Role of anion doping on electronic structure and magnetism of GdN by first principles calculations

Abstract

We have investigated the electronic structure and magnetism of anion doped GdN_1−yX_y (X = B, C, O, F, P, S and As) systems by first-principles calculations based on density functional theory. GdN_1−yX_y systems doped by O, C, F, P, and S atoms are more stable than those doped by B and As atoms because of relatively high binding energies. The anion doping and the N defect states modify the density of states at the Fermi level, resulting in a decrease in spin polarization and a slight increase in the magnetic moment at the Gd and N sites.

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1. Introduction

Rare-earth nitrides (ReN) exhibit very interesting magnetic, electronic and optical properties, despite their common and simple lattice structure, the face-centered cubic structure of sodium chloride. The highly localized 4f states determine the magnetic properties while the electronic properties are determined principally by the itinerant s–d electrons.¹ GdN is a more popular material compared to the other Gd pnictides or rare-earth nitrides, but the nature of its magnetism and electronic structure are still under debate.^2,3 A clear-cut picture did not emerge from a series of studies by Kaldis and co-workers in the 1970s and 1980s.^4–6 They pointed out that the specific resistivity decreased with an increase in temperature, suggesting that GdN is semiconducting.⁴ Their later experiments on high quality samples showed a very large carrier density of 1.9 × 10²³ cm⁻³, revealing the possibility of a semimetal matherial.⁶ Room-temperature resistivity of GdN covers a wide range from 10⁻⁴ Ω cm for epitaxial films^7–9 to 1 Ω cm for polycrystalline films.^10,11 It is difficult to prepare fully stoichiometric GdN without N vacancies and rare-earth nitrides have a strong propensity to oxidize in the presence of water vapor in the atmosphere. Theoretically, the band structure and optical response functions of GdN were investigated by Lambrecht¹² using the linear muffin-tin orbital (LMTO) method taking into account quasiparticle corrections using a simplified GW approximation, showing that GdN is an indirect narrow gap semiconductor. Aerts et al.,¹³ using density functional theory in the local-spin-density approximation (LSDA) with a self-interaction correction, found that exchange splitting of the predominantly Gd s–d-like and N p-like conduction band states cause GdN to be half-metallic, meaning that the electrons at the Fermi level only have one spin direction. Such materials are of particular interest in the field of spintronic devices. Duan et al.¹⁴ investigated the electronic structure and magnetism of GdN as a function of unit cell volume using the LSDA + U method. They observed a transformation in the conduction properties associated with an increase in lattice volume: first from half-metallic to semimetallic, then ultimately to semiconducting. The electronic and magnetic properties of GdN are also calculated using the LSDA + U method by Larson et al., and ferromagnetism was predicted by applying U on f and d orbitals.¹⁵ Abdelouahed et al. used the generalized gradient approximation GGA + U to calculate the magnetic anisotropy energy of bulk GdN, which agreed best with the experimental value.¹⁶

After a controversial discussion over three decades, GdN now seems to be recognized as a ferromagnet. It has a Curie temperature T_C around 60 K and a magnetic saturation moment near 7 μ_B/Gd ion that is consistent with the ⁸S_7/2 half filled 4f shell configuration of Gd³⁺ with zero orbital angular momentum.¹⁷ Recently, large optical splitting in the spin-states leading to a sharp magnetic switching, N-vacancy tuned optical and ferromagnetic properties have been observed in GdN films.^18,19 Electric-field and photo-excited control of the carrier concentration are possible in GdN.²⁰ Epitaxial ferromagnetic nanoislands of cubic GdN are fabricated in a hexagonal GaN matrix.²¹ In our previous work, a large magnetoresistance is observed in polycrystalline GdN films with different N vacancies.²² The electrical transport and magnetic properties of GdN films are significantly affected by different kinds of anion defects, such as N vacancies, oxidizations, etc. In this paper, we consider GdN as a ferromagnet. The hole or the electron carriers are introduced by N defect states and anion doping by B, C, O, F, and S atoms. The band structures and density of states were obtained by using a first-principles spin-polarized calculation. We found that a slight increase of magnetic moment and the loss of half-metal properties of GdN_1−yX_y systems with X = B, C, O, F, P, S, and As.

2. Calculation details and model

The calculation is performed using the PAW (projector-augmented wave) method implemented in VASP (Vienna ab initio simulation package) code²³ and the GGA (generalized gradient approximation) PBE (Perdew–Burke–Ernzerhof) function²⁴ with the DFT (density functional theory) + U (ref. 25) technique on the f orbitals of Gd. We used a Hubbard U = 6.7 eV and an exchange J = 0.7 eV for Gd compounds in the GGA + U scheme.^14,26–28 In order to find the theoretical equilibrium static geometries for all the cases, a Γ-centered 6 × 6 × 6 k mesh together with an energy cutoff of 600 eV was used in the geometry optimization process and static calculations. The convergence criteria for total energy were 10⁻⁵ eV. All of the atoms were relaxed using a conjugated gradient method until the Hellmann–Feynmann forces on each atom were reduced to less than 0.01 eV Å⁻¹.

GdN has a rock salt structure at ambient conditions. The structural optimization is performed using an experimental lattice constant of a = 4.97 Å as a starting point.⁸ Subsequently, the ionic positions and the cell volume are fully relaxed to ensure that the output structure is convincing. The theoretically calculated equilibrium lattice parameter is a = 5.00 Å, which agrees well with the experimental value. The original unit cell of eight atoms is extended to three supercells with 16, 32 and 64 atoms in each of these supercells one N atom is removed or replaced by an X atom, an example is shown in Fig. 1, resulting in impurity concentrations of y = 0.12, 0.06 and 0.03, respectively.

Fig. 1 Schematic diagram of the calculated supercell, where the blue balls are N, the cyan ones are Gd, and the red, yellow and magenta ones are nitrogen vacancies or impurity atoms.

3. Results and discussion

The optimized lattice constants are shown in Table 1. Comparing with pure GdN, the lattice constants of GdN_1−yX_y (y = 0.03, 0.06 and 0.12) are slightly higher for B, C, P, As, and S doping, but are slightly lower for O and F doping, which can be attributed to the variations in covalent radii of X relative to N. To check the stability of different dopants, we have calculated the binding energies as summarized in Fig. 2. The binding energy is defined as E_b = E_ν − E_d + μ, where E_ν is the energy of a relaxed GdN with one N vacancy, E_d is the energy of a relaxed GdN with one N atom replaced by the X and μ is the energy of the doped atom.^29,30 The value of E_b for different dopants varies from 4.4 to 10.9 eV. N self-substitution yields the binding energy of one N atom, which is 10.7 eV. In Fig. 2, one can see that the substitutional doping with O atoms is stable. The binding energy of C and F atoms is 7.5 eV, which is smaller than for an O atom. However, doping of B and As atoms in GdN is difficult because of the low binding energies.

Table 1 The geometric optimized lattice constants for X-doped GdN systems (X = B, C, O, F, P, S and As)

System	Lattice constant (Å)			Angle (°)
	a	b	c	α	β	γ
Gd32N32	5.004	5.004	5.004	90	90	90
Gd32N31B1	5.014	5.014	5.014	90	90	90
Gd32N31C1	5.008	5.008	5.008	90	90	90
Gd32N31O1	5.000	5.000	5.000	90	90	90
Gd32N31F1	5.000	5.000	5.000	90	90	90
Gd32N31P1	5.031	5.031	5.031	90	90	90
Gd32N31S1	5.025	5.025	5.025	90	90	90
Gd32N31As1	5.037	5.037	5.037	90	90	90

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Fig. 2 Binding energies of cubic GdN doped by anion X (X = B, C, O, F, P, S and As).

Table 2 summarizes the atomic magnetic moment in GdN_0.97X_0.03. Magnetism of GdN_0.97X_0.03 is determined by the large spin magnetic moment of the highly localized 4f electron states. It is found that the calculated magnetic moment of each Gd atom is slightly larger than the 4f value of 7 μ_B in undoped GdN, suggesting that the Gd 5d moment is parallel to the 4f moment. This arises from the spin splitting of the d orbital by f–d coupling.³ From Table 2, the magnetic moment of Gd f almost remains unchanged in all of the doped systems, but the magnetic moment of Gd d increases slightly. For electron doped cases, such as O, F, S impurities and N defect states, the Fermi level will move upward compared with that of the undoped system. Therefore, the unoccupied spin-up states of Gd 5d increases slightly, while the change of the density of the spin-down states is not obvious, which results in the slight increase in the magnetic moment for Gd 5d. At y = 0.12 and 0.06, the magnetic moment of Gd 5d is larger than that of y = 0.03 due to the increase in free charge carrier density. For hole-doped systems, the Fermi level will move to the opposite direction compared with electron doped systems. Moreover, the hybridization effect of Gd 5d with X 2p in the vicinity of the Fermi level in the minority spin channel also leads to a slight increase in the magnetic moment for Gd 5d. For P and As impurities, the magnetic moment of Gd remains almost unchanged, because P and As are isovalent to N and no redundant free carriers were introduced.

Table 2 The average magnetic moment of the N and Gd atoms in GdN_0.97X_0.03, the magnetic moment of the X site and one of the Gd sites at the nearest X and the magnetic moment of a Gd_nea df-orbital

System	Site
	Nav	X	Gdav	Gdnea	Gd d	Gd f
GdN	−0.116	—	7.051	7.051	0.097	6.946
GdN0.97□0.03	−0.109	—	7.082	7.110	0.138	6.950
GdN0.97B0.03	−0.102	0.595	7.077	7.150	0.172	6.957
GdN0.97C0.03	−0.112	0.053	7.054	7.059	0.102	6.948
GdN0.97O0.03	−0.111	−0.067	7.062	7.058	0.102	6.948
GdN0.97F0.03	−0.108	−0.019	7.069	7.068	0.111	6.948
GdN0.97P0.03	−0.116	−0.078	7.051	7.049	0.097	6.944
GdN0.97As0.03	−0.115	−0.079	7.052	7.050	0.098	6.944
GdN0.97S0.03	−0.111	−0.053	7.062	7.057	0.102	6.947

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The total density of states (TDOS) and partial density of states (PDOS) of cubic ferromagnetic GdN_0.97X_0.03 (X = C, O and P) are obtained for the GGA + U calculations in Fig. 3. We discuss in detail results for C, O and P doping, since the other anions present similar electronic structures. Fig. 3(a) shows that the half-metallic behavior of the ground state in pure GdN, which acts as a conductor to electrons in the majority spin states but as an insulator for spin minority states, with a gap of 0.6 eV. Our GGA + U calculation gives the unoccupied 4f states 5 eV above E_f and occupied 4f states 6 eV below, which qualitatively is in good agreement with the experimental results.³¹ The majority 4f electrons create an exchange field that leads to spin splitting of the N p band. Furthermore, there is visible Gd d-N sp as well as Gd 4f-N p hybridization in the occupied part of the GdN valence band. One of the consequences is that the N anion should carry a magnetic moment, as given in Table 2. The minority f states are above the E_f hybrid with Gd 5d and N 2p states. From the TDOS of GdN_0.97X_0.03 (shown in Fig. 3(b)–(d)) it is obvious that the spin polarization of GdN_0.97X_0.03 decreases compared with pure GdN. The magnetic moment of C is 0.053 μ_B in the GdN_0.97C_0.03 system (see Table 2), which arises clearly from the spin splitting of C sp by the exchange field coming from the neighboring Gd atoms. However, in GdN_0.88C_0.12, the magnetic moment of C increases to 0.106 μ_B followed by the Fermi level moving. The calculation gives a magnetic moment of 0.595 μ_B on the B in GdN_0.97B_0.03 (see Table 2). In Fig. 3(b), C 2p states and Gd 5d states dominate the DOS of the minority spin channel at the Fermi level, indicating the presence of hybridization between the Gd and C atoms. The hybridization results in a sharp decrease of spin polarization from 100% to 0. Herewith, the spin polarization is defined as P = (N_↑ − N_↓)/(N_↑ + N_↓), where N_↑(↓) is the density of electronic states at the Fermi level. In view of the DOS in Fig. 3(c), the spin polarization of GdN_0.97O_0.03 decreases to 66%, because the Fermi level moves upward and a small minority of the spin density of states of Gd 5d exist at the Fermi level. In GdN_0.94O_0.06 and GdN_0.88O_0.12 systems, the spin polarization becomes 46% and 51%. Due to the increase of the P radius relative to N, a small minority of the spin density of states of P 2p exist at the Fermi level (Fig. 3(d)), resulting in the decrease of spin polarization to 35%. At y = 0.06 and 0.12, the GdN_1−yP_y systems have spin polarizations of 30%.

Fig. 3 The total density of states (TDOS) and the partial density of states (PDOS) of (a) pure GdN, (b) GdN_0.97C_0.03, (c) GdN_0.97O_0.03 and (d) GdN_0.97P_0.03. The insert in the first panel represents the zoom of the TDOS near the Fermi energy.

Fig. 4 shows the calculated electronic band structure of GdN_0.88X_0.12 (X = C, O, and P). The Fermi level was set to 0 eV on the energy axis. The blue lines refer to the majority spin states, while the red ones refer to the minority spin states. After introducing C, O and P into GdN, the band gap in the minority spin states decreases. It can be seen from Fig. 4(a) that the pure GdN is half-metallic, with a gap of 0.6 eV in the minority spin states, which is similar to the calculated value of 0.6 eV using the LSDA + U method.¹⁴ In Fig. 4(b), we find that the impurity bands from C 2p states appear in the spin minority band gap of GdN, leading to a decrease in spin polarization to 0%. In Fig. 4(c), the Fermi level moves upward into the conduction band, resulting in the electrons at the Fermi level having the minority spin direction for GdN_0.88O_0.12 and a decrease in spin polarization, which should be the reason for the experimental difference concerning the carrier density and ferromagnetic exchange mechanism of GdN due to the exposure of the sample in air. Fig. 4(d) represents the band structure of GdN_0.88P_0.12. With the introduction of a heavier anion, GdN_0.88P_0.12 becomes metallic in either a majority or minority spin state, because of the increase of the anion radius and the overlap of the conduction band and the valence band.

Fig. 4 The calculated electronic band structure of (a) pure GdN, (b) GdN_0.88C_0.12, (c) GdN_0.88O_0.12 and (d) GdN_0.88P_0.12.

4. Conclusion

We found that anion doping of O, C, F, P and S atoms in GdN are energetically favorable relative to B and As doping. The spin polarization decreases due to the N defect states and introduction of O, C, F, S, P into GdN systems. The analysis of TDOS and PDOS of cubic ferromagnetic anion doped GdN indicates that the magnetic moments of N and Gd sites slightly increase, except for P and As doped systems, but the half-metallic character disappears. Because of the narrow band gap of the minority spin, the magnetism of GdN is very sensitive to the doping.

Acknowledgements

This work was supported by the National Natural Foundation of China (51172126), Key Project of Natural Foundation of Tianjin City (12JCZDJC27100), Program for New Century Excellent Talents in University (NCET-13-0409) and Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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