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Understanding spin and lattice excitations in a metallic magnetic ordered system form the basis to unveil the magnetic and lattice exchange couplings and their interactions with itinerant electrons. Kagome lattice antiferromagnet FeGe is interesting because it displays rare charge density wave (CDW) deep inside the antiferromagnetic ordered phase that interacts with the magnetic order. We use neutron scattering to study the evolution of spin and lattice excitations across the CDW transition $T_{\rm CDW}$ in FeGe. While spin excitations below $\sim$100 meV can be well described by spin waves of a spin-1 Heisenberg Hamiltonian, spin excitations at higher energies are centered around the Brillouin zone boundary and extend up to $\sim180$ meV consistent with quasiparticle excitations across spin-polarized electron-hole Fermi surfaces. Furthermore, $c$-axis spin wave dispersion and Fe-Ge optical phonon modes show a clear hardening below $T_{\rm CDW}$ due to spin-charge-lattice coupling but with no evidence for a phonon Kohn anomaly. By comparing our experimental results with density functional theory calculations in absolute units, we conclude that FeGe is a Hund's metal in the intermediate correlated regime where magnetism has contributions from both itinerant and localized electrons arising from spin polarized electronic bands near the Fermi level.

A quantum spin liquid (QSL) arises from a highly entangled superposition of many degenerate classical ground states in a frustrated magnet, and is characterized by emergent gauge fields and deconfined fractionalized excitations (spinons). Because such a novel phase of matter is relevant to high-transition-temperature superconductivity and quantum computation, the microscopic understanding of QSL states is a long-sought goal in condensed matter physics. The 3D pyrochlore lattice of corner-sharing tetrahedra can host a QSL with U(1) gauge fields called quantum spin ice (QSI), which is a quantum (with effective $S=1/2$) analog of the classical (with large effective moment) spin ice. A key difference between QSI and classical spin ice is the predicted presence of the linearly dispersing collective excitations near zero energy, dubbed the "photons", arising from emergent quantum electrodynamics, in addition to the spinons at higher energies. Recently, 3D pyrochlore systems Ce2M2O7 (M = Sn, Zr, Hf) have been suggested as effective $S=1/2$ QSI candidates, but there has been no evidence of quasielastic magnetic scattering signals from photons, a key signature for a QSI. Here, we use polarized neutron scattering experiments on single crystals of Ce2Zr2O7 to conclusively demonstrate the presence of magnetic excitations near zero energy at 50 mK in addition to signatures of spinons at higher energies. By comparing the energy (E), wave vector (Q), and polarization dependence of the magnetic excitations with theoretical calculations, we conclude that Ce2Zr2O7 is the first example of a dipolar-octupolar $\pi$ flux QSI with dominant dipolar Ising interactions, therefore identifying a microscopic Hamiltonian responsible for a QSL.

We present high-quality angle-resolved photoemission (ARPES) and density functional theory calculations (DFT+U) of SmCoIn$_5$. We find broad agreement with previously published studies of LaCoIn$_5$ and CeCoIn$_5$, confirming that the Sm $4f$ electrons are mostly localized. Nevertheless, our model is consistent with an additional delocalized Sm component, stemming from hybridization between the $4f$ electrons and the metallic bands at "hot spot" positions in the Brillouin zone. The dominant hot spot, called $\gamma_Z$, is similar to a source of delocalized $f$ states found in previous experimental and theoretical studies of CeCoIn$_5$. In this work, we identify and focus on the role of the Co $d$ states in exploring the relationship between heavy quasiparticles and the magnetic interactions in SmCoIn$_5$, which lead to a magnetically ordered ground state from within an intermediate valence scenario. Specifically, we find a globally flat band consisting of Co $d$ states near $E=-0.7$ eV, indicating the possibility of enhanced electronic and magnetic interactions in the "115" family of materials through localization in the Co layer, and we discuss a possible origin in geometric frustration. We also show that the delocalized Sm $4f$ states can hybridize directly with the Co $3d_{xz}$/$3d_{yz}$ orbitals, which occurs in our model at the Brillouin zone boundary point $R$ in a band that is locally flat and touches the Fermi level from above. Our work identifies microscopic ingredients for additional magnetic interactions in the "115" materials beyond the RKKY mechanism, and strongly suggests that the Co $d$ bands are an important ingredient in the formation of both magnetic and superconducting ground states., Comment: 11 pages, 5 figures

The microscopic mechanism of heavy band formation, relevant for unconventional superconductivity in CeCoIn$_5$ and other Ce-based heavy fermion materials, depends strongly on the efficiency with which $f$ electrons are delocalized from the rare earth sites and participate in a Kondo lattice. Replacing Ce$^{3+}$ ($4f^1$, $J=5/2$) with Sm$^{3+}$ ($4f^5$, $J=5/2$), we show that a combination of crystal field and on-site Coulomb repulsion causes SmCoIn$_5$ to exhibit a $\Gamma_7$ ground state similar to CeCoIn$_5$ with multiple $f$ electrons. Remarkably, we also find that with this ground state, SmCoIn$_5$ exhibits a temperature-induced valence crossover consistent with a Kondo scenario, leading to increased delocalization of $f$ holes below a temperature scale set by the crystal field, $T_v$ $\approx$ 60 K. Our result provides evidence that in the case of many $f$ electrons, the crystal field remains the most important tuning knob in controlling the efficiency of delocalization near a heavy fermion quantum critical point, and additionally clarifies that charge fluctuations play a general role in the ground state of "115" materials., Comment: 12 pages, 5 figures

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe$_2$As$_2$, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature $T_s$. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature $T_N$ ($

The existence of orbital-dependent electronic correlations has been recognized as an essential ingredient to describe the physics of iron-based superconductors. NaFeAs, a parent compound of iron based superconductors, exhibits a tetragonal-to-orthorhombic lattice distortion below $T_s\approx 60$ K, forming an electronic nematic phase with two 90$^\circ$ rotated (twinned) domains, and orders antiferromagnetically below $T_N\approx 42$ K. We use inelastic neutron scattering to study spin waves in uniaxial pressure-detwinned NaFeAs. By comparing the data with combined density functional theory and dynamical mean-field theory calculations, we conclude that spin waves up to an energy scale of $E_\text{crossover} \approx 100$ meV are dominated by $d_{yz}$-$d_{yz}$ intra-orbital scattering processes, which have the two-fold ($C_2$) rotational symmetry of the underlying lattice. On the other hand, the spin wave excitations above $E_\text{crossover}$, which have approximately fourfold ($C_4$) rotational symmetry, arise from the $d_{xy}$-$d_{xy}$ intra-orbital scattering that controls the overall magnetic bandwidth in this material. In addition, we find that the low-energy ($E\approx 6$ meV) spin excitations change from approximate $C_4$ to $C_2$ rotational symmetry below a temperature $T^\ast$ ($>T_s$), while spin excitations at energies above $E_\text{crossover}$ have approximate $C_4$ rotational symmetry and are weakly temperature dependent. These results are consistent with angle resolved photoemission spectroscopy measurements, where the presence of an uniaxial strain necessary to detwin NaFeAs also raises the onset temperature $T^\ast$ of observable orbital-dependent band splitting to above $T_s$, thus supporting the notion of orbital selective spin waves in the nematic phase of iron-based superconductors., Comment: 12 pages, 7 figures

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (Er = 3.6 meV) of superconducting FeSe (Tc = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasi-particle excitations between the hole and electron Fermi surfaces., Comment: To be published as a Rapid Communication in Physical Review B

The optimal superconductivity ($T_c \approx 30 $ K) in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ can be reached when the coupled antiferromagnetic (AF) order ($T_N$) and orthorhombic lattice distortion ($T_s$) are suppressed to zero temperature with increasing of P concentration or hydrostatic pressure. Here we use transport and neutron scattering to study the $c$-axis pressure effects on electronic phases in underdoped BaFe$_2$(As$_{0.72}$P$_{0.28}$)$_2$, which has $T_N = T_s\approx 40$ K and $T_c \approx $ 28 K at zero pressure. With increasing $c$-axis pressure, $T_N$ and $T_s$ are slightly enhanced around $P_c \sim 20 $ MPa. Upon further increasing pressure, AF order is gradually suppressed to zero, while $T_c$ is enhanced to 30 K. Our results reveal the importance of magnetoelastic couplings in BaFe$_2$(As$_{1-x}$P$_x$)$_2$, suggesting that the $c$-axis pressure can be used as a tuning parameter to manipulate the electronic phases in iron pnictides.

We use inelastic neutron scattering to show that long-range spin waves arising from the static bicollinear antiferromagnetic (AF) order in FeTe, which have twofold rotational symmetry in a fully detwinned crystal, rapidly dissolve above $E\approx 26$ meV into ridges of scattering with fourfold rotational symmetry and a nearly isotropic magnetic fluctuation spectrum. With increasing temperature above $T_N\approx 68$ K, the twofold spin waves change into broad regions of scattering with fourfold symmetry. Since the scattering patterns from plaquette magnetic order generated within a bilinear biquadratic Hamiltonian have fourfold rotational symmetry consistent with the high-energy, spin-isotropic spin waves of FeTe, we conclude that the bicollinear AF state in FeTe is quasidegenerate with plaquette magnetic order, providing evidence for the strongly frustrated nature of the local moments in iron chalcogenide family of iron-based superconductors., Comment: 12 pages, 11 figures

Understanding the nature of the electronic nematic phase in iron pnictide superconductors is important for elucidating its impact on high-temperature superconductivity. Here we use transport and inelastic neutron scattering to study spin excitations and in-plane resistivity anisotropy in uniaxial pressure detwinned BaFe$_2$As$_2$ and SrFe$_2$As$_2$, the parent compounds of iron pnictide superconductors. While BaFe$_2$As$_2$ exhibits weakly first order tetragonal-to-orthorhombic structural and antiferromagnetic (AF) phase transitions below $T_s > T_N\approx 138$ K, SrFe$_2$As$_2$ has strongly coupled first order structural and AF transitions below $T_s= T_N\approx 210$ K. We find that the direct signatures of the nematic phase persist to lower temperatures above the phase transition in the case of SrFe$_2$As$_2$ compared to BaFe$_2$As$_2$. Our findings support the conclusion that the strongly first-order nature of the magnetic transition in SrFe$_2$As$_2$ weakens the nematic phase and resistivity anisotropy in the system., Comment: 9 pages, 8 figures

A quantum spin liquid (QSL) is a state of matter where unpaired electrons' spins in a solid are quantum entangled, but do not show magnetic order in the zero-temperature limit. Because such a state may be important to the microscopic origin of high-transition temperature superconductivity and useful for quantum computation, the experimental realization of QSL is a long-sought goal in condensed matter physics. Although neutron scattering experiments on the two-dimensional (2D) spin-1/2 kagome-lattice ZnCu3(OD)6Cl2 and effective spin-1/2 triangular lattice YbMgGaO4 have found evidence for a continuum of magnetic excitations, the hallmark of a QSL carrying 'fractionalized quantum excitations', at very low temperature, magnetic and nonmagnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional (3D) Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 QSL candidate, but there is no evidence of a spin excitation continuum. Here we use thermodynamic, muon spin relaxation ({\mu} SR), and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK, consistent with the expectation of a QSL. Since our neutron diffraction and diffuse scattering measurements on Ce2Zr2O7 reveal no evidence of oxygen deficiency and magnetic/nonmagnetic ion disorder as seen in other pyrochlores, Ce2Zr2O7 may be the first example of a 3D QSL material with minimum magnetic and nonmagnetic chemical disorder.

Superconductivity in BaFe2(As1-xPx)2 iron pnictides emerges when its in-plane two-dimensional (2D) orthorhombic lattice distortion associated with nematic phase at Ts and three-dimensional (3D) collinear antiferromagnetic (AF) order at TN (Ts = TN) are gradually suppressed with increasing x, reaching optimal superconductivity around x = 0.30 with Tc $\approx$ 30 K. Here we show that a moderate uniaxial pressure along the c-axis in BaFe2(As0.70P0.30)2 spontaneously induces a 3D collinear AF order with TN = Ts > 30 K, while only slightly suppresses Tc. Although a ~ 400 MPa pressure compresses the c-axis lattice while expanding the in-plane lattice and increasing the nearest-neighbor Fe-Fe distance, it barely changes the average iron-pnictogen height in BaFe2(As0.70P0.30)2. Therefore, the pressure- induced AF order must arise from a strong in-plane magnetoelastic coupling, suggesting that the 2D nematic phase is a competing state with superconductivity., Comment: 13 pages, 5 figures

Understanding magnetic interactions in the parent compounds of high-temperature superconductors forms the basis for determining their role for the mechanism of superconductivity. For parent compounds of iron pnictide superconductors such as $A$Fe$_2$As$_2$ ($A=$ Ba, Ca, Sr), although spin excitations have been mapped out throughout the entire Brillouin zone (BZ), measurements were carried out on twinned samples and did not allow for a conclusive determination of the spin dynamics. Here we use inelastic neutron scattering to completely map out spin excitations of $\sim$100\% detwinned BaFe$_2$As$_2$. By comparing observed spectra with theoretical calculations, we conclude that the spin excitations can be well described by an itinerant model with important contributions from electronic correlations., Comment: 6 pages, 4 figures, with supplemental material

Using random-phase approximation spin-fluctuation theory, we study the influence of the hybridization between iron $d$-orbitals and pnictide $p$-orbitals on the superconducting pairing state in iron-based superconductors. The calculations are performed for a 16-orbital Hubbard-Hund tight-binding model of BaFe$_2$As$_2$ that includes the As-$p$ orbital degrees of freedom in addition to the Fe-$d$ orbitals and compared to calculations for a 10-orbital Fe-$d$ only model. In both models we find a leading $s^\pm$ pairing state and a subleading $d_ {x^2-y^2}$-wave state in the parent compound. Upon doping, we find that the $s^\pm$ state remains the leading state in the 16-orbital model up to a doping level of 0.475 electrons per unit cell, at which the hole Fermi surface pockets at the zone center start to disappear. This is in contrast to the 10-orbital model, where the $d$-wave state becomes the leading state at a doping of less than 0.2 electrons. This improved stability of $s^\pm$ pairing is found to arise from a decrease of $d_{xy}$ orbital weight on the electron pockets due to hybridization with the As-$p$ orbitals and the resulting reduction of near $(\pi,\pi)$ spin-fluctuation scattering which favors the competing $d$-wave state. These results show that the orbital dependent hybridization of Fermi surface Bloch states with the usually neglected $p$-orbital states is an important ingredient in an improved itinerant pairing theory., Comment: 6 pages, 4 figures

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 increasing x. The combination of magnetic and superconducting volumes implies that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reduction of both the ordered moment size and the volume fraction is observed below the superconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other iron pnictides in which one of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further enhanced with increased Ni doping, leading to a reentrant non-magnetic state below T_C for x = 1.3 %. The reentrant behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the same electrons. These observations are consistent with the sign-changing s-wave superconducting state, which is expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering temperature TN across a variety of iron-based superconductors. We argue that this linear relationship is consistent with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering., Comment: 20 pages, 14 figures, Correspondence should be addressed to Prof. Yasutomo Uemura: tomo@phys.columbia.edu

Two phase transitions in the tetragonal strongly correlated electron system CeNiAsO were probed by neutron scattering and zero field muon spin rotation. For $T

We use neutron diffraction and muon spin relaxation to study the effect of in-plane uniaxial pressure on the antiferromagnetic (AF) orthorhombic phase in BaFe$_2$As$_2$ and its Co- and Ni-substituted members near optimal superconductivity. In the low temperature AF ordered state, uniaxial pressure necessary to detwin the orthorhombic crystals also increases the magnetic ordered moment, reaching an 11$\%$ increase under 40 MPa for BaFe$_{1.9}$Co$_{0.1}$As$_2$, and a 15$\%$ increase for BaFe$_{1.915}$Ni$_{0.085}$As$_2$. We also observe an increase of the AF ordering temperature ($T_N$) of about 0.25 K/MPa in all compounds, consistent with density functional theory calculations that reveal better Fermi surface nesting for itinerant electrons under uniaxial pressure. The doping dependence of the magnetic ordered moment is captured by combining dynamical mean field theory with density functional theory, suggesting that the pressure-induced moment increase near optimal superconductivity is closely related to quantum fluctuations and the nearby electronic nematic phase., Comment: 6 pages, 4 figures, 12 supplementary pages, 12 supplementary figures, PRB accepted as Rapid Communication

We use neutron scattering to study spin excitations in single crystals of LiFe$_{0.88}$Co$_{0.12}$As, which is located near the boundary of the superconducting phase of LiFe$_{1-x}$Co$_{x}$As and exhibits non-Fermi-liquid behavior indicative of a quantum critical point. By comparing spin excitations of LiFe$_{0.88}$Co$_{0.12}$As with a combined density functional theory (DFT) and dynamical mean field theory (DMFT) calculation, we conclude that wave-vector correlated low energy spin excitations are mostly from the $d_{xy}$ orbitals, while high-energy spin excitations arise from the $d_{yz}$ and $d_{xz}$ orbitals. Unlike most iron pnictides, the strong orbital selective spin excitations in LiFeAs family cannot be described by anisotropic Heisenberg Hamiltonian. While the evolution of low-energy spin excitations of LiFe$_{1-x}$Co$_x$As are consistent with electron-hole Fermi surface nesting condition for the $d_{xy}$ orbital, the reduced superconductivity in LiFe$_{0.88}$Co$_{0.12}$As suggests that Fermi surface nesting conditions for the $d_{yz}$ and $d_{xz}$ orbitals are also important for superconductivity in iron pnictides., Comment: 14 pages, 10 figures,Accepted for publication in PRL

We use inelastic neutron scattering to study the temperature and energy dependence of the spin excitation anisotropy in uniaxial-strained electron-doped iron pnictide BaFe$_{1.9}$Ni$_{0.1}$As$_2$ near optimal superconductivity ($T_c=20$ K). Our work has been motivated by the observation of in-plane resistivity anisotropy in the paramagnetic tetragonal phase of electron-underdoped iron pnictides under uniaxial pressure, which has been attributed to a spin-driven Ising-nematic state or orbital ordering. Here we show that the spin excitation anisotropy, a signature of the spin-driven Ising-nematic phase, exists for energies below $\sim$60 meV in uniaxial-strained BaFe$_{1.9}$Ni$_{0.1}$As$_2$. Since this energy scale is considerably larger than the energy splitting of the $d_{xz}$ and $d_{yz}$ bands of uniaxial-strained Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal superconductivity, spin Ising-nematic correlations is likely the driving force for the resistivity anisotropy and associated electronic nematic correlations.

High-temperature superconductivity in iron pnictides occurs when electrons are doped into their antiferromagnetic (AF) parent compounds. In addition to inducing superconductivity, electron-doping also changes the static commensurate AF order in the undoped parent compounds into short-range incommensurate AF order near optimal superconductivity. Here we use neutron scattering to demonstrate that the incommensurate AF order in BaFe$_{2-x}$Ni$_{x}$As$_{2}$ is not a spin-density-wave arising from the itinerant electrons in nested Fermi surfaces, but consistent with a cluster spin glass in the matrix of the superconducting phase. Therefore, optimal superconductivity in iron pnictides coexists and competes with a mesoscopically separated cluster spin glass phase, much different from the homogeneous coexisting AF and superconducting phases in the underdoped regime., Comment: 4 figures