The influence of the structural transition on magnetic fluctuations in NaFeAs
NaFeAs belongs to a class of Fe-based superconductors which parent compounds show separated structural and magnetic transitions. Effects of the structural transition on spin dynamics therefore can be investigated separately from the magnetic transition. A plateau in dynamic spin response is observed in a critical region around the structural transition temperature . It is interpreted as due to the stiffening of spin fluctuations along the in-plane magnetic hard axis due to the and orbital ordering. The appearance of anisotropic spin dynamics in the critical region above the at offers a dynamic magnetic scattering mechanism for anisotropic electronic properties in the commonly referred “nematic phase”.
It is well known that in the phase diagrams of the LaFeAsO (1111) Kamihara et al. (2008), BaFeAs (122) Rotter et al. (2008) and FeSe (11) Hsu et al. (2008) superconductors, there exists an antiferromagnetic order in a distorted lattice phase which breaks the four-fold tetragonal symmetry de la Cruz et al. (2008); Huang et al. (2008); Bao et al. (2009). For all parent antiferromagnetic orders of the 1111, 122 and 11 families Qiu et al. (2008); Huang et al. (2008); Bao et al. (2009) as well as the antiferromagnetic order of KFeSe Bao et al. (2011), neutron diffraction experiments, which simultaneously measure crystalline and magnetic structures, have shown that the antiferromagnetic bond between neighboring Fe ions has expanded lattice spacing while the ferromagnetic bond has contracted lattice spacing. Such a close relation between the sign of magnetic interaction and the lattice spacing is a hallmark of the orbital ordering phenomenon Qiu et al. (2008); Huang et al. (2008); Bao et al. (2009, 2011); Bao (2013); Imada et al. (1998). Together with theoretical calculation Yildirim (2008), it has been further stated specifically in 2008 that the orbital ordering involves the and orbitals in the Fe-based material Qiu et al. (2008). The two types of Fe bonds of different and occupancy have since been shown to account for the three kinds of commensurate antiferromagnetic structures which have been observed so far for the Fe-based superconductor parent compounds Bao (2013); Yin et al. (2012), and different and occupancy in the structural distorted phase has also been subsequently observed in ARPES experiments Yi et al. (2011).
When the number of electrons is less than available orbitals, an ordered occupation pattern of the orbitals by the electrons leads to a regular orbital-pair pattern Bao (2013); Yin et al. (2012). The hopping parameter between the transition-metal ion pair determines not only the magnetic exchange interaction, but also the lattice bonding strength, thus the lattice spacing, as well as the transport property. This was demonstrated by Goodenough Goodenough (1955) in his classic explanation of the rich magnetic phases in perovskite manganites observed in neutron diffraction experiments Wollan and Koehler (1955). Orbital ordering has also been identified through such lattice and magnetic interaction corresponding relation more recently in neutron scattering studies on classic transition metal oxides Bao et al. (1997a, b). Since the orbital ordering changes the bonding between the transition-metal ions, it automatically manifests itself by a structural transition Bao et al. (1997a, b). The effective spin Hamiltonian is also altered by the orbital ordering transition. When (I) the Néel temperature of the effective spin Hamiltonian in the orbital ordered state is higher than the orbital order temperature , the antiferromagnetic transition will necessarily concur with the structural transition, such as in the case of VO Bao et al. (1997a), BaFeAs Huang et al. (2008) and FeTe Bao et al. (2009). When (II) is lower than , the antiferromagnetic transition will occur in a separated phase transition upon further cooling after the structural transition, such as in the case of the -type perovskite manganite Bao et al. (1997b), LaFeAsO de la Cruz et al. (2008) and NaFeAs (111) Chen et al. (2009); Wang et al. (2012); Li et al. (2009).
Since the antiferromagnetic bond along the -axis and the ferromagnetic bond along the -axis have different spacing Huang et al. (2008), detwinned 122 crystals would reveal the different hopping parameters of the two different bonds in transport measurements along the and -axis Chu et al. (2010); Tanatar et al. (2010). The in-plane anisotropy expected to occur in the orbital ordered state has also been observed in resonant ultrasound spectroscopy Fernandes et al. (2010), torque magnetometry Kasahara et al. (2012), magnetic inelastic neutron scattering Lu et al. (2014), time-resolved polarimetry Patz et al. (2014) measurements of the 122 systems. However, theoretical debate has been going on concerning the relative importance of the orbital Yin et al. (2012); Lv et al. (2009); Lee et al. (2009); Chen et al. (2010); Lee and Phillips (2012); Liu et al. (2011), lattice Liang et al. (2013) and spin Fang et al. (2008); Xu et al. (2008) degrees of freedom, and a spontaneous symmetry breaking Fermi liquid state, the so-called “nematic phase”, has been introduced Fernandes et al. (2014). In this connection, the class II orbital-ordered Fe-based superconductors such as the LaFeAsO de la Cruz et al. (2008) and NaFeAs Li et al. (2009) families of separated and offer experimental advantage. LaFeAsO and Co-doped BaFeAs have been investigated in NMR and inelastic neutron scattering studies to reveal the effect of the structural transition on spin dynamics Fu et al. (2012); Zhang et al. (2015). Here we report inelastic neutron scattering investigation on NaFeAs.
Single crystals were synthesized as described in Wang et al. (2012). About 2.5 grams of samples were co-aligned with the mosaic in the scattering plane of the low-temperature orthorhombic unit cell. Both nuclear and magnetic Bragg peaks are accessible in this plane Li et al. (2009), see inset to Fig. 1. The lattice parameters , and at 1.5 K. Neutron scattering experiments were performed at the thermal neutron triple-axis spectrometer Taipan Danilkin et al. (2007) in Bragg Institute, Australia Nuclear Science and Technology Organization (ANSTO). The Pyrolytic Graphite (PG) monochromator was in the double focusing mode and the PG analyzer in the vertical focusing mode. The final energy of the neutron beam was fixed at 14.7 meV, a PG filter was used after the sample to remove higher order neutrons and a 40 collimator was put after the sample. The sample temperature was regulated using an ILL Orange cryostat in the 1.4 K to 300 K range. Fig. 1 shows the temperature dependence of the nuclear Bragg peak (4,0,0) and magnetic Bragg peak (1,0,1.5). The anomaly of the nuclear peak marks the the tetragonal to orthorhombic structural transition at K, and the magnetic peak appears below the Néel temperature K. The two phase transitions are well separated.
The constant energy scans along the -axis across the magnetic zone center (1,0,1.5) are displayed in Fig. 2. At meV, no peak was visible at 1.5 K, consistent with a spin gap formation due to the long-range magnetic order Song et al. (2013). The most intense peak appears at K when the gap closes and magnetic critical scattering maximizes. The low energy magnetic fluctuation persists into the paramagnetic state, both below and above the structural transition at K. At meV, a finite peak at the magnetic zone center can be detected at the base temperature 1.4 K. Its intensity increases upon approaching the , then decreases upon further rising of temperature, as expected for magnetic excitations.
The fitting parameters of these constant- scans across (1,0,1.5) are shown in Fig. 3. A comparison with the results of similar scans in a recent neutron scattering study on LaFeAsO and Ba(FeCo)As Zhang et al. (2015) would be beneficial. The maximum of the magnetic signal at in Fig. 3(a) is the same as the cases for LaFeAsO and Ba(FeCo)As. However, this is a universal critical phenomenon of the second order antiferromagnetic transition, which occurs in any class II orbital ordered material. Such a critical behavior has also been picked up in the NMR study on NaFeAs Ma et al. (2011). For LaFeAsO and Ba(FeCo)As, the peak width reduces drastically below by and , respectively Zhang et al. (2015). For NaFeAs, however, our data statistics does not allow such a solid conclusion, putting the upper limit of the peak narrowing at 0.04 .
Due to the hydrogen-containing glue used in assembling the single crystals, it contributed substantial background scattering, such as those shown in Fig. 2 beneath the magnetic peak. Thus, in order to extract magnetic signal from the inelastic neutron scattering signal , we performed const- scans from 1.4 to 80 K and covered the energy range up to 10 meV. Magnetic signal in our investigation range is sharp enough in the reciprocal space, it reaches background level at and 1.3 in the const- scan along the (,0,1.5). Therefore we obtain at from measurement of at subtracted by background measured at and . Fig. 4 shows at the peak position in energy scans at various temperatures. There is an energy gap at 1.5 K, consistent with the measurement from a previous neutron scattering experiment at 2 K Song et al. (2013). At K, the gap is closed and an overdamped critical spin dynamic response appears. The critical spin dynamics extend above the structural or orbital transition at .
To pin down the elusive influence of the structural transition on spin dynamics, we now focus on the most temperature sensitive part of dynamic magnetic correlation function at and meV. Fig. 5(a) shows the raw data of the peak intensity and background measured at as a function of temperature. The longer counting time was used to ensure adequate data statistics for the background subtracted shown in Fig. 5(b). The energy gap at 1.5 K, demonstrated in Fig. 2(a) and Fig. 4, disappears rather abruptly upon warming the sample to the Néel temperature , where low energy spin fluctuations peak and then decrease upon further warming the sample. The otherwise -shaped signal of magnetic critical fluctuations is modified prominently by a plateau around the . The abnormal behavior is rather puzzling, in particularly if one follows the building up of the magnetic correlations from high temperature to the base temperature: more and more spins join the dynamic magnetic correlations at the magnetic wave vector, as signified by the increasing intensity with lowering the temperature. However, the build-up is arrested in the neighborhood of the tetragonal-to-orthorhombic structural transition K. Only with further lowering the temperature, the dynamic spin correlations resume the normal magnetic behavior with increasing intensity, which finally condense to the long-range antiferromagnetic order at and gap out the low energy spin fluctuations.
While our measurements shown in Fig. 5 were performed at a low energy in the energy gap, a possible explanation of the arrest of the spin dynamics at the plateau may be provided from the polarized neutron scattering results at 6 meV above the gap Song et al. (2013). Song et al. show that while spin fluctuations above are isotropic, the transverse component along the ferromagnetic bond direction is partially frozen out at . If such a behavior holds also below the gap energy caused by the spin-space anisotropy, one may explain the reduced intensity in the plateau region of our data. Thus, the orbital ordering renders the ferromagnetic bond along the -axis the magnetic hard axis through the usual spin-orbital coupling mechanism, consistent with the observed alignment of the magnetic moments along the easy axis in the -axis discovered in the 1111 Qiu et al. (2008), 122 Huang et al. (2008) and 111 Li et al. (2009) families of Fe-based materials.
Resistivity anisotropy along the and -axis has also been observed in the NaFeAs family of the Fe-based superconductors Deng et al. (2015) similar to the 122 family materials Chu et al. (2010); Tanatar et al. (2010), as expected for orbital ordered materials. Such a behavior usually starts above the at a higher temperature . Anisotropic electronic state has also been deduced from the quasiparticle interference (QPI) measurements Rosenthal et al. (2014); Cai et al. (2014) and observed in ARPES measurements He et al. (2010); Zhang et al. (2012); Yi et al. (2012) on the 111 materials. The is reported to be 70 K for NaFeAs. If we take the partial frozen picture discussed above, the upper end of the plateau in Fig. 5 indicates the appearance of the spin space anisotropy, namely the K. Our is lower than the value 70 K for two possible reasons: 1) One would expect higher value of if the measurement energy of spin fluctuations is reduced from 2 meV to . 2) the uniaxial stress to detwin the sample is similar to the uniform magnetic field applying to a ferromagnet, and it is well known that the field increases the . The plateau extends above and below the approximately symmetrically, it is likely attributed to the critical fluctuations of the orbital degree of freedom of the orbital ordering transition at .
In summary, we performed inelastic neutron scattering investigation on NaFeAs which shows separated structural and antiferromagnetic transitions upon cooling. The prominent influence of the structural transition on spin dynamics manifests in the plateau in the temperature dependence of the low energy dynamic magnetic fluctuations. It reflects the stiffening of spin fluctuations along the ferromagnetic bond in the -axis and is consistent with the eventual condensation of the dynamic magnetic correlations to the long range antiferromagnetic order with the easy axis along the antiferromagnetic bond direction in the -axis. High statistics data allow us to detect the plateau feature, which could be a consequence of the orbital fluctuations and extends the anisotropic spin fluctuations to above the . Therefore, an orbital ordering picture involving the and orbitals which we have proposed since 2008 Qiu et al. (2008); Huang et al. (2008) basing on the pioneering idea of Goodenough Goodenough (1955) seems to consistently explain all experimental data on NaFeAs.
The works at RUC and USTC were supported by National Basic Research Program of China (Grant Nos. 2012CB921700 and 2011CBA00112) and the National Natural Science Foundation of China (Grant Nos. 11034012 and 11190024).
- Kamihara et al. (2008) Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
- Rotter et al. (2008) M. Rotter, M. Tegel, and D. Johrendt, Phys. Rev. Lett. 101, 107006 (2008).
- Hsu et al. (2008) F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W. Huang, P. M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu, D.-C. Yan, and M.-K. Wu, PNAS 105, 14262 (2008).
- de la Cruz et al. (2008) C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N. L. Wang, and P. Dai, Nature 453, 899 (2008).
- Huang et al. (2008) Q. Huang, Y. Qiu, W. Bao, M. Green, J. Lynn, Y. Gasparovic, T. Wu, G. Wu, and X. H. Chen, Phys. Rev. Lett. 101, 257003 (2008).
- Bao et al. (2009) W. Bao, Y. Qiu, Q. Huang, M. A. Green, P. Zajdel, M. R. Fitzsimmons, M. Zhernenkov, M. Fang, B. Qian, E. Vehstedt, J. Yang, H. Pham, L. Spinu, and Z. Mao, Phys. Rev. Lett. 102, 247001 (2009).
- Qiu et al. (2008) Y. Qiu, W. Bao, Q. Huang, T. Yildirim, J. Simmons, M. Green, J. Lynn, Y. Gasparovic, J. Li, T. Wu, G. Wu, and X. Chen, Phys. Rev. Lett. 101, 257002 (2008).
- Bao et al. (2011) W. Bao, Q. Huang, G. F. Chen, M. A. Green, D. M. Wang, J. B. He, X. Q. Wang, and Y. Qiu, Chin. Phys. Lett. 28, 086104 (2011).
- Bao (2013) W. Bao, Chinese Phys. B 22, 087405 (2013).
- Imada et al. (1998) M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).
- Yildirim (2008) T. Yildirim, Phys. Rev. Lett. 101, 057010 (2008).
- Yin et al. (2012) W.-G. Yin, C.-H. Lin, and W. Ku, Phys. Rev. B 86, 081106(R) (2012).
- Yi et al. (2011) M. Yi, D. Lu, J.-H. Chu, J. G. Analytis, A. P. Sorini, A. F. Kemper, B. Moritz, S.-K. Mo, R. G. Moore, M. Hashimoto, W.-S. Lee, Z. Hussain, T. P. Devereaux, I. R. Fisher, and Z.-X. Shen, PNAS 108, 6878 (2011).
- Goodenough (1955) J. B. Goodenough, Phys. Rev. 100, 564 (1955).
- Wollan and Koehler (1955) E. O. Wollan and W. C. Koehler, Phys. Rev. 100, 545 (1955).
- Bao et al. (1997a) W. Bao, C. Broholm, G. Aeppli, P. Dai, J. M. Honig, and P. Metcalf, Phys. Rev. Lett. 78, 507 (1997a).
- Bao et al. (1997b) W. Bao, J. D. Axe, C. H. Chen, and S.-W. Cheong, Phys. Rev. Lett. 78, 543 (1997b).
- Chen et al. (2009) G. F. Chen, W. Z. Hu, J. L. Luo, and N. L. Wang, Phys. Rev. Lett. 102, 227004 (2009).
- Wang et al. (2012) A. F. Wang, X. G. Luo, Y. J. Yan, J. J. Ying, Z. J. Xiang, G. J. Ye, P. Cheng, Z. Y. Li, W. J. Hu, and X. H. Chen, Phys. Rev. B 85, 224521 (2012).
- Li et al. (2009) S. Li, C. de la Cruz, Q. Huang, G. F. Chen, T.-L. Xia, J. L. Luo, N. L. Wang, and P. Dai, Phys. Rev. B 80, 020504 (2009).
- Chu et al. (2010) J.-H. Chu, J. G. Analytis, K. D. Greve, P. L. McMahon, Z. Islam, Y. Yamamoto, and I. R. Fisher, Science 329, 824 (2010).
- Tanatar et al. (2010) M. A. Tanatar, E. C. Blomberg, A. Kreyssig, M. G. Kim, N. Ni, A. Thaler, S. L. Budâko, P. C. Canfield, A. I. Goldman, I. I. Mazin, and R. Prozorov, Phys. Rev. B 81, 184508 (2010).
- Fernandes et al. (2010) R. M. Fernandes, L. H. VanBebber, S. Bhattacharya, P. Chandra, V. Keppens, D. Mandrus, M. A. McGuire, B. C. Sales, A. S. Sefat, and J. Schmalian, Phys. Rev. Lett. 105, 157003 (2010).
- Kasahara et al. (2012) S. Kasahara, H. J. Shi, K. Hashimoto, S. Tonegawa, Y. Mizukami, T. Shibauchi, K. Sugimoto, T. Fukuda, T. Terashima, A. H. Nevidomskyy, and Y. Matsuda, Nature 486, 382 (2012).
- Lu et al. (2014) X. Lu, J. T. Park, R. Zhang, H. Luo, A. H. Nevidomskyy, Q. Si, and P. Dai, Science 345, 657 (2014).
- Patz et al. (2014) A. Patz, T. Li, S. Ran, R. M. Fernandes, J. Schmalian, S. L. Budâko, P. C. Canfield, I. E. Perakis, and J. Wang, Nat Commun 5, 3229 (2014).
- Lv et al. (2009) W. Lv, J. Wu, and P. Phillips, Phys. Rev. B 80, 224506 (2009).
- Lee et al. (2009) C.-C. Lee, W.-G. Yin, and W. Ku, Phys. Rev. Lett. 103, 267001 (2009).
- Chen et al. (2010) C.-C. Chen, J. Maciejko, A. P. Sorini, B. Moritz, R. R. P. Singh, and T. P. Devereaux, Phys. Rev. B 82, 100504 (2010).
- Lee and Phillips (2012) W.-C. Lee and P. W. Phillips, Phys. Rev. B 86, 245113 (2012).
- Liu et al. (2011) D.-Y. Liu, Y.-M. Quan, D.-M. Chen, L.-J. Zou, and H.-Q. Lin, Phys. Rev. B 84, 064435 (2011).
- Liang et al. (2013) S. Liang, A. Moreo, and E. Dagotto, Phys. Rev. Lett. 111, 047004 (2013).
- Fang et al. (2008) C. Fang, H. Yao, W.-F. Tsai, J. Hu, and S. A. Kivelson, Phys. Rev. B 77, 224509 (2008).
- Xu et al. (2008) C. Xu, M. MÃ¼ller, and S. Sachdev, Phys. Rev. B 78, 020501 (2008).
- Fernandes et al. (2014) R. M. Fernandes, A. V. Chubukov, and J. Schmalian, Nat Phys 10, 97 (2014).
- Fu et al. (2012) M. Fu, D. A. Torchetti, T. Imai, F. L. Ning, J.-Q. Yan, and A. S. Sefat, Phys. Rev. Lett. 109, 247001 (2012).
- Zhang et al. (2015) Q. Zhang, R. M. Fernandes, J. Lamsal, J. Yan, S. Chi, G. S. Tucker, D. K. Pratt, J. W. Lynn, R. McCallum, P. C. Canfield, T. A. Lograsso, A. I. Goldman, D. Vaknin, and R. J. McQueeney, Phys. Rev. Lett. 114, 057001 (2015).
- Danilkin et al. (2007) S. A. Danilkin, G. Horton, R. Moore, G. Braoudakis, and M. Hagen, Journal of Neutron Research 15, 55 (2007).
- Song et al. (2013) Y. Song, L.-P. Regnault, C. Zhang, G. Tan, S. V. Carr, S. Chi, A. D. Christianson, T. Xiang, and P. Dai, Phys. Rev. B 88, 134512 (2013).
- Ma et al. (2011) L. Ma, G. F. Chen, D.-X. Yao, J. Zhang, S. Zhang, T.-L. Xia, and W. Yu, Phys. Rev. B 83, 132501 (2011).
- Deng et al. (2015) Q. Deng, J. Liu, J. Xing, H. Yang, and H.-H. Wen, Phys. Rev. B 91, 020508 (2015).
- Rosenthal et al. (2014) E. P. Rosenthal, E. F. Andrade, C. J. Arguello, R. M. Fernandes, L. Y. Xing, X. C. Wang, C. Q. Jin, A. J. Millis, and A. N. Pasupathy, Nat. Phys. 10, 225 (2014), article.
- Cai et al. (2014) P. Cai, W. Ruan, X. Zhou, C. Ye, A. Wang, X. Chen, D.-H. Lee, and Y. Wang, Phys. Rev. Lett. 112, 127001 (2014).
- He et al. (2010) C. He, Y. Zhang, B. P. Xie, X. F. Wang, L. X. Yang, B. Zhou, F. Chen, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, X. H. Chen, J. P. Hu, and D. L. Feng, Phys. Rev. Lett. 105, 117002 (2010).
- Zhang et al. (2012) Y. Zhang, C. He, Z. R. Ye, J. Jiang, F. Chen, M. Xu, Q. Q. Ge, B. P. Xie, J. Wei, M. Aeschlimann, X. Y. Cui, M. Shi, J. P. Hu, and D. L. Feng, Phys. Rev. B 85, 085121 (2012).
- Yi et al. (2012) M. Yi, D. H. Lu, R. G. Moore, K. Kihou, C.-H. Lee, A. Iyo, H. Eisaki, T. Yoshida, A. Fujimori, and Z.-X. Shen, New J. Phys. 14, 073019 (2012).