- Email: [email protected]
The effect of Sr doping on the magnetic properties of Co perovskite
17 May 1999
Physics Letters A 255 Ž1999. 354–360
The effect of Sr doping on the magnetic properties of Co perovskite Min Zhuang
a,1
, Weiyi Zhang
a,b
, Tiejun Zhou a , Naiben Ming
a,b
a b
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniÕersity, Nanjing 210093, China Department of Physics, The Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Received 14 December 1998; received in revised form 2 March 1999; accepted 4 March 1999 Communicated by L.J. Sham
Abstract Within the unrestricted Hartree–Fock approximation and the real space recursion method, we calculated the electronic structure of the La 1yx Sr x CoO 3 in whole doping range 0.0 F x F 1.0. The low-spin ŽLS, t 26 g e g0 ., the intermediate-spin ŽIS, t 25 g e 1g ., and the high-spin ŽHS, t 24 g e g2 . states as well as their combinations in the doubled cell were taken as the initial 0. configurations. It is found that the system is a nonmagnetic low-spin state Ž t 26yx g e g for x F 0.25 and a ferromagnetic 5 1yx . Ž intermediate-spin state t 2 g e g for 0.25 - x F 0.41. For 0.41 - x - 0.95, the ground state of the system is a IS–HS Ž t 25 g e 1yx -t 24 g e g2yx . nearest neighbor ferromagnetically ordered state, which is followed by the HS state up to x s 1.0. The g ground state properties as a function of Sr doping are in accord with the experimental observations. q 1999 Elsevier Science B.V. All rights reserved. PACS: 75.25.q z; 75.50.q y; 75.30.Vn
1. Introduction Since the giant magnetoresistance effects were observed in the doped LaMnO 3 perovskite w1–3x similar results have also been reported for the doped LaCoO 3 perovskite w4–7x. Very different from the A-type antiferromagnetic Žlayered AFM. ground state of LaMnO 3 , the ground state of undoped Co perovskite is a nonmagnetic insulator, the so called low-spin state ŽLS, S s 0, t 26 g e g0 . w8–11x. However, the low-spin state is only stable at low temperature, 1
Corresponding author, current address: Department of Physics, University of Minnesota, 116 Church St. SE, Minneapolis MN 55455, USA; E-mail: [email protected]
the compound experiences a thermally assisted magnetic transition from the low-spin state to a high-spin state ŽHS, S s 2, t 24 g e g2 . at around 90 K w12x. In addition, another unclear transition takes place at 500 K, where the system changes from an activated semiconductor to a metallic conductor w13x. Recently, Korotin et al. w14x proposed that the low temperature transition most likely takes place between the low-spin state and the intermediate-spin state ŽIS, t 25 g e 1g .. Upon Sr substitution, both photoemission spectra w15x and electrical resistivity measurements w4,16x also revealed that there appears an insulator-metal transition for a doping concentration x s 0.2 due to the overlap among the doping induced hole states
0375-9601r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 1 6 8 - 1
M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
and the valence band. Because the ionic radius of the Sr 2q is larger than that of the La3q, the crystal field strength Dq is reduced, which favors the magnetic state in the system. Thus, the insulator-metal transition is accompanied by a magnetic transition from the nonmagnetic state to the ferromagnetically ordered state w8–11,16,17x. While most of the studies suggested that two transitions occur almost at the same doping concentration, another result has also been reported w18x. Furthermore, the thorough investigation showed that the compound is in the spin-glass state for low doping concentration w19,20x and in the ferromagnetic cluster-glass state for high doping concentration w11,19x. As a result, the ferromagnetic state here seems to lack the proper long range order in contrast to that in the Mn perovskite, this difference may also reflect in the physical mechanisms of magnetoresistance in these materials. The nature of the various spin-states in this compound is still a controversial issue; there is no consensus reached on the spin state of Co 3q and Co 4q in the system. While Sathe et al. w21x proposed that the Co 3q ions are in a mixed low-spin high-spin state and the Co 4q ions are in the low-spin state for the ferromagnetic region 0.2 F x F 0.5, Taguchi et al. w17x indicated that Co 3q ions are in the high-spin state in the doping range 0.5 F x F 1.0. More recently, photoemission results also suggested that the possible intermediate-spin state is realized in the ferromagnetic phase w22x. In fact, the spin-state of different Co ions not only depends on the doping concentration x, but also depends on the temperature due to the entropy effect. Thus, it is of great interest to make a systematic study in the whole doping range to elucidate the properties of the various Co ions, the spin-states, as well as the magnetic transition so that the giant magnetoresistance can be understood. Previously, the magnetoresistance of this material was explained in terms of the so-called double exchange model w23x and La 1y x Sr x CoO 3 is also classified as the double exchange system w5,18x. Nevertheless, one has observed the negative magnetoresistance in the insulator regime w7x and the positive ones in the doping range x ) 0.4 w4,24x, which are not found in the Mn perovskite. Mahendiran and Raychaudhuri suggested that the spin-state transition and the spin-cluster freezing both play an important
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role in the curious negative magnetoresistance in the insulating samples w24x. Therefore, in this paper we have studied the Sr doping effect on the spin state of the Co perovskite, periodic structures with both primary cell and doubled cell are considered to allow the existence of various magnetic states. Although the periodicity condition restricts the structures of magnetic states under investigation, the doubled cell structures accommodate all interested magnetic states proposed so far. It is well known that LaCoO 3 has a pseudo-cubic perovskite structure with a rhombohedral distortion, with Sr doping the system gradually approaches to an ideal perovskite. For simplicity, we treated the materials as a pure perovskite and considered Sr doping merely reducing the valence electrons. The calculation is performed within the unrestricted Hartree–Fock approximation on a realistic perovskite-type lattice model. Various initial configurations for the single and doubled cell are given to imitate the LS, IS, and HS states as well as their superpositions, the selfconsistent solutions are sought using the iteration method. With the band structure parameters deduced from the photoemission spectra as input, we obtained the nonmagnetic low-spin state of LaCoO 3 and the ferromagnetic intermediate-spin state of SrCoO 3 Ž t 24 g e 1g , S s 3r2.., which are in agreement with the experiments w8–11,25x. Moreover, we also obtained modulated structures consisting of the superposition of above three spin-states, ´ which were emphasized by Senaris-Rodriguez and ˜ ´ Goodenough w11x for LaCoO 3 . To compare the relative stability of the various states, we have computed their energies as functions of x. Our results show that the first magnetic transition takes place at x G 0.25 between the LS state and the ferromagnetic IS state; as the doping concentration increases to x s 0.41, the magnetic ground state of the system changes from the ferromagnetic IS state into the superposition of intermediate-spin high-spin ordered state; the high-spin state becomes the ground state only near the doping concentration x G 0.94. It is interesting to find that t 2 g electrons remain localized after doping, the system possesses the half-metallic behavior as in the La 1y x Ca x MnO 3 w26x. The total density of states at the Fermi energy is extremely low when x - 0.2, this suggests that any insulator metal transition occurs only after x s 0.2. Also the character of the
M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
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valence band becomes more O–p weighted as doping removes d electrons from the system. All these features are consistent with the experimental observations. In Section 2, we first introduce the multiband Hubbard model proposed for the real perovskite-type material, then the real space recursion method is also briefly outlined together with the unrestricted Hartree–Fock approximation. In Section 3, we analyze the Sr doping effect on the properties of Co perovskite based on the numerical results. The conclusion is drawn in Section 4.
Ž pps ., and Ž ppp . w28x. Sidm is the total spin operator of Co ion extracting the one in orbital m, u˜ s u y 5 jr2. The parameter u is related to the multiplet averaged d y d Coulomb interaction U via u s U q 209 j. Next, we linearize the Hamiltonian within the unrestricted Hartree–Fock approximation, and obtain the effective tight-binding Hamiltonian as below j H s Ý e d0m q un di m s y s Ž m td y m md . 2 im s qu˜ Ž n dt y n dm . d i†m s d i m s q
Ý e p p†jn s pjn s jn s
q
2. Theoretical formalism
Ý Ž
t imj n d i†m s
pjn s q h.c. .
ijmn s
To study the perovskite compounds, the following multiband d-p model w27x, which includes the full degeneracy of the transition metal 3d orbitals and oxygen 2 p orbitals as well as on-site Coulomb and exchange interactions, are generally adopted.
Ž 1a .
H s H0 q H1 H0 s
Ý
e d0m d i†m s
dims q Ý
im s
e p p†jn s
pjn s
jn s
Ý Ž t imj nd i†m s pjn s q h.c. .
q
ijmn s X
Ý Ž t injn p†i n s pjn s q h.c. .
q
Ž 1b .
X
X
ijnn s
H1 s Ý ud i†m ≠ d i m ≠ d i†m x d i m x im
q 12
˜ i†m s d i m s d i†m s Ý ud X
X
im/m ss
yj
Ý im ss
X
X
d i†m s s d i m s X P Sidm .
X
d i mX s X
X
q
Ý Ž t injn p†i n s pjn s q h.c. . . X
Ž 2.
X
ijnn s
Here, n dm s s ² d m† s d m s :, m md s n dm ≠ y n dm x , and n dt and m td are the total electron numbers and magnetization of the Co–d orbitals, which are to be determined self-consistently. For simplicity, we choose the z-axis as the spin quantization axis so that all the magnetic states are Ising-type structures. For the tight-binding Hamiltonian Eq. Ž2., the density of states can be easily calculated using the real space recursion method w29x. Instead of diagonalizing the Hamiltonian with the dimension of the number of orbitals in the primitive cell, the recursion method choose one particular lattice site, where the density of states is acquired, and tridiagonalizes the Hamiltonian to a certain number of levels; one then writes the Green’s function as
Ž 1c .
Here d i m s Ž d i†m s . and pjn s Ž p†jn s . denote the annihilation Žcreation. operators of an electron on Co–d m orbital at site i and O–p n orbital at site j with the spin s , respectively. The on-site energy of O–p orbital is set to be zero. The crystal-field-splitting energy is included in the on-site energy of the Co–d orbital e d0m as e d0 Ž t 2 g . s e d0 y 4 Dq and e d0 Ž e g . s e d0 q 6 Dq, where e d0 X is the bare on-site energy of d orbital. t imj n and t injn are the nearest neighbor hopping integrals for p-d and p-p which is expressed in terms of Slater–Koster parameters Ž pd s ., Ž pdp .,
Ž3.
The coefficients a i and bi are obtained from the tridiagonalization of the tight-binding Hamiltonian matrix for a given starting orbital. The multiband terminator w30x is chosen in our calculation to close the continuous fractional. Once the Green’s function is obtained, the density of states could be worked out
M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
with the relation rms Ž v . s yŽ1rp .ImGmsŽ v .. This allows us to calculate the electron numbers, magnetic moments, as well as the energies of various possible stable states. To accommodate both the single-cell and doublecell magnetic structures, the numerical calculation are carried out uniformly in the doubled cell. For every trial state there are 38 independent orbitals to be calculated for each iteration, and we compute 25 levels for the continuous fractional coefficients of each orbital. The whole procedure is iterated selfconsistently till convergence of electron numbers in each orbitals, hence the magnetic moment and energy. We have checked our results for different levels to ensure the accuracy of energy calculation and better than 5 meV in energy accuracy is secured. Note that the 5 meV energy accuracy in our numerical calculation is much smaller than the energy difference ; 0.1 eV between the different spin states. 3. Numerical results and discussions The parameter set of the compound can be derived from the cluster model analysis of the photoemission spectra w16x as well as the ab initio local spin density approximation ŽLSDA. calculations w31x. The densities of states ŽDOS. of the end members LaCoO 3 and SrCoO 3 using these parameters are in a excellent agreement with both experiments and ab initio calculations. Furthermore, we found that the dependence of DOS as a function of doping level is also in consistent with the photoemission experiments w15x. The parameter set thus obtained is as follows: The bare on-site energies of Co–d and O–p orbitals are taken as e d0 s y28.0 eV and e p s 0 eV. The Slater–Koster parameters are Ž pd s . s y2.0 eV, Ž pdp . s 0.922 eV, Ž pps . s 0.6 eV, and Ž ppp . s y0.15 eV, respectively. The on-site Coulomb repulsion is U s 5.0 eV. The crystal field strength and Hund’s coupling are set as Dq s 0.16 eV and j s 0.84 eV. As will be shown below, this parameter set does reproduce the low-spin ground state of LaCoO 3 and the intermediate-spin ground state of SrCoO 3 which are observed experimentally w8–11,25x. We use the spin-states of Coq3 as references and study the evolution of the LS state, IS state, and HS state as well as their neighboring ordered states as a function of Sr doping concentration. The densities of
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states are calculated, stabilities of various states are analyzed, and phase diagram as function of doping is obtained. According to our numerical calculations, we found that t 2 g electrons in these states remain localized and the number of itinerant e g electrons is reduced with the doping, except for the low-spin state without e g electrons. The main magnetic moment of the system is due to the localized t 2 g electrons, which can be clearly seen from the spinresolved density of states discussed below. To save space, only the spin-states which become the ground states at certain doping range are discussed in detail. In Fig. 1, we present the energies of four spinstates as a function of doping concentration x. They are the LS state, the IS state, the HS state, and the IS–HS ferromagnetically ordered state. All energies decrease monotonically with x and with different slopes, the crossover points between different spinstates separate the doping parameter into several regions where one of the four spin-states becomes the ground state. For x F 0.25, the system is in the nonmagnetic LS state as LaCoO 3 . The ferromagnetic IS state becomes the energetically most favorable state between x s 0.25 and 0.41, which is followed by the IS–HS ferromagnetically ordered state. The HS state only exists near the doping concentration x s 1.0. From the ion configuration of Co 4q, the HS state here for x s 1.0 is exactly the IS state of SrCoO 3 as expected. Next, we illustrate the electronic structures of each ground state of different x one by one.
Fig. 1. The energies per doubled cell of the various spin states as a x 0 5 1y x x function of x. The configurations t 26y and t 24 g e 2y g e g , t2 g e g g refer to the low-spin, the intermediate-spin, and the high-spin states, respectively.
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M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
We first calculate the densities of states of end members LaCoO 3 and SrCoO 3 . As shown in Fig. 2, LaCoO 3 is a LS insulator. The first peak near the top of valence band comes mostly from the occupied t 2 g band, the other two peaks below the Fermi energy are mainly contributed by the O–p orbitals. The e g band is located above the Fermi energy and is nearly unoccupied. These main features are in agreement both with the photoemission spectra w16x and with the previous results obtained using LSDA method w31x. In Fig. 3, the density of states of SrCoO 3 is also presented. One can see clearly that SrCoO 3 is in the metallic IS state with a magnetic moment of 2.96 m B per Co ions. Quite different from LaCoO 3 , the contribution of Co t 2 g electrons is shifted towards the low energy. The density of states near the Fermi energy is dominated by the O–p orbitals. These features of SrCoO 3 can be well compared with the experiments w25x. Upon Sr doping, significant changes take place in electrical and magnetic properties of the system. For low doping concentration Ž x - 0.2., the system remains a nonmagnetic LS state. Fig. 4 also shows that the density of states at Fermi energy is extremely low and Fermi energy still stays in the tail regime
Fig. 2. The density of states of the low-spin state of LaCoO 3 . From top to bottom are the partial densities of states for the Co– d orbitals, O– p orbitals, and total density of states, respectively. The upward and downward curves represent the spin-up and spin-down states. The other parameters are described in the text.
Fig. 3. The density of states of the intermediate-spin state of SrCoO 3 . The other parameters and notation are the same as in Fig. 2.
which reminisces the localized states. Thus, the insulator-metal transition might result from doping induced Mott–Anderson delocalization transition. When 0.25 - x F 0.41, the ground state of the system turns out to be the IS state and its typical density
Fig. 4. The density of states of the low-spin state at doping concentration x s 0.2. The other parameters and notation are the same as in Fig. 2.
M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
of states is shown in Fig. 5 for x s 0.3. This spin-state has the metallic nature due to the presence of finite density of states at Fermi energy. In comparison with that of the LS state, the Co–d bands shifts slightly downwards while the O–p bands shifts upwards, the trend is even more pronounced with the increase of doping. Especially, the Co t 2 g peaks diminish so that the spectral distribution becomes broader. As doping increases further, some IS Co ions are replaced by the HS ions with the same moment direction. Our numerical search reveals that the IS–HS ferromagnetically ordered state is the ground state for 0.41 - x F 0.95, the partial densities of states of the two different Co ions are shown in Fig. 6Ža. and Žb.. It is found that e g bands of two Co ions are always flat and broad, while t 2 g bands of the IS Co ions ŽFig. 6Ža.. show several splitted peaks at edges of the valence band. On the contrary, the small t 2 g peaks of HS Co ions ŽFig. 6Žb.. move to the bottom of the valence band. These peaks result from the moment formation and thus band splitting. From the total density of states, it is clear that the main feature of the valence band comes from the O–p orbitals, while the total band width is mainly determined by the Co–d bands and increases with doping. This feature is consistent with the photoemission experiments w15x. The magnetic moments of two Co
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Fig. 6. The density of states of the intermediate-spin high-spin ferromagnetically ordered state at doping concentration x s 0.7. From top to bottom are the partial densities of states for the IS Co– d orbitals, HS Co– d orbitals, O– p orbitals, and total density of states, respectively. The other parameters are the same as in Fig. 2.
ions are 1.61 m B and 3.16 m B and their average moment is 2.385m B . It is worthwhile to mention that doped LaCoO 3 compound belongs to the half-metal category according to Pickett and Singh w26x, which resembles the electronic structures of La 1y x Ca xMnO 3 .
4. Conclusion
Fig. 5. The density of states of the intermediate-spin state at doping concentration x s 0.3. The other parameters and notation are the same as in Fig. 2.
In summary, we have studied the effect of Sr doping on the magnetic and electronic properties of LaCoO 3 . Starting with the initial configurations of LaCoO 3 , we calculated various spin states using the unrestricted Hartree–Fock approximation of the multiband d-p model and real space recursion method. Our result shows that four possible ground states are stable at different doping ranges, the system changes consecutively from the low-spin state to the intermediate-spin state, then to the intermediatespin high-spin ordered state, and finally to the highspin state as doping varies from 0 to 1. The evolution of the spectral shapes is also in accord with the experimental observations.
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M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
Acknowledgements The present work is supported in part by the National Natural Science Foundation of China under Grant Nos. NNSF 19677202 and 19674027 and the key research project in ‘Climbing Program’ by the National Science and Technology Commission of China.
References w1x R. von Helmholt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer, Phys. Rev. Lett. 71 Ž1993. 2331. w2x M. McCormack, S. Jin, T.H. Tiefl, R.M. Fleming, J.M. Phillips, R. Ramesh, Appl. Phys. Lett. 64 Ž1994. 3045. w3x P. Schiffer, A.P. Ramirez, W. Bao, S.W. Cheong, Phys. Rev. Lett. 75 Ž1995. 3336. w4x R. Mahendiran, A.K. Raychaudhuri, A. Chainani, adn D.D. Sarma, J. Phys.: Condens. Matter 7 Ž1995. L561. w5x S. Yamaguchi, H. Taniguchi, H. Takagi, T. Arima, Y. Tokura, J. Phys. Soc. Jpn. 54 Ž1995. 1885. w6x G. Briceno, H. Chang, X. Sun, P.G. Schultz, X.D. Xiang, Science 270 Ž1995. 273. w7x V. Golovanov, L. Mihaly, A.R. Moodenbaugh, Phys. Rev. B 53 Ž1996. 8207. w8x P.M. Raccah, J.B. Goodenough, Phys. Rev. 155 Ž1967. 932. w9x G.H. Jonker, J.H. Van Santen, Physica 19 Ž1953. 120. w10x V.G. Bhide, D.S. Rajoria, G.R. Rao, C.N.R. Rao, Phys. Rev. B 6 Ž1972. 1021. ´ w11x M.A. Senaris-Rodriguez, J.B. Goodenough, J. Solid state ˜ ´ Chem. 116 Ž1995. 224; 118 Ž1995. 323. w12x K. Asai, P. Gehring, H. Chou, G. Shirane, Phys. Rev. B 40 Ž1989. 10982. w13x S. Yamaguchi, Y. Okimoto, H. Taniguchi, Y. Tokura, Phys. Rev. B 53 Ž1996. R2926.
w14x M.A. Korotin, S.Yu. Ezhov, I.V. Solovyev, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. B 54 Ž1996. 5309. w15x A. Chainani, M. Mathew, D.D. Sarma, Phys. Rev. B 46 Ž1992. 9976. w16x P.M. Raccah, J.B. Goodenough, J. Appl. Phys. 39 Ž1967. 1209. w17x H. Taguchi, M. Shimada, M. Koizumi, Mater. Res. Bull. 13 Ž1978. 1225; J. Solid State Chem. 29 Ž1979. 221; 33 Ž1980. 169. w18x P. Ganguly, P.S. Anil Kumar, P.N. Santhosh, I.S. Mulla, J. Phys.: Condens. Matter. 6 Ž1994. 533. w19x M. Itoh, I. Natori, S. Kuboto, K. Motoya, J. Phys. Soc. Jpn. 63 Ž1994. 1486. w20x K. Asai, O. Yokokura, N. Nishimori, H. Chou, J.M. Tranquada, G. Shirane, S. Higuchi, Y. Okajima, K. Kohn, Phys. Rev. B 50 Ž1994. 3025. w21x V.G. Sathe, A.V. Pimpale, V. Siruguri, S.K. Paranjpe, J. Phys.: Comdens. Matter 8 Ž1996. 3889. w22x T. Saitoh, T. Mizokawa, A. Fujimori, M. Abbate, T. Takeda, M. Takano, Phys. Rev. B 56 Ž1997. 1290. w23x C. Zener, Phys. Rev. 81 Ž1951. 440; P.G. de Gennes, Phys. Rev. 118 Ž1960. 141. w24x R. Mahendiran, A.K. Raychaudhuri, Phys. Rev. B 54 Ž1996. 16044. w25x R.H. Potze, G.A. Sawatzky, M. Abbate, Phys. Rev. B 51 Ž1995. 11501. w26x W.E. Pickett, D.J. Singh, Phys. Rev. B 53 Ž1996. 1146. w27x T. Mizokawa, A. Fujimori, Phys. Rev. B 53 Ž1996. R4201; B 54 Ž1996. 5368; B 51 Ž1995. 12880. w28x J.C. Slater, G.F. Koster, Phys. Rev. 94 Ž1954. 1498. w29x V. Heine, R. Haydock, M.J. Kelly, in: H. Ehrenreich, F. Seitz, D. Turnbull ŽEds.., Solid state Physics: Advances in Research and Applications, vol. 35, Academic, New York, 1980, p. 215. w30x R. Haydock, C.M.M. Nex, J. Phys. C 17 Ž1984. 4783. w31x D.D. Sarma, N. Shanthi, S.R. Barman, N. Hamada, H. Sawada, K. Terakura, Phys. Rev. Lett. 75 Ž1995. 1126.
Physics Letters A 255 Ž1999. 354–360
The effect of Sr doping on the magnetic properties of Co perovskite Min Zhuang
a,1
, Weiyi Zhang
a,b
, Tiejun Zhou a , Naiben Ming
a,b
a b
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniÕersity, Nanjing 210093, China Department of Physics, The Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Received 14 December 1998; received in revised form 2 March 1999; accepted 4 March 1999 Communicated by L.J. Sham
Abstract Within the unrestricted Hartree–Fock approximation and the real space recursion method, we calculated the electronic structure of the La 1yx Sr x CoO 3 in whole doping range 0.0 F x F 1.0. The low-spin ŽLS, t 26 g e g0 ., the intermediate-spin ŽIS, t 25 g e 1g ., and the high-spin ŽHS, t 24 g e g2 . states as well as their combinations in the doubled cell were taken as the initial 0. configurations. It is found that the system is a nonmagnetic low-spin state Ž t 26yx g e g for x F 0.25 and a ferromagnetic 5 1yx . Ž intermediate-spin state t 2 g e g for 0.25 - x F 0.41. For 0.41 - x - 0.95, the ground state of the system is a IS–HS Ž t 25 g e 1yx -t 24 g e g2yx . nearest neighbor ferromagnetically ordered state, which is followed by the HS state up to x s 1.0. The g ground state properties as a function of Sr doping are in accord with the experimental observations. q 1999 Elsevier Science B.V. All rights reserved. PACS: 75.25.q z; 75.50.q y; 75.30.Vn
1. Introduction Since the giant magnetoresistance effects were observed in the doped LaMnO 3 perovskite w1–3x similar results have also been reported for the doped LaCoO 3 perovskite w4–7x. Very different from the A-type antiferromagnetic Žlayered AFM. ground state of LaMnO 3 , the ground state of undoped Co perovskite is a nonmagnetic insulator, the so called low-spin state ŽLS, S s 0, t 26 g e g0 . w8–11x. However, the low-spin state is only stable at low temperature, 1
Corresponding author, current address: Department of Physics, University of Minnesota, 116 Church St. SE, Minneapolis MN 55455, USA; E-mail: [email protected]
the compound experiences a thermally assisted magnetic transition from the low-spin state to a high-spin state ŽHS, S s 2, t 24 g e g2 . at around 90 K w12x. In addition, another unclear transition takes place at 500 K, where the system changes from an activated semiconductor to a metallic conductor w13x. Recently, Korotin et al. w14x proposed that the low temperature transition most likely takes place between the low-spin state and the intermediate-spin state ŽIS, t 25 g e 1g .. Upon Sr substitution, both photoemission spectra w15x and electrical resistivity measurements w4,16x also revealed that there appears an insulator-metal transition for a doping concentration x s 0.2 due to the overlap among the doping induced hole states
0375-9601r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 1 6 8 - 1
M. Zhuang et al.r Physics Letters A 255 (1999) 354–360
and the valence band. Because the ionic radius of the Sr 2q is larger than that of the La3q, the crystal field strength Dq is reduced, which favors the magnetic state in the system. Thus, the insulator-metal transition is accompanied by a magnetic transition from the nonmagnetic state to the ferromagnetically ordered state w8–11,16,17x. While most of the studies suggested that two transitions occur almost at the same doping concentration, another result has also been reported w18x. Furthermore, the thorough investigation showed that the compound is in the spin-glass state for low doping concentration w19,20x and in the ferromagnetic cluster-glass state for high doping concentration w11,19x. As a result, the ferromagnetic state here seems to lack the proper long range order in contrast to that in the Mn perovskite, this difference may also reflect in the physical mechanisms of magnetoresistance in these materials. The nature of the various spin-states in this compound is still a controversial issue; there is no consensus reached on the spin state of Co 3q and Co 4q in the system. While Sathe et al. w21x proposed that the Co 3q ions are in a mixed low-spin high-spin state and the Co 4q ions are in the low-spin state for the ferromagnetic region 0.2 F x F 0.5, Taguchi et al. w17x indicated that Co 3q ions are in the high-spin state in the doping range 0.5 F x F 1.0. More recently, photoemission results also suggested that the possible intermediate-spin state is realized in the ferromagnetic phase w22x. In fact, the spin-state of different Co ions not only depends on the doping concentration x, but also depends on the temperature due to the entropy effect. Thus, it is of great interest to make a systematic study in the whole doping range to elucidate the properties of the various Co ions, the spin-states, as well as the magnetic transition so that the giant magnetoresistance can be understood. Previously, the magnetoresistance of this material was explained in terms of the so-called double exchange model w23x and La 1y x Sr x CoO 3 is also classified as the double exchange system w5,18x. Nevertheless, one has observed the negative magnetoresistance in the insulator regime w7x and the positive ones in the doping range x ) 0.4 w4,24x, which are not found in the Mn perovskite. Mahendiran and Raychaudhuri suggested that the spin-state transition and the spin-cluster freezing both play an important
355
role in the curious negative magnetoresistance in the insulating samples w24x. Therefore, in this paper we have studied the Sr doping effect on the spin state of the Co perovskite, periodic structures with both primary cell and doubled cell are considered to allow the existence of various magnetic states. Although the periodicity condition restricts the structures of magnetic states under investigation, the doubled cell structures accommodate all interested magnetic states proposed so far. It is well known that LaCoO 3 has a pseudo-cubic perovskite structure with a rhombohedral distortion, with Sr doping the system gradually approaches to an ideal perovskite. For simplicity, we treated the materials as a pure perovskite and considered Sr doping merely reducing the valence electrons. The calculation is performed within the unrestricted Hartree–Fock approximation on a realistic perovskite-type lattice model. Various initial configurations for the single and doubled cell are given to imitate the LS, IS, and HS states as well as their superpositions, the selfconsistent solutions are sought using the iteration method. With the band structure parameters deduced from the photoemission spectra as input, we obtained the nonmagnetic low-spin state of LaCoO 3 and the ferromagnetic intermediate-spin state of SrCoO 3 Ž t 24 g e 1g , S s 3r2.., which are in agreement with the experiments w8–11,25x. Moreover, we also obtained modulated structures consisting of the superposition of above three spin-states, ´ which were emphasized by Senaris-Rodriguez and ˜ ´ Goodenough w11x for LaCoO 3 . To compare the relative stability of the various states, we have computed their energies as functions of x. Our results show that the first magnetic transition takes place at x G 0.25 between the LS state and the ferromagnetic IS state; as the doping concentration increases to x s 0.41, the magnetic ground state of the system changes from the ferromagnetic IS state into the superposition of intermediate-spin high-spin ordered state; the high-spin state becomes the ground state only near the doping concentration x G 0.94. It is interesting to find that t 2 g electrons remain localized after doping, the system possesses the half-metallic behavior as in the La 1y x Ca x MnO 3 w26x. The total density of states at the Fermi energy is extremely low when x - 0.2, this suggests that any insulator metal transition occurs only after x s 0.2. Also the character of the
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valence band becomes more O–p weighted as doping removes d electrons from the system. All these features are consistent with the experimental observations. In Section 2, we first introduce the multiband Hubbard model proposed for the real perovskite-type material, then the real space recursion method is also briefly outlined together with the unrestricted Hartree–Fock approximation. In Section 3, we analyze the Sr doping effect on the properties of Co perovskite based on the numerical results. The conclusion is drawn in Section 4.
Ž pps ., and Ž ppp . w28x. Sidm is the total spin operator of Co ion extracting the one in orbital m, u˜ s u y 5 jr2. The parameter u is related to the multiplet averaged d y d Coulomb interaction U via u s U q 209 j. Next, we linearize the Hamiltonian within the unrestricted Hartree–Fock approximation, and obtain the effective tight-binding Hamiltonian as below j H s Ý e d0m q un di m s y s Ž m td y m md . 2 im s qu˜ Ž n dt y n dm . d i†m s d i m s q
Ý e p p†jn s pjn s jn s
q
2. Theoretical formalism
Ý Ž
t imj n d i†m s
pjn s q h.c. .
ijmn s
To study the perovskite compounds, the following multiband d-p model w27x, which includes the full degeneracy of the transition metal 3d orbitals and oxygen 2 p orbitals as well as on-site Coulomb and exchange interactions, are generally adopted.
Ž 1a .
H s H0 q H1 H0 s
Ý
e d0m d i†m s
dims q Ý
im s
e p p†jn s
pjn s
jn s
Ý Ž t imj nd i†m s pjn s q h.c. .
q
ijmn s X
Ý Ž t injn p†i n s pjn s q h.c. .
q
Ž 1b .
X
X
ijnn s
H1 s Ý ud i†m ≠ d i m ≠ d i†m x d i m x im
q 12
˜ i†m s d i m s d i†m s Ý ud X
X
im/m ss
yj
Ý im ss
X
X
d i†m s s d i m s X P Sidm .
X
d i mX s X
X
q
Ý Ž t injn p†i n s pjn s q h.c. . . X
Ž 2.
X
ijnn s
Here, n dm s s ² d m† s d m s :, m md s n dm ≠ y n dm x , and n dt and m td are the total electron numbers and magnetization of the Co–d orbitals, which are to be determined self-consistently. For simplicity, we choose the z-axis as the spin quantization axis so that all the magnetic states are Ising-type structures. For the tight-binding Hamiltonian Eq. Ž2., the density of states can be easily calculated using the real space recursion method w29x. Instead of diagonalizing the Hamiltonian with the dimension of the number of orbitals in the primitive cell, the recursion method choose one particular lattice site, where the density of states is acquired, and tridiagonalizes the Hamiltonian to a certain number of levels; one then writes the Green’s function as
Ž 1c .
Here d i m s Ž d i†m s . and pjn s Ž p†jn s . denote the annihilation Žcreation. operators of an electron on Co–d m orbital at site i and O–p n orbital at site j with the spin s , respectively. The on-site energy of O–p orbital is set to be zero. The crystal-field-splitting energy is included in the on-site energy of the Co–d orbital e d0m as e d0 Ž t 2 g . s e d0 y 4 Dq and e d0 Ž e g . s e d0 q 6 Dq, where e d0 X is the bare on-site energy of d orbital. t imj n and t injn are the nearest neighbor hopping integrals for p-d and p-p which is expressed in terms of Slater–Koster parameters Ž pd s ., Ž pdp .,
Ž3.
The coefficients a i and bi are obtained from the tridiagonalization of the tight-binding Hamiltonian matrix for a given starting orbital. The multiband terminator w30x is chosen in our calculation to close the continuous fractional. Once the Green’s function is obtained, the density of states could be worked out
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with the relation rms Ž v . s yŽ1rp .ImGmsŽ v .. This allows us to calculate the electron numbers, magnetic moments, as well as the energies of various possible stable states. To accommodate both the single-cell and doublecell magnetic structures, the numerical calculation are carried out uniformly in the doubled cell. For every trial state there are 38 independent orbitals to be calculated for each iteration, and we compute 25 levels for the continuous fractional coefficients of each orbital. The whole procedure is iterated selfconsistently till convergence of electron numbers in each orbitals, hence the magnetic moment and energy. We have checked our results for different levels to ensure the accuracy of energy calculation and better than 5 meV in energy accuracy is secured. Note that the 5 meV energy accuracy in our numerical calculation is much smaller than the energy difference ; 0.1 eV between the different spin states. 3. Numerical results and discussions The parameter set of the compound can be derived from the cluster model analysis of the photoemission spectra w16x as well as the ab initio local spin density approximation ŽLSDA. calculations w31x. The densities of states ŽDOS. of the end members LaCoO 3 and SrCoO 3 using these parameters are in a excellent agreement with both experiments and ab initio calculations. Furthermore, we found that the dependence of DOS as a function of doping level is also in consistent with the photoemission experiments w15x. The parameter set thus obtained is as follows: The bare on-site energies of Co–d and O–p orbitals are taken as e d0 s y28.0 eV and e p s 0 eV. The Slater–Koster parameters are Ž pd s . s y2.0 eV, Ž pdp . s 0.922 eV, Ž pps . s 0.6 eV, and Ž ppp . s y0.15 eV, respectively. The on-site Coulomb repulsion is U s 5.0 eV. The crystal field strength and Hund’s coupling are set as Dq s 0.16 eV and j s 0.84 eV. As will be shown below, this parameter set does reproduce the low-spin ground state of LaCoO 3 and the intermediate-spin ground state of SrCoO 3 which are observed experimentally w8–11,25x. We use the spin-states of Coq3 as references and study the evolution of the LS state, IS state, and HS state as well as their neighboring ordered states as a function of Sr doping concentration. The densities of
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states are calculated, stabilities of various states are analyzed, and phase diagram as function of doping is obtained. According to our numerical calculations, we found that t 2 g electrons in these states remain localized and the number of itinerant e g electrons is reduced with the doping, except for the low-spin state without e g electrons. The main magnetic moment of the system is due to the localized t 2 g electrons, which can be clearly seen from the spinresolved density of states discussed below. To save space, only the spin-states which become the ground states at certain doping range are discussed in detail. In Fig. 1, we present the energies of four spinstates as a function of doping concentration x. They are the LS state, the IS state, the HS state, and the IS–HS ferromagnetically ordered state. All energies decrease monotonically with x and with different slopes, the crossover points between different spinstates separate the doping parameter into several regions where one of the four spin-states becomes the ground state. For x F 0.25, the system is in the nonmagnetic LS state as LaCoO 3 . The ferromagnetic IS state becomes the energetically most favorable state between x s 0.25 and 0.41, which is followed by the IS–HS ferromagnetically ordered state. The HS state only exists near the doping concentration x s 1.0. From the ion configuration of Co 4q, the HS state here for x s 1.0 is exactly the IS state of SrCoO 3 as expected. Next, we illustrate the electronic structures of each ground state of different x one by one.
Fig. 1. The energies per doubled cell of the various spin states as a x 0 5 1y x x function of x. The configurations t 26y and t 24 g e 2y g e g , t2 g e g g refer to the low-spin, the intermediate-spin, and the high-spin states, respectively.
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We first calculate the densities of states of end members LaCoO 3 and SrCoO 3 . As shown in Fig. 2, LaCoO 3 is a LS insulator. The first peak near the top of valence band comes mostly from the occupied t 2 g band, the other two peaks below the Fermi energy are mainly contributed by the O–p orbitals. The e g band is located above the Fermi energy and is nearly unoccupied. These main features are in agreement both with the photoemission spectra w16x and with the previous results obtained using LSDA method w31x. In Fig. 3, the density of states of SrCoO 3 is also presented. One can see clearly that SrCoO 3 is in the metallic IS state with a magnetic moment of 2.96 m B per Co ions. Quite different from LaCoO 3 , the contribution of Co t 2 g electrons is shifted towards the low energy. The density of states near the Fermi energy is dominated by the O–p orbitals. These features of SrCoO 3 can be well compared with the experiments w25x. Upon Sr doping, significant changes take place in electrical and magnetic properties of the system. For low doping concentration Ž x - 0.2., the system remains a nonmagnetic LS state. Fig. 4 also shows that the density of states at Fermi energy is extremely low and Fermi energy still stays in the tail regime
Fig. 2. The density of states of the low-spin state of LaCoO 3 . From top to bottom are the partial densities of states for the Co– d orbitals, O– p orbitals, and total density of states, respectively. The upward and downward curves represent the spin-up and spin-down states. The other parameters are described in the text.
Fig. 3. The density of states of the intermediate-spin state of SrCoO 3 . The other parameters and notation are the same as in Fig. 2.
which reminisces the localized states. Thus, the insulator-metal transition might result from doping induced Mott–Anderson delocalization transition. When 0.25 - x F 0.41, the ground state of the system turns out to be the IS state and its typical density
Fig. 4. The density of states of the low-spin state at doping concentration x s 0.2. The other parameters and notation are the same as in Fig. 2.
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of states is shown in Fig. 5 for x s 0.3. This spin-state has the metallic nature due to the presence of finite density of states at Fermi energy. In comparison with that of the LS state, the Co–d bands shifts slightly downwards while the O–p bands shifts upwards, the trend is even more pronounced with the increase of doping. Especially, the Co t 2 g peaks diminish so that the spectral distribution becomes broader. As doping increases further, some IS Co ions are replaced by the HS ions with the same moment direction. Our numerical search reveals that the IS–HS ferromagnetically ordered state is the ground state for 0.41 - x F 0.95, the partial densities of states of the two different Co ions are shown in Fig. 6Ža. and Žb.. It is found that e g bands of two Co ions are always flat and broad, while t 2 g bands of the IS Co ions ŽFig. 6Ža.. show several splitted peaks at edges of the valence band. On the contrary, the small t 2 g peaks of HS Co ions ŽFig. 6Žb.. move to the bottom of the valence band. These peaks result from the moment formation and thus band splitting. From the total density of states, it is clear that the main feature of the valence band comes from the O–p orbitals, while the total band width is mainly determined by the Co–d bands and increases with doping. This feature is consistent with the photoemission experiments w15x. The magnetic moments of two Co
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Fig. 6. The density of states of the intermediate-spin high-spin ferromagnetically ordered state at doping concentration x s 0.7. From top to bottom are the partial densities of states for the IS Co– d orbitals, HS Co– d orbitals, O– p orbitals, and total density of states, respectively. The other parameters are the same as in Fig. 2.
ions are 1.61 m B and 3.16 m B and their average moment is 2.385m B . It is worthwhile to mention that doped LaCoO 3 compound belongs to the half-metal category according to Pickett and Singh w26x, which resembles the electronic structures of La 1y x Ca xMnO 3 .
4. Conclusion
Fig. 5. The density of states of the intermediate-spin state at doping concentration x s 0.3. The other parameters and notation are the same as in Fig. 2.
In summary, we have studied the effect of Sr doping on the magnetic and electronic properties of LaCoO 3 . Starting with the initial configurations of LaCoO 3 , we calculated various spin states using the unrestricted Hartree–Fock approximation of the multiband d-p model and real space recursion method. Our result shows that four possible ground states are stable at different doping ranges, the system changes consecutively from the low-spin state to the intermediate-spin state, then to the intermediatespin high-spin ordered state, and finally to the highspin state as doping varies from 0 to 1. The evolution of the spectral shapes is also in accord with the experimental observations.
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Acknowledgements The present work is supported in part by the National Natural Science Foundation of China under Grant Nos. NNSF 19677202 and 19674027 and the key research project in ‘Climbing Program’ by the National Science and Technology Commission of China.
References w1x R. von Helmholt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer, Phys. Rev. Lett. 71 Ž1993. 2331. w2x M. McCormack, S. Jin, T.H. Tiefl, R.M. Fleming, J.M. Phillips, R. Ramesh, Appl. Phys. Lett. 64 Ž1994. 3045. w3x P. Schiffer, A.P. Ramirez, W. Bao, S.W. Cheong, Phys. Rev. Lett. 75 Ž1995. 3336. w4x R. Mahendiran, A.K. Raychaudhuri, A. Chainani, adn D.D. Sarma, J. Phys.: Condens. Matter 7 Ž1995. L561. w5x S. Yamaguchi, H. Taniguchi, H. Takagi, T. Arima, Y. Tokura, J. Phys. Soc. Jpn. 54 Ž1995. 1885. w6x G. Briceno, H. Chang, X. Sun, P.G. Schultz, X.D. Xiang, Science 270 Ž1995. 273. w7x V. Golovanov, L. Mihaly, A.R. Moodenbaugh, Phys. Rev. B 53 Ž1996. 8207. w8x P.M. Raccah, J.B. Goodenough, Phys. Rev. 155 Ž1967. 932. w9x G.H. Jonker, J.H. Van Santen, Physica 19 Ž1953. 120. w10x V.G. Bhide, D.S. Rajoria, G.R. Rao, C.N.R. Rao, Phys. Rev. B 6 Ž1972. 1021. ´ w11x M.A. Senaris-Rodriguez, J.B. Goodenough, J. Solid state ˜ ´ Chem. 116 Ž1995. 224; 118 Ž1995. 323. w12x K. Asai, P. Gehring, H. Chou, G. Shirane, Phys. Rev. B 40 Ž1989. 10982. w13x S. Yamaguchi, Y. Okimoto, H. Taniguchi, Y. Tokura, Phys. Rev. B 53 Ž1996. R2926.
w14x M.A. Korotin, S.Yu. Ezhov, I.V. Solovyev, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. B 54 Ž1996. 5309. w15x A. Chainani, M. Mathew, D.D. Sarma, Phys. Rev. B 46 Ž1992. 9976. w16x P.M. Raccah, J.B. Goodenough, J. Appl. Phys. 39 Ž1967. 1209. w17x H. Taguchi, M. Shimada, M. Koizumi, Mater. Res. Bull. 13 Ž1978. 1225; J. Solid State Chem. 29 Ž1979. 221; 33 Ž1980. 169. w18x P. Ganguly, P.S. Anil Kumar, P.N. Santhosh, I.S. Mulla, J. Phys.: Condens. Matter. 6 Ž1994. 533. w19x M. Itoh, I. Natori, S. Kuboto, K. Motoya, J. Phys. Soc. Jpn. 63 Ž1994. 1486. w20x K. Asai, O. Yokokura, N. Nishimori, H. Chou, J.M. Tranquada, G. Shirane, S. Higuchi, Y. Okajima, K. Kohn, Phys. Rev. B 50 Ž1994. 3025. w21x V.G. Sathe, A.V. Pimpale, V. Siruguri, S.K. Paranjpe, J. Phys.: Comdens. Matter 8 Ž1996. 3889. w22x T. Saitoh, T. Mizokawa, A. Fujimori, M. Abbate, T. Takeda, M. Takano, Phys. Rev. B 56 Ž1997. 1290. w23x C. Zener, Phys. Rev. 81 Ž1951. 440; P.G. de Gennes, Phys. Rev. 118 Ž1960. 141. w24x R. Mahendiran, A.K. Raychaudhuri, Phys. Rev. B 54 Ž1996. 16044. w25x R.H. Potze, G.A. Sawatzky, M. Abbate, Phys. Rev. B 51 Ž1995. 11501. w26x W.E. Pickett, D.J. Singh, Phys. Rev. B 53 Ž1996. 1146. w27x T. Mizokawa, A. Fujimori, Phys. Rev. B 53 Ž1996. R4201; B 54 Ž1996. 5368; B 51 Ž1995. 12880. w28x J.C. Slater, G.F. Koster, Phys. Rev. 94 Ž1954. 1498. w29x V. Heine, R. Haydock, M.J. Kelly, in: H. Ehrenreich, F. Seitz, D. Turnbull ŽEds.., Solid state Physics: Advances in Research and Applications, vol. 35, Academic, New York, 1980, p. 215. w30x R. Haydock, C.M.M. Nex, J. Phys. C 17 Ž1984. 4783. w31x D.D. Sarma, N. Shanthi, S.R. Barman, N. Hamada, H. Sawada, K. Terakura, Phys. Rev. Lett. 75 Ž1995. 1126.