- Email: [email protected]
Fermi surfaces of LaFePO and the related compounds
Physica C 470 (2010) S320–S321
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Fermi surfaces of LaFePO and the related compounds Tomoaki Kanai a,*, Hisatomo Harima a,b a b
Department of Physics, Faculty of Science, Kobe University, Hyogo 657-8501, Japan JST, Transformative Research-Project on Iron Pnictides (TRIP), Chiyoda 102-0075, Japan
a r t i c l e
i n f o
Article history: Accepted 4 November 2009 Available online 10 November 2009 Keywords: Iron-pnictides Band structure calculation Fermi surfaces
a b s t r a c t Full-potential band structure calculations within LDA have been carried out for new iron-based superconductors LaFePO and the related compounds. Cylindrical Fermi surfaces characterise the conduction bands in these iron-based superconductors. Obtained Fermi surfaces are compared with the experimental dHvA results, then quantitatively better agreement is realised in our full-potential results. Ó 2009 Published by Elsevier B.V.
1. Introduction
2. Calculation
The iron-based oxyarsenides superconductors have attracted much attention, because of their high T c for superconductivity and the adjacent magnetic phases [1]. For example, antiferromagnetic LaFeAsO, when F is doped, undergoes superconductivity with T c ¼ 26 K [2]. Now SmFeAsO shows the highest T c of 55 K [3]. While, an isostructural compound LaFePO, the first discovered iron-oxypnictide superconductor, shows superconductivity with relatively low T c ¼ 7 K [4]. Even when electron or hole is doped to LaFePO, the T c does not increase so much. Therefore, it is important to investigate electronic structures and Fermi surfaces of these materials for the research of the higher T c superconductivity. These iron-pnictide compounds RTPnO (R ¼ rare earth; T ¼ Fe; Co; Ni, and Ru, Pn ¼ P or As) are the tetragonal ZrCuSiAs-type (P4/nmm) layered structure, which consists of alternating RO and TPn layered structure stacked along the [0 0 1] direction. Another iron-based superconductors AT 2 Pn2 (A: alkari metal) with the ThCr2 Si2 -type (I4/mmm) tetragonal structure are also studied extensively. Among the above pnictide superconductors, the dHvA measurements are already done for LaFePO [5] and for LaRuPO and LaFe2 P2 [6]. Bandstructure calculation for LaFePO [5,7] and LaRuPO and LaFe2 P2 [6] are also reported. However, the agreement is not satisfied quantitatively [5,6]. In this paper, we have applied a full potential scheme to analyse the origin of the discrepancy, because the Muffin-tin approximation; i.e. LAPW is used in the previous analysis [5,6].
Energy band calculations have been carried out for LaFePO, LaRuPO and LaFe2 P2 based on a relativistic full potential linearized augmented-plane-wave method (FLAPW) within a local density approximation (LDA). The program codes TSPACE and KANSAI-04 are used. Scalar relativistic effect is included for all electrons and the spin–orbit interaction is considered for valence electrons. The experimental lattice parameters are used in the calculations, as follows: LaFePO; a ¼ 3:957Å; c ¼ 8:507Å, and zP ¼ 0:36 for the 4e site of P [8], LaRuPO; a ¼ 4:047Å; c ¼ 8:406Å, and zP ¼ 0:35 [8], LaFe2 P2 ; a ¼ 3:838Å; c ¼ 11:006Å, and zP ¼ 0:35 [9].
* Corresponding author. E-mail address: [email protected] (T. Kanai). 0921-4534/$ - see front matter Ó 2009 Published by Elsevier B.V. doi:10.1016/j.physc.2009.11.030
3. Results and discussion Our FLAPW calculation for LaFePO has obtained Fermi surfaces very similar to the previous results calculated by using VASP (Vienna ab initio simulation package) [7]. The Fermi surfaces consist of four cylindrical sheets and one closed pocket. The similarity is realized not only in topology, but also in the sizes. The LAPW calculations show only four sheets of cylindrical Fermi surface [5]. Although, the dHvA frequencies and cyclotron masses are not obtained in the VASP calculation, cylindrical Fermi surfaces obtained by VASP (and also our FLAPW) look larger than the LAPW ones. Actually the a branch has the measured frequency 2:38 107 Oe for Hk½0 0 1, while the calculations are 0:979 107 Oe in LAPW [5] and 2:62 107 Oe in our FLAPW. Therefore, our results explain the dHvA frequencies qualitatively well. Now we can compare the cyclotron masses. The calculated cyclotron masses are about twice smaller than the measured cyclotron masses. For example, mex ¼ 2:28m0 for a dHvA branch named a in Ref. [5], while, the cor-
T. Kanai, H. Harima / Physica C 470 (2010) S320–S321
Fig. 1. The calculated density of states for (a) LaFePO and (b) LaRuPO. Green lines shows 3d or 4d components. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
responding calculated band mass is mb ¼ 0:97m0 , Therefore the mass enhancement is not so large in LaFePO. For LaRuPO, we have obtained very similar Fermi surfaces to those of LaFePO. Since the measured dHvA frequencies are also similar in LaRuPO and LaFePO [6], the calculated Fermi surfaces explain the measurements well. As for cyclotron masses, mex ¼ 0:85m0 for a dHvA branch named a in Ref. [6], while the corresponding calculated mass mb ¼ 0:54m0 . Then, the mass enhancement in LaRuPO is much smaller than that in LaFePO. The smaller correlation effect for 4d electrons can be generally accepted. The density of states (DOS) of LaFePO and LaRuPO are shown in Fig. 1. Ru-4d electrons in LaRuPO have wider band width than the Fe-3d electrons of LaFePO, then the DOS at the Fermi level of LaRuPO is smaller than that of LaFePO, due to the smaller contributions of d electrons. Then, smaller cyclotron masses and the smaller mass enhancement are introduced in LaRuPO. In the above two materials, two dimensional Fermi surfaces characterise the conduction bands, while three dimensional Fermi surfaces are obtained for LaFe2 P2 in the previous study [6]. From our FLAPW approach to LaFe2 P2 , the three sheets of Fermi surfaces are obtained, though the topology is slightly different with previous ones. As shown in Fig. 5 of Ref. [6]. The Fermi surfaces of LaFe2 P2 are rather three dimensional and the agreement in the
S321
dHvA frequencies is rather good. However, the calculated band masses are also much smaller than the measured cyclotron masses. For example, mex ¼ 2:7m0 for a dHvA branch named c in Ref. [6], while mb = 0.77m0 for the corresponding band mass. LaFePO and LaRuPO are a compensated metal, where the volume of electrons is the same as holes. While LaFe2P2 is an uncompensated metal, then the sum of the electron volume is just a half of the BZ. Therefore, the dHvA frequencies tend to be predicted better in an uncompensated metal, even larger mass enhancement indicates strong electron–electron correlation. For compensated metals, the volume of each carrier can be obtained as any number. In this study, the calculated volumes of the Fermi surfaces are in good agreement with experiments even for compensated metal, LaFePO and LaRuPO. This indicates the LDA with a full potential scheme is working well in describing the Fermi surfaces in these materials. The success is not related to the many body effect causing mass enhancement, because the mass enhancement factor is very different in the two compounds. Recently, a single crystal of KFe2 As2 is synthesised, and the Fermi surfaces are expected to be cylindrical [10]. The reported large specific heat coefficient c, which is about 70 mJ=ðK2 molÞ, strongly indicates large electron– electron correlation [11]. Now the Fermi surface study for KFe2 As2 is in progress to check whether the LDA works well in such large electron–electron correlation system. In summary, we have calculated the energy band structures for iron-pnictide superconductor, LaFePO, LaRuPO and LaFe2 P2 , by using a full potential scheme within LDA. Cylindrical Fermi surfaces characterise the conduction bands in LaFePO and LaRuPO. The good agreement in the dHvA frequencies suggests that LDA treatment works well for these superconductors with a relatively lower T c , though the mass enhancements are different. It means that the electron–electron correlation is not so crucial in Fermi surface topology of these materials. Acknowledgement This work is partly supported by a Grant-in-Aid for Scientific Research on Innovative Areas ”Heavy Electrons” (No. 20102002) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan. References [1] K. Ishida, Y. Nakai, H. Hosono, J. Phys. Sci. Jpn. 78 (2009) 062001. [2] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [3] Ren Zhi-An, Lu Wei, Yang Jie, Yi Wei, Shen Xiao-Li, Zheng-Cai, Che Guang-Can, Dong Xiao-Li, Sun Li-Ling, Zhou Fang, Zhao Zhong-Xian, Chin. Phys. Lett. 25 (2008) 2215. [4] Y. Kamihara, H. Hiranmatsu, M. Hirabo, R. Kawamura, H. Yanagi, T. Kamiya, H. Hosono, J. Am. Chem. Soc. 128 (2008) 10012. [5] H. Sugawara, R. Settai, Y. Doi, H. Muranaka, K. Katayama, H. Yamagami, Y. ¯ nuki, J. Phys. Sci. Jpn. 77 (2008) 113711. O [6] H. Muranaka, Y. Doi, K. Katayama, H. Sugawara, R. Settai, F. Honda, T.D. ¯ nuki, J. Phys. Sci. Jpn. 78 (2009) 053705. Matsuda, Y. Haga, H. Yamagami, Y. O [7] S. Lebègue, Phys. Rev. B 75 (2007) 035110. [8] B.I. Zimmer, W. Jeitschko, J.H. Albering, R. Glaum, M. Reehuis, J. Alloys Compd. 229 (1995) 238. [9] M. Reehuis, W. Jeitschko, J. Phys. Chem. Solids 51 (1990) 961. [10] T. Terashima, M. Kimata, H. Satsukawa, A. Harada, K. Hazama, S. Uji, H. Harima, Gen-Fu Chen, Jian-Lin Luo, Nan-Lin Wang, J. Phys. Soc. Jpn. 78 (2009) 063702. [11] H. Fukazawa, Y. Yamada, K. Kondo, T. Saito, Y. Kohori, K. Kuga, Y. Matsumoto, S. Nakatsuji, H. Kito, P.M. Shirage, K. Kihou, N. Takeshita, C.-H. Lee, A. Iyo, H. Eisaki, J. Phys. Soc. Jpn. 78 (2009) 083712.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Fermi surfaces of LaFePO and the related compounds Tomoaki Kanai a,*, Hisatomo Harima a,b a b
Department of Physics, Faculty of Science, Kobe University, Hyogo 657-8501, Japan JST, Transformative Research-Project on Iron Pnictides (TRIP), Chiyoda 102-0075, Japan
a r t i c l e
i n f o
Article history: Accepted 4 November 2009 Available online 10 November 2009 Keywords: Iron-pnictides Band structure calculation Fermi surfaces
a b s t r a c t Full-potential band structure calculations within LDA have been carried out for new iron-based superconductors LaFePO and the related compounds. Cylindrical Fermi surfaces characterise the conduction bands in these iron-based superconductors. Obtained Fermi surfaces are compared with the experimental dHvA results, then quantitatively better agreement is realised in our full-potential results. Ó 2009 Published by Elsevier B.V.
1. Introduction
2. Calculation
The iron-based oxyarsenides superconductors have attracted much attention, because of their high T c for superconductivity and the adjacent magnetic phases [1]. For example, antiferromagnetic LaFeAsO, when F is doped, undergoes superconductivity with T c ¼ 26 K [2]. Now SmFeAsO shows the highest T c of 55 K [3]. While, an isostructural compound LaFePO, the first discovered iron-oxypnictide superconductor, shows superconductivity with relatively low T c ¼ 7 K [4]. Even when electron or hole is doped to LaFePO, the T c does not increase so much. Therefore, it is important to investigate electronic structures and Fermi surfaces of these materials for the research of the higher T c superconductivity. These iron-pnictide compounds RTPnO (R ¼ rare earth; T ¼ Fe; Co; Ni, and Ru, Pn ¼ P or As) are the tetragonal ZrCuSiAs-type (P4/nmm) layered structure, which consists of alternating RO and TPn layered structure stacked along the [0 0 1] direction. Another iron-based superconductors AT 2 Pn2 (A: alkari metal) with the ThCr2 Si2 -type (I4/mmm) tetragonal structure are also studied extensively. Among the above pnictide superconductors, the dHvA measurements are already done for LaFePO [5] and for LaRuPO and LaFe2 P2 [6]. Bandstructure calculation for LaFePO [5,7] and LaRuPO and LaFe2 P2 [6] are also reported. However, the agreement is not satisfied quantitatively [5,6]. In this paper, we have applied a full potential scheme to analyse the origin of the discrepancy, because the Muffin-tin approximation; i.e. LAPW is used in the previous analysis [5,6].
Energy band calculations have been carried out for LaFePO, LaRuPO and LaFe2 P2 based on a relativistic full potential linearized augmented-plane-wave method (FLAPW) within a local density approximation (LDA). The program codes TSPACE and KANSAI-04 are used. Scalar relativistic effect is included for all electrons and the spin–orbit interaction is considered for valence electrons. The experimental lattice parameters are used in the calculations, as follows: LaFePO; a ¼ 3:957Å; c ¼ 8:507Å, and zP ¼ 0:36 for the 4e site of P [8], LaRuPO; a ¼ 4:047Å; c ¼ 8:406Å, and zP ¼ 0:35 [8], LaFe2 P2 ; a ¼ 3:838Å; c ¼ 11:006Å, and zP ¼ 0:35 [9].
* Corresponding author. E-mail address: [email protected] (T. Kanai). 0921-4534/$ - see front matter Ó 2009 Published by Elsevier B.V. doi:10.1016/j.physc.2009.11.030
3. Results and discussion Our FLAPW calculation for LaFePO has obtained Fermi surfaces very similar to the previous results calculated by using VASP (Vienna ab initio simulation package) [7]. The Fermi surfaces consist of four cylindrical sheets and one closed pocket. The similarity is realized not only in topology, but also in the sizes. The LAPW calculations show only four sheets of cylindrical Fermi surface [5]. Although, the dHvA frequencies and cyclotron masses are not obtained in the VASP calculation, cylindrical Fermi surfaces obtained by VASP (and also our FLAPW) look larger than the LAPW ones. Actually the a branch has the measured frequency 2:38 107 Oe for Hk½0 0 1, while the calculations are 0:979 107 Oe in LAPW [5] and 2:62 107 Oe in our FLAPW. Therefore, our results explain the dHvA frequencies qualitatively well. Now we can compare the cyclotron masses. The calculated cyclotron masses are about twice smaller than the measured cyclotron masses. For example, mex ¼ 2:28m0 for a dHvA branch named a in Ref. [5], while, the cor-
T. Kanai, H. Harima / Physica C 470 (2010) S320–S321
Fig. 1. The calculated density of states for (a) LaFePO and (b) LaRuPO. Green lines shows 3d or 4d components. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
responding calculated band mass is mb ¼ 0:97m0 , Therefore the mass enhancement is not so large in LaFePO. For LaRuPO, we have obtained very similar Fermi surfaces to those of LaFePO. Since the measured dHvA frequencies are also similar in LaRuPO and LaFePO [6], the calculated Fermi surfaces explain the measurements well. As for cyclotron masses, mex ¼ 0:85m0 for a dHvA branch named a in Ref. [6], while the corresponding calculated mass mb ¼ 0:54m0 . Then, the mass enhancement in LaRuPO is much smaller than that in LaFePO. The smaller correlation effect for 4d electrons can be generally accepted. The density of states (DOS) of LaFePO and LaRuPO are shown in Fig. 1. Ru-4d electrons in LaRuPO have wider band width than the Fe-3d electrons of LaFePO, then the DOS at the Fermi level of LaRuPO is smaller than that of LaFePO, due to the smaller contributions of d electrons. Then, smaller cyclotron masses and the smaller mass enhancement are introduced in LaRuPO. In the above two materials, two dimensional Fermi surfaces characterise the conduction bands, while three dimensional Fermi surfaces are obtained for LaFe2 P2 in the previous study [6]. From our FLAPW approach to LaFe2 P2 , the three sheets of Fermi surfaces are obtained, though the topology is slightly different with previous ones. As shown in Fig. 5 of Ref. [6]. The Fermi surfaces of LaFe2 P2 are rather three dimensional and the agreement in the
S321
dHvA frequencies is rather good. However, the calculated band masses are also much smaller than the measured cyclotron masses. For example, mex ¼ 2:7m0 for a dHvA branch named c in Ref. [6], while mb = 0.77m0 for the corresponding band mass. LaFePO and LaRuPO are a compensated metal, where the volume of electrons is the same as holes. While LaFe2P2 is an uncompensated metal, then the sum of the electron volume is just a half of the BZ. Therefore, the dHvA frequencies tend to be predicted better in an uncompensated metal, even larger mass enhancement indicates strong electron–electron correlation. For compensated metals, the volume of each carrier can be obtained as any number. In this study, the calculated volumes of the Fermi surfaces are in good agreement with experiments even for compensated metal, LaFePO and LaRuPO. This indicates the LDA with a full potential scheme is working well in describing the Fermi surfaces in these materials. The success is not related to the many body effect causing mass enhancement, because the mass enhancement factor is very different in the two compounds. Recently, a single crystal of KFe2 As2 is synthesised, and the Fermi surfaces are expected to be cylindrical [10]. The reported large specific heat coefficient c, which is about 70 mJ=ðK2 molÞ, strongly indicates large electron– electron correlation [11]. Now the Fermi surface study for KFe2 As2 is in progress to check whether the LDA works well in such large electron–electron correlation system. In summary, we have calculated the energy band structures for iron-pnictide superconductor, LaFePO, LaRuPO and LaFe2 P2 , by using a full potential scheme within LDA. Cylindrical Fermi surfaces characterise the conduction bands in LaFePO and LaRuPO. The good agreement in the dHvA frequencies suggests that LDA treatment works well for these superconductors with a relatively lower T c , though the mass enhancements are different. It means that the electron–electron correlation is not so crucial in Fermi surface topology of these materials. Acknowledgement This work is partly supported by a Grant-in-Aid for Scientific Research on Innovative Areas ”Heavy Electrons” (No. 20102002) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan. References [1] K. Ishida, Y. Nakai, H. Hosono, J. Phys. Sci. Jpn. 78 (2009) 062001. [2] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [3] Ren Zhi-An, Lu Wei, Yang Jie, Yi Wei, Shen Xiao-Li, Zheng-Cai, Che Guang-Can, Dong Xiao-Li, Sun Li-Ling, Zhou Fang, Zhao Zhong-Xian, Chin. Phys. Lett. 25 (2008) 2215. [4] Y. Kamihara, H. Hiranmatsu, M. Hirabo, R. Kawamura, H. Yanagi, T. Kamiya, H. Hosono, J. Am. Chem. Soc. 128 (2008) 10012. [5] H. Sugawara, R. Settai, Y. Doi, H. Muranaka, K. Katayama, H. Yamagami, Y. ¯ nuki, J. Phys. Sci. Jpn. 77 (2008) 113711. O [6] H. Muranaka, Y. Doi, K. Katayama, H. Sugawara, R. Settai, F. Honda, T.D. ¯ nuki, J. Phys. Sci. Jpn. 78 (2009) 053705. Matsuda, Y. Haga, H. Yamagami, Y. O [7] S. Lebègue, Phys. Rev. B 75 (2007) 035110. [8] B.I. Zimmer, W. Jeitschko, J.H. Albering, R. Glaum, M. Reehuis, J. Alloys Compd. 229 (1995) 238. [9] M. Reehuis, W. Jeitschko, J. Phys. Chem. Solids 51 (1990) 961. [10] T. Terashima, M. Kimata, H. Satsukawa, A. Harada, K. Hazama, S. Uji, H. Harima, Gen-Fu Chen, Jian-Lin Luo, Nan-Lin Wang, J. Phys. Soc. Jpn. 78 (2009) 063702. [11] H. Fukazawa, Y. Yamada, K. Kondo, T. Saito, Y. Kohori, K. Kuga, Y. Matsumoto, S. Nakatsuji, H. Kito, P.M. Shirage, K. Kihou, N. Takeshita, C.-H. Lee, A. Iyo, H. Eisaki, J. Phys. Soc. Jpn. 78 (2009) 083712.