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Uniaxial strain is a powerful tuning parameter that can control symmetry and anisotropic electronic properties in iron-based superconductors. However, accurately characterizing anisotropic strain can be challenging and complex. Here, we utilize a cryogenic optical system equipped with a high-spatial-resolution microscope to characterize surface strains in iron-based superconductors using the digital image correlation method. Compared with other methods such as high-resolution X-ray diffraction, strain gauge, and capacitive sensor, digital image correlation offers a non-contact, full-field measurement approach, acting as an optical virtual strain gauge that provides high spatial resolution. The results measured on detwinned {\BFA} are quantitatively consistent with the distortion measured by X-ray diffraction and neutron Larmor diffraction. These findings highlight the potential of cryogenic digital image correlation as an effective and accessible tool for probing the isotropic and anisotropic strains, facilitating the application of uniaxial strain tuning in the study of quantum materials., Comment: 6 pages, 4 figures. Published online in Chinese Physics Letters. DOI 10.1088/0256-307X/41/10/107102

In iron-based superconductors (FeSCs), the interplay between electronic nematicity and superconductivity is essential for understanding the exotic superconducting ground state. In the nematic regime, uniaxial-strain ($\varepsilon$) tuning of the superconducting transition temperature $T_c$ [$\Delta T_c(\varepsilon)=\alpha\varepsilon+\beta\varepsilon^2$] offers a unique approach to investigating the evolution of pairing symmetry if both $s$ and $d$ wave pairing instabilities are relevant. Here, we employ uniaxial strain to tune the $T_c$ of FeSe$_{1-x}$S$_x$, in which both nematicity and superconductivity undergo significant changes with doping. While $T_c$ is usually suppressed quadratically with $\varepsilon$ in optimally doped BaFe$_2$As$_2$, $\Delta T_c(\varepsilon)$ in FeSe$_{1-x}$S$_x$ dominated by $\Delta T_c(\varepsilon)=\beta\varepsilon^2$ changes its sign from $\beta$ < $0$ in FeSe to $\beta$ > $0$ in FeSe$_{1-x}$S$_x$ ($x\gtrsim0.10$), indicating an evolution of the pairing symmetry from an $s_{\pm}$ state towards an $s+d$ wave state. These findings highlight the $\Delta T_c(\varepsilon)$ as a powerful probe for elucidating the superconducting pairing symmetry in the nematic regime of FeSCs and provide new insights into the evolution of pairing symmetry in FeSCs., Comment: 6 pages, 4 figures. Supplementary is available upon reasonable request

An eutectic LiCl/KCl flux method in a horizontal configuration has been used to grow a series of homogeneous Fe$_{1+\delta}$Se$_{1-x}$Te$_x$ single crystals of high quality with 0.5 $\leq$ $x$ $\leq$ 1. Compared with previously used melt-growth method, the stable crystallization process in LiCl/KCl flux below their peritectic temperatures results in better homogeneity and crystalline perfection identified by energy dispersive spectrometer and x-ray diffraction. The interstitial Fe value $\delta$ remains small within 0.5 $\leq$ $x$ $\leq$ 0.85 where the superconducting temperature $T_C$ is not sensitive to the Te content with sharp superconducting transition widths $\Delta$$T_C$ < 1 K and a maximum of $T_C$ = 14.3 K at $x$ = 0.61. The value $\delta$ starts to increase quickly accompanied by a deviation of linear behavior of crystal lattice parameters as well as the broadening of $\Delta$$T_C$ = 2.1 K at $x$ = 0.91, then suddenly rises up to $\delta$ > 0.1 followed by the disappearance of superconductivity and emergence of antiferromagnetic order at x $\geq$ 0.96. We also observed a metallic to semiconducting transition in the normal state resistivity of Fe$_{1+\delta}$Se$_{1-x}$Te$_x$ with increasing Te content which is related to a localized electronic state induced by the interstitial Fe. The interstitial Fe value $\delta$ might be a key physical parameter to understand various properties of Fe$_{1+\delta}$Se$_{1-x}$Te$_x$ system.

Magnetic field is expelled from a superconductor, unless it forms quantum vortices, consisting of a core singularity with current circulating around it. The London quantization condition implies that there is one core singularity per quantum of magnetic flux in single-component superconductors, while in multiband materials fractional vortices are possible. Here, we report the first observation of quantum vortex core fractionalization on the potassium terminated surface of multiband superconductor KFe2As2 by scanning tunneling microscopy. We observe splitting of an integer-flux vortex into several fractional vortices, leading to disparity between numbers of flux quanta and vortex cores. Our findings demonstrate that fractionalized core singularities are possible in a multiband superconductor, opening avenue for new experimental platforms with quasiparticles with fractional statistics., Comment: 16 pages, 4 figures

Supersolid is an exotic quantum state of matter that spontaneously hosts the features of both solid and superfluid, which breaks the translation and U(1) gauge symmetries. Here we study the spin dynamics in the triangular-lattice compound Na$_2$BaCo(PO$_4$)$_2$, which is revealed in [Xiang et al., Nature 625, 270-275 (2024)] as a quantum magnetic analog of supersolid. We simulate the easy-axis Heisenberg model with tensor network approach and uncover unique dynamic traits. These features are manifested in two branches of excitations that can be associated with the spin solidity and superfluidity, respectively. One branch contains the U(1) Goldstone and roton modes, while the other comprises pseudo-Goldstone and roton modes. The gapless Goldstone modes of the in-plane superfluid order are confirmed by our inelastic neutron scattering measurements. Together with the evident out-of-plane solid order indicated by the magnetic Bragg peaks, our findings provide spectroscopic evidence for spin supersolidity in this easy-axis antiferromagnet. Akin to the role of phonon-roton modes -- Landau elementary excitations -- in shaping the helium superfluid thermodynamics, the intriguing double magnon-roton dispersion here determines the low-temperature thermodynamics of spin supersolid down to sub-Kelvin regime, explaining the recently observed giant magnetocaloric effect in Na$_2$BaCo(PO$_4$)$_2$., Comment: 8+9 pages, 4+9 figures

Determination of the magnetic structure and confirmation of the presence or absence of inversion ($\mathcal{P}$) and time reversal ($\mathcal{T}$) symmetry is imperative for correctly understanding the topological magnetic materials. Here high-quality single crystals of the layered manganese pnictide CaMnSb$_2$ are synthesized using the self-flux method. De Haas-van Alphen oscillations indicate a nontrivial Berry phase of $\sim$ $\pi$ and a notably small cyclotron effective mass, supporting the Dirac semimetal nature of CaMnSb$_2$. Neutron diffraction measurements identify a C-type antiferromagnetic (AFM) structure below $T\rm_{N}$ = 303(1) K with the Mn moments aligned along the $a$ axis, which is well supported by the density functional theory (DFT) calculations. The corresponding magnetic space group is $Pn'm'a'$, preserving a $\mathcal{P}\times\mathcal{T}$ symmetry. Adopting the experimentally determined magnetic structure, band crossings near the Y point in momentum space and linear dispersions of the Sb $5p_{y,z}$ bands are revealed by the DFT calculations. Furthermore, our study predicts the possible existence of an intrinsic second-order nonlinear Hall effect in CaMnSb$_2$, offering a promising platform to study the impact of topological properties on nonlinear electrical transports in antiferromagnets., Comment: 7 Pages, 6 figures

Noncentrosymmetric magnets usually host intriguing magnetic interactions inherent the crystal structure with broken inversion symmetry, which can give rise to rich magnetic behaviors. We report herein the high-pressure synthesis, crystal structure, magnetizations and magnetic structure of a so-called Nowotny chimney ladder compound Cr4Ge7. Our analysis on the powder neutron diffraction data revises the crystal structure as a noncentrosymmetric space group (P-4c2, No.116). It exhibits two magnetic orders within the temperature range of 2 - 400 K. The first order at ~ 207 K associated with a small magnetic moment of ~ 0.75 miuB is assigned to a commensurate ferromagnetic structure with a propagation vector k = (0, 0, 0). The weak itinerant ferromagnet nature should be caused by the complex Cr spin orders from different Wyckoff positions. The second order at ~ 18 K is assumed to arise from a competition between the Dzyaloshinskii-Moria and Heisenberg interactions. The results provide an excellent platform for study on intricate interactions between various magnetic exchanges as well as for the exploration of high temperature exotic magnetic properties which host potential applications in next-generation spintronics., Comment: 21 pages, 5 figures, 2 tables; Supporting Information is not included

The unusual quantum-disordered magnetic ground state intertwined with superconductivity and electronic nematicity in FeSe has been a research focus in iron-based superconductors. However, the intrinsic spin excitations across the entire Brillouin zone in detwinned FeSe, which forms the basis for a microscopic understanding of the magnetic state and superconductivity, remain to be determined. Here, we use inelastic neutron scattering to map out the spin excitations of FeSe dewtinned with a uniaxial-strain device. We find that the stripe spin excitations (Q=(1, 0)/(0, 1)) exhibit the $C_2$ symmetry up to $E\approx120$ meV, while the N{\'e}el spin excitations (Q=(1, 1)) retain their $C_4$ symmetry in the nematic state. The temperature dependence of the difference in the spin excitations at Q=(1, 0) and (0, 1) for temperatures above the structural phase transition unambiguously shows the establishment of the nematic quantum disordered state. The similarity of the N\'eel excitations in FeSe and NaFeAs suggests that the N\'eel excitations are driven by the enhanced electron correlations in the $3d_{xy}$ orbital. By determining the key features of the stripe excitations and fitting their dispersions using a Heisenberg Hamiltonian with biquadratic interaction ($J_1$-$K$-$J_2$), we establish a spin-interaction phase diagram and conclude that FeSe is close to a crossover region between the antiferroquadrupolar, N\'eel, and stripe ordering regimes. The results provide an experimental basis for establishing a microscopic theoretical model to describe the origin and intertwining of the emergent orders in iron-based superconductors., Comment: 9 pages, 5 figures

The occurrence of charge-density-wave (CDW) order is a common thread in the phase diagram of cuprate high-transition-temperature ($T_c$) superconductors. In iron-based superconductors (FeSCs), nematic order and fluctuations play a decisive role in driving other emergent orders. CDW order has been observed by scanning tunneling microscopy for various FeSCs such as FeSe thin films, uniaxially strained LiFeAs, and tetragonal FeSe$_{0.81}$S$_{0.19}$. However, it remains elusive if the CDW in these materials is a bulk phenomenon as well as if and how it intertwines with the electronic nematicity. Using energy-resolved resonant X-ray scattering at the Fe-L$_3$ edge, we report the discovery of a local-strain-induced incommensurate isotropic CDW order in FeSe$_{0.82}$S$_{0.18}$. A highly anisotropic CDW response under uniaxial strain unambiguously manifests that the CDW is directly coupled to the nematicity. Transforming part of Fe$^{2+}$ to Fe$^{3+}$ on the surface of FeSe$_{1-x}$S$_{x}$ reveals that the same isotropic CDW can be induced, enhanced, and stabilized in the whole nematic regime measured ($x=0-0.19$). As Fe$^{3+}$ can create local lattice distortions on the surface, the CDW could arise from the interaction between the local strain around Fe$^{3+}$ and the nematic electron correlations. Our experimental observation of a local-strain-induced CDW gives vital information for understanding the interplay between electron correlations and the electronic nematicity in FeSCs., Comment: 7 pages, 4 figures

We use resonant inelastic X-ray scattering (RIXS) at the Fe-L$_3$ edge to study the spin excitations of uniaxial-strained and unstrained FeSe$_{1-x}$S$_{x}$ ($0\leq x\leq0.21$) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range $0< x\leq0.21$ of FeSe$_{1-x}$S$_{x}$. The spin-excitation anisotropy persists to a high temperature up to $T>200$ K in $x=0.18$ and reaches a maximum around the nematic quantum critical doping ($x_c\approx0.17$). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and open the door for uniaxial strain tuning of spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity., Comment: 6 pages, 4 figures, supplemental materials uploaded

An experimental determination of electronic phase diagrams of high-transition temperature (high-$T_c$) superconductors forms the basis for a microscopic understanding of unconventional superconductivity. For most high-$T_c$ superconductors, the electronic phase diagrams are established through partial chemical substitution, which also induces lattice disorder. Here we show that symmetry-specific uniaxial strain can be used to study electronic phases in iron-based superconductors, composed of two-dimensional nearly square iron lattice planed separated by other elements. By applying tunable uniaxial strain along different high symmetry directions and carrying out transport measurements, we establish strain-tuning dependent electronic nematicity, antiferromagnetic (AF) order, and superconductivity of BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ superconductor. We find that uniaxial strain along the nearest Fe-Fe direction can dramatically tune the AF order and superconductivity, producing an electronic phase diagram clearly different from the chemical substitution-induced one. Our results thus establish strain tuning as a way to study the intertwined orders in correlated electron materials without using chemical substitution.

Na$_{4-\delta}$NiTeO$_{6}$ is a rare example in the transition-metal tellurate family of realizing an $S$ = 1 spin-chain structure. By performing neutron powder diffraction measurements, the ground-state magnetic structure of Na$_{4-\delta}$NiTeO$_{6}$ is determined. These measurements reveal that below $T\rm_{N}$ ${\sim}$ 6.8(2) K, the Ni$^{2+}$ moments form a screwed ferromagnetic (FM) spin-chain structure running along the crystallographic $a$ axis but these FM spin chains are coupled antiferromagnetically along the $b$ and $c$ directions, giving rise to a magnetic propagation vector of $k$ = (0, 1/2, 1/2). This zigzag magnetic order is well supported by first-principles calculations. The moment size of Ni$^{2+}$ spins is determined to be 2.1(1) $\mu$$\rm_{B}$ at 3 K, suggesting a significant quenching of the orbital moment due to the crystalline electric field (CEF) effect. The previously reported metamagnetic transition near $H\rm_{C}$ ${\sim}$ 0.1 T can be understood as a field-induced spin-flip transition. The relatively easy tunability of the dimensionality of its magnetism by external parameters makes Na$_{4-\delta}$NiTeO$_{6}$ a promising candidate for further exploring various types of novel spin-chain physics., Comment: 10 pages, 6 figures

The origin of the electronic nematicity in FeSe is one of the most important unresolved puzzles in the study of iron-based superconductors. In both spin- and orbital-nematic models, the intrinsic magnetic excitations at $\mathbf{Q}_1=(1, 0)$ and $\mathbf{Q}_2=(0, 1)$ of twin-free FeSe are expected to provide decisive criteria for clarifying this issue. Although a spin-fluctuation anisotropy below 10 meV between $\mathbf{Q}_1$ and $\mathbf{Q}_2$ has been observed by inelastic neutron scattering around $T_c\sim 9$ K ($<

We studied the magnetic properties of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] ($x$ = 0.33), where Cu$^{2+}$ ions form two-dimensional kagome layers. There is no magnetic order down to 50 mK while the Curie-Weiss temperature is on the order of -100 K. At zero magnetic field, the low-temperature specific heat shows a $T^2$ dependence. Above 2 T, a linear temperature dependence term in specific heat emerges, and the value of $\gamma = C/T$ increases linearly with the field. Furthermore, the magnetic susceptibility tends to a constant value at $T = 0$. Our results suggest that the magnetic ground state of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] is consistent with a Dirac quantum-spin-liquid state with a linearly dispersing spinon strongly coupled to an emergent gauge field, which has long been theoretically proposed as a candidate ground state in the two-dimensional kagome Heisenberg antiferromagnetic system., Comment: 7 pages, 3 figures

It has been well established experimentally that the interplay of electronic correlations and spin-orbit interactions in Ir$^{4+}$ and Ir$^{5+}$ oxides results in insulating J$_{\rm eff}$=1/2 and J$_{\rm eff}$=0 ground states, respectively. However, in compounds where the structural dimerization of iridum ions is favourable, the direct Ir $d$--$d$ hybridisation can be significant and takes a key role. Here, we investigate the effects of direct Ir $d$--$d$ hybridisation in comparison with electronic correlations and spin-orbit coupling in Ba$_5$AlIr$_2$O$_{11}$, a compound with Ir dimers. Using a combination of $ab$ $initio$ many-body wave function quantum chemistry calculations and resonant inelastic X-ray scattering (RIXS) experiments, we elucidate the electronic structure of Ba$_5$AlIr$_2$O$_{11}$. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to the expectations, the analysis of the many-body wave function shows that the two Ir (Ir$^{4+}$ and Ir$^{5+}$) ions in the Ir$_2$O$_9$ dimer unit in this compound preserve their local J$_{\rm eff}$ character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir sites assumes an important role, significantly limiting the direct $d$--$d$ hybridisation. Our results emphasize that minute details in the local crystal field (CF) environment can lead to dramatic differences in electronic states in iridates and 5$d$ oxides in general., Comment: 5 pages with 3 figures

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 the connection between superconductivity, magnetism and electronic correlations. Here we use X-ray absorption spectroscopy and resonant inelastic X-ray scattering to study the valence state of Fe and spin dynamics in two NaFe$_{1-x}$Cu$_x$As compounds ($x=0$ and 0.47). We find that magnetism in both compounds arises from Fe$^{2+}$ atoms, and exhibits underdamped dispersive spin waves in their respective ordered states. The dispersion of spin excitations in NaFe$_{0.53}$Cu$_{0.47}$As is consistent with being quasi-one-dimensional. Compared to NaFeAs, the band top of spin waves in NaFe$_{0.53}$Cu$_{0.47}$As is slightly softened with significantly more spectral weight of the spin excitations. Our results indicate the spin dynamics in NaFe$_{0.53}$Cu$_{0.47}$As arise from localized magnetic moments and suggest the iron-based superconductors are proximate to a correlated insulating state with localized iron moments., Comment: accepted for publication in Phys. Rev. B

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 $T_N$ ($

Triangular lattice of rare-earth ions with interacting effective spin-$1/2$ local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh$_2$ (Ch=O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and muon spin rotation measurements on NaYbCh$_2$ have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystalline NaYbSe$_2$ samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe$_2$ is a QSL with a spinon Fermi surface., Comment: 18 pages, 6 figures

We use neutron scattering to study vanadium (hole)-doped LiFe$_{1-x}$V$_x$As. In the undoped state, LiFeAs exhibits superconductivity at $T_c=18$ K and transverse incommensurate spin excitations similar to electron overdoped iron pnictides. Upon vanadium-doping to form LiFe$_{0.955}$V$_{0.045}$, the transverse incommensurate spin excitations in LiFeAs transform into longitudinally elongated in a similar fashion as that of potassium (hole) doped Ba$_{0.7}$K$_{0.3}$Fe$_2$As$_2$, but with dramatically enhanced magnetic scattering and elimination of superconductivity. This is different from the suppression of the overall magnetic excitations in hole doped BaFe$_2$As$_2$ and the enhancement of superconductivity near optimal hole doping. These results are consistent with density function theory plus dynamic mean field theory calculations, suggesting that vanadium-doping in LiFeAs may induce an enlarged effective magnetic moment $S_{eff}$ with a spin crossover ground state arising from the inter-orbital scattering of itinerant electrons., Comment: Accepted by npj Quantum Materials

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe$_{0.8}$Ag$_{1.2}$Te$_2$ (K$_5$Fe$_4$Ag$_6$Te$_{10}$, KFAT) is a local-moment magnet consisting of well-separated 2$\times$2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the $2\times2$ clusters act as the spin analogue of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergent-like increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter., Comment: accepted for publication in Physical Review Letters

Unconventional superconductivity arises at the border between the strong coupling regime with local magnetic moments and the weak coupling regime with itinerant electrons, and stems from the physics of criticality that dissects the two. Unveiling the nature of the quasiparticles close to quantum criticality is fundamental to understand the phase diagram of quantum materials. Here, using resonant inelastic x-ray scattering (RIXS) and Fe-K$_\beta$ emission spectroscopy (XES), we visualize the coexistence and evolution of local magnetic moments and collective spin excitations across the superconducting dome in isovalently-doped BaFe$_2$(As$_{1-x}$P$_x$)$_2$ (0.00$\leq$x$\leq0.$52). Collective magnetic excitations resolved by RIXS are gradually hardened, whereas XES reveals a strong suppression of the local magnetic moment upon doping. This relationship is captured by an intermediate coupling theory, explicitly accounting for the partially localized and itinerant nature of the electrons in Fe pnictides. Finally, our work identifies a local-itinerant spin fluctuations channel through which the local moments transfer spin excitations to the particle-hole (paramagnons) continuum across the superconducting dome., Comment: Accepted in Communications Physics

We use inelastic neutron scattering to study spin excitation anisotropy in mechanically detwinned Ba(Fe1-xCox)2As2 with x = 0.048 and 0.054. Both samples exhibit a tetragonal-to-orthorhombic structural transition at Ts, a collinear static antiferromagnetic (AF) order at wave vector Q1 = QAF = (1, 0) below the Neel temperature TN, and superconductivity below Tc (Ts > TN > Tc). In the high temperature paramagnetic tetragonal phase (T > Ts), spin excitations centered at Q1 and Q2 = (0, 1) are gapless and have four-fold (C4) rotational symmetry. On cooling to below TN but above Tc, spin excitations become highly anisotropic, developing a gap at Q2 but still are gapless at Q1. Upon entering into the superconducting state, a neutron spin resonance appears at Q1 with no magnetic scattering at Q2. By comparing these results with those from angle resolved photoemission spectroscopy experiments, we conclude that the anisotropic shift of the dyz and dxz bands in detwinned Ba(Fe1-xCox)2As2 below Ts is associated with the spin excitation anisotropy, and the superconductivity-induced resonance arises from the electron-hole Fermi surface nesting of quasiparticles with the dyz orbital characters.

Elucidating the nature of spin excitations is important to understanding the mechanism of superconductivity in the iron pnictides. Motivated by recent inelastic neutron scattering measurements in the nearly 100% detwinned BaFe$_{2}$As$_{2}$, we study the spin dynamics of an $S=1$ frustrated bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with wavevector $(\pi,0)$. The biquadratic interactions are treated in a dynamical way using a flavor-wave theory in an $SU(3)$ representation. Besides the magnon (dipolar) excitations, the biquadratic interactions give rise to quadrupolar excitations at high energies. We find that the quadrupolar wave significantly influences, in an energy dependent way, the anisotropy between the spin excitation spectra along the $(\pi,0)$ and $(0,\pi)$ directions in the wave vector space. Our theoretical results capture the essential behavior of the spin dynamics measured in the antiferromagnetic phase of the detwinned BaFe$_2$As$_2$. More generally, our results underscore the importance of electron correlation effects for the microscopic physics of the iron pnictides., Comment: 8 pages, 4 figures, published version

Understanding and controlling the electronic structure of thin layers of quantum materials is a crucial first step towards designing heterostructures where new phases and phenomena, including the metal-insulator transition (MIT), emerge. Here, we demonstrate control of the MIT via tuning electronic bandwidth and local site environment through selection of the number of atomic layers deposited. We take CaVO3, a correlated metal in its bulk form that has only a single electron in its V4+ 3d manifold, as a representative example. We find that thick films and ultrathin films (6 unit cells, uc, and below) are metallic and insulating, respectively, while a 10 uc CaVO3 film exhibits a clear thermal MIT. Our combined X-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) study reveals that the thickness-induced MIT is triggered by electronic bandwidth reduction and local moment formation from V3+ ions, that are both a consequence of the thickness confinement. The thermal MIT in our 10 uc CaVO3 film exhibits similar changes in the RIXS response to that of the thickness-induced MIT in terms of reduction of bandwidth and V 3d - O 2p hybridization., Comment: 27 pages, 6 figures

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

Electron correlations play a dominant role in the charge dynamics of the cuprates. We use resonant inelastic x-ray scattering (RIXS) to track the doping dependence of the collective charge excitations in electron doped La$_{2-x}$Ce$_{x}$CuO$_{4}$(LCCO). From the resonant energy dependence and the out-of-plane momentum dependence, the charge excitations are identified as three-dimensional (3D) plasmons, which reflect the nature of the electronic structure and Coulomb repulsion on both short and long length scales. With increasing electron doping, the plasmon excitations show monotonic hardening in energy, a consequence of the electron correlation effect on electron structure near the Fermi surface (FS). Importantly, the plasmon excitations evolve from a broad feature into a well defined peak with much increased life time, revealing the evolution of the electrons from incoherent states to coherent quasi-particles near the FS. Such evolution marks the reduction of the short-range electronic correlation, and thus the softening of the Mottness of the system with increasing electron doping.

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations, or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.7 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations., Comment: accepted for Nature Materials

A series of high quality BaFe$_{2-x}$Ni$_x$As$_2$ pnictide superconductors were studied using magnetic relaxation and isothermal magnetic measurements in order to study the second magnetization peak (SMP) and critical current behaviour in Ni-doped 122 family. The temperature dependence of the magnetic relaxation rate suggests a pinning crossover, whereas, it's magnetic field dependence hints a vortex-lattice structural phase-transition. The activation energy ($U$) estimated using the magnetic relaxation data was analyzed in detail for slightly-underdoped, slightly-overdoped and an overdoped samples, using Maley's method and collective creep theory. Our results confirm that the SMP in these samples is due to the collective (elastic) to plastic creep crossover as has been observed for the other members of 122-family. In addition, we also investigated the doping dependence of the critical current density ($J_c$) and the vortex-pinning behaviour in these compounds. The observed $J_c$ is higher than the threshold limit (10$^5$ A/cm$^2$) considered for the technological potential and even greater than 1 MA/cm$^2$ for slightly underdoped Ni-content, x = 0.092 sample. The pinning characteristics were analyzed in terms of the models developed by Dew-Hughes and Griessen $et$ $al$, which suggest the dominant role of $\delta l$-type pinning., Comment: 26 pages, 13 figures, Accepted for publication in ACS Applied Electronic Materials 2019

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

We use transport and inelastic neutron scattering measurements to investigate single crystals of iron pnictide BaFe$_{2-x}$Ni$_{x}$As$_{2}$ ($x=0,0.03$), which exhibit a tetragonal-to-orthorhombic structural transition at $T_s$ and stripe antiferromagnetic order at $T_N$ ($T_s\geq T_N$). Using a tunable uniaxial pressure device, we detwin the crystals and study their transport and spin excitation properties at antiferromagnetic wave vector $S_1(1,0)$ and its 90$^\circ$ rotated wave vector $S_2(0,1)$ under different pressure conditions. We find that uniaxial pressure necessary to detwin and maintain single domain orthorhombic antiferromagnetic phase of BaFe$_{2-x}$Ni$_{x}$As$_{2}$ induces resistivity and spin excitation anisotropy at temperatures above zero pressure $T_s$. In uniaxial pressure-free detwinned sample, spin excitation anisotropy between $S_1(1,0)$ and $S_2(0,1)$ first appear in the paramagnetic orthorhombic phase below $T_s$. These results are consistent with predictions of spin nematic theory, suggesting the absence of structural or nematic phase transition above $T_s$ in iron pnictides., Comment: 6 pages, 4 figures

Unconventional superconductivity typically emerges in the presence of quasi-degenerate ground states, and the associated intense fluctuations are likely responsible for generating the superconducting state. Here we use polarized neutron scattering to study the spin space anisotropy of spin excitations in Fe$_{1.07}$Te exhibiting bicollinear antiferromagnetic (AF) order, the parent compound of FeTe$_{1-x}$Se$_x$ superconductors. We confirm that the low energy spin excitations are transverse spin waves, consistent with a local-moment origin of the bicollinear AF order. While the ordered moments lie in the $ab$-plane in Fe$_{1.07}$Te, it takes less energy for them to fluctuate out-of-plane, similar to BaFe$_2$As$_2$ and NaFeAs. At energies above $E\gtrsim20$ meV, we find magnetic scattering to be dominated by an isotropic continuum that persists up to at least 50 meV. Although the isotropic spin excitations cannot be ascribed to spin waves from a long-range ordered local moment antiferromagnet, the continuum can result from the bicollinear magnetic order ground state of Fe$_{1.07}$Te being quasi-degenerate with plaquette magnetic order., Comment: accepted for publication in Phys. Rev. B

Resonant inelastic X-ray scattering (RIXS) experiments performed at the oxygen-$K$ edge on the iridate perovskites {\SIOS} and {\SION} reveal a sequence of well-defined dispersive modes over the energy range up to $\sim 0.8$ eV. The momentum dependence of these modes and their variation with the experimental geometry allows us to assign each of them to specific collective magnetic and/or electronic excitation processes, including single and bi-magnons, and spin-orbit and electron-hole excitons. We thus demonstrated that dispersive magnetic and electronic excitations are observable at the O-$K$ edge in the presence of the strong spin-orbit coupling in the $5d$ shell of iridium and strong hybridization between Ir $5d$ and O $2p$ orbitals, which confirm and expand theoretical expectations. More generally, our results establish the utility of O-$K$ edge RIXS for studying the collective excitations in a range of $5d$ materials that are attracting increasing attention due to their novel magnetic and electronic properties. Especially, the strong RIXS response at O-$K$ edge opens up the opportunity for investigating collective excitations in thin films and heterostructures fabricated from these materials., Comment: 6 pages, 4 figures with supplementary material. Accepted by PRB Rapid Communications

We use unpolarized and polarized neutron scattering to study the temperature and polarization dependence of low-energy magnetic fluctuations in nearly-optimal-doped NaFe$_{0.9785}$Co$_{0.0215}$As, with coexisting superconductivity ($T_{\rm c}\approx19$ K) and weak antiferromagnetic order ($T_{\rm N}\approx30$ K, ordered moment $\approx0.02$ $\mu_{\rm B}$/Fe). A single spin resonance mode with intensity tracking the superconducting order parameter is observed, although energy of the mode only softens slightly on approaching $T_{\rm c}$. Polarized neutron scattering reveals that the single resonance is mostly isotropic in spin space, similar to overdoped NaFe$_{0.935}$Co$_{0.045}$As but different from optimal electron-, hole-, and isovalent-doped BaFe$_2$As$_2$ compounds, all featuring an additional prominent anisotropic component. Spin anisotropy in NaFe$_{0.9785}$Co$_{0.0215}$As is instead present at energies below the resonance, which becomes partially gapped below $T_{\rm c}$, similar to the situation in optimal-doped YBa$_2$Cu$_3$O$_{6.9}$. Our results indicate that anisotropic spin fluctuations in NaFe$_{1-x}$Co$_x$As appear in the form of a resonance in the underdoped regime, become partially gapped below $T_{\rm c}$ near optimal doping and disappear in overdoped compounds., Comment: to be published in PRB

We report infrared studies of AFe$_{2}$As$_{2}$ (A = Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a $\sqrt{B}$ dependence of the LL transition energies, the zero-energy intercepts at B = 0 T under the linear extrapolations of the transition energies and the energy ratio ($\sim$ 2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in antiferromagnetic BaFe$_{2}$As$_{2}$. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction $k_{z}$ indicate that massless Dirac fermions in BaFe$_{2}$As$_{2}$ are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe$_{2}$As$_{2}$ by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected., Comment: Magneto-infrared study, Landau level spectroscopy, DFT+DMFT calculations

We use neutron polarization analysis to study temperature dependence of the spin excitation anisotropy in BaFe$_2$As$_2$, which has a tetragonal-to-orthorhombic structural distortion at $T_s$ and antiferromagnetic (AF) phase transition at $T_N$ with ordered moments along the orthorhombic $a$-axis below $T_s\approx T_N\approx 136$ K. In the paramagnetic tetragonal state at 160 K, spin excitations are isotropic in spin space with $M_a=M_b=M_c$, where $M_a$, $M_b$, and $M_c$ are spin excitations polarized along the $a$, $b$, and $c$-axis directions of the orthorhombic lattice, respectively. On cooling towards $T_N$, significant spin excitation anisotropy with $M_a>M_b\approx M_c$ develops below 3 meV with a diverging $M_a$ at $T_N$. The in-plane spin excitation anisotropy in the tetragonal phase of BaFe$_2$As$_2$ is similar to those seen in the tetragonal phase of its electron and hole-doped superconductors, suggesting that spin excitation anisotropy is a direct probe of doping dependence of spin-orbit coupling and its connection to superconductivity in iron pnictides., Comment: 6 pages,4 figures, in press with PRB rapid

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 polarized inelastic neutron scattering to study the temperature and energy dependence of spin space anisotropies in the optimally hole-doped iron pnictide Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ ($T_{{\rm c}}=38$ K). In the superconducting state, while the high-energy part of the magnetic spectrum is nearly isotropic, the low-energy part displays a pronouced anisotropy, manifested by a $c$-axis polarized resonance. We also observe that the spin anisotropy in superconducting Ba$_{0.67}$K$_{0.33}$Fe$_{2}$As$_{2}$ extends to higher energies compared to electron-doped BaFe$_{2-x}TM_{x}$As$_{2}$ ($TM=$Co, Ni) and isovalent-doped BaFe$_{2}$As$_{1.4}$P$_{0.6}$, suggesting a connection between $T_{\rm c}$ and the energy scale of the spin anisotropy. In the normal state, the low-energy spin anisotropy for optimally hole- and electron-doped iron pnictides onset at temperatures similar to the temperatures at which the elastoresistance deviate from Curie-Weiss behavior, pointing to a possible connection between the two phenomena. Our results highlight the relevance of the spin-orbit coupling to the superconductivity of the iron pnictides., Comment: accepted for publication in Physical Review B, Supplementary information is appended at the end of the arxiv version

We use resonant elastic and inelastic X-ray scattering at the Ir-$L_3$ edge to study the doping-dependent magnetic order, magnetic excitations and spin-orbit excitons in the electron-doped bilayer iridate (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$ ($0 \leq x \leq 0.065$). With increasing doping $x$, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order from $x = 0$ to $0.05$, followed by a transition to two-dimensional short range order between $x = 0.05$ and $0.065$. Following the evolution of the antiferromagnetic order, the magnetic excitations undergo damping, anisotropic softening and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ into a correlated metallic state hosting two-dimensional short range antiferromagnetic order and strong antiferromagnetic fluctuations of $J_{\text{eff}} = \frac{1}{2}$ moments, with the magnon gap strongly suppressed., Comment: 6 Pages, 3 Figures, with supplementary in Source

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,$\pi$) should decrease with decreasing temperature below the structural transition temperature $T_s$. Here we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe$_{1.935}$Ni$_{0.065}$As$_2$ under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,$\pi$) happens just below $T_s$, suggesting strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order., Comment: 5 pages, 4 figures

We have systematically studied the low-temperature specific heat of the BaFe$_{2-x}$Ni$_x$As$_2$ single crystals covering the whole superconducting dome. Using the nonsuperconducting heavily overdoped x = 0.3 sample as a reference for the phonon contribution to the specific heat, we find that the normal-state electronic specific heats in the superconducting samples may have a nonlinear temperature dependence, which challenges previous results in the electron-doped Ba-122 iron-based superconductors. A model based on the presence of ferromagnetic spin fluctuations may explain the data between x = 0.1 and x = 0.15, suggesting the important role of Fermi-surface topology in understanding the normal-state electronic states., Comment: 7 pages, 5 figures

We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe$_{2-x}$Ni$_x$As$_2$ by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions, or more exotically, a higher symmetry may be present around optimal doping., Comment: 5 pages, 3 figures. This Letter only contains parts of the former version 1511.05784

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.

The upper critical field ($H_{c2}$) in superconducting BaFe$_{2-x}$Ni$_{x}$As$_2$ single crystals has been determined by magnetotransport measurements down to 0.6 K over the whole superconducting dome with $0.065 \leqslant x \leqslant 0.22$, both for the inter-plane ($H \parallel c$, $H_{c2}^{c}$) and in-plane ($H \parallel ab$, $H_{c2}^{ab}$) field directions in static magnetic fields up to 16 T and pulsed magnetic fields up to 60 T. The temperature dependence of $H_{c2}^{ab}$ follows the Werthamer-Helfand-Hohenberg (WHH) model incorporating orbital and spin paramagnetic effects, while $H_{c2}^{c}(T)$ can only be described by the effective two-band model with unbalanced diffusivity. The anisotropy of the upper critical fields, $\gamma (T)=H_{c2}^{ab}/H_{c2}^{c}$ monotonically increases with increasing temperature for all dopings, and its zero-temperature limit, $\gamma (0)$, has an asymmetric doping dependence with a significant enhancement in the overdoped regime, where the optimally doped compound has the most isotropic superconductivity. Our results suggest that the anisotropy in the superconductivity of iron pnictides is determined by the topology of the Fermi surfaces together with the doping-induced impurity scattering., Comment: 7 pages, 7 figures, Accepted by Phys. Rev. B