Magnetic order driven by orbital ordering in the semiconducting KFe_1.5Se₂

Abstract

The two-orbital Hubbard model is studied numerically by using the Hartree-Fock approximation in both real space and momentum space, and the ground-state properties of the alkali metal iron selenide semiconducting KFe_1.5Se₂ are investigated. A rhombus-type Fe vacancy order with stripetype antiferromagnetic (AFM) order is found, as was observed in neutron scattering experiments [J. Zhao, et al., Phys. Rev. Lett. 109, 267003 (2012)]. Hopping parameters are obtained by fitting the experimentally observed stripe AFM phase in real space. These hopping parameters are then used to study the ground-state properties of the semiconductor in momentum space. It is found to be a strongly correlated system with a large on-site Coulomb repulsion U, similar to the AFM Mott insulator — the parent compound of copper oxide superconductors. We also find that the electronic occupation numbers and magnetizations in the d_xz and d_yz orbitals become different simultaneously when U>U_c (∼3.4 eV), indicating orbital ordering. These results imply that the rotational symmetry between the two orbitals is broken by orbital ordering and thus drives the strong anisotropy of the magnetic coupling that has been observed by experiments and that the stripe-type AFM order in this compound may be caused by orbital ordering together with the observed large anisotropy.

Keywords

iron-based superconductor / two-orbital model / stripe AFM phase / rhombus Fe vacancy order / orbital ordering

References

[1] J. G. Guo, S. F. Jin, G. Wang, S. C. Wang, K. X. Zhu, T. T. Zhou, M. He, and X. L. Chen, Superconductivity in the iron selenide K_xFe₂Se₂ (0≤x≤1.0), Phys. Rev. B 82(18), 180520 (2010)

[2] A. Krzton-Maziopa, Z. Shermadini, E. Pomjakushina, V. Pomjakushin, M. Bendele, A. Amato, R. Khasanov, H. Luetkens, and K. Conder, Synthesis and crystal growth of Cs_0.8(FeSe_0.98)₂: A new iron-based superconductor with Tc= 27 K, J. Phys.: Condens. Matter 23(5), 052203 (2011)

[3] H. D. Wang, C. H. Dong, Z. J. Li, Q. H. Mao, S. S. Zhu, C. M. Feng, H. Q. Yuan, and M. H. Fang, Superconductivity at 32 K and anisotropy in Tl_0.58Rb_0.42Fe_1.72Se₂ crystals, Europhys. Lett. 93(4), 47004 (2011)

[4] A. F. Wang, J. J. Ying, Y. J. Yan, R. H. Liu, X. G. Luo, Z. Y. Li, X. F. Wang, M. Zhang, G. J. Ye, P. Cheng, Z. J. Xiang, and X. H. Chen, Superconductivity at 32 K in single-crystalline Rb_xFe_2-ySe₂, Phys. Rev. B 83, 060512(R) (2011)

[5] E. Dagotto, Colloquium: The unexpected properties of alkali metal iron selenide superconductors, Rev. Mod. Phys. 85(2), 849 (2013)

[6] M. Guidry and Y. Sun, Superconductivity and superfluidity as universal emergent phenomena, Front. Phys. 10(4), 107404 (2015)

[7] Y. Zhang, L. X. Yang, M. Xu, Z. R. Ye, F. Chen, C. He, H. C. Xu, J. Jiang, B. P. Xie, J. J. Ying, X. F. Wang, X. H. Chen, J. P. Hu, M. Matsunami, S. Kimura, and D. L. Feng, Nodeless superconducting gap in A_xFe₂Se₂ (A=K,Cs) revealed by angle-resolved photoemission spectroscopy, Nat. Mater. 10(4), 273 (2011)

[8] T. Qian, X. P. Wang, W. C. Jin, P. Zhang, P. Richard, G. Xu, X. Dai, Z. Fang, J. G. Guo, X. L. Chen, and H. Ding, Absence of a holelike fermi surface for the iron-based K_0.8F_1.7Se₂ superconductor revealed by angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 106(18), 187001 (2011)

[9] X. P. Wang, T. Qian, P. Richard, P. Zhang, J. Dong, H. D. Wang, C. H. Dong, M. H. Fang, and H. Ding, Strong nodeless pairing on separate electron Fermi surface sheets in (Tl, K)Fe_1.78Se₂ probed by ARPES, Europhys. Lett. 93(5), 57001 (2011)

[10] F. J. Ma and Z. Y. Lu, Iron-based layered compound LaFeAsO is an antiferromagnetic semimetal, Phys. Rev. B 78(3), 033111 (2008)

[11] J. Dong, H. J. Zhang, G. Xu, Z. Li, G. Li, W. Z. Hu, D. Wu, G. F. Chen, X. Dai, J. L. Luo, Z. Fang, and N. L. Wang, Competing orders and spin-density-wave instability in La(O_1-xF_x)FeAs, Europhys. Lett. 83(2), 27006 (2008)

[12] F. Chen, M. Xu, Q. Q. Ge, Y. Zhang, Z. R. Ye, L. X. Yang, J. Jiang, B. P. Xie, R. C. Che, M. Zhang, A. F. Wang, X. H. Chen, D. W. Shen, J. P. Hu, and D. L. Feng, Electronic identification of the parental phases and mesoscopic phase separation of K_xFe_2-ySe₂ superconductors, Phys. Rev. X 1(2), 021020 (2011)

[13] A. Ricci, N. Poccia, G. Campi, B. Joseph, G. Arrighetti, L. Barba, M. Reynolds, M. Burghammer, H. Takeya, Y. Mizuguchi, Y. Takano, M. Colapietro, N.L. Saini, and A. Bianconi, Nanoscale phase separation in the iron chalcogenide superconductor K_0.8Fe_1.6Se₂ as seen via scanning nanofocused X-ray diffraction, Phys. Rev. B 84, 060511(R) (2011)

[14] D. X. Mou, L. Zhao, and X. J. Zhou, Structural, magnetic and electronic properties of the iron-chalcogenide A_xFe_2-ySe₂ (A=K, Cs, Rb, and Tl, etc.) superconductors, Front. Phys. 6(4), 410 (2011)

[15] W. Bao, Q. Z. Huang, G. F. Chen, M. A. Green, D. M. Wang, J. B. He, and Y. M. Qiu, A novel large moment antiferromagnetic order in K_0.8Fe_1.6Se₂ superconductor, Chin. Phys. Lett. 28(8), 086104 (2011)

[16] W. Bao, G. N. Li, Q. Z. Huang, G. F. Chen, J. B. He, D. M. Wang, M. A. Green, Y. M. Qiu, J. L. Luo, and M. M. Wu, Superconductivity tuned by the iron vacancy order in K_xF_2-ySe₂, Chin. Phys. Lett. 30(2), 027402 (2013)

[17] J. Zhao, H. Cao, E. Bourret-Courchesne, D. H. Lee, and R. J. Birgeneau, Neutron-diffraction measurements of an antiferromagnetic semiconducting phase in the vicinity of the high-temperature superconducting state of K_xFe_2-ySe₂, Phys. Rev. Lett. 109(26), 267003 (2012)

[18] M. Wang, W. Tian, P. Valdivia, S. X. Chi, E. Bourret-Courchesne, P. C. Dai, and R. J. Birgeneau, Two spatially separated phases in semiconducting Rb_0.8Fe_1.5S₂, Phys. Rev. B 90(12), 125148 (2014)

[19] J. Zhao, Y. Shen, R. J. Birgeneau, M. Gao, Z. Y. Lu, D. H. Lee, X. Z. Lu, H. J. Xiang, D. L. Abernathy, and Y. Zhao, Neutron scattering measurements of spatially anisotropic magnetic exchange interactions in semiconducting K_0.85Fe_1.54Se₂ (TN= 280 K), Phys. Rev. Lett. 112(17), 177002 (2014)

[20] M. Wang, P. Valdivia, J. X. Chen, W. L. Zhang, R. A. Ewings, T. G. Perring, Y. Zhao, L. W. Harriger, J. W. Lynn, E. Bourret-Courchesne, D. H. Lee, D. X. Yao, and R. J. Birgeneau, Spin waves and spatially anisotropic exchange interactions in the S= 2 stripe antiferromagnet Rb_0.8Fe_1.5S₂, Phys. Rev. B 92, 041109(R) (2015)

[21] L. Boeri, O. V. Dolgov, and A. A. Golubov, Is LaFeAsO_1-xF_x an electron-phonon superconductor? Phys. Rev. Lett. 101(2), 026403 (2008)

[22] Y. Liang, X. X. Wu, W. F. Tsai, and J. P. Hu, Pairing symmetry in layered BiS₂ compounds driven by electron-electron correlation, Front. Phys. 9(2), 194 (2014)

[23] S. Raghu, X.-L. Qi, C.-X. Liu, D. J. Scalapino, and S.-C. Zhang, A minimal two-band model for the superconducting Fe-pnictides, Phys. Rev. B 77, 220503(R) (2008)

[24] M. Daghofer, A. Moreo, J. A. Riera, E. Arrigoni, D. J. Scalapino, and E. Dagotto, Model for the magnetic order and pairing channels in Fe pnictide superconductors, Phys. Rev. Lett. 101(23), 237004 (2008)

[25] Q. Jiang, Y. T. Kang, and D. X. Yao, Spin, charge, and orbital orderings in iron-based superconductors, Chin. Phys. B 22(8), 087402 (2013)

[26] Q. L. Luo, D. X. Yao, A. Moreo, and E. Dagotto, Charge stripes in the two-orbital Hubbard model for iron pnictides, Phys. Rev. B 83(17), 174513 (2011)

[27] M. Wang, C. Fang, D. X. Yao, G. Tan, L. W. Harriger, Y. Song, T. Netherton, C. Zhang, M. Wang, M. B. Stone, W. Tian, J. Hu, and P. Dai, Spin waves and magnetic exchange interactions in insulating Rb_0.89Fe_1.58Se₂, Nat Commun. 2, 580 (2011)

[28] W. Li, C. Setty, X. H. Chen, and J. P. Hu, Electronic and magnetic structures of chain structured iron selenide compounds, Front. Phys. 9(4), 465 (2014)

[29] R. Yu, K. T. Trinh, A. Moreo, M. Daghofer, J. A. Riera, S. Haas, and E. Dagotto, Magnetic and metallic state at intermediate Hubbard U coupling in multiorbital models for undoped iron pnictides, Phys. Rev. B 79(10), 104510 (2009)

[30] X. W. Yan, M. Gao, Z. Y. Lu, and T. Xiang, Electronic structures and magnetic order of ordered-Fe-vacancy ternary iron selenides TlFe_1.5Se₂ and AFe_1.5Se₂ (A=K, Rb, or Cs), Phys. Rev. Lett. 106(8), 087005 (2011)

[31] C. C. Lee, W. G. Yin, and W. Ku, Ferro-orbital order and strong magnetic anisotropy in the parent compounds of iron-pnictide superconductors, Phys. Rev. Lett. 103(26), 267001 (2009)

[32] W. C. Lv, W. C. Lee, and P. Phillips, Vacancy-driven orbital and magnetic order in (K,Tl,Cs)yFe_2-xSe₂, Phys. Rev. B 84(15), 155107 (2011)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg