NaFe$_{0.5}$Cu$_{0.5}$As represents a rare exception in the metallic iron pnictide family, in which a small insulating gap is opened. Based on first-principles study, we provide a comprehensive theoretical characterization of this insulating compound. The Fe$^{3+} $spin degree of freedom is quantified as a quasi-1D $S=\frac{5}{2}$ Heisenberg model. The itinerant As hole state is downfolded to a $p_{xy}$-orbital hopping model on a square lattice. A unique orbital-dependent Hund's coupling between the spin and the hole is revealed. Several important material properties are analyzed, including (a) factors affecting the small $p-d$ charge-transfer gap; (b) role of the extra interchain Fe; and (c) the quasi-1D spin excitation in the Fe chains. The experimental manifestations of these properties are discussed.
Quasi-one-dimensional spin excitations in the iron pnictide NaFe$_{0.53}$Cu$_{0.47}$As
Zhejiang University（浙江大学）；Rice University（莱斯大学）；STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普顿实验室）；Oak Ridge National Laboratory（橡树岭国家实验室）；Renmin University of China（中国人民大学）
A central question in a large class of strongly correlated electron systems, including heavy fermion compounds and iron pnictides, is the identification of different phases and their origins. It has been shown that the antiferromagnetic (AFM) phase in some heavy fermion compounds is induced by Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized moments, and that the competition between this interaction and Kondo effect is responsible for quantum criticality. However, conclusive experimental evidence of the RKKY interaction in pnictides is lacking. Here, using high resolution $^{…
In the studies of iron-pnictides, a key question is whether their bad-metal state from which the superconductivity emerges lies in close proximity with a magnetically ordered insulating phase. Recently it was found that at low temperatures, the heavily Cu-doped NaFe$_{1-x}$Cu$_x$As ($x > 0.3$) iron-pnictide is an insulator with long-range antiferromagnetic order, similar to the parent compound of cuprates but distinct from all other iron-pnictides. Using angle-resolved photoemission spectroscopy, we determined the momentum-resolved electronic structure of NaFe$_{1-x}$Cu$_x$As ($x = 0.44$) and …
In copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe$_{1-x}$Cu$_x$As single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\approx1.8\%$. …
We present the results of extended theoretical LDA+DMFT calculations for a new iron-pnictide high temperature superconductor NaFeAs compared with the recent high quality angle-resolved photoemission (ARPES) experiments on this system [1]. The universal manifestation of correlation effects in iron-pnictides is narrowing of conducting bands near the Fermi level. Our calculations demonstrate that for NaFeAs the effective mass is renormalized on average by a factor of the order of 3, in good agreement with ARPES data. This is essentially due to correlation effects on Fe-3d orbitals only and no add…
The parent compounds of iron-based superconductors are magnetically-ordered bad metals, with superconductivity appearing near a putative magnetic quantum critical point. The presence of both Hubbard repulsion and Hund's coupling leads to rich physics in these multiorbital systems, and motivated descriptions of magnetism in terms of itinerant electrons or localized spins. The NaFe$_{1-x}$Cu$_x$As series consists of magnetically-ordered bad metal ($x=0$), superconducting ($x\approx0.02$) and magnetically-ordered semiconducing/insulating ($x\approx0.5$) phases, providing a platform to investigate…
Using angle-resolved photoemission spectroscopy, we studied the electronic structure of NaFe$_{1-x}$Co$_x$As from an optimally doped superconducting compound ($x=0.028$) to a heavily overdoped non-superconducting one ($x=0.109$). Similar to the case of "122" type iron pnictides, our data suggest that Co dopant in NaFe$_{1-x}$Co$_x$As supplies extra charge carriers and shifts the Fermi level accordingly. In the $x=0.109$ compound, the hole-like bands around the zone center $Γ$ move to deeper binding energies and an electron pocket appears instead. The overall band renormalization remains basica…
Iron-based superconductivity develops near an antiferromagnetic order and out of a bad metal normal state, which has been interpreted as originating from a proximate Mott transition. Whether an actual Mott insulator can be realized in the phase diagram of the iron pnictides remains an open question. Here we use transport, transmission electron microscopy, X-ray absorption spectroscopy, and neutron scattering to demonstrate that NaFe$_{1-x}$Cu$_x$As near $x\approx 0.5$ exhibits real space Fe and Cu ordering, and are antiferromagnetic insulators with the insulating behavior persisting above the …
Recent neutron scattering measurements indicate that NaFe$_{1-x}$Cu$_{x}$As forms an antiferromagnetic stripe phase near $x\approx 0.5$ in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, $x < 0.04$. We have investigated the development of magnetism in this compound using $^{23}$Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals ($x$ = 0.13, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest neighbo…
Similar to the cuprate high TC superconductors, the iron pnictide superconductors also lie in close proximity to a magnetically ordered phase. A central debate concerning the superconducting mechanism is whether the local magnetic moments play an indispensable role or the itinerant electron description is sufficient. A key step for resolving this issue is to acquire a comprehensive picture regarding the nature of various phases and interactions in the iron compounds. Here we report the doping, temperature, and spatial evolutions of the electronic structure of NaFe1-xCoxAs studied by scanning t…
We use inelastic neutron scattering to study acoustic phonons and spin excitations in single crystals of NaFeAs, a parent compound of iron pnictide superconductors. NaFeAs exhibits a tetragonal-to-orthorhombic structural transition at $T_s\approx 58$ K and a collinear antiferromagnetic (AF) order at $T_N\approx 45$ K. While longitudinal and out-of-plane transverse acoustic phonons behave as expected, the in-plane transverse acoustic phonons reveal considerable softening on cooling to $T_s$, and then harden on approaching $T_N$ before saturating below $T_N$. In addition, we find that spin-spin …
Neutron spin resonance, a collective magnetic excitation coupled to superconductivity, is one of the most prominent features shared by a broad family of unconventional superconductors including copper oxides, iron pnictides, and heavy fermions. In this work, we study the doping evolution of the resonances in NaFe$_{1-x}$Co$_x$As covering the entire superconducting dome. For the underdoped compositions, two resonance modes coexist. As doping increases, the low-energy resonance gradually loses its spectral weight to the high-energy one but remains at the same energy. By contrast, in the overdope…
The superconductivity discovered in iron-pnictides is intimately related to a nematic ground state, where the C4 rotational symmetry is broken via the structural and magnetic transitions. We here study the nematicity in NaFeAs with the polarization dependent angle-resolved photoemission spectroscopy. A uniaxial strain was applied on the sample to overcome the twinning effect in the low temperature C2-symmetric state, and obtain a much simpler electronic structure than that of a twinned sample. We found the electronic structure undergoes an orbital-dependent reconstruction in the nematic state,…
One of the major puzzles regarding unconventional superconductivity is how some of the most interesting superconductors are related to an insulating phase that lies in close proximity. Here we report scanning tunneling microscopy studies of the local electronic structure of Cu doped NaFeAs across the superconductor to insulator transition. We find that in the highly insulating regime the electronic spectrum develops an energy gap with diminishing density of state at the Fermi level. The overall lineshape and strong spatial variations of the spectra are strikingly similar to that of lightly dop…
A series of high quality NaFe$_{1-x}$Cu$_x$As single crystals has been grown by a self-flux technique, which were systematically characterized via structural, transport, thermodynamic, and high pressure measurements. Both the structural and magnetic transitions are suppressed by Cu doping, and bulk superconductivity is induced by Cu doping. Superconducting transition temperature ($T_c$) is initially enhanced from 9.6 to 11.5 K by Cu doping, and then suppressed with further doping. A phase diagram similar to NaFe$_{1-x}$Co$_x$As is obtained except that insulating instead of metallic behavior is…
In a conventional superconductor, the spin-lattice relaxation rate on all nuclei should have the same temperature dependence below Tc. We performed $^{23}$Na, $^{75}$As, and $^{59}$Co NMR studies on single crystals of NaFe0.95Co0.05As, and found that spin-lattice relaxation rates show very different temperature dependent power-law behavior on three sites. We propose that such site-dependent behavior is due to the facts that the superconductor has two gaps of very different sizes. The power-law exponent of each nucleus is affected by the strength of the hyperfine coupling to the small gap. We a…
We study an inhomogeneous three-orbital Hubbard model for the Cu-substituted iron pnictides using an extended real-space Green's function method combined with density functional calculations. We find that the onsite interactions of the Cu ions are the principal determinant of whether an electron dopant or a hole dopant is caused by the Cu substitution. It is found that the Cu substitution could lead to a hole doping when its onsite interactions are smaller than a critical value, as opposed to an electron doping when the interactions of Cu ions are larger than the critical value, which may expl…
We report Hall measurement of the normal state in K- and Co-doped BaFe$_2$As$_2$, as well NaFe$_{1-x}$Co$_x$As. We found that a power-law temperature dependence of Hall angle, cot$θ_{\rm H}$$\propto$ $T^β$, prevails in normal state with temperature range well above the structural, spin-density-wave and superconducting transitions for the all samples with various doping levels. The power $β$ is nearly 4 for the parent compounds and the heavily underdoped samples, while around 3 for the superconducting samples. The $β$ suddenly changes from 4 to 3 at a doping level that is close to the emergence…
The multiband nature of iron pnictides gives rise to a rich temperature-doping phase diagram of competing orders and a plethora of collective phenomena. At low dopings, the tetragonal-to-orthorhombic structural transition is closely followed by a spin density wave transition both being in close proximity to the superconducting phase. A key question is the nature of high-$T_c$ superconductivity and its relation to orbital ordering and magnetism. Here we study the NaFe$_{1-x}$Co$_{x}$As superconductor using polarization-resolved Raman spectroscopy. The Raman susceptibility displays critical enha…
We report results of inelastic-neutron-scattering measurements of low-energy spin-wave excitations in two structurally distinct families of iron-pnictide parent compounds: Na(1-δ)FeAs and BaFe2As2. Despite their very different values of the ordered magnetic moment and Néel temperatures, T_N, in the antiferromagnetic state both compounds exhibit similar spin gaps of the order of 10 meV at the magnetic Brillouin-zone center. The gap opens sharply below T_N, with no signatures of a precursor gap at temperatures between the orthorhombic and magnetic phase transitions in Na(1-δ)FeAs. We also find a…
Iron-based superconductors have been found to exhibit an intimate interplay of orbital, spin, and lattice degrees of freedom, dramatically affecting their low-energy electronic properties, including superconductivity. Albeit the precise pairing mechanism remains unidentified, several candidate interactions have been suggested to mediate the superconducting pairing, both in the orbital and in the spin channel. Here, we employ optical spectroscopy (OS), angle-resolved photoemission spectroscopy (ARPES), ab initio band-structure, and Eliashberg calculations to show that nearly optimally doped NaF…
Muon spin rotation and relaxation studies have been performed on a "111" family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for higher x than 0.4 % magnetic order becomes more disordered and is completely suppressed for x = 1.5 %. The magnetic volume fraction continuously decreases with …
The bad-metal behavior of the iron pnictides has motivated a theoretical description in terms of a proximity to Mott localization. Since the parent compounds of the iron pnictides contain an even number of 3d-electrons per Fe, it is important to determine whether a Mott transition robustly exists and the nature of the possible Mott insulating phases. We address these issues in a minimal two-orbital model and a more realistic four-orbital model for the parent iron pnictides using a slave-spin approach. In the two-orbital model with two electrons per Fe, we identify a transition from metal to Mo…
X-ray emission and absorption spectroscopies are jointly used as fast probes to determine the evolution as a function of doping of the fluctuating local magnetic moments in K- and Cr- hole-doped BaFe2As2. An increase in the local moment with hole-doping is found, supporting the theoretical scenario in which a Mott insulating state that would be realized for half-filled conduction bands has an influence throughout the phase diagram of these iron-pnictides.
A U(1) slave-spin representation is introduced for multi-orbital Hubbard models. As with the $Z_2$ form of L. de'Medici et al. (Phys. Rev. B 72, 205124 (2005)), this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For non-degenerate multi-orbital models, our U(1) approach is advantageous in that it captures the non-interacting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the U(1) and $Z_2$ slave-spin approachs yield the same results in the slave-spin-condensed phase. I…
Density-functional-theory-based electronic structure calculations are made to consider the novel electronic states of Ru-pnictides RuP and RuAs where the intriguing phase transitions and superconductivity under doping of Rh have been reported. We find that there appear nearly degenerate flat bands just at the Fermi level in the high-temperature metallic phase of RuP and RuAs; the flat-band states come mainly from the $4d_{xy}$ orbitals of Ru ions and the Rh doping shifts the Fermi level just above the flat bands. The splitting of the flat bands caused by their electronic instability may then b…
The Coulomb repulsion, impeding electrons' motion, has an important impact on the charge dynamics. It mainly causes a reduction of the effective metallic Drude weight (proportional to the so-called optical kinetic energy), encountered in the optical conductivity, with respect to the expectation within the nearly-free electron limit (defining the so-called band kinetic energy), as evinced from band-structure theory. In principle, the ratio between the optical and band kinetic energy allows defining the degree of electronic correlations. Through spectral weight arguments based on the excitation …
We present a high-pressure NMR study of the overdoped iron pnictide superconductor NaFe$_{0.94}$Co$_{0.06}$As. The low-energy antiferromagnetic spin fluctuations in the normal state, manifest as the Curie-Weiss upturn in the spin-lattice relaxation rate $1/^{75}T_1T$, first increase strongly with pressure but fall again at $P > P_{\rm opt} =$ 2.2 GPa. Neither long-ranged magnetic order nor a structural phase transition is encountered up to 2.5 GPa. The superconducting transition temperature $T_c$ shows a pressure-dependence identical to the spin fluctuations. Our observations demonstrate that …
We use neutron scattering to study temperature dependent spin excitations in insulating antiferromagnetic (AF) Rb$_{0.8}$Fe$_{1.6}$Se$_2$. In the low-temperature AF state, spin waves can be accurately described by a local moment Heisenberg Hamiltonian. On warming to around the Neel temperature of T_N=500$ K, low-energy (E<30meV) paramagnetic spin excitations form Lorentzian-like quasielastic peaks centered at the AF wave vectors associated with spin waves, while high-energy (E>50meV) spin excitations become heavily damped. Upon further warming to above the structural distortion temperature of …
Superconductivity in the iron pnictides and chalcogenides is closely connected to a bad-metal normal state and a nearby antiferromagnetic order. Therefore, considerable attention has been focused on the role of electron correlations and spin dynamics. In this article, we summarize some key experiments that quite directly imply strong electron correlations in these materials, and discuss aspects of the recent theoretical studies on these issues. In particular, we outline a $w$-expansion, which treats the correlation effects using the Mott transition as the reference point. For the parent system…
The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the superconducting dome. In this review, we critically examine these claims and highlight significant diffe…
The correlation and competition between antiferromagnetism and superconductivity are one of the most fundamental issues in all of high temperature superconductors. The superconductivity in high temperature cuprate superconductors arises from suppressing an antiferromagnetic (AFM) Mott insulator phase by doping1 while that in iron-pnictide high temperature superconductors arises from AFM semimetals and can coexist with AFM orders2-9. This key difference marked in their phase diagrams has raised many intriguing debates about whether the two materials can be placed in the same category to underst…
In Fe pnictide (Pn) superconducting materials, neither Mn- nor Cr- doping to the Fe site induces superconductivity, even though hole carriers are generated. This is in strong contrast with the superconductivity appearing when holes are introduced by alkali metal substitution on the insulating blocking layers. We investigate in detail the effects of Mn doping on magneto-transport properties in Ba(Fe$_{1-x}$Mn$_x$As)$_2$ for elucidating the intrinsic reason. The negative Hall coefficient for $x$ = 0 estimated in the low magnetic field ($B$) regime gradually increases as $x$ increases, and its si…
We investigated the reliability and applicability of so-called magnetic force linear response method to calculate spin-spin interaction strengths from first-principles. We examined the dependence on the numerical parameters including the number of basis orbitals and their cutoff radii within non-orthogonal LCPAO (linear combination of pseudo-atomic orbitals) formalism. It is shown that the parameter dependence and the ambiguity caused by these choices are small enough in comparison to the other computation approach and experiments. Further, we tried to pursue the possible extension of this tec…
The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconv…
Bad metal properties have motivated a description of the parent iron pnictides as correlated metals on the verge of Mott localization. What has been unclear is whether interactions can push these and related compounds to the Mott insulating side of the phase diagram. Here we consider the iron oxychalcogenides La2O2Fe2O(Se,S)2, which contain an Fe square lattice with an expanded unit cell. We show theoretically that they contain enhanced correlation effects through band narrowing compared to LaOFeAs, and we provide experimental evidence that they are Mott insulators with moderate charge gaps. W…
The bad metal behavior in the normal state of the iron-based superconductors suggests an intimate connection between the superconductivity and a proximity to a Mott transition. At the same time, there is strong evidence for the multi-orbital nature of the electronic excitations. It is then important to understand the orbital-dependent effects of electron correlations. In this paper we review the recent theoretical progresses on the metal-to-insulator transition in multiorbital models for the iron-based superconductors. These include studies of models that contain at least the 3d xy and 3d xz/y…
To elucidate the role played by the transition metal ion in the pnictide materials, we compare the electronic and magnetic properties of BaFe_{2}As_{2} with BaMn_{2}As_{2}. To this end we employ the LDA+Gutzwiller method to analyze the mass renormalizations and the size of the ordered magnetic moment of the two systems. We study a model that contains all five transition metal 3d orbitals together with the Ba-5d and As-4p states (ddp-model) and compare these results with a downfolded model that consists of Fe/Mn d-states only (d-model). Electronic correlations are treated using the multiband Gu…
This is a report on the new 122 ternary transition-metal pnictide of BaMn2Bi2, which is crystallized from bismuth flux. BaMn2Bi2 adopts ThCr2Si2-type structure (I4/mmm) with a = 4.4902(3) Å and c = 14.687(1) Å; it is antiferromagnetic with anisotropic magnetic susceptibility and semiconducting with a band gap of Eg = 6 meV. Heat capacity result confirms the insulating ground state in BaMn2Bi2 with the electronic residual Sommerfeld coefficient of γ ~ 0. The high temperature magnetization results show that magnetic ordering temperature is TN ~ 400 K. Hole-doping in BaMn2Bi2 via potassium in Ba1…
Moiré in $Γ$-valley square lattice: Copper- and iron-based superconductor simulation in a single device
International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science（物质纳米结构国际中心（WPI-MANA），国立材料研究所）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics, University of Connecticut（康涅狄格大学物理系）；School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）
