Half-metallicity and giant magneto-optical Kerr effect in N-doped NaTaO 3
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov Half-metallicity and giant magneto-optical Kerr effect in N-dopedNaTaO Y. Saeed , N. Singh , , and U. Schwingenschlgl Physical Science & Engineering division, KAUST,Thuwal 23955-6900, Kingdom of Saudi Arabia and Solar and Photovoltaic Energy Research Center,KAUST, Thuwal 23955-6900, Kingdom of Saudi Arabia
Abstract
We employ density functional theory using the modified Becke-Johnson (mBJ) approach toinvestigate the electronic and magneto-optical properties of N-doped NaTaO . The mBJ resultsreveal a half metallic nature of NaTaO N, in contrast to results obtained by the generalized gradientapproximation. We find a giant polar Kerr rotation of 2.16 ◦ at 725 nm wave length (visible region),which is high as compared to other half metallic perovskites as well as to the prototypical half metalPtMnSb. . INTRODUCTION Room temperature ferromagnetism has been reported for different doped oxides such asC/N-doped ZnO [1–3], TiO [4–6], SnO [7, 8] and confirmed recently [9–11]. Room tem-perature ferromagnetism with half metallicity is reported for N-doped SrTiO and BaTiO [12, 13], in which the magnetic interactions between the nearest and next-nearest N dopantsresult in a strong ferromagnetic coupling [14]. Ferromagnetic half-metals have potential ap-plications in spintronics devices [15, 16] and also show unusual magneto-optical effects dueto a metallic state for one spin channel and an insulating state for the other. Yang et al .have reported that a high concentration of N is required for achieving a magnetic long rangorder in perovskite oxide [14].The perovskite oxide NaTaO (NTO) is a ferroelectric material with high permittivityand low dielectric loss, which suggests usage in microwave devices [17–19]. Several ab-initiocalculations have been performed to described the electronic properties of bulk NTO [20] buta detailed study of the electronic structure and magneto-optical properties of N-doped NTOis missing in the literature. The magneto-optical Kerr effect of doped NTO is interesting formagneto-optical reading and recording devices [21]. The N-doped perovskite oxide NTO isa 5 d system. Therefore, electron correlation effects are expected to be small as compared to3 d systems such as SrTiO and BaTiO . In the following we establish a half metallic naturefor NaTaO − x N x ( x = 0 . − .
33) and discuss the electronic structure in comparison to thestrongly correlated perovskites SrTiO and BaTiO . We also address the magneto-opticalKerr effect in N-doped NTO. II. COMPUTATIONAL METHOD
Our calculations are based on density functional theory, using the full-potential linearizedaugmented plane wave approach as implemented in the WIEN2k code [22]. We use themodified Becke-Johnson (mBJ) exchange correlation potential [23]. The popular generalizedgradient approximation (GGA) [24] is employed to optimize the volume and the internalatomic coordinates. In general, the unit cell is divided into non-overlapping atomic spherescentered at the atomic sites and an interstitial region. The convergence parameter R mt K max ,where K max is the plane-wave cut-off and R mt is the smallest muffin-tin radius, controls the2
10 20 30 40
N concentration in % s p i n po l a r i za ti on ( % ) N concentration in % n ( m - ) (a) (b) FIG. 1: Calculated spin polarization and majority spin hole density n as a function of N-concentration, as obtained by the GGA+SOC approximation. size of the basis set. This convergence parameter is set to 7 together with G max = 24. Weuse 66 k -points in the irreducible wedge of the Brillouin zone for calculating the electronicstructure and a dense mesh of 480 k -points in the magneto-optical calculations. The cubicphase Pm m ( a = b = c = 3 .
93 ˚A and α = β = γ = 90 ◦ ) of NTO [25] is used in the presentcalculations for simplicity because the differences to the monoclinic phase P /m ( a = 3 . b = 3 . c = 3 . α = γ = 90 ◦ , and β = 90 . ◦ ) are subordinate [26]. Asa consequence, the electronic band structures and density of states (DOS) are found to bevery similar in both phases [27, 28]. III. RESULTS AND DISCUSSION
Our optimized lattice parameter (using the GGA) of cubic NTO is 3.98 ˚A, which is ingood agreement with the experimental value of 3.93 ˚A [25]. We replace one O with oneN to form the oxynitrate (NaTaO N). The optimized lattice parameters of NaTaO N isslightly increased to 4.03 ˚A. In order to find the magnetic ground state, we construct a1 × × E mag = E F M − E AF M = − . ∼ µ B per cell (or 1 µ B per N atom) inFM case. The Curie temperature T C is calculated using the mean-field Heisenberg model,i.e., T C = (2 / E mag /k B [29, 30]. The calculated T C for NaTaO N is 396 K, which is closeto that of N-doped SrTiO and BaTiO at the same N-N distance [14]. In order to observethe long range FM order, we study a high N-doping of 33% by replacing one O by one N3 Γ X M Γ -6-4-20246 E - E F ( e V ) z N 2p x +p y PDOS
Ta 5dO 2pN 2p z N 2p x +p y R Γ X M Γ -6-4-20246 E - E F ( e V ) FIG. 2: Band structure and DOS of NaTaO N as obtained by the mBJ approximation. in a single unit cell. A magnetic moment is induced as the delocalized N p states becomepolarized, where 0.15 µ B come from the interstitial, 0.13 µ B come from O and 0.61 µ B comefrom N, summing upto 1 µ B per N atom.To explain the induced spin-polarization in NaTaO N, we analyzes DOS and electronicband structure obtained by GGA approximation (not shown here). The DOS shows a half-metallic character with a metallic state for the minority spin and an insulating state for themajority spin. To confirm the half-metallicity, we include spin orbit coupling (SOC) alongwith GGA in the calculations, finding that NaTaO N becomes a metal since the majorityspin states crosses the Fermi level. The spin polarization (= N ↑− N ↓ N ↑ + N ↓ , where N is the numberof states at the Fermi level) of NaTaO N is obtained ∼ × × ∼ ∼
94% at 33% N-doping. In Fig. 1(b), we plot the hole density (holes per volume)for the majority spin channel. Similar to the spin-polarization, the hole density increasesrapidly upto 46.8 × m − as the N-concentration increases to 33%, while the hole densityis almost constant for low N-concentration.Recently, Guo et al. [31] have applied the mBJ approach successfully to improve the4 P o l a r K e rr e ff ec t ( d e g r ee ) θ K ε K E=1.71 eV θ K =2.16 o { FIG. 3: Calculated polar Kerr angle θ K and Kerr ellipticity ε K of NaTaO N. half-metallic ferromagnetism in zincblende MnAs, which turns into a half-metal withoutaffecting the d t g bands. We apply the same method to NaTaO N. The calculated bandstructure and DOS in Fig. 2 show a truly half-metallic nature for NaTaO N. The majorityspin bands are similar to pristine NTO with a gap of 3.96 eV, which is in excellent agreementwith experiments [28] and the previous GW calculations [27]. The minority spin channel ismetallic due to a non-zero DOS at the Fermi level. The band splitting at the Fermi levelalong R-Γ and M-Γ is very small, while along Γ-X-M, it is large. The calculated plasmafrequency ω p from the minority spin channel due to metallic nature, is 2.7 eV, which issmaller in the ferromagnetic half-metal PtMnSb ( ω p = 4 . p and O 2 p states. The bottom of the conduction bands is composed of Ta 5 d states(see Fig. 2). For the minority spin channel, the N 2 p bands cross the Fermi level (withsmall O 2 p contributions). The N 2 p ↑↓ states split into ( p x + p y ) ↑↓ and p ↑↓ z bands. Thereis no shifting of peak position with respect to energy is observed at the Fermi level in N2( p x + p y ) ↑↓ and N 2 p ↑↓ z states from the N-doped SrTiO and BaTiO [14] where N 2 p y + p z and N 2 p x have different peak position at the Fermi level. There is a strong hybridizationbetween the N 2 p ↑↓ and O 2 p ↑↓ states for the minority spin channel. The Ta 5 d ↑↓ bands donot change with the N-concentration. 5ntense search aim at materials with large magneto-optical peaks in the low wave-lengthregion to be used for high-density storage [33]. Both borates [34] and Zintl compounds[35, 36], can shows a remarkable Kerr signal in the low energy range. The Kerr rotation θ K and Kerr ellipticity ε K of half metallic NaTaO N are shown in Fig. 3. We find a value of θ K = 2 . ◦ at 1.71 eV ( ∼
725 nm), which is higher than in BiNiO ( θ K = 1 . ◦ ) [37] andthe Heusler compound PtMnSb ( θ K = 1 . ◦ ) [38, 39]. The high Kerr angle is an intrabandeffect, and not due to the SOC (which creates an imbalance in the optical transitions inPtMnSb and NiMnSb [40], for example. For the minority spin channel, the band structureof NaTaO N shows a set of parallel bands across the Fermi level (R-Γ, Γ-X-M, and Γ-M)which consist of N 2( p x + p y ) ↓ states. These parallel bands give rise to intraband transitionswhich contribute significantly to the Kerr spectrum in the low energy range. In NaTaO N,the separation between these bands is much smaller than in PtMnSb [40]. This past explainthe higher magneto-optical Kerr effect in NaTaO N. The calculated Kerr ellipticity ε K hasa maximum of ∼ ◦ at 1.6 eV. IV. CONCLUSION
In conclusion, we have presented first principles results of the band structure, DOS,and magneto-optical properties of N-doped NaTaO , as obtained from density functionaltheory. Our results for NaTaO − x N x ( x = 0 . − .
33) show that the GGA+SOC approachgives a 99% spin-polarization at low N-concentrations upto 16%. The mBJ+SOC approachresults in a pure ferromagnetic half-metal in contrast to the GGA+SOC. We observe a giantmagneto-optical Kerr signal of θ K =2.16 ◦ at ∼
725 nm in NaTaO N, which is the highest Kerrangle among the ferromagnetic half-metals in UV-visible region. The origin of the high Kerrangle is attributed to intraband transitions involving the N 2( p x + p y ) ↓ orbital due to parallelbands around the Fermi level. The large Kerr rotation in NaTaO N in the visible region mayfind applications in red/infrared laser magneto-optical devices and the half metallic natureof NaTaO N is interesting for spintronics devices. [1] H. Pan, J. B. Yi, L. Shen, R. Q. Wu, J. H. Yang, J. Lin, Y. P. Feng, J. Ding, L.H. Van, andJ. H. Yin, Phys. Rev. Lett. 99, 127201 (2007).
2] L. Shen, R. Q. Wu, H. Pan, G. W. Peng, M. Yang, Z. D. Sha, and Y. P. Feng, Phys. Rev. B78, 073306 (2008).[3] K. Yang, R. Wu, L. Shen, Y. P. Feng, Y. Dai, and B. Huang, Phys. Rev. B 81, 125211 (2010).[4] K. Yang, Y. Dai, B. Huang, and M.-H. Whangbo, Appl. Phys. Lett. 93, 132507 (2008).[5] K. Yang, Y. Dai, B. Huang, and M.-H. Whangbo, Chem. Phys. Lett 481, 99 (2009).[6] J. G. Tao, L. X. Guan, J. S. Pan, C. H. A. Huan, L.Wang, J. L. Kuo, Z. Zhang, J. W. Chai,and S. J. Wang, Appl. Phys. Lett. 95, 062505 (2009).[7] G. Rahman and V. M. Garc´ıa-Su´arez, Appl. Phys. Lett. 96, 052508 (2010).[8] W.-Z. Xiao, L.-L. Wang, L. Xua, Q. Wan, and B. S. Zou, Solid State Commun. 149, 1304(2009).[9] B. J. Nagare, S. Chack, and D. G. Kanhere, J. Phys. Chem. A 114, 2689 (2010).[10] N. N. Bao, H. M. Fan, J. Ding, and J. B. Yi, J. Appl. Phys. 109, 07C302 (2011).[11] N. H. Hong, J.-H. Song, A. T. Raghavender, T. Asaeda, and M. Kurisu, Appl. Phys. Lett. 99,052505 (2011).[12] C. M. Liu, X. Xiang, and X. T. Zu, Chin. J. Phys. 47, 893 (2009).[13] X. Tan, C. Chen, K. Jin, and B. Luo, J. Alloy. Compd. 509, L311 (2011).[14] K. Yang, Y. Dai, and B. Huang, Appl. Phys. Lett. 100, 062409 (2012).[15] P. G. van Engen, K. H. J. Buschow, and R. Jongebreur, Appl. Phys. Lett. 42, 202 (1982).[16] R. A. de Groot, F. M. Mueller, P. G. van Engen, and K. H. J. Buschow, Phys. Rev. Lett. 50,2024 (1983).[17] K. Rabe, C. H. Ahn, and J.-M. Triscone, Physics of Ferroelectrics: A Modern Perspective,Topics in Applied Physics (Springer, Berlin, 2007), Vol. 105.[18] R. G. Geyer, B. Riddle, J. Krupka, and L. A. Boatner, J. Appl. Phys. 97, 104111 (2005).[19] A.-K. Axelsson, Y. Pan, M. Valant, and N. Alford, J. Am. Ceram. Soc. 92, 1773 (2009).[20] M. Choi, F. Oba, and I. Tanaka, Phys. Rev. B 83, 214107 (2011).[21] M. Fiebig, J. Phys. D: Appl. Phys. 38, R123 (2005).[22] P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka, and J. Luitz, WIEN2k, An Augmented PlaneWave + Local Orbitals Program for Calculating Crystal Properties (TU Vienna, Vienna,2001).[23] F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).[24] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
25] International Center for Diffraction Data, JCPDS Card No. 742488 (2001).[26] International Center for Diffraction Data, JCPDS Card No. 742479 (2001).[27] H. Wang, F. Wu, and H. Jiang, J. Phys. Chem. C 115, 16180 (2011).[28] W. H. Lin, C. Cheng, C. C. Hu, and H. Teng, Appl. Phys. Lett. 89, 211904 (2006).[29] J. Kudrnovsk´y, I. Turek, V. Drchal, F. M´aca, P. Weinberger, and P. Bruno, Phys. Rev. B 69,115208 (2004).[30] F. M´aca, J. Kudrnovs´k, V. Drchal, and G. Bouzerar, Appl. Phys. Lett. 92, 212503 (2008).[31] S.-D. Guo and B.-G. Liu, Euro. Phys. Lett. 93, 47006 (2011).[32] S. Picozzi, A. Continenza, and A. J. Freeman, J. Phys. D: Appl. Phys. 39, 851 (2006).[33] P. J. Grundy, in Electronic and Magnetic Properties of Metals and Ceramics, Materials Scienceand Technology, edited by K. H. J. Buschow (VCH, 1994), Vol. 3B, p. 575.[34] Y. Saeed, N. Singh, and U. Schwingenschl¨ogl, J. Appl. Phys. 110, 103512 (2011).[35] N. Singh and U. Schwingenschl¨ogl, Chem. Phys. Lett. 508, 29 (2011).[36] N. Singh and U. Schwingenschl¨ogl, Appl. Phys. Lett. 100, 151906 (2012).[37] M. Q. Cai, X. Tan, G. W. Yang, L. Q. Wen, L. L. Wang, W. Y. Hu, and Y. G. Wang, J. Phys.Chem. C 112, 16638 (2008).[38] P. G. van Engen, K. H. J. Buschow, R. Jongebreur, and M. Erman, Appl. Phys. Lett. 42, 202(1983).[39] I. D. Lobov, A. A. Makhnev, and M. M. Kirillova, Phys. Met. Metallogr. 113, 135 (2012), andreferences therein.[40] J. van Ek and J. M. Maclaren, Phys. Rev. B 56, R2924 (1997).25] International Center for Diffraction Data, JCPDS Card No. 742488 (2001).[26] International Center for Diffraction Data, JCPDS Card No. 742479 (2001).[27] H. Wang, F. Wu, and H. Jiang, J. Phys. Chem. C 115, 16180 (2011).[28] W. H. Lin, C. Cheng, C. C. Hu, and H. Teng, Appl. Phys. Lett. 89, 211904 (2006).[29] J. Kudrnovsk´y, I. Turek, V. Drchal, F. M´aca, P. Weinberger, and P. Bruno, Phys. Rev. B 69,115208 (2004).[30] F. M´aca, J. Kudrnovs´k, V. Drchal, and G. Bouzerar, Appl. Phys. Lett. 92, 212503 (2008).[31] S.-D. Guo and B.-G. Liu, Euro. Phys. Lett. 93, 47006 (2011).[32] S. Picozzi, A. Continenza, and A. J. Freeman, J. Phys. D: Appl. Phys. 39, 851 (2006).[33] P. J. Grundy, in Electronic and Magnetic Properties of Metals and Ceramics, Materials Scienceand Technology, edited by K. H. J. Buschow (VCH, 1994), Vol. 3B, p. 575.[34] Y. Saeed, N. Singh, and U. Schwingenschl¨ogl, J. Appl. Phys. 110, 103512 (2011).[35] N. Singh and U. Schwingenschl¨ogl, Chem. Phys. Lett. 508, 29 (2011).[36] N. Singh and U. Schwingenschl¨ogl, Appl. Phys. Lett. 100, 151906 (2012).[37] M. Q. Cai, X. Tan, G. W. Yang, L. Q. Wen, L. L. Wang, W. Y. Hu, and Y. G. Wang, J. Phys.Chem. C 112, 16638 (2008).[38] P. G. van Engen, K. H. J. Buschow, R. Jongebreur, and M. Erman, Appl. Phys. Lett. 42, 202(1983).[39] I. D. Lobov, A. A. Makhnev, and M. M. Kirillova, Phys. Met. Metallogr. 113, 135 (2012), andreferences therein.[40] J. van Ek and J. M. Maclaren, Phys. Rev. B 56, R2924 (1997).