Session W22: Focus Session: Fe-based Superconductivity - Magnetism in AxFe(1-y)Se2

NMR Study of Superconductivity and Spin Fluctuations in Intercalated Iron Selenides A$_y$Fe$_{2-x}$Se$_2$

The role of spin fluctuations in superconductivity is an essential topic in both cuprate and Fe-based superconductors. NMR works in several Fe-based superconductors proposed that the low-energy antiferromagnetic spin fluctuations (AFSF) is a possible pairing glue for superconductivity. However, studies on other systems such as KFe$_2$As$_2$ and Li$_{1-x}$FeAs does not support a strong correlation between low-energy spin fluctuations and superconductivity. In the newly discovered A$_y$Fe$_{2-x}$Se$_2$ superconductors with $T_c\sim$ 32 K, our NMR study identifies unambiguously a paramagnetic superconducting phase, which is phase separated from the block antiferromagnetic state. The low-energy AFSF is not seen at all, even though the T$_c$ is high. The A$_y$Fe$_{2-x}$Se$_2$ are singlet superconductors evidenced from the NMR Knight shift $K$; However, the absence of the coherence peak in the spin-lattice relaxation rate $1/T_1$ suggests an unconventional behavior of superconductivity. In fact, we found that both the $K$ and the $1/T_1T$ increase dramatically with temperature and follow a $a+bT^2$ form from Tc up to 300 K. Such behavior is strong evidence for spin fluctuations with a high-energy, local nature in 3D systems, and inconsistent with a band-gap effect. Furthermore, $K$ and $1/T_1T$ saturate above 400 K, indicating an energy scale of 35 meV, which is distinct from the low-energy spin fluctuations. The above temperature enhanced spin fluctuations seem to be universal in Fe-based superconductors. \\[4pt] References: W. Yu et al., Phys. Rev. Lett. 106, 197001 (2011); Long Ma et al., Phys. Rev. B 83, 174510 (2011); L. Ma et al., arXiv:1103.4960.   

Spin Waves and magnetic exchange interactions in insulating Rb0.89Fe1.58Se2

Superconductivity in alkaline iron selenide AFe$_{1.6+x}$Se$_{2}$ (A = K, Rb, Cs) may have a different origin from the sign reversed s-wave electron pairing mechanism, because they are insulators near x = 0 and form a blocked AF structure that is completely different from the iron pnictides. We use neutron scattering to map out spin waves in the AF insulating Rb$_{0.89}$Fe$_{1.58}$Se$_{2}$. A comparison of the fitted effective exchange couplings using a local moment Heisenberg Hamiltonian in Rb$_{0.89}$Fe$_{1.58}$Se$_{2}$, (Ba,Ca,Sr)Fe$_{2}$As$_{2}$, and iron chalcogenide Fe1.05Te reveals that their next nearest neighbor (NNN) exchange couplings are similar. Therefore, superconductivity in all Fe-based materials may have a common magnetic origin that is intimately associated with the NNN magnetic exchange interactions, even though they have metallic or insulating ground states, different AF orders and electronic band structures.   

77Se NMR Study of K{x}Fe{2-y}Se{2-z}S{z}

We will present a $^{77}$Se NMR study of the superconducting properties of the recently discovered K$_{x}$Fe$_{2-y}$Se$_{2}$ (T$_{c} \sim$ 33 K), in a temperature range of 4 to 250 K [1]. Our Knight shift data reflect the progressive decrease in uniform spin susceptibility with temperature, in analogy with FeSe and iron-arsenide systems. Nuclear spin-lattice relaxation rate data shows no Hebel-Slichter coherence peak, nor any enhancement of antiferromagnetic spin fluctuations (AFSF) toward T$_{c}$. We have also conducted $^{77}$Se NMR measurements on K$_{x}$Fe$_{2-y}$Se$_{0.4}$S$_{1.6}$ (non-superconducting) and K$_{x}$Fe$_{2-y}$Se$_{1.2}$S$_{0.8}$ (T$_{c} \sim$ 21 K) to study the effect of sulphur substitution in this superconductor [2]. Sulphur applies a chemical pressure on the lattice, because it has the same valence as Selenium but less than half the ionic radius. We again measure NMR Knight shift and nuclear spin-lattice relaxation rate 1/T$_{1}$, and find that both are suppressed with S substitution. We will discuss these results in comparison with K$_{x}$Fe$_{2-y}$Se$_{2}$. \\[4pt] [1] D. Torchetti et. al., PRB 83, 104508 (2011)\\[0pt] [2] D. Torchetti et. al., arXiv:1111.2552 (2011)   

Magnetic state of K$_{0.8}$Fe$_{1.6}$Se$_2$ from a five-orbital Hubbard model in the Hartree-Fock approximation

The five-orbital Hubbard model (without lattice distortions) is investigated to study theoretically the recently discovered Fe-based superconductors K$_{0.8}$Fe$_{1.6}$Se$_2$, by using the real-space Hartree-Fock approximation and employing a 10$\times$10 Fe cluster with Fe vacancies in a $\sqrt{5}\times\sqrt{5}$ pattern[1]. The phase diagram contains an insulating state with the same spin pattern as observed experimentally, involving 2$\times$2 ferromagnetic plaquettes coupled with one another antiferromagnetically. The magnetic moment $\sim$3$\mu_B$/Fe is in good agreement with experiments. Several other competing phases are also stabilized in the phase diagram, in agreement with recent calculations using phenomenological models. [1] Qinlong Luo {\it et al.}, Phys. Rev. B {\bf 84}, 140506(R) (2011), and references therein.   

Electronic structure and magnetic excitations in iron selenides

We calculate the electronic structure and magnetic excitations in the K$_{4}$Fe$_{4+x}$Se$_{5}$ alloy, with x between 0 and 1, within the local-density approximation. Analysis of the electronic structure with varying x leads to a prediction of the coexistence of two phases: one, strongly magnetic and another, weakly or nonmagnetic. Using linear response techniques we calculate spin wave spectra in K$_{4}$Fe$_{4+x}$Se$_{5}$, and find it is in excellent agreement with a recent experiment. The spectrum can be described rather well by an anisotropic J$_{1}$-J$_{2}$ model. We confirm that exchange coupling between NN Fe magnetic moments is strongly anisotropic, and show directly that in the ideal system this anisotropy can be associated with higher order terms in spin Hamiltonian (biquadratic coupling). Structural relaxation provides an additional source of the exchange anisotropy of approximately the same strength. The dependence of spin wave spectra on filling of Fe vacancy sites is discussed.   

Novel Magnetism in K$_{0.8}$Fe$_{1.6}$Se$_2$ Explained in the Unified Picture

The novel block checkerboard antiferromagnetism in Fe-vacancy-ordered insulating K$_{0.8}$Fe$_{1.6}$Se$_2$ is investigated theoretically [1]. Neither of the Fermi surface nesting and the Mott insulator scenarios, which were widely employed to model previous Fe-vacancy-free iron-based superconductors, is supported by our first-principles analysis of its electronic structure including unfolded Fermi surface, band gap, and orbital polarization. Instead, the orbital-degenerate double-exchange model, previously proposed to unify the metallic collinear and bicollinear antiferromagnetism of iron-based superconductors, is found sufficient to explain this insulating spin order as well as associated quantum magnetic transition induced by tetramer lattice distortion. Our findings demonstrate that the iron-based superconductors be universally described in the framework of coexisting itinerant and localized electronic states, which are coupled by Hund's rule coupling on the Fe atoms. Work supported by DOE DE-AC02-98CH10886.\\[4pt] [1] W.-G. Yin, C.-H. Lin, and W. Ku, arXiv:1106.0881v1.   

Vacancy-driven orbital and magnetic order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$

We investigate the effects of the $\sqrt{5}\times\sqrt{5}$ Fe vacancy ordering on the orbital and magnetic order in (K,Tl,Cs)$_y$Fe$_{2-x}$Se$_2$ using a three-orbital ($t_{2g}$) tight-binding Hamiltonian with generalized Hubbard interactions. We find that vacancy order enhances electron correlations, resulting in the onset of a block antiferromagnetic phase with large moments at smaller interaction strengths. In addition, vacancy ordering modulates the kinetic energy differently for the three $t_{2g}$ orbitals. This results in a breaking of the degeneracy between the $d_{xz}$ and $d_{yz}$ orbitals on each Fe site, and the onset of orbital order. Consequently, we obtain a novel inverse relation between orbital polarization and the magnetic moment. We predict that a transition from high-spin to low-spin states accompanied by a crossover from orbitally-disordered to orbitally-ordered states will be driven by doping the parent compound with electrons, which can be verified by neutron scattering and soft X-ray measurements.   

Phase separation and magnetic order in K-doped iron selenide superconductor

The newly discovered alkali-doped iron selenide superconductors exhibit unique characters that are absent in other iron-based superconductors, such as anti-ferromagnetically ordered insulating phases, extremely high Neel transition temperatures, and the presence of Fe vacancies and ordering. We have grown high-quality K$_{x}$Fe$_{2-y}$Se$_{2}$ thin films on graphene by molecular beam epitaxy and measured their atomic and electronic structures by low-temperature scanning tunneling microscopy. We demonstrate that a typical K$_{x}$Fe$_{2-y}$Se$_{2}$ sample contains two distinct phases: an insulating phase with well-defined $\surd 5 \times \surd $5 order of Fe vacancies, and a superconducting KFe$_{2}$Se$_{2}$ phase containing no Fe vacancies. An individual Fe vacancy can locally destroy superconductivity in a similar way as a magnetic impurity in conventional superconductors. The measurement of magnetic field dependence of the Fe-vacancy-induced bound states reveals a magnetically-related bipartite order in the tetragonal iron lattice. These findings elucidate the existing controversies on this new superconductor and provide atomistic information on the interplay between magnetism and superconductivity in iron-based superconductors.   

Magnetism and Superconductivity in Rb$_{1-x}$Fe$_{2-y}$Se$_2$

We report on the structural, magnetic, and superconducting properties of Rb$_{1-x}$Fe$_{2-y}$Se$_2$ single crystals. The system exhibits a strongly anisotropic antiferromagnetic behavior below 400~K. For 1.53 $<2-y<$ 1.6 superconductivity is found, whereas for Fe concentrations $2-y<$ 1.5 and $2-y>$ 1.6 insulating and semiconducting behavior is observed, respectively. The sharpest transition to the superconducting state and the highest transition temperature $T_c$ of 32.4~K is found for compositions close to Rb$_2$Fe$_4$Se$_5$. Comparison of the magnetic behavior of non-superconducting and superconducting samples provides evidence for the coexistence of superconductivity and static antiferromagnetic order [1]. THz time-domain transmission spectroscopy in superconducting samples evidences a metallic response and the superconducting transition of the system [2].\\[4pt] [1] V. Tsurkan et al., Phys. Rev. B 84, 144520 (2011).\\[0pt] [2] A. Charnukha et al., arXiv:1108.5698.   

Defect formation, magnetic interaction and electron phonon coupling in iron selenides M$_{1-x}$Fe$_{2-y}$Se$_{2}$

We perform a systematic study to explore the electronic and magnetic structures in iron selenide superconductors M$_{1-x}$Fe$_{2-y}$Se$_{2}$ using first principles calculations. We show that there is an intimate relationship between Se-height and the underneath Fe-spin square in M$_{1-x}$Fe$_{2-y}$Se$_{2}$. A displacement of the Se atom by as small as 0.2{\AA} is enough to change the amount of charge in the Fe-plane as much as 0.7 e per Fe. The Se-height increases as the number of ferromagnetic Fe-Fe bonds increases, yielding an expansion of 2{\AA} expansion in the c-axis for fully ferromagnetic spin configuration, which indicates a giant magneto-elastic coupling in these systems. Our calculations also explain why the formation of Fe vacancies is favorable in iron selenides, but not in iron pnictides. Finally, we calculate the spin-resolved electron-phonon coupling in MFe$_{2}$Se$_{2}$ and M$_{1-x}$Fe$_{2-y}$Se$_{2}$ to shed light on the mechanism of superconductivity in these materials.   

Phononic, magnetic, and inter-band Raman scattering in K$_{0.75}$Fe$_{1.75}$Se$_{2}$ superconductor

We have analyzed collective excitations in K$_{0.75}$Fe$_{1.75}$Se$_{2}$ single crystal ($T_{c}\sim $ 32 K) by polarized Raman scattering in the energy shift range of 20-8000 cm$^{-1}$, the temperature range of 10-300 K, and laser excitation energies from 1.8 to 3.0 eV. Seven $B_{g}$ and nine $A_{g}$ phonon modes are observed at 300K. Below $\sim $150 K an extra $A_{g}$ mode appears at 165 cm$^{-1}$. The amplitudes of the $A_{g}$ modes at $\sim $67, 112, and 124 cm$^{-1}$ are reduced, while the amplitude of 183 cm$^{-1} \quad A_{g}$ mode is enhanced by factor of five as temperature decreases from 300 to 40 K. Magnetic scattering bands at 1000-2000 cm$^{-1 }$consist of at least three distinct peaks each, implying different Fe-Fe AFM exchange coupling constants for underlying structure. Inter-band transitions are observed at $\sim $3700 and 4600 cm$^{-1}$ at 300 K in the $A_{g}$ and $B_{g}$ channels, respectively. Below 140 K these excitations are hardened to $\sim $4040 and 4820 cm$^{-1}$.   

Electronic structure and magnetism of doped $A_{x}Fe_{2-y}Se_{2}$

We develop a new multiorbital t-J Hamiltonian with realistic tight-binding and Heisenberg parameters to study the electronic and magnetic structure of $A_xFe_{2-y}Se_2$ superconductors for 0$<$y$<$0.4. The ARPES experiments are fitted by a tight-binding lattice model with random vacancy order. We find that the vacancy order greatly affects the electronic band structure. For intermediate doping levels 0 $<$ y $<$ 0.4, the stable electronic structure is a compromise between the solution for y=0 and y=0.4. Based on this model, we study the paramagnetic and antiferromagnetic (AFM) phases of $A_{0.8}Fe_{1.6}Se_2$. In the AFM phase the calculated spin susceptibility for the bare band structure agrees with a block-spin structure. This theoretical result is in good agreement with neutron scattering experiments of the spin structure. Furthermore, we show the results on the evolution of low-energy quasiparticle states with electron filling factor in the vacancy-ordered magnetic state.   

Nodeless d-wave Superconductivity and spin resonance in iron-selenide superconductors

Iron-selenide based layered compounds have been realized to be high-transition temperature superconductor in December, 2010. The superconductivity is tuned by varying number of iron vacancies in the crystal. This unique tunability of the high-temperature superconducting properties has reinforces the debate of universal properties in Fe based superconductors. Experiments and band structure calculations have shown that the electronic and magnetic structures of these compounds are significantly different from other iron-based superconductors. This fact leads us to propose that the superconducting state is nodeless d-wave pairing which is still driven by magnetic interactions. Nodeless gap leads to the fully gapped quasiparticle spectrum. Sign-changing gap lends itself naturally to the sharp feature in neutron scattering spectrum, the so called spin resonance. We predict the upward ``horseshoe'' dispersion of the spin resonance, in a sharp contrast with the ``hourglass'' dispersion in high\_Tc oxides where similar spin resonance is ubiquitously seen. In conclusion, despite iron-selenide systems exhibit very different observables, we show that the underlying pairing mechanism is driven by similar spin-fluctuation instabilities as in other high-temperature superconductors.