Probing FeSi, a d-electron topological Kondo insulator candidate, with magnetic field, pressure, and microwaves.

Recently, evidence for a conducting surface state (CSS) below 19 K was reported for the correlated d-electron small gap semiconductor FeSi. In the work reported herein, the CSS and the bulk phase of FeSi were probed via electrical resistivity ρ measurements as a function of temperature T, magnetic field B to 60 T, and pressure P to 7.6 GPa, and by means of a magnetic field-modulated microwave spectroscopy (MFMMS) technique. The properties of FeSi were also compared with those of the Kondo insulator SmB6 to address the question of whether FeSi is a d-electron analogue of an f-electron Kondo insulator and, in addition, a "topological Kondo insulator" (TKI). The overall behavior of the magnetoresistance of FeSi at temperatures above and below the onset temperature TS = 19 K of the CSS is similar to that of SmB6. The two energy gaps, inferred from the ρ(T) data in the semiconducting regime, increase with pressure up to about 7 GPa, followed by a drop which coincides with a sharp suppression of TS. Several studies of ρ(T) under pressure on SmB6 reveal behavior similar to that of FeSi in which the two energy gaps vanish at a critical pressure near the pressure at which TS vanishes, although the energy gaps in SmB6 initially decrease with pressure, whereas in FeSi they increase with pressure. The MFMMS measurements showed a sharp feature at TS ≈ 19 K for FeSi, which could be due to ferromagnetic ordering of the CSS. However, no such feature was observed at TS ≈ 4.5 K for SmB6.

Crystal Chemistry and Physics of UCd11.

In the phase diagram U-Cd, only one compound has been identified so far─UCd11 (space group Pm3̅m). Since the discovery of this material, the physical properties of UCd11 have attracted a considerable amount of attention. In particular, its complex magnetic phase diagram─as a result of tuning with magnetic field or pressure─is not well-understood. From a chemical perspective, a range of lattice parameter values have been reported, suggesting a possibility of a considerable homogeneity range, i.e., UCd11-x. In this work, we perform a simultaneous study of crystallographic features coupled with measurements of physical properties. This work sheds light on the delicate relationship between the intrinsic crystal chemistry and magnetic properties of UCd11.

Transport gap in SmB6 protected against disorder.

The inverted resistance method was used in this study to extend the bulk resistivity of [Formula: see text] to a regime where the surface conduction overwhelms the bulk. Remarkably, regardless of the large off-stoichiometric growth conditions (inducing disorder by samarium vacancies, boron interstitials, etc.), the bulk resistivity shows an intrinsic thermally activated behavior that changes ∼7-10 orders of magnitude, suggesting that [Formula: see text] is an ideal insulator that is immune to disorder.

Topological surface states interacting with bulk excitations in the Kondo insulator SmB6 revealed via planar tunneling spectroscopy.

Samarium hexaboride (SmB6), a well-known Kondo insulator in which the insulating bulk arises from strong electron correlations, has recently attracted great attention owing to increasing evidence for its topological nature, thereby harboring protected surface states. However, corroborative spectroscopic evidence is still lacking, unlike in the weakly correlated counterparts, including Bi2Se3 Here, we report results from planar tunneling that unveil the detailed spectroscopic properties of SmB6 The tunneling conductance obtained on the (001) and (011) single crystal surfaces reveals linear density of states as expected for two and one Dirac cone(s), respectively. Quite remarkably, it is found that these topological states are not protected completely within the bulk hybridization gap. A phenomenological model of the tunneling process invoking interaction of the surface states with bulk excitations (spin excitons), as predicted by a recent theory, provides a consistent explanation for all of the observed features. Our spectroscopic study supports and explains the proposed picture of the incompletely protected surface states in this topological Kondo insulator SmB6.

Evidence for Ferromagnetic Clusters in the Colossal-Magnetoresistance Material EuB_{6}.

We combined scanning tunneling microscopy and locally resolved magnetic stray field measurements on the ferromagnetic semimetal EuB_{6}, which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect. In a zero magnetic field, scanning tunneling spectroscopy visualizes the existence of local inhomogeneities in the electronic density of states, which we interpret as the localization of charge carriers due to the formation of magnetic polarons. Micro-Hall magnetometry measurements of the total stray field emanating from the end of a rectangular-shaped platelike sample reveals evidence for magnetic clusters also in finite magnetic fields. In contrast, the signal detected below the faces of the magnetized sample measures a local stray field indicating the formation of pronounced magnetic inhomogeneities consistent with large clusters of percolated magnetic polarons.

Multi-q Mesoscale Magnetism in CeAuSb_{2}.

We report the discovery of a field driven transition from a single-q to multi-q spin density wave (SDW) in the tetragonal heavy fermion compound CeAuSb_{2}. Polarized along c, the sinusoidal SDW amplitude is 1.8(2)µ_{B}/Ce for T≪T_{N}=6.25(10) K with a wave vector q_{1}=(η,η,1/2) [η=0.136(2)]. For H∥c, harmonics appearing at 2q_{1} evidence a striped magnetic texture below µ_{∘}H_{1}=2.78(1) T. Above H_{1}, these are replaced by coupled harmonics at q_{1}+q_{2}=(2η,0,0)+c^{*} until µ_{∘}H_{2}=5.42(5) T, where satellites vanish and magnetization nonlinearly approaches saturation at 1.64(2)µ_{B}/Ce for µ_{∘}H≈7 T.

Visualizing heavy fermions emerging in a quantum critical Kondo lattice.

In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to the appearance of unconventional superconductivity and non-Fermi-liquid behaviour observed in actinide- and lanthanide-based compounds. Here we use spectroscopic mapping with the scanning tunnelling microscope to detect the emergence of heavy excitations with lowering of temperature in a prototypical family of cerium-based heavy-fermion compounds. We demonstrate the sensitivity of the tunnelling process to the composite nature of these heavy quasiparticles, which arises from quantum entanglement of itinerant conduction and f electrons. Scattering and interference of the composite quasiparticles is used to resolve their energy-momentum structure and to extract their mass enhancement, which develops with decreasing temperature. The lifetime of the emergent heavy quasiparticles reveals signatures of enhanced scattering and their spectral lineshape shows evidence of energy-temperature scaling. These findings demonstrate that proximity to a quantum critical point results in critical damping of the emergent heavy excitation of our Kondo lattice system.

Hybridization gap and Fano resonance in SmB6.

Hybridization between conduction electrons and the strongly interacting f-electrons in rare earth or actinide compounds may result in new states of matter. Depending on the exact location of the concomitant hybridization gap with respect to the Fermi energy, a heavy fermion or an insulating ground state ensues. To study this entanglement locally, we conducted scanning tunneling microscopy and spectroscopy (STS) measurements on the "Kondo insulator" SmB6. The vast majority of surface areas investigated were reconstructed, but infrequently, patches of varying sizes of nonreconstructed Sm- or B-terminated surfaces also were found. On the smallest patches, clear indications for the hybridization gap with logarithmic temperature dependence (as expected for a Kondo system) and for intermultiplet transitions were observed. On nonreconstructed surface areas large enough for coherent cotunneling, we were able to observe clear-cut Fano resonances. Our locally resolved STS indicated considerable finite conductance on all surfaces independent of their structure, not proving but leaving open the possibility of the existence of a topologically protected surface state.

Radio Frequency Tunable Oscillator Device Based on a SmB_{6} Microcrystal.

Radio frequency tunable oscillators are vital electronic components for signal generation, characterization, and processing. They are often constructed with a resonant circuit and a "negative" resistor, such as a Gunn diode, involving complex structure and large footprints. Here we report that a piece of SmB_{6}, 100 µm in size, works as a current-controlled oscillator in the 30 MHz frequency range. SmB_{6} is a strongly correlated Kondo insulator that was recently found to have a robust surface state likely to be protected by the topology of its electronics structure. We exploit its nonlinear dynamics, and demonstrate large ac voltage outputs with frequencies from 20 Hz to 30 MHz by adjusting a small dc bias current. The behaviors of these oscillators agree well with a theoretical model describing the thermal and electronic dynamics of coupled surface and bulk states. With reduced crystal size we anticipate the device to work at higher frequencies, even in the THz regime. This type of oscillator might be realized in other materials with a metallic surface and a semiconducting bulk.

Lattice strain accompanying the colossal magnetoresistance effect in EuB6.

The coupling of magnetic and electronic degrees of freedom to the crystal lattice in the ferromagnetic semimetal EuB(6), which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect, is studied by high-resolution thermal expansion and magnetostriction experiments. EuB(6) may be viewed as a model system, where pure magnetism-tuned transport and the response of the crystal lattice can be studied in a comparatively simple environment, i.e., not influenced by strong crystal-electric field effects and Jahn-Teller distortions. We find a very large lattice response, quantified by (i) the magnetic Grüneisen parameter, (ii) the spontaneous strain when entering the ferromagnetic region, and (iii) the magnetostriction in the paramagnetic temperature regime. Our analysis reveals that a significant part of the lattice effects originates in the magnetically driven delocalization of charge carriers, consistent with the scenario of percolating magnetic polarons. A strong effect of the formation and dynamics of local magnetic clusters on the lattice parameters is suggested to be a general feature of colossal magnetoresistance materials.

Scaling the Kondo lattice.

The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between 'local-moment' magnetism and 'itinerant-electron' magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons' response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram.

Kondo physics in a rare earth ion with well localized 4f electrons.

Dilute Nd in simple cubic LaB(6) shows electrical resistance and specific heat features at low temperature consistent with a Kondo scale of T(K)

Exploring itinerant states in divalent hexaborides using rare-earth L edge resonant inelastic x-ray scattering.

We present a study of resonant inelastic x-ray scattering (RIXS) spectra collected at the rare-earth L edges of divalent hexaborides YbB6 and EuB6. In both systems, RIXS-active features are observed at two distinct resonances separated by [Formula: see text] eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak resemble the unoccupied 5d density of states calculated using density functional theory. We discuss possible origins of this correspondence including a scenario which changes the 4f  valence. In addition, anomalous resonant scattering is observed at higher incident energy, where no corresponding absorption feature is present. Our results demonstrate the potential for L-edge RIXS to assess the itinerant-state properties of f -electron materials.

Flux growth and structure of two compounds with the EuIn2P2 structure type, AIn2P2 (A = Ca and Sr), and a new structure type, BaIn2P2.

Single crystals of the new Zintl phases AIn2P2 [A = Ca (calcium indium phosphide), Sr (strontium indium phosphide) and Ba (barium indium phosphide)] have been synthesized from a reactive indium flux. CaIn2P2 and SrIn2P2 are isostructural with EuIn2P2 and crystallize in the space group P63/mmc. The alkaline earth cations A are located at a site with 3m symmetry; In and P are located at sites with 3m symmetry. The structure type consists of layers of A2+ cations separated by [In2P2]2- anions that contain [In2P6] eclipsed ethane-like units that are further connected by shared P atoms. This yields a double layer of six-membered rings in which the In-In bonds are parallel to the c axis and to one another. BaIn2P2 crystallizes in a new structure type in the space group P2(1)/m with Z = 4, with all atoms residing on sites of mirror symmetry. The structure contains layers of Ba2+ cations separated by [In2P2]2- layers of staggered [In2P6] units that form a mixture of four-, five- and six-membered rings. As a consequence of this more complicated layered structure, both the steric and electronic requirements of the large Ba2+ cation are met.

Localized magnetic moments in metallic SrB6 single crystals.

The specific heat [Formula: see text] of metallic SrB6 single crystals shows an anomalous behavior for [Formula: see text] K which varies strongly with an applied magnetic field. This is consistent with a two-level Schottky system. We ascribe the excess of [Formula: see text] in this temperature range to localized magnetic moments. In addition, features that are attributable to a partial ferromagnetic polarization of a conduction electron gas are observed. These results are supported by magnetization measurements and are compatible with the transport properties reported previously (Stankiewicz 2016 Phys. Rev. B 94 125141).

Magnetic and defect probes of the SmB6 surface state.

The impact of nonmagnetic and magnetic impurities on topological insulators is a central focus concerning their fundamental physics and possible spintronics and quantum computing applications. Combining scanning tunneling spectroscopy with transport measurements, we investigate, both locally and globally, the effect of nonmagnetic and magnetic substituents in SmB6, a predicted topological Kondo insulator. Around the so-introduced substitutents and in accord with theoretical predictions, the surface states are locally suppressed with different length scales depending on the substituent's magnetic properties. For sufficiently high substituent concentrations, these states are globally destroyed. Similarly, using a magnetic tip in tunneling spectroscopy also resulted in largely suppressed surface states. Hence, a destruction of the surface states is always observed close to atoms with substantial magnetic moment. This points to the topological nature of the surface states in SmB6 and illustrates how magnetic impurities destroy the surface states from microscopic to macroscopic length scales.

Atomic-scale visualization of surface-assisted orbital order.

Orbital-related physics attracts growing interest in condensed matter research, but direct real-space access of the orbital degree of freedom is challenging. We report a first, real-space, imaging of a surface-assisted orbital ordered structure on a cobalt-terminated surface of the well-studied heavy fermion compound CeCoIn5. Within small tip-sample distances, the cobalt atoms on a cleaved (001) surface take on dumbbell shapes alternatingly aligned in the [100] and [010] directions in scanning tunneling microscopy topographies. First-principles calculations reveal that this structure is a consequence of the staggered d xz -d yz orbital order triggered by enhanced on-site Coulomb interaction at the surface. This so far overlooked surface-assisted orbital ordering may prevail in transition metal oxides, heavy fermion superconductors, and other materials.

Quantum phase transition and destruction of Kondo effect in pressurized SmB6.

SmB6 has been a well-known Kondo insulator for decades, but recently attracts extensive new attention as a candidate topological system. Studying SmB6 under pressure provides an opportunity to acquire the much-needed understanding about the effect of electron correlations on both the metallic surface state and bulk insulating state. Here we do so by studying the evolution of two transport gaps (low temperature gap El and high temperature gap Eh) associated with the Kondo effect by measuring the electrical resistivity under high pressure and low temperature (0.3 K) conditions. We associate the gaps with the bulk Kondo hybridization, and from their evolution with pressure we demonstrate an insulator-to-metal transition at ∼4 GPa. At the transition pressure, a large change in the Hall number and a divergence tendency of the electron-electron scattering coefficient provide evidence for a destruction of the Kondo entanglement in the ground state. Our results raise the new prospect for studying topological electronic states in quantum critical materials settings.