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J. Phys. Chem. C 2008, 112, 16638–16642
Giant Magneto-Optical Kerr Effects in Ferromagnetic Perovskite BiNiO3 with Half-Metallic State M. Q. Cai,†,‡ X. Tan,† G. W. Yang,*,† L. Q. Wen,‡ L. L. Wang,‡ W. Y. Hu,‡ and Y. G. Wang‡ State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics Science & Engineering, Zhongshan UniVersity, Guangzhou 510275, China and School of Physics and Microelectronics Science and Micro-Nanotechnologies Research Centre, Hunan UniVersity, Changsha, 410082, China ReceiVed: March 4, 2008; ReVised Manuscript ReceiVed: August 13, 2008
We theoretically show that the giant magneto-optical Kerr effects are induced by the electronic structure of half-metallic ferromagnetism in the perovskite BiNiO3 with the orthorhombic structure by first-principles calculation. A Kerr rotation is up to 1.28° at 1.87 eV, which is comparative to the recognized maximum polar Kerr rotation of 1.35° at 1.75 eV in the Heusler compound PtMnSb. The strong p-d exchange interaction causes the half-metallic ferromagnetism, i.e., the majority-spin electrons are semiconducting and the minorityspin electrons are metallic, which finally leads to the large Kerr rotation in the half-metallic ferromagnetic perovskite BiNiO3. 1. Introduction Multiferroic materials with magnetic and electric ordering united in a single phase have been studied extensively because of a number of device applications for including multiple state memory elements such as electric field controlled ferromagnetic resonance devices and variable transducers with either magnetically modulated piezoelectricity or electrically modulated piezomagnetism.1 Thus, the ability to couple with either magnetic or the electric polarization not only offers an extra degree of freedom in the design of conventional actuators, transducers, and storage devices but also exhibits many novel physical properties.2 There are two classes of simple multiferroic materials: transition-metal oxides of Bi- and Ni-containing perovskite ABO3 structures. For the Bi-based multiferroics such as BiFeO3, BiMnO3, BiCrO3, and BiCoO3,3-6 the intensive research focuses on the physical origins of ferroelectricity and ferromagnetism and the couple of the magnetoelectric effect. For the Ni-based compounds RNiO3 (R ) rare earth), much attention focused is on the metal-insulator (MI) transition with the change of charge ordering.7,8 It is well known that the halfmetal materials, which have a metallic nature for electrons with one spin orientation and an insulating nature for electrons with the other, have potential applications in realizing spin-based electronics.9,10 Meanwhile, the half-metal ferromagnets possess unusual magneto-optical (MO) effects due to their metallic state for majority-spin electrons but the insulating state for minority ones, which will naturally induce the extraordinary optical properties.9 Would the half-metallic state appear in the perovskite transition-metal oxides? This is really an interesting issue. However, besides ferroelectric, ferromagnetic, or antiferromagnetic, there have not been any findings about the half-metallic properties and related MO effects in the perovskite transitionmetal oxides.2 BiNiO3 is a typical magnetic perovskite with a Curie temperature about 513 K that has been scrutinized for its structural, magnetic, and electronic properties.11,12 In an ambient * To whom correspondence should be addressed. E-mail: stsygw@ mail.sysu.edu.cn. † Zhongshan University. ‡ Hunan University.
environment, BiNiO3 exhibits an antiferromagnetic insulating ground state with triclinic structure. When a pressure of about 3 GPa is applied, the phase transition from an antiferromagnetic insulating ground state with a triclinic structure to a ferromagnetic melting state with an orthorhombic structure can take place.13-15 Our recent calculations showed that the high-pressure phase of BiNiO3, i.e., the orthorhombic structure, has a halfmetallic state.16 In this constribution, we further reveal the giant MO effect with a Kerr rotation of about 1.28° at 1.87 eV in the half-metallic state in orthorhombic BiNiO3 using the firstprinciples calculations. Remarkably, our findings expand the concept of MO effects into the new field of optical recording materials, i.e., the perovskite transition-metal oxides. 2. Computational Method In our calculations, the magnetization is taken along the [001] direction for the Pnma structure of BiNiO3. In this configuration, the polar Kerr effect (KE) is given by the well-known formula for the complex Kerr angle in the two-media approach17
-σxy(ω)
θK(ω) + iεK(ω) )
(1)
4iπ 1+ σ (ω) ω xx
σxx(ω)
with θK(ω) being the Kerr rotation angle and εK(ω) the socalled Kerr ellipticity. This macroscopical model has been widely and successfully used in calculations of MOKE spectra for many systems such as element metals, simple or complex compounds, and multilayered systems. σRβ (R, β ≡ x, y, z) is the element of optical conductivity tensor, which is calculated within the electric dipole approximation using the Kubo linearresponse formula18 β R 2 f (E ) - f (E )
σRβ(ω) )
-ie m2pV
∑∑ k
j, j′
jk
j′k
ωjj′
[∏∏ j′j
jj′
ω - ωjj′ + iτ-1
+
(∏j′jR ∏jj′β )*
ω + ωjj′ + iτ-1
]
(2)
where f(Ejk) is the Fermi function, pωjj′ ) Ejk - Ej′k is the energy difference of the Kohn-Sham energies Ejk, and τ-1 is the inverse
10.1021/jp801889b CCC: $40.75 2008 American Chemical Society Published on Web 09/27/2008
Magneto-Optical Kerr Effects in Ferromagnetic Perovskite BiNiO3
J. Phys. Chem. C, Vol. 112, No. 42, 2008 16639
Figure 2. Calculated total and partial orbital-resolved densities of states (DOS) of BiNiO3 by LSDA+U.
Figure 1. Crystal structure of BiNiO3 with the orthorhombic Pbnm space group. The magnetocrystalline anisotropy calculations show the preferable the [001] spin direction with spin-orbit coupling.
of the lifetime of the excited Bloch electron states, taken as 0.4 eV, which is thought to be large enough for the transition-metal R compounds.19 ∏ j′j are the elements of the dipole optical tranzhysition matrix. Because of the metallic nature, the intraband transitions will make a great contribution to the optical tensor in the lowerenergy region, which is usually described by the Drude formula20
σD(ω) )
ωP2 4π(τD-1 - iω)
(3)
where ωP is the unscreened plasma frequency and τD is the phenomenological Drude electron relaxation time, characterizing the scattering of charge carriers, which depends on the amount of defects and therefore varies from sample to sample. τD is different from the interband relaxation time parameter τ,21 which can be frequency dependent and should be nonzero because the excited states always have a finite lifetime, whereas τD will approach zero for very pure materials. Similarly, in the halfmetallic systems, τD-1 of about 0.3 eV can well reproduce the experimental spectra. We calculate the plasma frequency ωP by22
ωP2 )
4πe2 m2V
∑ δ(Ejk - EF)|∏Rjj|2
(4)
jk
Accordingly, the Drude-type intraband contribution to the MOKE is considered in our calculations. The orthorhombic Pbnm structure (the high-pressure phase of BiNiO3) is shown in Figure 1. The highly accurate all-electron full-potential linearized augmented plane-wave method (FLAPW) plus local orbital (LO) implemented in the latest WIEN2K code is used for electronic structure calculations. For modeling of strong on-site Coulomb and exchange interactions for the local d electron between neighbor Ni atoms, we used a so-called LSDA+U method that comnines one calculation scheme local density approximation (LASD) and Hubbard model approaches.23 Relativistic effects are taken into account within the scalar approximation. The spin-orbit coupling (SOC) is taken
into account using the second-variation method self-consistently. An orbital-dependent potential with an associated on-site Coulomb and exchange interactions U ) 7 eV is considered. The cutoff energy is as high as 2.5 Ryd. A separated calculation with the cufoff energy of 3.5 Ryd gives nearly the same results. The muffin-tin sphere radii are Ri )2.4, 1.8, and 1.6 au for Bi, Ni, and O atoms, respectively. Local orbitals were used to treat the high-lying valence states of Bi and Ni as well as relax linearization errors. In the FLAPW method the relevant convergence parameter is RmtKmax, defined by the product of the smallest atomic sphere radius (Rmt) times the largest reciprocal lattice vector of the planewave basis (Kmax). For controlling the size of the basis set for the wave functions, The parameter RmtKmax is set to 7.0 and make the expansion up to l ) 14 in the muffin tins containing a well-converged basis set of about 1700 LAPW’s plus 35 local orbits for the primitive cell. In our calculations, there are in all about 1000 k points sampled in the Brillouin zone for integration over k space in the self-consistent calculation. In order to get the accurate optical conductivity tensor, much denser k-space sampling, as many as 10 000 k points, is used. The upper limit of band index j and j′ is taken as the band lying at as high as 2.5 Ryd above the Fermi level, and the convergence is carefully checked by varying it from 1.5 to 3.5 Ryd. Convergence tests indicate that only small changes result from going to a denser k mesh or to a larger value of RmtKmax. The self-consistent calculations are considered to be converged only when the integrated charge difference performula unit, ∫|Fn - Fn-1|dr, between input charge density [Fn-1] is less than 0.0001. 3. Results and Discussion Figure 2 shows the calculated total and partial orbital-resolved densities of states (DOS) of BiNiO3 by LSDA+U.15 As shown in Figure 2a, the DOS, in order of increasing energy, consists of two split-off Bi 6s-derived peaks, approximately 10 eV below the Fermi energy, followed by a manifold of the O 2p- and Ni 3d-derived bands. In the conduct band, there is mainly Ni 3-d and Bi 6p-derived bands. Now the orthorhombic phase of BiNiO3 with FM ordering (U ) 0 eV) shows the metal property and the majority and minority spin in the Fermi level are all coexistent. Generally, for the transition-metal oxides there are strong on-site Coulomb and exchange interactions for the d electrons between neighbor transition-metal ions due to the local d orbitals. Considering that the LSDA often underestimates the size of band gap in systems with strongly localized d orbitals
16640 J. Phys. Chem. C, Vol. 112, No. 42, 2008
Cai et al.
Figure 3. Energy gap and local spin magnetic Ni moment versus U value using the LSDA+U approximation for BiNiO3 in the highpressure phase.
and even predicts the metallic behavior of materials that are known to be insulators, we calculate the electronic structure of BiNiO3 in the Pbnm structure within LSDA+U. In a general way, the Hubbard parameter U can be taken from either experimental or estimated values using the restricted LSDA supercell calculation. It is generally agreed that for this type of compound the value of U is in the range of several electronvolts up to about 8 eV. In order to obtain the right U value, we plot the curve of the spin magnetic moment of Ni and the band gap of BiNiO3 with the Ueff (shown in Figure 3), where we define the Ueff ) U - J (J ) 0). We see that the spin magnetic moment of Ni and the band gap of BiNiO3 increase with the increment of the Ueff below 7 eV but slightly change about 7 eV. Moreover, we used the restricted LSDA supercell calculation and got an exact U of about 6.91 eV for BiNiO3. Therefore, we think that, based on the U value of 7 eV, LSDA+U can well describe the strong correction effect of Ni 3d and give the right electronic properties of the ground state for BiNiO3. Interestingly, the electronic structure shows the halfmetal property (Figure 2b), in which there is only complete spin polarization of electrons at the Fermi level. From Figure 2b we know that the minority electrons are in the metallic states while the majority electrons are insulating. The energy band gap about 1.96 eV appears in the majority DOS. In Figure 2d, at the top of the valance band, there are mainly the Ni 3d2g states, which are partially filled and cross the Fermi surface to cause the metallic nature, which corresponds to the Ni3+ of d7 configuration in the orthorhombic structure based on Hunt’s rule with the difference of Ni2+ of d8 configuration in the triclinic structure.16 In detail, the spin splitting of Ni 3d orbitals should cause the high-spin states.16 However, we can see in Figure 2c and 2d some electrons of O ions transfer to the Ni ions because the density of states of Ni 3d and O 2p orbitals overlap in the same energy positions, indicating the occurrence of hybridization of O 2p-Ni 3d. Thus, the Ni ions do not show the 3+ state. In our calculations the spin magnetic moments of Bi, O1, O2, and Ni are about -0.00771, 1.67514, -0.17538, and -0.16637 µB, respectively. The total magnetic moments are about 4.637 µB for the unit cell with 4 Bi atoms, 4 Ni atoms, 4 O1 atoms, and 8 O2 atoms. Moreover, the orbital magnetic moments of Ni are about 0.13055 µB. The hybridization of O 2p-Ni 3d is responsible for the small spin magnetic moment of about 1.67 µB. Therefore, a well-developed splitting of Ni d states by the quasicubic crystal field together with the strong exchange interaction in the Ni-sited bonding induce the half-metallic nature of BiNiO3. The corresponding band structures of BiNiO3 are shown in Figure 4. The spin-polarized band structures in the left-hand panels (Figure 4a and 4b) and right-hand panel are calculated without SOC and with SOC, respectively. We also find out that
Figure 4. Band structures of half-metallic ferromagnetic BiNiO3 in the Pbnm structure without (left-hand panels) the spin-orbit coupling (SOC) for the (a) majority-spin direction and (b) minority-spin direction and (c) with (right-hand panel) SOC. Fermi energy is set to zero.
the electronic structures of BiNiO3 show the typical half-metallic properties with the metallic nature for the majority band structure (Figure 4a) and the insulating nature with a band gap 1.96 eV for the minority band structure (Figure 4b) in Figure 4. Compared with the band structure with SOC (Figure 4c), the half-metallic state is stable no matter whether SOC is included or not. As we known, the spin-down and spin-up band structures would be apart from 2-fold states because of the spin-orbit coupling. Indeed, we could see the separate two states in the bottom of the conduct bands Γ point of Brillouin zone (BZ) in Figure 4c, whereas there is only one state at the top of the valance-band Γ point of BZ for the half-metallic property. The SOC does not change the half-metallic property. Although the asymmetric electronic states for different spins have been predicted in some ferromagnetic metals such as the Heusler compounds, CrO2, transition-metal pnictides and chalcogenides with wurtzite and zinc-blende structures, and self-doped oxide spinels of LiM2O4,10,24-26 there are no reports on the halfmetallic properties in the perovskite-type ABO3 transition-metal oxides. As we know, the perovskite-type ABO3 transition-metal oxides such as BiFeO3, BiMnO3, and BiCoO3 are promising for the information memory due to the antiferromagnetic nature in the room structures.3-6 In spite of good magnetic control for electric storage, it is not convenient to realize magnetic storage under electric control because of the antiferromagnetic properties. Therefore, our studies, for the first time, reveal the halfmetallic state in perovskite-type ABO3 transition-metal oxides. BiNiO3 with the orthorhombic structure has a quite large MOKE with a maximum polar Kerr rotation of about 1.28° at 1.87 eV as shown in Figure 5a, which is comparative to the recognized maximum polar Kerr rotation of about 1.35° at 1.75 eV in the Heusler compound PtMnSb with the polycrystal structure at room temperature.9 Additionally, the height of the second peak is about 0.61° at 4.6 eV in the Kerr rotation spectrum. Note that when the Kerr ellipticity crosses the zero line, the peak always appears in the Kerr rotation spectra and
Magneto-Optical Kerr Effects in Ferromagnetic Perovskite BiNiO3
Figure 5. (a) Calculated Kerr rotation (θK, solid line) and Kerr ellipticity (εK, dotted line) spectra vs photon energy for half-metallic ferromagnetism BiNiO3 in the Pbnm structure. (b) Separate contributions to the Kerr rotation spectra of BiNiO3 from Im[εσxy (solid line) and Im[εD]-1 (dotted line).
vice versa due to the Kramers-Kronig relations in Figure 5a. This result means that our calculations about the magneticoptical spectra are pretty good. The large Kerr rotation of BiNiO3 near 1.87 and 4.6 eV could find possible applications in red or ultraviolet laser light MO effect devices. In general, spin-polarization, spin-orbit interaction, and plasma resonance play important roles in determining the MO Kerr spectra.27 For the influences on the polar Kerr rotation spectrum from spin polarization, spin-orbit interaction, and interaction between the two, the off-diagonal conductivity spectrum of IM[ωσxy] could account for them, whereas the effects for the polar Kerr rotation spectrum by the plasma edge (plasma resonance), due to the metallic feature, could be reflected through Im[ωD]-1, which is confirmed to play a crucial role for the polar Kerr rotation spectrum by Feil and Haas28 based on model calculations for some magnetic metallic rareearth or transition-metal compounds. D(ω) can be expressed as
1 + 4iπω σ (ω)
D(ω) ) σxx(ω)
xx
In order to show the effects on the polar Kerr rotation spectrum for the plasma resonance and spin-orbit interaction in the different energy region, the separate contributions to the Kerr rotation spectra of BiNiO3 from Im[σxy] (solid line) and Im[D]-1 (dotted line) are also shown in Figure 5b. As shown in Figure 5b, the Kerr rotation and ellipticity are very compatible with each other. It is clearly seen that when the Kerr ellipticity crosses the zero line, a peak always appears in the Kerr rotation spectra and vice versa due to the Kramers-Kronig relations, which means our direct calculation of eq 2 is quite good. Considering the Kerr rotation associating with the ellipticity by the Kramers-Kronig relations, we only discuss the relationship between the Kerr rotation and Im[ωD]-1. In fact, the Kerr ellipticity is also related to Im[ωD]-1. Although the peak position of the Kerr rotation is somewhat different from that of Im[ωD]-1, as a whole the shape of the spectra of the Kerr rotation are quite similar to that of Im[ωD]-1 in the lowenergy region. The small difference between the peak positions of the Kerr rotation spectra and Im[ωD]-1 could be due to the missing p1/2 radial basis function in the scalar-relativistic basis for calculation of the optical conductivity tensor. Moreover, we see that the imaginary part Im[ωD]-1 exhibits a similar structure to the Kerr rotation spectrum in
J. Phys. Chem. C, Vol. 112, No. 42, 2008 16641 the energy region lower than about 2.8 eV, while the imaginary part of off-off-diagonal optical conductivity Im[ωσxy] is very small in the same region. This result thus shows no such structure. On the contrary, in the energy region higher than 2.8 eV, Im[ωσxy] contributes most to the Kerr rotation spectra while Im[ωD]-1 keeps nearly a small constant. Evidently there exist different mechanisms for the Kerr rotation peaks in the high- and low-energy region. It is known that because of the metallic nature of the electronic structure of BiNiO3, these electronics near the Fermi face could be excited easily to become plasma resonance as for the Ni, Fe, and so on. Thus, the large Kerr rotation peak in the low-energy peak at about 1.87 eV is induced by the plasma resonance due to the metallic nature for the majority electronic structure. The high-energy peak at about 4.60 eV mostly originates from the off-diagonal conductivity due to the interband transitions between the SOC-split bands. 4. Conclusion We theoretically predicted the giant MOKE in a new class of half-metallic materials, i.e., the perovskite BiNiO3 with the orthorhombic structure, using first-principles calculations. The physical mechanisms of the unusual MOKE are attributed to the unique electronic structure of the half-metallic state. These findings seem to open a door toward applications of perovskite transition-metal oxides in red and ultraviolet laser light recording. Acknowledgment. The NSFC (50525206), China Postdoctoral Science Foundation (20060390763), and NSFG (06300333) supported this work. M.Q.C. expresses thanks to the Supercomputer Centers of Hunan University and Shanghai. References and Notes (1) Kimura, T.; GoTo, T.; Shintani, H.; Ishizaka, K.; Arima, T.; Tokura, Y. Nature 2003, 426, 55. (2) Fiebig, M. J. Phys. D: Appl. Phys. 2005, 38, R123. (3) Wang, J.; Neaton, J. B.; Zheng, H.; Nagarajan, V.; Ogale, S. B.; Liu, B.; Viehland, D.; Vaithyanathan, V.; Schlom, D. G.; Waghmare, U. V.; Spaldin, N. A.; Wuttig, M.; Ramesh, R. Science 2003, 299, 1719. (4) Hill, N. A.; Rabe, K. M. Phys. ReV. B 1999, 59, 8759. (5) Hill, N. A.; Ba¨ttig, P.; Daul, C. J. Phys. Chem. B 2002, 106, 3383. (6) Cai, M. Q.; Liu, J. C.; Yang, G. W.; Tan, X.; Cao, Y. L.; Wang, L. L.; Hu, Y. Y.; Wang, Y. G. J. Chem. Phys. 2007, 126, 154708. (7) Torrance, J. B.; Lacorre, P.; Nazzal, A. I.; Ansaldo, E. J.; Niedermayer, C. Phys. ReV. B 1992, 45, 8209. (8) Alonso, J. A.; Martinez-Pope, M. J.; Casais, M. T.; Garcı´a-Mun˜oz, J. L.; Ferna´ndez-Dı´az, M. T. Phys. ReV. B 2000, 61, 1765. (9) van Engen, P. G.; Buschow, K. H. J.; Jongebreur, R. Appl. Phys. Lett. 1982, 42, 202. (10) de Groot, R. A.; Mueller, F. M.; van Engen, P. G.; Buschow, K. H. J. Phys. ReV. Lett. 1983, 50, 2024. (11) Ishiwata, S.; Azuma, M.; Takano, M.; Nishibori, E.; Takata, M.; Sakata, M.; Kato, K. J. Mater. Chem. 2002, 12, 3733. (12) Cai, M. Q.; Yang, G. W.; Cao, Y. L.; Hu, W. Y.; Wang, L. L.; Wang, Y. G. Appl. Phys. Lett. 2007, 90, 242911. (13) Wadati, H.; Takizawa, M.; Tran, T. T.; Tanaka, K.; Mizokawa, T.; Fujimori, A.; Chikamatsu, A.; Kumigashira, H.; Oshima, M.; Ishiwata, S.; Azuma, M.; Takano, M. Phys. ReV. B 2005, 72, 155103. (14) Ishiwata, S.; Azuma, M.; Hanawa, M.; Moritomo, Y.; Ohishi, Y.; Kato, K.; Takata, M.; Nishibori, E.; Sakata, M.; Terasaki, I.; Takanol, M. Phys. ReV. B 2005, 72, 045104. (15) Ishiwata, S.; Azuma, M.; Takanol, M.; Nishibori, E.; Sakata, M. Physica B 2003, 329-333, 813. (16) Cai, M. Q.; Yang, G. W.; Tan, X.; Cao, Y. L.; Wang, L. L.; Hu, W. Y.; Wang, Y. G. Appl. Phys. Lett. 2007, 91, 101901. (17) Antonov, V. N.; Oppeneer, P. M.; Yaresko, A. N.; Perlov, A. Y.; Kraft, T. Phys. ReV. B 1997, 56, 13012. (18) Ebert, H. Rep. Prog. Phys. 1996, 59, 1665.
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