Local Spin Susceptibility Research Articles

Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet.

The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of active debate. We conducted oxygen-17 single-crystal nuclear magnetic resonance (NMR) measurements of the spin-1/2 kagome lattice in herbertsmithite [ZnCu3(OH)6Cl2], which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrated that the intrinsic local spin susceptibility χ(kagome), deduced from the oxygen-17 NMR frequency shift, asymptotes to zero below temperatures of 0.03J, where J ~ 200 kelvin is the copper-copper superexchange interaction. Combined with the magnetic field dependence of χ(kagome) that we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.

Fermi-liquid theory for the single-impurity Anderson model

We generalize Nozi\`eres' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozi\`eres that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the $\sim B^2$, $\sim T^2$, and $\sim V^2$ terms \textit{exactly} in terms of the Fermi-liquid parameters. The coefficients of $T^2$, $V^2$ and $B^2$ are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

Anomalous local spin susceptibilities in noncentrosymmetricLa2C3superconductor

We report on $^{139}\mathrm{La}$ and $^{13}\mathrm{C}$ nuclear magnetic resonance (NMR) study of noncentrosymmetric superconductor ${\mathrm{La}}_{2}{\mathrm{C}}_{3}$ with superconducting critical temperature ${T}_{\mathrm{c}}=11.8$ K. In the normal state $^{139}\mathrm{La}$ NMR spectra show a characteristic quadrupole polycrystalline broadening yielding a quadrupole frequency ${\ensuremath{\nu}}_{\mathrm{Q}}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}3.1$ MHz and a very large shift of $\ensuremath{\sim}3000$ ppm. A significant part of this shift arises from the Van Vleck-like susceptibility as a result of a sizable spin-orbit coupling. In the superconducting phase ${\mathrm{La}}_{2}{\mathrm{C}}_{3}$ shows abnormal behavior that dramatically deviates from the conventional $s$-wave superconductors. Namely, (i) $^{139}\mathrm{La}$ and $^{13}\mathrm{C}$ NMR shifts in the superconducting state do not change from their normal-state values, and (ii) the $^{139}\mathrm{La}$ spin-lattice relaxation rate is strongly enhanced below ${T}_{\mathrm{c}}$. Such unconventional response in the local static and dynamic spin susceptibilities is discussed in terms of possible mixture of spin-singlet and spin-triplet Cooper pairs, which is promoted by the asymmetric spin-orbit coupling in the system without the center of inversion.

Metal–Insulator Transition and Superconductivity in the Two-Orbital Hubbard–Holstein Model for Iron-Based Superconductors

We investigate a two-orbital model for iron-based superconductors to elucidate the effect of interplay between electron correlation and Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory combined with the exact diagonalization method. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $\chi_{s}$ and $\chi_{o}$, increase with $\chi_{s}=\chi_{o}$ in the absence of the Hund's rule coupling $J$ and the electron-phonon coupling $g$. In the presence of $J$ and $g$, there are distinct two regimes: for $J \stackrel{>}{_\sim} 2g^2/\omega_0$ with the phonon frequency $\omega_0$, $\chi_{s}$ is enhanced relative to $\chi_{o}$ and shows a divergence at $J=J_c$ above which the system becomes Mott insulator, while for $J \stackrel{<}{_\sim} 2g^2/\omega_0$, $\chi_{o}$ is enhanced relative to $\chi_{s}$ and shows a divergence at $g=g_c$ above which the system becomes bipolaronic insulator. In the former regime, the superconductivity is mediated by antiferromagnetic fluctuations enhanced due to Fermi-surface nesting and is found to be largely dependent on carrier doping. On the other hand, in the latter regime, the superconductivity is mediated by ferro-orbital fluctuations and is observed for wide doping region including heavily doped case without the Fermi-surface nesting.

Spin susceptibility in superconducting LiFeAs studied by polarized neutron diffraction

The local spin susceptibility in superconducting LiFeAs was studied by polarized neutron diffraction as a function of temperature. In the superconducting phase the spin susceptibility is clearly suppressed and it can be well described by the Yosida function suggesting a singlet pairing to occur at low temperature. The spin susceptibility in the normal state and its suppression in the superconducting phase are fully comparable to observations in Co-doped BaFe${}_{2}$As${}_{2}$.

Quantum criticality in the pseudogap Bose-Fermi Anderson and Kondo models: Interplay between fermion- and boson-induced Kondo destruction

We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like |\epsilon|^r at the Fermi energy (\epsilon=0) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to |\omega|^s. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<1/2 and 1/2<s<1, and applying the numerical renormalization-group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and \omega/T scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum critical point.

Local spin susceptibilities of low-dimensional electron systems

We investigate, assess, and suggest possibilities for a measurement of the local spin susceptibility of a conducting low-dimensional electron system. The basic setup of the experiment we envisage is a source-probe one. Locally induced spin density (e.g., by a magnetized atomic force microscope tip) extends in the medium according to its spin susceptibility. The induced magnetization can be detected as a dipolar magnetic field, for instance, by an ultrasensitive nitrogen-vacancy center based detector, from which the spatial structure of the spin susceptibility can be deduced. We find that one-dimensional systems, such as semiconducting nanowires or carbon nanotubes, are expected to yield a measurable signal. The signal in a two-dimensional electron gas is weaker, though materials with a high enough $g$-factor (such as InGaAs) seem promising for successful measurements.

Local quantum criticality out of equilibrium: Effective temperatures and scaling in the steady-state regime

We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point–dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities.

Spin-state crossover model for the magnetism of iron pnictides.

We propose a minimal model describing magnetic behavior of Fe-based superconductors. The key ingredient of the model is a dynamical mixing of quasidegenerate spin states of Fe(2+) ion by intersite electron hoppings, resulting in an effective local spin S(eff). The moments S(eff) tend to form singlet pairs and may condense into a spin nematic phase due to the emergent biquadratic exchange couplings. The long-range ordered part m of S(eff) varies widely, 0 ≤ m ≤ S(eff), but magnon spectra are universal and scale with S(eff), resolving the puzzle of large but fluctuating Fe moments. Unusual temperature dependences of a local moment and spin susceptibility are also explained.

Surface states and local spin susceptibility in doped three-dimensional topological insulators with odd-parity superconducting pairing symmetry

We investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the local spin susceptibility, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments. Because of their different decay lengths, the Majorana modes can be observed and clearly distinguished from the Dirac modes of the topological insulator by local probes which allow for a depth-controlled study of the electron spins on the nanometer length scale.

3d Electron Quadrupole Moments in Vanadium Oxides

We report the local spin susceptibility and the 3d quadrupole moment in V5O9. The metal-insulator transition accompanies with the spin singlet formation without an apparent dimerization in the V lattice. Based on the angle dependence of the 51V quadrupole frequency, we suggest that the orbital ordering assists the spin singlet formation in the quasi-one-dimensional chain in V5O9. At high temperatures, the paramagnetic metallic state has nonuniform spin susceptibility depending on V sites, which indicates that the magnetically active and inactive V sites are already separated in the metallic state due to the strong electron correlation.

Quantum criticality out of equilibrium in the pseudogap Kondo model

We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels {\mu}_L/R, {\rho}_c,L(R) ({\omega}) \propto |{\omega} - {\mu}_L(R) |r, and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.

Quantum criticality of the sub-Ohmic spin-boson model

We revisit the critical behavior of the sub-ohmic spin-boson model. Analysis of both the leading and subleading terms in the temperature dependence of the inverse static local spin susceptibility at the quantum critical point, calculated using a numerical renormalization-group method, provides evidence that the quantum critical point is interacting in cases where the quantum-to-classical mapping would predict mean-field behavior. The subleading term is shown to be consistent with an w/T scaling of the local dynamical susceptibility, as is the leading term. The frequency and temperature dependences of the local spin susceptibility in the strong-coupling (delocalized) regime are also presented. We attribute the violation of the quantum-to-classical mapping to a Berry-phase term in a continuum path-integral representation of the model. This effect connects the behavior discussed here with its counterparts in models with continuous spin symmetry.

Zn-induced spin dynamics in overdoped La2−xSrxCu1−yZnyO4

Spin fluctuations and the local spin susceptibility in isovalently Zn-substituted La${}_{2\ensuremath{-}x}$Sr${}_{x}$Cu${}_{1\ensuremath{-}y}$Zn${}_{y}$O${}_{4}$ ($x=0.25$, $y\ensuremath{\approx}0.01$) are measured via inelastic neutron-scattering techniques. As Zn${}^{2+}$ is substituted onto the Cu${}^{2+}$-sites, an anomalous enhancement of the local spin susceptibility ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$ appears due to the emergence of a commensurate antiferromagnetic excitation centered at wave vector Q $=(\ensuremath{\pi},\ensuremath{\pi},0)$ that coexists with the known incommensurate spin-density wave excitations at Q${}_{HK}=(\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta},\ensuremath{\pi}),(\ensuremath{\pi},\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})$. Our results support a picture of Zn-induced antiferromagnetic (AF) fluctuations appearing through a local staggered polarization of Cu${}^{2+}$ spins, and the simultaneous suppression of T${}_{c}$ as AF fluctuations are slowed in proximity to Zn impurities suggests the continued importance of high-energy AF fluctuations at the far overdoped edge of superconductivity in the cuprates.

Charge and spin criticality for the continuous Mott transition in a two-dimensional organic conductor

We study the continuous bandwidth-controlled Mott transition in the two-dimensional single-band Hubbard model with a focus on the critical scaling behavior of charge and spin degrees of freedom. Using plaquette cluster dynamical mean-field theory, we find charge and spin criticality consistent with experimental results for organic conductors. In particular, the charge degree of freedom measured via the local density of states at the Fermi level shows a smoother transition than expected for the Ising universality class and in single-site dynamical mean-field theory, revealing the importance of short-ranged nonlocal correlations in two spatial dimensions. The spin criticality measured via the local spin susceptibility agrees quantitatively with nuclear magnetic resonance measurements of the spin-lattice relaxation rate.

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau–Ginzburg–Wilson paradigm. The Landau–Ginzburg–Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Local spin susceptibility in the orbital-frustrated vanadium oxide BaV10O15

BaV10O15 having a bilayer triangular lattice exhibits a semiconductor-insulator transition accompanied by the structural phase transition at Tc ∼130 K. We show the microscopic properties of the phase transition investigated by 51V NMR measurements on a single crystal. We have observed 51V NMR spectra from two of the three inequivalent V sites at high temperatures. The Knight shift tensors are determined at 300 K for the two V sites. The local spin susceptibility strongly depends on the V sites and temperature despite the nearly independent magnetic susceptibility. Each spectrum is split into two below 200 K far above Tc, suggesting a charge/order ordering transition. The local spin susceptibilities of the three sites gradually vanish with decreasing temperature, consistent with the V trimer formation. The microscopic evidence for the spin singlet state is clearly observed below Tc.

13C NMR study on the charge-disproportionated conducting state in the quasi-two-dimensional organic conductorα-(BEDT-TTF)2I3

The conducting state of the quasi-two-dimensional organic conductor, $\alpha$-(BEDT-TTF)$_2$I$_3$, at ambient pressure is investigated with $^{13}$C NMR measurements, which separate the local electronic states at three nonequivalent molecular sites (A, B, and C). The spin susceptibility and electron correlation effect are revealed in a locally resolved manner. While there is no remarkable site-dependence around room temperature, the local spin susceptibility gradually disproportionates among the nonequivalent sites with decreasing temperature. The disproportionation-ratio yields 5:4:6 for A:B:C molecules at 140 K. Distinct site- and temperature-dependences are also observed in the Korringa ratio, $\mathcal{K}_i \propto (1/T_{1}T)_iK^{-2}_i$ ($i$ = A, B, and C), which is a measure of the strength and the type of electron correlations. The values of $\mathcal{K}_i$ point to sizable antiferromagnetic spin correlation. We argue the present results in terms of the theoretical prediction of the peculiar site-specific reciprocal-space ($\bm{k}$-space) anisotropy on the tilted Dirac cone, and discuss the $\bm{k}$-dependent profiles of the spin susceptibility and electron correlation on the cone.

Local Spin Susceptibility of α-D2I3(D = bis(ethylendithio)tetraselenafulvalene (BETS) and bis(ethylendithio)dithiadiselenafulvalene (BEDT-STF)) Studied by77Se NMR

We performed static susceptibility and 77 Se NMR measurements on α-(BETS) 2 I 3 and α-(BEDT-STF) 2 I 3 which are analogues of the “zero gap” system, α-(BEDT-TTF) 2 I 3 to systematically compare the electronic properties of the α-type I 3 systems, where BETS, BEDT-STF, and BEDT-TTF are bis(ethylendithio)tetraselenafulvalene, bis(ethylendithio)dithiadiselenafulvalene, and bis(ethylendithio)tetrathiafulvalene, respectively. From the analysis of the NMR lineshape for a polycrystalline sample at high temperatures, which are explained as an admixture of several powder patterns, we found that the local spin susceptibility is not uniform but at least one of the molecular sites has very small susceptibility. It was confirmed from single crystal data that there are three kinds of molecules with different local susceptibilities in a unit cell. The analysis of the angular dependence on a single crystal clarified that the relative magnitude of the local susceptibilities of A, B, and C molecules, χ loc A , χ loc B , and χ loc C , are similar to those of the BEDT-TTF salt; χ loc C > χ loc A > χ loc B . On the contrary, the temperature dependence of spin susceptibility and relaxation rate suggested a gap opening well above the metal–insulator transition, whereas no indication of symmetry breaking of the lattice was detected.

Coexistence of localized and itinerant electronic states in the multiband iron-based superconductorFeSe0.42Te0.58

We report X-band EPR and $^{125}$Te and $^{77}$Se NMR measurements on single-crystalline superconducting FeSe$_{0.42}$Te$_{0.58}$ ($T_c$ = 11.5(1) K). The data provide evidence for the coexistence of intrinsic localized and itinerant electronic states. In the normal state, localized moments couple to itinerant electrons in the Fe(Se,Te) layers and affect the local spin susceptibility and spin fluctuations. Below $T_c$, spin fluctuations become rapidly suppressed and an unconventional superconducting state emerges in which $1/T_1$ is reduced at a much faster rate than expected for conventional $s$- or $s_\pm$-wave symmetry. We suggest that the localized states arise from the strong electronic correlations within one of the Fe-derived bands. The multiband electronic structure together with the electronic correlations thus determine the normal and superconducting states of the FeSe$_{1-x}$Te$_x$ family, which appears much closer to other high-$T_c$ superconductors than previously anticipated.