Kondo Spin Research Articles

Magnetism in frustrated Kondo and non-Kondo intermetallics: CeInCu2 versus NdInCu2

Single crystalline intermetallics ${\mathrm{CeInCu}}_{2}$ and ${\mathrm{NdInCu}}_{2}$, where the rare earth ions occupy geometrically frustrated fcc lattice of Heusler-type structure, have been studied comparatively to shed light on the ground-state magnetism derived from Kondo physics and/or spin frustration competing with the Ruderman-Kittel-Kasuya-Yosida interaction. ${\mathrm{CeInCu}}_{2}$ is distinct from ${\mathrm{NdInCu}}_{2}$ due to the significant Kondo effect that is absent in the latter. They order antiferromagnetically at ${T}_{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}1.4$ and 2.0 K with large paramagnetic Curie-Weiss temperature of $\ensuremath{-}35.4$ K and $\ensuremath{-}41.1$ K, respectively. The electronic specific-heat coefficient $\ensuremath{\gamma}$ = $C/T$ ($T\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}0$) = 870 mJ ${\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ in ${\mathrm{CeInCu}}_{2}$ is significantly enhanced, much larger than 180 mJ ${\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ of the latter that is also enhanced albeit its non-Kondo nature. For both compounds, the Kadowaki-Woods ratio deviates greatly from the standard value expected from a Kramers doublet ground state, which, however, can be restored if one considers a smaller but still sizable $\ensuremath{\gamma}$ estimated from the paramagnetic state. Likewise, the Kondo temperature of ${\mathrm{CeInCu}}_{2}$ is revised to be ${T}_{K}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}$ 13 K that is double the literature values, manifesting a major effect of spin frustration to low-temperature thermodynamics beyond the Kondo physics. Similarities between the two compounds is also noticed in their temperature-field phase diagrams in spite of their thermodynamic distinctions in the thermal expansion and the Gr\"uneisen ratio, which are much more sensitive to Kondo hybridization than to geometrical frustration.

Quantum spin liquid in an RKKY-coupled two-impurity Kondo system

We consider a 2-impurity Kondo system with spin-exchange coupling within the conduction band. Our numerical renormalization group calculations show that for strong intraband spin correlations the competition of these correlations with Kondo spin screening stabilizes a metallic spin-liquid phase of the localized spins without geometric frustration. For weak Kondo coupling the spin liquid and the Kondo singlet phase are separated by two quantum phase transitions and an intermediate RKKY spin-dimer phase, while beyond a critical coupling they are connected by a crossover. The results suggest how a quantum spin liquid may be realized in heavy-fermion systems near a spin-density wave instability.

Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems.

Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.

Entanglement measure for Kondo spin at finite temperatures

Universal Thermal Entanglement of Multichannel Kondo Effects Authors: Donghoon Kim, Jeongmin Shim, and H.-S. Sim Phys. Rev. Lett. 127, 226801 (2021); DOI: 10.1103/PhysRevLett.127.226801 Recommended with a commentary by Masaki Oshikawa, University of Tokyo |View Commentary (pdf)| This commentary may be cited as: DOI: 10.36471/JCCM_August_2022_02 https://doi.org/10.36471/JCCM_August_2022_02

Spin relaxation in copper channels with submicron cross sections

We review our recent experimental studies of the spin relaxation processes in the submicron copper channels of nonlocal spin valves (NLSV). Long spin relaxation lengths up to 3.0 μm at low temperatures are demonstrated in highly conductive copper channels with residual resistivity ratios up to 6. An unexpected anisotropy of spin relaxation is observed and can be attributed to the surface spin–orbit effects. An unusual scaling of the Kondo spin relaxation is established experimentally and can be explained by overlapping Kondo screening clouds. Our results demonstrate the technological potential of copper as a spin transport channel in spintronics and highlights unanswered fundamental questions related to the spin relaxation processes.

Magnetic Interactions in Substitutional Core-Doped Graphene Nanoribbons.

The design of a spin imbalance within the crystallographic unit cell of bottom-up engineered 1D graphene nanoribbons (GNRs) gives rise to nonzero magnetic moments within each cell. Here, we demonstrate the bottom-up assembly and spectroscopic characterization of a one-dimensional Kondo spin chain formed by a chevron-type GNR (cGNR) physisorbed on Au(111). Substitutional nitrogen core doping introduces a pair of low-lying occupied states per monomer within the semiconducting gap of cGNRs. Charging resulting from the interaction with the gold substrate quenches one electronic state for each monomer, leaving behind a 1D chain of radical cations commensurate with the unit cell of the ribbon. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal the signature of a Kondo resonance emerging from the interaction of S = 1/2 spin centers in each monomer core with itinerant electrons in the Au substrate. STM tip lift-off experiments locally reduce the effective screening of the unpaired radical cation being lifted, revealing a robust exchange coupling between neighboring spin centers. First-principles DFT-LSDA calculations support the presence of magnetic moments in the core of this GNR when it is placed on Au.

Electrically Controllable Kondo Correlation in Spin-Orbit-Coupled Quantum Point Contacts

Integrating the Kondo correlation and spin-orbit interactions, each of which have individually offered unprecedented means to manipulate electron spins, in a controllable way can open up new possibilities for spintronics. We demonstrate electrical control of the Kondo correlation by coupling the bound spin to leads with tunable Rashba spin-orbit interactions, realized in semiconductor quantum point contacts. We observe a transition from single to double peak zero-bias anomalies in nonequilibrium transport-the manifestation of the Kondo effect-indicating a controlled Kondo spin reversal using only spin-orbit interactions. Universal scaling of the Kondo conductance is demonstrated, implying that the spin-orbit interactions could enhance the Kondo temperature. A theoretical model based on quantum master equations is also developed to calculate the nonequilibrium quantum transport.

Impact of Kondo correlations and spin–orbit coupling on spin-polarized transport in carbon nanotube quantum dot

Spin polarized transport through a quantum dot coupled to ferromagnetic electrodes with noncollinear magnetizations is discussed in terms of nonequilibrium Green functions formalism in the finite-U slave boson mean field approximation. The difference of orientations of the magnetizations of electrodes opens off-diagonal spin–orbital transmission and apart from spin currents of longitudinal polarization also spin-flip currents appear. We also study equilibrium pure spin current at zero bias and discuss its dependence on magnetization orientation, spin–orbit coupling strength and gate voltage. Impact of these factors on tunneling magnetoresistance (TMR) is also undertaken. In general spin–orbit coupling weakens TMR, but it can change its sign.

Probing Kondo spin fluctuations with scanning tunneling microscopy and electron spin resonance

We theoretically analyze a state-of-the-art experimental method based on a combination of electron spin resonance and scanning tunneling microscopy (ESR-STM), to directly probe the spin fluctuations in the Kondo effect. The Kondo impurity is exchange coupled to the probe spin, and the ESR-STM setup detects the small level shifts in the probe spin induced by the spin fluctuations of the Kondo impurity. We use the open quantum system approach by regarding the probe spin as the "system" and the Kondo impurity spin as the fluctuating "bath" to evaluate the resonance line shifts in terms of the dynamic spin susceptibility of the Kondo impurity. We consider various common adatoms on surfaces as possible probe spins and estimate the corresponding level shifts. It is found that the sensitivity is most pronounced for the probe spins with transverse magnetic anisotropy.

Kondo effect and spin\u2013orbit coupling in graphene quantum dots

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction.

Scaling of Kondo spin relaxation: Experiments on Cu-based nonlocal spin valves with Fe impurities

The relation between the Kondo spin-relaxation rate ${{\ensuremath{\tau}}_{sK}}^{\ensuremath{-}1}$ and the Kondo momentum-relaxation rate ${{\ensuremath{\tau}}_{eK}}^{\ensuremath{-}1}$ is explored by using nonlocal spin valves with submicron copper channels that contain dilute iron impurities. A linear relation between ${{\ensuremath{\tau}}_{sK}}^{\ensuremath{-}1}$ and ${{\ensuremath{\tau}}_{eK}}^{\ensuremath{-}1}$ is established under varying temperatures for any given device. Among 20 devices, however, ${{\ensuremath{\tau}}_{sK}}^{\ensuremath{-}1}$ remains nearly constant, despite variation of ${{\ensuremath{\tau}}_{eK}}^{\ensuremath{-}1}$ by a factor of 10. This surprising relation can be understood by considering spin relaxation through overlapping Kondo screening clouds and supports the physical existence of the elusive Kondo clouds.

Manipulation of Molecular Spin State on Surfaces Studied by Scanning Tunneling Microscopy.

The adsorbed magnetic molecules with tunable spin states have drawn wide attention for their immense potential in the emerging fields of molecular spintronics and quantum computing. One of the key issues toward their application is the efficient controlling of their spin state. This review briefly summarizes the recent progress in the field of molecular spin state manipulation on surfaces. We focus on the molecular spins originated from the unpaired electrons of which the Kondo effect and spin excitation can be detected by scanning tunneling microscopy and spectroscopy (STM and STS). Studies of the molecular spin-carriers in three categories are overviewed, i.e., the ones solely composed of main group elements, the ones comprising 3d-metals, and the ones comprising 4f-metals. Several frequently used strategies for tuning molecular spin state are exemplified, including chemical reactions, reversible atomic/molecular chemisorption, and STM-tip manipulations. The summary of the successful case studies of molecular spin state manipulation may not only facilitate the fundamental understanding of molecular magnetism and spintronics but also inspire the design of the molecule-based spintronic devices and materials.

Spin dependent transmission of nickelocene-Cu contacts probed with shot noise

The current $I$ through nickelocene molecules and its noise are measured with a low temperature scanning tunneling microscope on a Cu(100) substrate. Density functional theory calculations and many-body modeling are used to analyze the data. During contact formation, two types of current evolution are observed, an abrupt jump to contact and a smooth transition. These data along with conductance spectra ($dI/dV$) recorded deep in the contact range are interpreted in terms of a transition from a spin-1 to a spin-1/2 state that is Kondo screened. Many-body calculations show that the smooth transition is also consistent with a renormalization of spin excitations of a spin-1 molecule by Kondo exchange coupling. The shot noise is significantly reduced compared to the Schottky value of $2eI$ but no influence of the Kondo effect or spin excitations are resolved. The noise can be described in the Landauer picture in terms of spin-polarized transmission of $\approx$35% through two degenerate $d_\pi$-orbitals of the Nickelocene molecule.

Coexistence of the Kondo effect and spin glass physics in Fe-doped NbS2

We report the coexistence of the Kondo effect and spin glass behavior in Fe-doped NbS2 single crystals. The FexNbS2 shows the resistance minimum and negative magnetoresistance due to the Kondo effect, and exhibits no superconducting behavior at low temperatures. The resistance curve follows a numerical renormalization-group theory using the Kondo temperature K for x = 0.01 as evidence of Kondo effect. Scanning tunneling microscope/spectroscopy (STM/STS) revealed the presence of Fe atoms near sulfur atoms and asymmetric spectra. The magnetic susceptibility exhibits a feature of spin glass. The static critical exponents determined by the universal scaling of the nonlinear part of the susceptibility suggest a three-dimensional Heisenberg spin glass. The doped-Fe atoms in the intra- and inter-layers revealed by the x-ray result can realize the coexistence of the Kondo effect and spin glass.

Self-doped Mott insulator for parent compounds of nickelate superconductors

We propose the parent compound of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ as a self-doped Mott insulator, in which the low-density Nd-$5d$ conduction electrons couple to localized Ni-3$% d_{x^{2}-y^{2}}$ electrons to form Kondo spin singlets at low temperatures. This proposal is motivated with our analyses of the reported resistivity and Hall coefficient data in the normal state, showing logarithmic temperature dependence at low temperatures. In the strong Kondo coupling limit, we derive a generalized $t$-$J$ model with both Kondo singlets and nickel holons moving through the lattice of otherwise nickel spin-1/2 background. The antiferromagnetic long-range order is therefore suppressed as observed in experiments. With Sr-doping, the number of holons on the nickel sites increases, giving rise to the superconductivity and a strange metal phase analogous to those in superconducting copper oxides.

The Mott to Kondo transition in diluted Kondo superlattices

In condensed matter, a tremendous effort has been generated to realise Kondo lattices both experimentally and theoretically. The pursuit of independent magnetic moments, via charge localization, is paramount for applications in nanotechnology. Particularly, systems with simultaneous charge/spin degrees of freedom can manifest both Kondo spin quenching and Mott–Hubbard charge localization. Experimental frameworks illuminating pathways between the two are physically and technologically significant, and hardly observed in reality. Recent developments in controlling densities/temperatures of strongly correlated impurities on surfaces has opened up new possibilities. Such systems introduce mechanisms to study Kondo/Mott-physics interplay methodically. However, the pathway between Kondo physics and charge localization remains elusive. In this work, we investigate the phase diagram of superlattice structures of f-elements on substrates, assessing required conditions for obtaining Kondo superlattices. We unveil pathways between Kondo quenching and Mott localization, and identify non-trivial charge density waves emerging from the competition of charge localization and Kondo physics.

From Kondo effect to weak-link regime in quantum spin- 12 spin chains

We analyze the crossover from Kondo to weak-link regime by means of a model of tunable bond impurities in the middle of a spin-1/2 XXZ Heisenberg chain. We study the Kondo screening cloud and estimate the Kondo length by combining perturbative renormalization group approach with the exact numerical calculation of the integrated real-space spin-spin correlation functions. We show that, when the spin impurity is symmetrically coupled to the two parts of the chain with realistic values of the Kondo coupling strengths and spin-parity symmetry is preserved, the Kondo length takes values within the reach of nowadays experimental technology in ultracold-atom setups. In the case of non-symmetric Kondo couplings and/or spin parity broken by a nonzero magnetic field applied to the impurity, we discuss how Kondo screening redistributes among the chain as a function of the asymmetry in the couplings and map out the shrinking of the Kondo length when the magnetic field induces a crossover from Kondo impurity to weak-link physics.

Aperiodic exchange modulation effect on the specific heat in the Kondo necklace model

In the present work we study the effect of the aperiodic exchange modulation on the spin gap at finite temperature as well as the specific heat of the Kondo necklace model in two and three dimensions. For this purpose, we use a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green’s functions is also used to find the dispersion relation for the excitations of the system. The influence of the aperiodic exchange modulation on the spin gap at low temperatures is discussed in the paramagnetic phase. Moreover, we investigate the specific heat as a function of the aperiodic exchange modulation at low temperatures in two cases: above the quantum critical point i.e., along the so-called non-Fermi liquid trajectory and in the Kondo spin liquid state. We have also compared our results with previous bond operator mean-field calculations.

Kondo effect with tunable spin–orbit interaction in LaTiO3/CeTiO3/SrTiO3 heterostructure

We have fabricated epitaxial films of CeTiO3 (CTO) on (0 0 1) oriented SrTiO3 (STO) substrates, which exhibit highly insulating and diamagnetic properties. X-ray photoelectron spectroscopy was used to establish the 3+ valence state of the Ce and Ti ions. Furthermore, we have also fabricated δ (CTO) doped LaTiO3 (LTO)/SrTiO3 thin films which exhibit variety of interesting properties including Kondo effect and spin–orbit interaction (SOI) at low temperatures. The SOI shows a non-monotonic behaviour as the thickness of the CTO layer is increased and is reflected in the value of characteristic SOI field () obtained from weak anti-localization fitting. The maximum value of is 1.00 T for δ layer thickness of 6 u.c. This non-monotonic behaviour of SOI is attributed to the strong screening of the confining potential at the interface. The screening effect is enhanced by the CTO layer thickness and the dielectric constant of STO which increases at low temperatures. Due to the strong screening, electrons confined at the interface are spread deeper into the STO bulk where it starts to populate the Ti subbands; consequently the Fermi level crosses over from to the subbands. At the crossover region of where there is orbital mixing, SOI goes through a maximum.

Spin-liquid state in an inhomogeneous periodic Anderson model

We studied the ground state of alkaline-earth-metal atoms confined in one-dimensional optical lattices with an effective hybridization generated by a suitable laser field. This system is modeled by the periodic Anderson model plus a quadratic confining potential, and we adopted the density-matrix renormalization group to calculate its ground state. We found a one-to-one correspondence between the local variance, the local von Neumann entropy, and the on-site spin-spin correlation. For low global densities, we observed the formation of local singlets between delocalized and localized atoms and found Kondo spin liquid domains that can be tuned with the confining potential, the hybridization, and the local repulsion. Band insulator, metallic, phase separation, and Kondo spin liquid regions coexist in the ground state.