Coexistence of ferromagnetic and stripe antiferromagnetic spin fluctuations in SrCo$_2$As$_2$

TL;DR

This study reveals coexistence of ferromagnetic and antiferromagnetic spin fluctuations in SrCo$_2$As$_2$, linked to orbital changes caused by Co substitution, impacting superconductivity.

Contribution

It demonstrates the coexistence of FM and AF spin fluctuations in SrCo$_2$As$_2$ and connects these to orbital switching from $t_{2g}$ to $e_g$ orbitals due to Co substitution.

Findings

Coexistence of AF and FM spin fluctuations at specific wave vectors.

Both types of fluctuations are associated with a flat $e_g$ band near the Fermi level.

FM fluctuations are detrimental to superconductivity due to orbital switching.

Abstract

We use inelastic neutron scattering to study energy and wave vector dependence of spin fluctuations in SrCo$_2$As$_2$, derived from SrFe$_{2-x}$Co$_x$As$_2$ iron pnictide superconductors. Our data reveals the coexistence of antiferromagnetic (AF) and ferromagnetic (FM) spin fluctuations at wave vectors $\textbf{Q}_{\rm AF}$=(1,0) and $\textbf{Q}_{\rm FM}$=(0,0)/(2,0), respectively. By comparing neutron scattering results with those of dynamic mean field theory calculation and angle-resolved photoemission spectroscopy experiments, we conclude that both AF and FM spin fluctuations in SrCo$_2$As$_2$ are closely associated with a flat band of the $e_g$ orbitals near the Fermi level, different from the $t_{2g}$ orbitals in superconducting SrFe$_{2-x}$Co$_x$As$_2$. Therefore, Co-substitution in SrFe$_{2-x}$Co$_x$As$_2$ induces a $t_{2g}$ to $e_g$ orbital switching, and is responsible for FM spin fluctuations detrimental to the singlet pairing superconductivity.

Full text

Flat electronic bands can give rise to a plethora of interaction-driven quantum phases, including ferromagnetism tasaki , Mott insulating phase due to electron correlations Cao1 , and superconductivity Cao2 . Therefore, an understanding how the flat electronic bands can influence the electronic, magnetic, and superconducting properties of solids is an important topic in condensed matter physics. In iron pnictide superconductors such as $A$Fe2-xCoxAs2 ($A=$ Ba, Sr) [Figs. 1(a)-1(d)], the dominate interactions are stripe antiferromagnetic (AF) order, and superconductivity, which has singlet electron pairing, arises by doping electron with Co-substitution to suppress static AF order Johnston ; Scalapino2012 ; RMP_Dai . While AF spin fluctuations and superconductivity in iron pnictides are believed to arise from nested hole Fermi surfaces at $\Gamma$ and electron Fermi surfaces at $M$ [Fig. 1(e)] Hirschfeld11 , the density functional theory (DFT) calculations suggest the competing ferromagnetic (FM) and AF spin fluctuations with the balance controlled by doping DFT_fm1 ; DFT_fm2 . For Co-overdoped $A$Co2As2 Sefat09 ; Pandey13 , where the DFT calculations find a tendency for both the FM and AF order, neutron scattering revealed only the AF spin fluctuations SCA_stripe while angle resolved photoemission spectroscopy (ARPES) experiments found no evidence of the Fermi surface nesting NXu13 ; Dhaka13 . On the other hand, nuclear magnetic resonance (NMR) measurements on $A$Fe2-xCoxAs2 provided evidence for FM spin fluctuations at all Co-doping levels in addition to the AF spin fluctuations NMR_SCA ; NMR_FM . In particular, strong FM spin fluctuations in $A$Fe2-xCoxAs2 are believed to compete with AF spin fluctuations and prevent superconductivity for Co-overdoped samples NMR_SCA ; NMR_FM , contrary to the Fermi surface nesting picture where superconductivity is suppressed via vanishing hole Fermi surfaces with increasing Co-doping Hirschfeld11 ; Meng2013 . Finally, action of physical, chemical pressure, or aliovalent substitution in $B$Co2As2 ($B=$ Eu, Ca) can drive these AF materials into ferromagnets XTan16 . In particular, CaCo1.84As2 with a collapsed tetragonal structure Kreyssig08 forms A-type AF ground state with coexisting FM spin fluctuations within the CoAs layer and A-type AF spin fluctuations between the CoAs layers Sapkota2017 . These features are different from those of Ca(Fe1-xCox)2As2 Sapkota18 ; jzhao09 and $A$Fe2-xCoxAs2 RMP_Dai .

Iron pnictides have five nearly degenerate $d$ orbitals which split into $t_{2g}$ and $e_{g}$ orbitals in a tetrahedral crystal field [Figs. 1(b), 1(c)]. The electronic structure of the system is dominated by Fe 3$d$ $t_{2g}$ orbitals near the Fermi level with hole-electron Fermi surfaces at $\Gamma$ and $M$, respectively [Fig. 1(e)]. The presence of multiple Fe 3$d$ orbitals near the Fermi level results in varying orbital characters on different parts of the Fermi surfaces MYi_npj_QM , and orbital-dependent strengths of electronic correlations Yin2011 ; Medici2014 ; Nica17 ; QMSi_NRM ; Zhonghao2018 . The electronic band structures of SrCo2As2 calculated by the DFT combined with dynamic mean field theory (DMFT) Kotliar06 ; Haule10 reveal the presence of a flat band near $M$ point with mixture of the $d_{z^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals [Fig. 1(d)]. If SrCo2As2 has strong ferromagnetism arising from the flat band as suggested from NMR NMR_SCA ; NMR_FM , one should be able to extract its energy and wave vector dependence by neutron scattering and determine its role to the suppressed superconductivity in Co-overdoped SrFe2-xCoxAs2 Johnston ; Scalapino2012 ; RMP_Dai .

In this Letter, we combine neutron scattering, ARPES and DFT+DMFT methods to study SrCo2As2, an electron-doped end member of SrFe2-xCoxAs2 exhibiting no structural, magnetic, or superconducting transitions Pandey13 . Besides confirming the longitudinally elongated AF spin fluctuations at wave vector $\textbf{Q}_{\rm AF}$=(1,0) [Figs. 1(f) and 2] SCA_stripe , we successfully observed the in-plane FM spin fluctuations at $\textbf{Q}_{\rm FM}$=(0,0) and its equivalent $(2,0)$ positions [Figs. 2 and 3]. From the DFT+DMFT calculations and ARPES measurements, we find a flat band consisting of the $e_{g}$ orbitals along the $\Gamma$-$M$ direction right above the Fermi level [Fig. 1(d)], leading to a prominent peak in the density-of-state (DOS) near Fermi level responsible for both the FM and AF spin fluctuations [Figs. 4(a)-4(d)]. Orbital analysis of the dynamic spin susceptibility $\chi^{\prime\prime}({\bf Q},E)$ in the DFT+DMFT calculations suggests that magnetism in SrCo2As2 is dominated by the $e_{g}$ orbitals [Figs. 1(d), 1(e), 4(e), 4(f)]. These results are beyond the prevailing orbital selective Mott picture in iron pnictides, where the $t_{2g}$ orbitals are most strongly correlated MYi_npj_QM ; QMSi_NRM ; Chenglin_NaFeAs ; YL_LiFeAs ; YSong16 and electron (Co) doping monotonously reduces correlations in all five $d$ orbitals Yin2011 ; Medici2014 . In addition, the FM spin correlations in SrCo2As2 are similar to the A-type AF order in CaCo1.86As2 AtypeCaCo2As2 . Therefore, our observation is consistent with the proposal that FM fluctuations are detrimental to superconductivity in Co-overdoped $A$Fe2-xCoxAs2 and may be responsible for the hole-electron asymmetry of the superconducting dome in iron pnictide families NMR_FM .

We begin by showing constant-energy slices of $\chi^{\prime\prime}({\bf Q},E)$ on SrCo2As2 at $T=5$ K [Figs. 2(a),(c),(e),(g)] SI ; YL_LiFeAs . At $E=8$ meV, the AF spin fluctuations at ${\bf Q}_{\rm AF}=(1,0)$ are longitudinally elongated similar to that in hole-doped BaFe2As2 [Fig. 2(a)] Meng2013 . With increasing energy, spin fluctuations along the longitudinal direction are further elongated while they barely change along the transverse direction, different from the transversely elongated spin fluctuations in $A$Fe2-xCoxAs2 RMP_Dai ; Meng2013 . At $E\geq 50$ meV, there are magnetic intensities at both the $\textbf{Q}_{\rm AF}=(1,0)$ and $\textbf{Q}_{\rm FM}=(2,0)$. Spin fluctuations form ridges of scattering across the whole Brillouin zone (BZ) forming a square network [Figs. 2(e), 2(g)], similar to those in CaCo2-yAs2 Sapkota2017 . Along the transverse direction, we observed a linearly broadening of the half-width at half-maximum (HWHM) of AF spin fluctuations with increasing energy at the speed of $\Delta HWHM/\Delta E\approx 1/(440$ meV$\cdot$ Å) SI and no peak splitting was identified.

We used the DFT+DMFT calculations to understand the electronic band structure [Fig. 1(d)] and spin dynamics of SrCo2As2 Yin2011 ; SI ; ZPYin14 . Figures 2(b), 2(d), 2(f) and 2(h) show the DFT+DMFT calculated results for $E=10,20,50,70$ meV. Although the calculated results look remarkably similar to experimental data in Figs. 2(a), 2(c), 2(e), and 2(g), there are also important differences. First, the AF spin fluctuations are weaker than the FM spin fluctuations in the DFT+DMFT calculation at $E=10$ meV, while they are stronger in experiments. This is mostly because the calculations are exceedingly sensitive to the position of the flat band with respect to the Fermi level. Second, the calculation suggests that FM spin fluctuations originating from $\Gamma$ (and equivalent) point merge into AF spin fluctuations at ${\bf Q}_{\rm AF}=(\pm 1,0)/(0,\pm 1)$ around 50 meV [Fig. 2(f)], while there is no clear evidence of FM spin fluctuations at $E=8,19$ meV [Figs. 2(a), 2(c)] SI . Figure 1(g) shows energy dependence of local dynamic susceptibility $\chi^{\prime\prime}(E)$, obtained by integrating both the FM and AF signal within the area of $(0,0)\rightarrow(1,1)\rightarrow(2,0)\rightarrow(1,-1)\rightarrow(0,0)$ RMP_Dai , and its comparison with those of BaFe2As2 leland11 . The total fluctuating moment is approximately $\langle m^{2}\rangle\approx 0.4\pm 0.1\ \mu^{2}_{B}$/f.u. leland11 ; SI , compared with 0.5 $\mu^{2}_{B}$/f.u. from the calculation. Due to the diffusive nature of the magnetic scattering, it is rather difficult to experimentally separate the integrated FM and AF signal and compare with that of the DFT+DMFT calculations.

To conclusively determine the FM signal in SrCo2As2, we carried out polarized neutron scattering experiments with the neutron polarization directions $x$, $y$, and $z$ shown in Fig. 3(a), which correspond to neutron spin-flip (SF) scattering cross sections $\sigma_{x}^{SF}$, $\sigma_{y}^{SF}$, and $\sigma_{z}^{SF}$, respectively moon ; polarized1 ; polarized2 ; polarized3 ; polarized4 ; YL_BaFe2As2 . The magnetic scattering of SrCo2As2 should then be $SIG=\sigma_{x}^{SF}-(\sigma_{y}^{SF}+\sigma_{z}^{SF})/2$ polarized1 ; polarized2 ; polarized3 ; polarized4 ; YL_BaFe2As2 . Figures 3(c) and 3(d) show the energy scans at $\textbf{Q}_{1}=(1,0,1)$ and $\textbf{Q}_{2}=(0,0,3)$ [Fig. 3(a)]. Figure 3(e) shows energy dependence of $SIG$ at $\textbf{Q}_{1}$ and $\textbf{Q}_{2}$, confirming the presence of magnetic fluctuations at the AF and FM wave vectors, respectively.

At $\textbf{Q}_{1}$ [Fig. 3(c)], $\sigma_{y}^{SF}\approx\sigma_{z}^{SF}$ implies that the AF spin fluctuations are isotropic in spin space, different from the anisotropic spin fluctuations in BaFe2-xCoxAs2 induced by spin-orbit coupling polarized1 ; polarized2 ; polarized3 ; polarized4 ; YL_BaFe2As2 . These results suggest that the spin-orbit coupling in SrCo2As2 is weaker than that of BaFe2As2. At $\textbf{Q}_{2}$ [Figs. 3(d), 3(e)], magnetic scattering increases with increasing energy with no spin gap above $E=3$ meV, providing direct evidence for the FM spin fluctuations in SrCo2As2 NMR_SCA ; SI . To further demonstrate the coexisting FM and AF spin fluctuations, we performed constant-energy scans along the $[H,0,3]$ and $[H,0,1]$ directions at $E=8$ meV [Fig. 3(b)]. Figure 3(f) indicates that the FM spin fluctuations are confined near $(0,0,3)$ and are about half the size as that of the AF signal around $(1,0,1)$. The DFT+DMFT calculations predict the dominant FM spin fluctuations around 10 meV [Fig. 2(b)]. Constant-energy scans along the $[1,0,L]$ [Fig. 3(g)] and $[0,0,L]$ [Fig. 3(h)] directions reveal weakly $L$ dependent scattering at both the AF and FM positions, respectively, confirming the quasi-two-dimensional nature of the magnetic scattering. Figure 1(h) shows energy dependence of $\chi^{\prime\prime}({\bf Q},E)$ at ${\bf Q}_{\rm AF}$ and ${\bf Q}_{\rm FM}$, where the peak in ${\bf Q}_{\rm FM}$ near 25 meV should be associated with the Van Hove singularity of the flat band.

To understand the origin of the FM and AF spin fluctuations in SrCo2As2 [Fig. 4(a)], we measured its band structure by ARPES and compared the outcome in Fig. 4(c) with the DFT+DMFT calculations in Fig. 4(d). Around the $\Gamma$ point, one shallow electron-like $\alpha$ band and one highly dispersive hole-like $\beta$ band were observed. Another electron-like band at the $M$ point was also found. These results agree well with the DFT+DMFT calculation in Fig. 4(d), supporting the existence of a flat band along $\Gamma$-$M$ direction right above the Fermi level [Figs. 1(d) and 4(d)] SI . Further ARPES data collected along the $Z$-$A$ direction with a different photon energy reveals the presence of the flat band (or band bottom) touching the Fermi level at $A$ point, mainly arising from the $d_{x^{2}-y^{2}}$ orbital hybridized with the $d_{z^{2}}$ [Fig. 1(d)] SI . In particular, the partial DOS of the Co 3$d_{x^{2}-y^{2}}$ orbital in the DFT+DMFT calculation exhibits a peak at about 35 meV above the Fermi level, similar to the maximum scattering of the FM spin fluctuations [Fig. 1(h)], suggesting a close relationship between the flat band and FM instability.

Flat electronic bands with high DOS near the Fermi level can influence the electronic and magnetic properties of solids through tuning the electron-electron correlations tasaki ; Cao1 ; Cao2 . In SrCo2As2, the flat band might affect spin fluctuations in two ways. First, the $d_{x^{2}-y^{2}}$ band ($\alpha$) dispersive along the $\Gamma$-$X/Y$ direction but flat along the $\Gamma$-$M$ direction [Fig. 1(d)] might lead to high DOS near the Fermi level and Stoner FM instability similar to that of Sr2RuO4 RMP214 ; FM214 . Both the DFT+DMFT calculations and ARPES experiments reveal a prominent peak in DOS near the Fermi level [Fig. 4(b)], supporting the existence of flat-band related FM fluctuations. Second, the flat band above the Fermi level provides many electron scattering channels as shown by the arrows in Fig. 4(d). These scattering processes result in the longitudinally elongated spin fluctuations extending from $\Gamma$ to $M$ [Fig. 1(f)]. This is different from the longitudinally elongated low-energy spin fluctuations in hole-doped BaFe2As2, where the longitudinal elongation is driven by mismatched sizes of the hole-electron Fermi surfaces Meng2013 ; JHZhang10 ; CLZhang11 ; RZhang18 . Figures 4(e) and 4(f) plot the DFT+DMFT calculated total dynamic spin susceptibility and contributions from the $d_{x^{2}-y^{2}}$ orbital SI . Surprisingly, both the AF and FM spin fluctuations are dominated by the $e_{g}$ orbitals (Fig. S5) SI , different from the majority $t_{2g}$ contributions to the spin dynamics in iron pnictides ZPYin14 . In SrFe2-xCoxAs2, the presence of AF spin fluctuations SCA_stripe is responsible for the superconductivity. The appearance of FM spin fluctuations in SrCo2As2 and their competition with the stripe AF spin fluctuations might be responsible the absence of superconductivity in heavily over-doped SrFe2-xCoxAs2. The underlying orbital characters might also be an important factor for superconductivity in iron pnictides.

The work at Rice is supported by the US NSF DMR-1700081 and the Robert A. Welch Foundation grant No. C-1839 (P.D.). ZPY was supported by the NSFC (Grant No. 11674030), the Fundamental Research Funds for the Central Universities (Grant No. 310421113), the National Key Research and Development Program of China grant 2016YFA0302300. The calculations used high performance computing clusters at BNU in Zhuhai and the National Supercomputer Center in Guangzhou. ZHL acknowledges the NSFC (Grant No. 11704394), and the Shanghai Sailing Program (Grant No.17YF1422900). We acknowledge the support of the HFIR/SNS, a DOE User Facility operated by ORNL. Experiments at the ISIS were supported by a beam time allocation from the STFC.