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Na0.75CoO2—an itinerant magnet?
Physica C 460–462 (2007) 495–496 www.elsevier.com/locate/physc
Na0.75CoO2—an itinerant magnet? Helmut Eschrig *, Klaus Koepernik IFW Dresden, P.O. Box 27 00 16, D-01171 Dresden, Germany Available online 27 March 2007
Abstract NaxCoO2 for x 0.75 is a rather unusual metal. It is an . . .ABAB. . . stack of CoO2 sheets intercalated with Na atoms. It has a large Curie–Weiss magnetic susceptibility. Neutron scattering sees spin correlations which are ferromagnetic in plane and antiferromagnetic in stack direction. Below about 22 K it orders in this way with an unusual small moment of about 0.2 lBohr per Co atom. Its Fermi surface measured by photoemission is a cylinder around the stack axis. Density functional calculations in local spin density approximation are presented which treat the partial Na occupation in a well justified virtual crystal approximation. They provide all those findings and yield an understanding as itinerant magnetism. In addition, a ferromagnetic order also in stack direction, which is a very clear half-metall, is nearly energetically degenerate with the antiferromagnetic ground state, with dramatic Fermi surface reconstruction. This could yield a clue to the anomalous thermopower and its strong field dependence. Ó 2007 Elsevier B.V. All rights reserved. PACS: 71.15.Mb; 71.18.+y; 71.20.Be; 75.50.Ee Keywords: Cobaltates; Magnetism; Fermi surface
Sodium cobaltate, NaxCoO2, 0 6 x < 1 is a currently very actively investigated material both because of its anomalous and badly understood properties and because of its application potential based on its superconductivity [1], its magnetic properties [2], its thermopower [3], possible half-metallicity [4,5], charge ordering [6] and others. Electronic structure calculations [4,5,7–17] come to no clear decision on the role of possible medium or strong correlations favored by [5,9–11,13,14,16] and/or charge and spin ordering effects favored by [4,7,8,12,15,17]. While the interest in low Na concentration (x 0.3) comes from superconductivity in hydrated samples, high Na concentration (x 0.75) is of interest because of the magnetic and thermoelectric properties. Photoemission (PES) sees a single large Fermi surface (FS) in this latter concentration region [18,19]. Quite early [4] there was theoretical evidence that NaxCoO2 could be weakly correlated and possibly instable against itinerant magnetism even for x 0.5. Further support for this point of view can be inferred from [5], if their *
Corresponding author. E-mail address: [email protected] (H. Eschrig).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.078
computed FS for x = 0.7 is compared with the PES data. The measured in-plane anisotropy is in much better agreement with computed results for local spin density approximation (LSDA) than for LSDA + U. However, this latter work neglects the dispersion in stacking direction which is quite sizable and which is distinct for ferro- and antiferromagnetic spin order in this direction by symmetry. Na disorder/order phenomena, in connection with Co valency disproportionation or not, are another very interesting issue [4,6,11,12,20–22]. Here, very accurate total energy and FS calculations for Na0.75CoO2 based on LSDA are reported using the FPLO code [23]. A complete disorder of the Na-sites in their planes is assumed and treated in virtual crystal approximation which should be not crucial due to the weak Na potential for valence electrons. The computational details will be published separately. The result is a ground state with the observed magnetic order, ferromagnetic layers in antiferromagnetic (AFM) stack with a site moment slightly below 0.2 lB per Co site (this is a not very accurately defined quantity in an itinerant picture), only 3 meV below the ferromagnetic (FM) state which is half-metallic and hence has a
496
H. Eschrig, K. Koepernik / Physica C 460–462 (2007) 495–496
References
Fig. 1. FS of FM (two sheets of upper two panels) and AFM (lower panel) Na0.75CoO2.
moment of 0.25 lB determined by the hole count. The nonmagnetic solution is 9 meV above the ground state. These results are in nice agreement with experimentally estimated magnetic in-plane and out-of-plane couplings [24], and with an explanation of the weak in-plane coupling [15]. Fig. 1 shows the FS of the AFM and FM states which, however, differ dramatically due to an symmetry enforced degeneracy of two minority spin bands for kz = ±p/c in the FM case which is split in the AFM order where only one spin degenerate FS sheet survives. The average Fermi velocity and the density of states at the Fermi level differ in both cases by more than a factor of 2, which must have dramatic effects on the thermopower and in temperature and magnetic field dependences of properties.
[1] K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422 (2003) 53. [2] A.T. Boothroyd, R. Coldea, D.A. Tennant, D. Prabhakaran, L.M. Helme, C.D. Frost, Phys. Rev. Lett. 92 (2004) 197201. [3] I. Terasaki, Y. Sasago, K. Uchinokura, Phys. Rev. B 56 (1997) R12685. [4] D.J. Singh, Phys. Rev. B 61 (2000) 13397. [5] P. Zhang, W. Luo, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 93 (2004) 236402. [6] J.L. Gavilano, D. Rau, B. Pedrini, J. Hinderer, H.R. Ott, S.M. Kazakov, J. Karpinski, Phys. Rev. B 69 (2004) 100404. [7] M.D. Johannes, D.J. Singh, Phys. Rev. B 70 (2004) 014507. [8] M.D. Johannes, D.A. Papaconstandtopoulos, D.J. Singh, M.J. Mehl, Europhys. Lett. 68 (2004) 433. [9] P. Zhang, W. Luo, V.C. Crespi, M.L. Cohen, S.G. Louie, Phys. Rev. B 70 (2004) 085108. [10] G. Khaliullin, W. Koshibae, S. Maekawa, Phys. Rev. Lett. 93 (2004) 176401. [11] K.-W. Lee, J. Kunesˇ, P. Novak, W.E. Pickett, Phys. Rev. Lett. 94 (2005) 026403. [12] P. Zhang, R.B. Capaz, M.L. Cohen, S.G. Louie, Phys. Rev. B 71 (2005) 153102. [13] H. Ishida, M.D. Johannes, A. Liebsch, Phys. Rev. Lett. 94 (2005) 196401. [14] S. Zhou, M. Gao, H. Ding, P.A. Lee, Z. Wang, Phys. Rev. Lett. 94 (2005) 206401. [15] M.D. Johannes, I.I. Mazin, D.J. Singh, Phys. Rev. B 71 (2005) 214410. [16] K.-W. Lee, W.E. Pickett, Phys. Rev. B 72 (2005) 115110. [17] K.-W. Lee, W.E. Pickett, Phys. Rev. Lett. 96 (2006) 096403. [18] M.Z. Hasan, Y.-D. Chuang, D. Qian, Y.W. Li, Y. Kong, A. Kuprin, A.V. Fedorov, R. Kimmerling, E. Rotenberg, K. Rossnagel, Z. Hussain, H. Koh, N.S. Rogado, M.L. Foo, R.J. Cava, Phys. Rev. Lett. 92 (2004) 246402. [19] H.-B. Yang, S.-C. Wang, A.K.P. Sekharan, H. Matsui, S. Souma, T. Sato, T. Takahashi, T. Takeuchi, J.C. Campuzano, R. Jin, B.C. Sales, D. Madrus, Z. Wang, H. Ding, Phys. Rev. Lett. 95 (2005) 146401. [20] M.L. Foo, Y. Wang, S. Watauchi, H.W. Zandbergen, T. He, R.J. Cava, N.P. Ong, Phys. Rev. Lett. 92 (2004) 247001. [21] C. Bernhard, A.V. Boris, N.N. Kovaleva, G. Khaliullin, A.V. Pimenov, L. Yu, D.P. Chen, C.T. Lin, B. Keimer, Phys. Rev. Lett. 93 (2004) 167003. [22] Q. Huang, M.L. Foo, R.A. Pascal Jr., W.J. Lynn, B.H. Toby, T. He, H.W. Zandbergen, R.J. Cava, Phys. Rev. B 70 (2004) 184110. [23] H. Eschrig, K. Koepernik, Phys. Rev. B 59 (1999) 1743. [24] L.M. Helme, A.T. Boothroyd, R. Coleda, D. Prabhakaran, D.A. Tennant, A. Hiess, J. Kulda, Phys. Rev. Lett. 94 (2005) 157206.
Na0.75CoO2—an itinerant magnet? Helmut Eschrig *, Klaus Koepernik IFW Dresden, P.O. Box 27 00 16, D-01171 Dresden, Germany Available online 27 March 2007
Abstract NaxCoO2 for x 0.75 is a rather unusual metal. It is an . . .ABAB. . . stack of CoO2 sheets intercalated with Na atoms. It has a large Curie–Weiss magnetic susceptibility. Neutron scattering sees spin correlations which are ferromagnetic in plane and antiferromagnetic in stack direction. Below about 22 K it orders in this way with an unusual small moment of about 0.2 lBohr per Co atom. Its Fermi surface measured by photoemission is a cylinder around the stack axis. Density functional calculations in local spin density approximation are presented which treat the partial Na occupation in a well justified virtual crystal approximation. They provide all those findings and yield an understanding as itinerant magnetism. In addition, a ferromagnetic order also in stack direction, which is a very clear half-metall, is nearly energetically degenerate with the antiferromagnetic ground state, with dramatic Fermi surface reconstruction. This could yield a clue to the anomalous thermopower and its strong field dependence. Ó 2007 Elsevier B.V. All rights reserved. PACS: 71.15.Mb; 71.18.+y; 71.20.Be; 75.50.Ee Keywords: Cobaltates; Magnetism; Fermi surface
Sodium cobaltate, NaxCoO2, 0 6 x < 1 is a currently very actively investigated material both because of its anomalous and badly understood properties and because of its application potential based on its superconductivity [1], its magnetic properties [2], its thermopower [3], possible half-metallicity [4,5], charge ordering [6] and others. Electronic structure calculations [4,5,7–17] come to no clear decision on the role of possible medium or strong correlations favored by [5,9–11,13,14,16] and/or charge and spin ordering effects favored by [4,7,8,12,15,17]. While the interest in low Na concentration (x 0.3) comes from superconductivity in hydrated samples, high Na concentration (x 0.75) is of interest because of the magnetic and thermoelectric properties. Photoemission (PES) sees a single large Fermi surface (FS) in this latter concentration region [18,19]. Quite early [4] there was theoretical evidence that NaxCoO2 could be weakly correlated and possibly instable against itinerant magnetism even for x 0.5. Further support for this point of view can be inferred from [5], if their *
Corresponding author. E-mail address: [email protected] (H. Eschrig).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.03.078
computed FS for x = 0.7 is compared with the PES data. The measured in-plane anisotropy is in much better agreement with computed results for local spin density approximation (LSDA) than for LSDA + U. However, this latter work neglects the dispersion in stacking direction which is quite sizable and which is distinct for ferro- and antiferromagnetic spin order in this direction by symmetry. Na disorder/order phenomena, in connection with Co valency disproportionation or not, are another very interesting issue [4,6,11,12,20–22]. Here, very accurate total energy and FS calculations for Na0.75CoO2 based on LSDA are reported using the FPLO code [23]. A complete disorder of the Na-sites in their planes is assumed and treated in virtual crystal approximation which should be not crucial due to the weak Na potential for valence electrons. The computational details will be published separately. The result is a ground state with the observed magnetic order, ferromagnetic layers in antiferromagnetic (AFM) stack with a site moment slightly below 0.2 lB per Co site (this is a not very accurately defined quantity in an itinerant picture), only 3 meV below the ferromagnetic (FM) state which is half-metallic and hence has a
496
H. Eschrig, K. Koepernik / Physica C 460–462 (2007) 495–496
References
Fig. 1. FS of FM (two sheets of upper two panels) and AFM (lower panel) Na0.75CoO2.
moment of 0.25 lB determined by the hole count. The nonmagnetic solution is 9 meV above the ground state. These results are in nice agreement with experimentally estimated magnetic in-plane and out-of-plane couplings [24], and with an explanation of the weak in-plane coupling [15]. Fig. 1 shows the FS of the AFM and FM states which, however, differ dramatically due to an symmetry enforced degeneracy of two minority spin bands for kz = ±p/c in the FM case which is split in the AFM order where only one spin degenerate FS sheet survives. The average Fermi velocity and the density of states at the Fermi level differ in both cases by more than a factor of 2, which must have dramatic effects on the thermopower and in temperature and magnetic field dependences of properties.
[1] K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422 (2003) 53. [2] A.T. Boothroyd, R. Coldea, D.A. Tennant, D. Prabhakaran, L.M. Helme, C.D. Frost, Phys. Rev. Lett. 92 (2004) 197201. [3] I. Terasaki, Y. Sasago, K. Uchinokura, Phys. Rev. B 56 (1997) R12685. [4] D.J. Singh, Phys. Rev. B 61 (2000) 13397. [5] P. Zhang, W. Luo, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 93 (2004) 236402. [6] J.L. Gavilano, D. Rau, B. Pedrini, J. Hinderer, H.R. Ott, S.M. Kazakov, J. Karpinski, Phys. Rev. B 69 (2004) 100404. [7] M.D. Johannes, D.J. Singh, Phys. Rev. B 70 (2004) 014507. [8] M.D. Johannes, D.A. Papaconstandtopoulos, D.J. Singh, M.J. Mehl, Europhys. Lett. 68 (2004) 433. [9] P. Zhang, W. Luo, V.C. Crespi, M.L. Cohen, S.G. Louie, Phys. Rev. B 70 (2004) 085108. [10] G. Khaliullin, W. Koshibae, S. Maekawa, Phys. Rev. Lett. 93 (2004) 176401. [11] K.-W. Lee, J. Kunesˇ, P. Novak, W.E. Pickett, Phys. Rev. Lett. 94 (2005) 026403. [12] P. Zhang, R.B. Capaz, M.L. Cohen, S.G. Louie, Phys. Rev. B 71 (2005) 153102. [13] H. Ishida, M.D. Johannes, A. Liebsch, Phys. Rev. Lett. 94 (2005) 196401. [14] S. Zhou, M. Gao, H. Ding, P.A. Lee, Z. Wang, Phys. Rev. Lett. 94 (2005) 206401. [15] M.D. Johannes, I.I. Mazin, D.J. Singh, Phys. Rev. B 71 (2005) 214410. [16] K.-W. Lee, W.E. Pickett, Phys. Rev. B 72 (2005) 115110. [17] K.-W. Lee, W.E. Pickett, Phys. Rev. Lett. 96 (2006) 096403. [18] M.Z. Hasan, Y.-D. Chuang, D. Qian, Y.W. Li, Y. Kong, A. Kuprin, A.V. Fedorov, R. Kimmerling, E. Rotenberg, K. Rossnagel, Z. Hussain, H. Koh, N.S. Rogado, M.L. Foo, R.J. Cava, Phys. Rev. Lett. 92 (2004) 246402. [19] H.-B. Yang, S.-C. Wang, A.K.P. Sekharan, H. Matsui, S. Souma, T. Sato, T. Takahashi, T. Takeuchi, J.C. Campuzano, R. Jin, B.C. Sales, D. Madrus, Z. Wang, H. Ding, Phys. Rev. Lett. 95 (2005) 146401. [20] M.L. Foo, Y. Wang, S. Watauchi, H.W. Zandbergen, T. He, R.J. Cava, N.P. Ong, Phys. Rev. Lett. 92 (2004) 247001. [21] C. Bernhard, A.V. Boris, N.N. Kovaleva, G. Khaliullin, A.V. Pimenov, L. Yu, D.P. Chen, C.T. Lin, B. Keimer, Phys. Rev. Lett. 93 (2004) 167003. [22] Q. Huang, M.L. Foo, R.A. Pascal Jr., W.J. Lynn, B.H. Toby, T. He, H.W. Zandbergen, R.J. Cava, Phys. Rev. B 70 (2004) 184110. [23] H. Eschrig, K. Koepernik, Phys. Rev. B 59 (1999) 1743. [24] L.M. Helme, A.T. Boothroyd, R. Coleda, D. Prabhakaran, D.A. Tennant, A. Hiess, J. Kulda, Phys. Rev. Lett. 94 (2005) 157206.