6
Fig. 5. Partial DOS projected on atoms in CrO2 xNx (x ¼0.5, 1 and 1.5) compounds. The positive and negative values denote the up-spin and down-spin channels. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
column of Table 2, for CrO2 compound the total magnetic moment is 1.975 μB per formula unit, which agree well with previous works [25,32–35]. It is also found that the change of the total magnetic moment with equivalent atom S doping in CrO2 compound is small except for x ¼1. The atomic magnetic moments also listed in Table 2, it can be seen that the total magnetic moment of CrO2 compound is mainly contributed by Cr atom and the magnetic moment of O atom is too small and negligible. Due to the same atomic environment, the magnetic moments of Cr1 and Cr2 atoms are nearly equal. Comparing with the CrO2 compound, the large changes of the Cr atomic magnetic moment in CrO2 xSx (x ¼0.5, 1 and 1.5) appear, except for Cr1 and Cr2 in CrOS compound, as well as Cr1 in CrO0.5S1.5 compound. This can be tentatively explained as follows: In CrOS compound, the Cr1 atom has two nearest O atoms and four next-nearest S atoms, while Cr2 atoms has four nearest O atoms and two next-nearest S atoms. As results, the electronic locality of Cr2 strengthens, while the electronic locality of Cr1 weakens; In CrO0.5S1.5 compound, the electronic locality of Cr1 becomes strong could be resulted from the bond length of Cr1–O is longer. From Table 2, we also can see that the same magnetic moment of 0.060 μB ( 0.209 μB) for O1 and O2 (S1 and S2) atoms in CrOS compound, which indicates the same atomic environment for O (S) atoms. With N doping, the total
magnetic moment decreases obviously. This is because the crystalline filed destroyed, resulting the spin splitting slightly and the electric structure of Cr atom became delocalized.
4. Conclusions The magnetic and electronic properties of S- and N-doped CrO2 have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). The following conclusions are obtained: (1) The optimized lattice constants for CrO2 agree well with the previous work. With increasing S (N)-doped, the lattice constants of CrO2 xSx (CrO2 xNx) (x¼ 0.5, 1 and 1.5) all increase (decrease), While these compounds remain the tetragonal structure. (2) The possibilities of spontaneous formation for all compounds occur except for CrO1.5S0.5. (3) CrO1.5S0.5, CrO1.5N0.5 and CrON compounds remain the halfmetallicity, while the band gap is determined by different factors. (4) For CrO2 compound the total magnetic moment is 1.975 μB per formula unit, which agrees well with previous works. It is also
Table 2 Atomic and total magnetic moment (μB) of CrO2 xSx (CrO2 xNx) (x ¼0, 0.5, 1 and 1.5) compounds.
CrO2 CrO1.5S0.5 CrOS CrO0.5S1.5 CrO1.5N0.5 CrON CrO0.5N1.5
MCr1 (μB)
MCr2 (μB)
MO1 (μB)
MO2 (μB)
MS1/N1 (μB)
2.146 2.263 1.887 2.467 1.883 1.400 0.032
2.118 2.196 2.423 2.084 1.706 1.384 0.030
0.078 0.067 0.060
0.078 0.086 0.060 0.056 0.092 0.037 0.006
0.257 0.209 0.173 0.265 0.255 0.006
0.058 0.037
MS2/N2 (μB)
0.209 0.214 0.255 0.007
Mtotal (μB) 1.975 1.980 1.885 1.970 1.540 1.105 0.000
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Y. Xie et al. / Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
found that the changes of the total magnetic moment with equivalent ion S doping in CrO2 compound are small except for x¼ 1. (5) With N doping, the total magnetic moment decreases obviously.
Acknowledgments The authors would like to acknowledge the Natural Science Basis Research Plan in Shaanxi Province of China (Program no. 2013JM8004), China Postdoctoral Science Foundation (2014M560798), National Natural Science Foundation of China (Grant No. 21276207), Shaanxi Province Postdoctoral Science Foundation (111), and Xi'an University of Science and Technology PhD Scientific Research Foundation (2013QDJ002) for providing financial support for this research.
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Effects of S and N doping on the structural, magnetic and electronic properties of rutile CrO2 You Xie a,b,n, An-Ning Zhou b, Kai-Gang Sun a, Ya-Ting Zhang b, Yi-Ping Huo c, Su-Fang Wang a, Jian-Min Zhang c a
College of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China College of Chemistry & Chemical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China c College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 11 April 2015 Received in revised form 2 November 2015 Accepted 21 December 2015 Available online 23 December 2015
Magnetic and electronic properties of S- and N-doped CrO2 are studied by using the first-principle projector augmented wave potential within the generalized gradient approximation. The optimized lattice constants for CrO2 agree well with the previous work. With increasing S doping (N doping), the lattice constants of CrO2 xSx (CrO2 xNx) (x ¼ 0.5, 1 and 1.5) all increase (decrease), While these compounds remain the tetragonal structure. CrO1.5S0.5, CrO1.5N0.5 and CrON compounds remain the halfmetallicity, while the band gap is determined by different factors. It is also found that the change of the total magnetic moment with equivalent atom S doping in CrO2 compound is small except for x ¼1. & 2015 Elsevier B.V. All rights reserved.
Keywords: CrO2 Half-metallic Magnetic properties First-principle
1. Introduction Increased interest in the field of magnetoelectronics or spin electronics during the last decade has intensified research on the so-called half-metallic ferromagnetic materials [1–6], a material that is a metal for one spin channel and an insulator for the other. Their characterization has attracted great attention, since a fully spin-polarized ferromagnetic material can be very useful for fabricating spin batteries and ideal magnetic tunnel junctions used in spintronics applications [7–9]. These offer opportunities for a new generation of devices combining standard microelectronic with spin-dependent effects such as nonvolatile magnetic random access memories and magnetic sensors [10]. This in turn has lead to the study of composites of ferromagnetic and ferroelectric materials, which can exhibit properties superior to a single-phase compound [11]. A potential candidate for spintronic applications is CrO2, which is a well established half-metallic ferromagnet (TC 400 K) [12– 15]. Since its early discovery, several works were devoted to its physical properties [16,17]. In pure CrO2, Cr atoms appear to have a single þ4 valence state and a magnetic moment of 2 μB. However, the electronic properties of CrO2 are still not fully understood. For instance, the resistivity between 10 and 300 K is usually described n
Corresponding author. Tel.: +86 29 85583136. E-mail address: [email protected] (Y. Xie).
http://dx.doi.org/10.1016/j.jmmm.2015.12.071 0304-8853/& 2015 Elsevier B.V. All rights reserved.
in terms of an excitation gap [18,19], while a clear connection with an electronic or spin gap excitation cannot be made. Also, different results have been reported with respect to the Hall effect. Recent theoretical works suggested that self-doping generates the maxed valence state of Cr atoms and oxygen-mediated the double exchange interaction [20,21]. Insight into the electronic properties can also be obtained though doping studies. Chetry et al. investigated the electronic and magnetic structure of CrO2–RuO2 interfaces [22]. The relatively good matching between the majority of the energy bands of CrO2 and both RuO2 channels in the (100), (110), and (001) directions was found. For (100) interfaces, they find a small induced Ru moment oriented opposite to that of the Cr moments. While the large negative moment that forms when a Ru ion substitutes for a Cr ion. Williams et al. also suggested that the Cr-doped rutile-phase material remained FM and half-metallic even for high concentrations in V1 xCrxO2 [23]. Recently, Ren et al. revealed the tuning of magnetic transition and associated reversible magnetocaloric effect in CrO2 xFx by manipulating the doping levels [24]. At x ¼0.12, the magnetic transition occurs at room temperature, with magnetic-entropy changes of around 4 J kg 1 K 1 and relative cooling power of 388 J kg 1 at magneticfield changes from 0 to 50 kOe. The reversibility was verified by negligible thermal and magnetic hysteresis, as well as the positive slope at Arrott plots. Up to now, the equivalent valence atom S doping in CrO2 compound has not been reported. So, it is interesting to investigate the effects of the S doping on magnetic and electronic properties of CrO2 compound.
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In this paper, we study systematically the effects of S- and Ndoped on the structural, magnetic and electronic properties of CrO2 by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). The paper is organized as follows. In Section 2, the computational method is described. In Section 3, the optimized lattice constants, formation energy, electric structure and magnetic properties are discussed. Finally in Section 4, we summarize our results and conclusions.
2. Computational method The calculations are performed using the Vienna ab initio simulation package (VASP) based on the density function theory (DFT) [25–28]. The electron–ionic core interaction is represented by the projector augmented wave (PAW) potentials [29] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew–Burke–Ernzerhof (PBE) [30] formulation of the generalized gradient approximation (GGA). A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 10 4 eV/ion and 0.01 eV/Å, respectively. The cutoff energy for the plane-waves is chosen to be 400 eV. A 5 5 9 Monkhorst–Pack grid for k-point sampling is adopted for Brillouin zone integration, together with a Gaussian smearing broadening of 0.2 eV.
3. Results and discussions See Fig. 1(a), CrO2 has a rutile structure (P42/mnm) with 2-formula-unit supercell (2 Cr atoms and 4 O atoms). With S (N) substituting O, CrO1.5S0.5 (CrO1.5N0.5), CrOS (CrON) and CrO0.5S1.5 (CrO0.5N1.5) compounds are got. As an example, here we only show the structures of CrO1.5S0.5, CrOS and CrO0.5S1.5 in Fig. 1 (b), (c) and (d), respectively. After completely relaxing, the structures of these compounds are optimized and the lattice constants are listed in Table 1. The optimized lattice constants of a ¼b¼4.454 Å and c ¼2.923 Å for CrO2 agree well with the previous work of a¼ b¼4.421 Å and c¼ 2.916 Å, respectively [31]. With increasing S-doped, the all of the lattice constants increase. The different case occurs in CrO2 compound with N-doped, the
lattice constants of c decrease with increasing N-doped, while the volume increases. The reason may be the atomic radius of 1.48 Å for S atom is slightly larger than that of 1.40 Å and 1.46 Å for O and N atoms, but the electronegativity of 2.58 for S is smaller than that of 3.44 and 3.04 for O and N atoms, respectively. We also calculate the distance lengths between Cr and O, Cr and S, as well as the distance lengths between Cr and N atoms. It can be seen that the Cr–O bonds (dCr1–O and dCr2–O) are obviously smaller than the Cr–S bonds (dCr1–S and dCr2–S) for the S-doped CrO2. But for N doping case, the Cr–O bonds (dCr1–O and dCr2–O) are equal to the Cr–N bonds (dCr1–N and dCr2–N) except for dCr2–N in CrO0.5N1.5 compound. With increasing both S- and N-doped, the compound maintains the tetragonal structure. The stability of the defective CrO2 compound is investigated, which can be deduced from the value of the formation energy. The defect formation energy Ef is calculated by
Ef = Edef − Eid −
∑ ni μ i
(1)
Where Edef and Eid represent the total energies of the compound with and without defect, respectively. The energy difference added or removed is represented by the last term ∑ ni μi . For the case of the substituting defect, ni is the number of atom transferred ( ni ¼ þ1 for the added atom and ni ¼ 1 for the removed atom) and μi is the chemical potential of these atoms in their stable solid or gas phase. As also listed in the last column of Table 1, we can see that with increasing S doping, the formation energy of the defective CrO2 decreases. That is to say, the impurity S facilitates stabilizing the structure. The formation energies of CrOS and CrO0.5S1.5 are negative values, suggesting the possibility of spontaneous formation of these kinds of the defective compounds. The same situations occur in CrO2 xNx (x¼ 0, 0.5, 1 and 1.5) compounds. While the positive value of the formation energy for CrO1.5S0.5 implies the formation processes of this defect is endothermic. Next, we further focus our attention on the electronic structure of CrO2 xSx and CrO2 xNx (x ¼0, 0.5, 1 and 1.5) compounds. Fig. 2 shows the total density of states (DOS) of CrO2 xSx with (a) x¼ 0, (b) x ¼0.5, (c) x¼ 1 and (d) x ¼1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. From Fig. 2(a), we can see that there is a positive spin-splitting between up-spin and down-spin channels around the Fermi level EF. Especially, the up-
Fig. 1. Crystal structures of CrO2 xSx (x ¼ 0, 0.5, 1, 1.5) compounds. (a), (b), (c) and (d) represent CrO2, CrO1.5S0.5, CrOS and CrO0.5S1.5, respectively.
Y. Xie et al. / Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
255
Table 1 The calculated Lattice constants (Å) and bond lengths (Å) of CrO2 xSx (CrO2 xNx) (x ¼0, 0.5, 1, 1.5) compounds, as well as the calculated formation energy Ef (eV) of CrO2 xSx (CrO2 xNx) (x¼ 0.5, 1, 1.5) compounds. Lattice constants (Å)
CrO2 CrO1.5S0.5 CrOS CrO0.5S1.5 CrO1.5N0.5 CrON CrO0.5N1.5
Bond lengths (Å)
Ef (eV)
a
b
c
dCr1 O
dCr1 S
dCr2 O
dCr2 S
4.454 4.752 5.095 5.286 4.461 4.585 4.595
4.454 4.752 5.095 5.286 4.461 4.585 4.595
2.923 3.031 3.051 3.296 2.850 2.791 2.644
1.91 1.91 1.92 2.02 1.89 1.74 1.85
2.33 2.29 2.28 1.89 1.86 1.87
1.91 1.94 1.95 1.86 1.91 1.74 2.03
2.24 2.36 2.30 1.87 1.86 1.86
spin channel crosses the Fermi level EF, while the down-spin channel forms a band gap of 1.046 eV around the Fermi level EF, which leads to a completely spin polarization (100%) at Fermi level EF and the realistic applications for spintronic devices [7–9]. It obviously can be found that the total DOS changes with increasing S-doped. For x ¼0.5, the compound remains the half-metallicity, while the gap width decreases and the Fermi level EF is close to the valence band maximum, as well as the total DOS contracts in the down-spin channel. However, for x ¼1 and 1.5, the half-metallic character disappears. Similar to the case of S doping, the halfmetallic character of CrO2 could be destroyed with increasing N-doped. In detail, the compound remains the half-metallicity until x ¼0.5, although the gap width of CrON compound is almost equal to zero (as shows in Fig. 3). It is interesting to note that the DOS of CrO0.5N1.5 compound are symmetrical, suggesting the compound is a nonmagnetic material. The partial DOSs (PDOSs) projected on atoms in S- and Ndoped CrO2 are shown in Figs. 4 and 5, respectively. From Fig. 4(a), it obviously can be seen that the band gap of CrO2 compound is determined by the valence band maximum of O atom and the conduction band minimum of Cr atom. It also can be seen that the
0.329 0.403 1.037 0.556 0.736 0.727
electronic structures for two Cr atoms are same, implying the same atomic environment, i.e., each Cr atom is surrounded by six O atoms. Although the half-metallicity disappears, the two Cr atoms in CrOS compound also have the similar feature of the electronic structures, except for some tiny difference (shown in Fig. 4(c)). The Cr1 atom has four nearest O atoms and two nextnearest S atoms, while Cr2 atom has two nearest O atoms and four next-nearest S atoms. We can see that the different atomic environments do not affect the electronic structure of Cr atom. This can be tentatively explained as follows: S atom substituting O atom doesn't destroy the symmetrical structure. For CrO1.5S0.5 compound, we can see that the band gap is determined by the valence band maximum of S atom and the conduction band minimum of Cr2 atom. Due to the asymmetrical structure, the electronic structures of Cr1 and Cr2 in CrO1.5S0.5 are different (shown in Fig. 4(b)). It is clearly seen in Fig. 4(d) that the similar electronic structure of Cr atom also can be observed in CrO0.5S1.5 compound. From Fig. 5, it is difference occurs in the case of S doping, the band gaps are still determined by the valence band maximum of O atom and the conduction band minimum of Cr atom in CrO1.5N0.5 and CrON compounds. We also can see that the
EF
EF
up-spin down-spin
4
DOS (states/eV)
0
-4
(a) CrO2
(b) CrO1.5S0.5
(c) CrOS
(d) CrO0.5S1.5
4
0
-4
-8
-6
-4
-2
0
2
4 -8 -6 Energy (eV)
-4
-2
0
2
4
Fig. 2. Calculated the total density of states of CrO2 xSx compounds with (a) x ¼0, (b) x¼ 0.5, (c) x ¼1 and (d) x¼ 1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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EF up-spin down-spin
3
DOS (states/eV)
0 -3 (a) CrO N 1.5 0.5
EF
3 0 -3
(c) CrO0.5N1.5
(b) CrON -8
-6
-4
-2
0
2
4 6 -8 -6 Energy (eV)
-4
-2
0
2
4
6
Fig. 3. Calculated the total density of states of CrO2 xNx compounds with (a) x ¼0.5, (b) x ¼1 and (c) x¼ 1.5. The black (red) line represents the up-spin (down-spin) channel. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
PDOS for each atom are almost symmetrical and across the Fermi level EF for CrO0.5N1.5 compound, that because the too small spin splitting occurs and the magnetic moment can be neglect for each atom (as list in Table 2). As elucidated above, only CrO1.5S0.5, CrO1.5N0.5 and CrON compounds still remain the half-metallicity, but the band gaps form in different factors, as shown in Figs. 4 and 5. While with further increasing the amount of S atoms, the partial DOS of S shifts to
high energy region and crosses the Fermi level EF in down spin channel, as well as the half-metallicity disappears (shown in Fig. 4 (c) and (d)). Magnetic moments vary due to the lattice constants change with the S- and N-doped CrO2. Total magnetic moment of 2 μB per formula unit for CrO2 was first predicted by Schwarz [32]. Since then, the magnetic property has been confirmed by several previous experiments and theories [25,33–36]. As listed in the last
EF
EF
2 (a) CrO 2
(b) CrO 1.5S0.5
PDOS (states/eV)
0 O Cr2
-2
O1 O2 Cr1
Cr1
S Cr2
2 (c) CrOS
(d) CrO 0.5S1.5
0 O Cr1
-2 -8
-6
-4
O S1 Cr1
S Cr2 -2
0
2
4 -8
-6
-4
S2 Cr2 -2
0
2
4
Energy (eV) Fig. 4. Partial DOS projected on atoms in CrO2 xSx (x¼ 0, 0.5, 1 and 1.5) compounds. The positive and negative values denote the up-spin and down-spin channels. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Y. Xie et al. / Journal of Magnetism and Magnetic Materials 405 (2016) 253–258
257
EF 1
(a) CrO1.5N0.5
PDOS (states/eV)
0 Cr1 O1 O2
-1
1
Cr2 N EF
(b) CrON
(c) CrO0.5N1.5
0 Cr1 O
-1 -8
-6
-4
Cr1 O N2
Cr2 N -2
0
2
4 6 -8 -6 Energy (eV)
-4
Cr2 N1 -2
0
2
4
6
Fig. 5. Partial DOS projected on atoms in CrO2 xNx (x ¼0.5, 1 and 1.5) compounds. The positive and negative values denote the up-spin and down-spin channels. The Fermi level EF is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
column of Table 2, for CrO2 compound the total magnetic moment is 1.975 μB per formula unit, which agree well with previous works [25,32–35]. It is also found that the change of the total magnetic moment with equivalent atom S doping in CrO2 compound is small except for x ¼1. The atomic magnetic moments also listed in Table 2, it can be seen that the total magnetic moment of CrO2 compound is mainly contributed by Cr atom and the magnetic moment of O atom is too small and negligible. Due to the same atomic environment, the magnetic moments of Cr1 and Cr2 atoms are nearly equal. Comparing with the CrO2 compound, the large changes of the Cr atomic magnetic moment in CrO2 xSx (x ¼0.5, 1 and 1.5) appear, except for Cr1 and Cr2 in CrOS compound, as well as Cr1 in CrO0.5S1.5 compound. This can be tentatively explained as follows: In CrOS compound, the Cr1 atom has two nearest O atoms and four next-nearest S atoms, while Cr2 atoms has four nearest O atoms and two next-nearest S atoms. As results, the electronic locality of Cr2 strengthens, while the electronic locality of Cr1 weakens; In CrO0.5S1.5 compound, the electronic locality of Cr1 becomes strong could be resulted from the bond length of Cr1–O is longer. From Table 2, we also can see that the same magnetic moment of 0.060 μB ( 0.209 μB) for O1 and O2 (S1 and S2) atoms in CrOS compound, which indicates the same atomic environment for O (S) atoms. With N doping, the total
magnetic moment decreases obviously. This is because the crystalline filed destroyed, resulting the spin splitting slightly and the electric structure of Cr atom became delocalized.
4. Conclusions The magnetic and electronic properties of S- and N-doped CrO2 have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). The following conclusions are obtained: (1) The optimized lattice constants for CrO2 agree well with the previous work. With increasing S (N)-doped, the lattice constants of CrO2 xSx (CrO2 xNx) (x¼ 0.5, 1 and 1.5) all increase (decrease), While these compounds remain the tetragonal structure. (2) The possibilities of spontaneous formation for all compounds occur except for CrO1.5S0.5. (3) CrO1.5S0.5, CrO1.5N0.5 and CrON compounds remain the halfmetallicity, while the band gap is determined by different factors. (4) For CrO2 compound the total magnetic moment is 1.975 μB per formula unit, which agrees well with previous works. It is also
Table 2 Atomic and total magnetic moment (μB) of CrO2 xSx (CrO2 xNx) (x ¼0, 0.5, 1 and 1.5) compounds.
CrO2 CrO1.5S0.5 CrOS CrO0.5S1.5 CrO1.5N0.5 CrON CrO0.5N1.5
MCr1 (μB)
MCr2 (μB)
MO1 (μB)
MO2 (μB)
MS1/N1 (μB)
2.146 2.263 1.887 2.467 1.883 1.400 0.032
2.118 2.196 2.423 2.084 1.706 1.384 0.030
0.078 0.067 0.060
0.078 0.086 0.060 0.056 0.092 0.037 0.006
0.257 0.209 0.173 0.265 0.255 0.006
0.058 0.037
MS2/N2 (μB)
0.209 0.214 0.255 0.007
Mtotal (μB) 1.975 1.980 1.885 1.970 1.540 1.105 0.000
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found that the changes of the total magnetic moment with equivalent ion S doping in CrO2 compound are small except for x¼ 1. (5) With N doping, the total magnetic moment decreases obviously.
Acknowledgments The authors would like to acknowledge the Natural Science Basis Research Plan in Shaanxi Province of China (Program no. 2013JM8004), China Postdoctoral Science Foundation (2014M560798), National Natural Science Foundation of China (Grant No. 21276207), Shaanxi Province Postdoctoral Science Foundation (111), and Xi'an University of Science and Technology PhD Scientific Research Foundation (2013QDJ002) for providing financial support for this research.
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