In this paper, we performed thermodynamic and electron spin resonance (ESR) measurements to study low-energy magnetic excitations, which were significantly affected by crystalline electric field (CEF) excitations due to relatively small gaps between the CEF ground state and the excited states. Based on the CEF and mean-field (MF) theories, we analyzed systematically and consistently the ESR experiments and thermodynamic measurements including susceptibility, magnetization, and heat capacity. The CEF parameters were successfully extracted by fitting high-temperature (> 20 K) susceptibilities in the ab-plane and along the c-axis, allowing to determine the Lande factors ($g_{ab,calc}$ = 5.98(7) and $g_{c,calc}$ = 2.73(3)). These values were consistent with the values of Lande factors determined by ESR experiments ($g_{ab,exp}$ = 5.69 and $g_{c,exp}$ = 2.75). By applying the CEF and MF theories to the susceptibility and magnetization results, we estimated the anisotropic spin-exchange energies and found that the CEF excitations in \ce{KErTe2} played a decisive role in the magnetism above 3 K, while the low-temperature magnetism below 10 K was gradually correlated with the anisotropic spin-exchange interactions. The CEF excitations were demonstrated in the low-temperature heat capacity, where both the positions of two broad peaks and their magnetic field dependence well corroborated our calculations. The present study provides a basis to explore the enriched magnetic and electronic properties of the QSL family.
We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb$^{3+}$ crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO$_4$. Three CEF excitations from the ground-state Kramers doublet are centered at the energies $\hbar ω$ = 39, 61, and 97\,meV in agreement with the effective \mbox{spin-1/2} $g$-factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg$^{2+}$ and Ga$^{3+}$ giving rise to a distribution of Yb--O distances and orientations …
Using the numerical renormalization group method, we investigate an extended Anderson model, in which correlated electrons with the $Γ_1$(singlet)-$\Gamma4$(triplet) f$^2$ crystalline-electric-field (CEF) configuration hybridize with conduction electrons of $Γ_7$(doublet) and $Γ_8$ (quartet) under cubic $O_h$ symmetry, from a strong spin-orbit interaction limit. For the case of the parameters relevant to PrFe4P12, the system is under competition between the CEF singlet fixed point and the multichannel Kondo non-Fermi liquid fixed point arising from the quadrupolar coupling between the impurity…
Frustrated magnetic systems exhibit many fascinating phases. Prime among them are quantum spin liquids, where the magnetic moments do not order even at zero temperature. A subclass of quantum spin liquids called Kitaev spin liquids are particularly interesting, because they are exactly solvable, can be realized in certain materials, and show a large variety of gapless and gapped phases. Here, we show that non-symmorphic symmetries can enrich spin liquid phases, such that the low-energy spinon degrees of freedom form three-dimensional Dirac cones or nodal chains. In addition, we suggest how suc…
A novel property of the quantum critical heavy fermion superconductor $β$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $β$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion driv…
Charge-transfer effect under odd-parity crystalline electric field (CEF) is analyzed theoretically. In quantum-critical metal $β$-YbAlB$_4$, seven-fold configuration of B atoms surrounding Yb atom breaks local inversion symmetry at the Yb site, giving rise to the odd-parity CEF. Analysis of the CEF on the basis of hybridization picture shows that admixture of 4f and 5d wave functions at Yb with pure imaginary coefficient occurs, which makes magnetic-toroidal (MT) and electric-dipole (ED) degrees of freedom active. By constructing the minimal model for periodic crystal $β$-YbAlB$_4$, we show th…
We investigate the crystal structure, magnetic properties, and crystalline-electric field of tetragonal, $I4_1/amd$, NaCeO$_2$. In this compound, Ce$^{3+}$ ions form a tetragonally elongated diamond lattice coupled by antiferromagnetic interactions ($Θ_{CW} = -7.69$ K) that magnetically order below $T_N = 3.18$ K. The Ce$^{3+}$ $J = 5/2$ crystalline-electric field-split multiplet is studied via inelastic neutron scattering to parameterize a $J_{eff} = 1/2$ ground state doublet comprised of states possessing mixed $|m_z \rangle$ character. Neutron powder diffraction data reveal the onset of $A$…
We have synthesized a new intermetallic compound with a distorted Heusler structure, YbRh$_{2}$Pb. We present a study of the magnetic, thermal, and transport properties. Heat capacity measurements revealed that YbRh$_{2}$Pb orders magnetically below T$_{N}$=0.57 K from a paramagnetic state with substantial crystal electric field splitting. Magnetic field further splits the ground state, which leads to the suppression of magnetic order in YbRh$_{2}$Pb.
We investigate the connection between the transport properties and the thermodynamics of electronic systems with a tendency to form broken-symmetry mesophases evocative of the physics of liquid crystals. Through a hydrodynamic approach to the electronic transport in inhomogeneous systems, we develop a perturbative expansion for the macroscopic conductivity to study the transport of two-dimensional smectic and nematic phases. At the fluctuation induced first order phase transition expected for the smectic to isotropic transition, a jump in the macroscopic conductivity is predicted, with a direc…
We argue that the ground state of a two-dimensional electron gas with Rashba spin-orbit coupling realizes one of several possible liquid crystalline or Wigner crystalline phases in the low-density limit, even for short-range repulsive electron-electron interactions (which decay with distance with a power larger than 2). Depending on specifics of the interactions, preferred ground-states include an anisotropic Wigner crystal with an increasingly anisotropic unit cell as the density decreases, a striped or electron smectic phase, and a ferromagnetic phase which strongly breaks the lattice point-…
The aspect of the quasiparticle interaction of a local Fermi liquid, the impurity version of f$^2$-based heavy fermions, is studied by the Wilson numerical renormalization group method. In particular, the case of the f$^2$-singlet crystalline-electric-field ground state is investigated assuming the case of UPt$_3$ with the hexagonal symmetry. It is found that the interorbital interaction becomes larger than the intraorbital one in contrast to the case of the bare Coulomb interaction for the parameters relevant to UPt$_3$. This result offers us a basis to construct a microscopic theory of the s…
We have succeeded in synthesizing of single crystals of a new intermetallic compound, Ce$_{3}$Rh$_{4}$Pb$_{13}$. Magnetic susceptibility measurements indicate that the Ce moments are highly localized, despite the metallic character of the electrical resistivity. Heat capacity measurements reveal that the cubic crystal electric field lifts the six-fold degeneracy of the Ce$^{3+}$ ground state, with the quartet state separated by approximately 60 K from the doublet ground state. The magnetic field dependence of the heat capacity at low temperature indicates a further splitting of the doublet, bu…
We describe a simple model of fermions in quasi-one dimension that features interaction induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on …
While the enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here we propose a new mechanism by which the $\mathrm{SU}(4)$ symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breaking hopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycomb structure, …
We report experimental evidence of emergent broken symmetry Fermi liquid state in an isolated single crystalline nanorod of $\rm Pr_2 Ir_2 O_7$. We find clear signature of the onset of the Fermi liquid behavior at low temperature marked by the sign inversion of magnetoresistance from negative at high temperature, characteristic of incoherent Kondo scattering, to positive as well as a $\rm T^2$ dependence of resistivity at low temperature. A resistive anomaly is observed, which is accompanied by thermal hysteresis in the presence of magnetic field, suggesting itinerant metamagnetism. The observ…
We study a magnetic field effect on the Non-Fermi Liquid (NFL) which arises around the quantum critical point (QCP) due to the competition between the f^2-crystalline-electric-field singlet and the Kondo-Yosida singlet states by using the numerical renormalization ground method. We show the characteristic temperature T_F^*, corresponding to a peak of a specific heat, is not affected by the magnetic field up to H_z^* which is determined by the distance from the QCP or characteristic energy scales of each singlet states. As a result, in the vicinity of QCP, there are parameter regions where the …
Neutron scattering experiments have been performed to elucidate magnetic properties of the quasicrystal approximant Au$_{70}$Si$_{17}$Tb$_{13}$, consisting of icosahedral spin clusters in a body-centered-cubic lattice. Bulk magnetic measurements performed on the single crystalline sample unambiguously confirm long-range ordering at $T_{\rm C} = 11.6 \pm 1$ K. In contrast to the simple ferromagnetic response in the bulk measurements, single crystal neutron diffraction confirms a formation of intriguing non-collinear and non-coplanar magnetic order. The magnetic moment direction was found to be …
Resistivity measurements were performed on Pr$_{1-x}$La$_x$Os$_4$Sb$_{12}$ single crystals at temperatures down to 20 mK and in fields up to 18 T. The results for dilute-Pr samples ($x=0.3$ and 0.67) are consistent with model calculations performed assuming a singlet crystalline-electric-field (CEF) ground state. The residual resistivity of these crystals features a smeared step centered around 9 T, the predicted crossing field for the lowest CEF levels. The CEF contribution to the magnetoresistance has a weaker-than-calculated dependence on the field direction, suggesting that interactions om…
We report on structural, magnetic and electrical properties of Sr-doped LaMnO_3 single crystals for doping levels 0.4 < x < 0.85. The complex structural and magnetic phase diagram can only be explained assuming significant contributions from the orbital degrees of freedom. Close to x = 0.6 a ferromagnetic metal is followed by an antiferromagnetic metallic phase below 200 K. This antiferromagnetic metallic phase exists in a monoclinic crystallographic structure. Following theoretical predictions this metallic antiferromagnet is expected to reveal an (x^2-y^2)-type orbital order. For higher Sr c…
We have performed X-ray powder diffraction, magnetization, electrical resistivity, heat capacity and inelastic neutron scattering (INS) to investigate the physical properties of the intermetallic series of compounds CeCuBi$_{2-x}$Sb$_{x}$. These compounds crystallize in a tetragonal structure with space group $P4/nmm$ and present antiferromagnetic transition temperatures ranging from 3.6 K to 16 K. Remarkably, the magnetization easy axis changes along the series, which is closely related to the variations of the tetragonal crystalline electric field (CEF) parameters. This evolution was analyze…
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
The temperature $T$ and magnetic field $H$ dependencies of the electrical resistivity $ρ$ of the recently discovered heavy fermion superconductor \PrOsSb{} have features that are associated with the splitting of the Pr$^{3+}$ Hund's rule multiplet by the crystalline electric field (CEF). These features are apparently due to magnetic exchange and aspherical Coulomb scattering from the thermally populated CEF-split Pr$^{3+}$ energy levels. The $ρ(T)$ data in zero magnetic field can be described well by calculations based on CEF theory for various ratios of magnetic exchange and aspherical Coulom…
We investigate the magnetic field dependence of the physical properties of f^2-configuration systems with a crystalline-electric field (CEF) singlet ground state, which gives rise to a non- Fermi liquid (NFL) fixed point due to the competition between the Kondo-Yosida singlet and CEF singlet states. On the basis of the numerical renormalization group method, we find that the magnetic field breaks this NFL fixed point via two mechanisms: one causing the polarization of f-electrons and the other giving the "channel" anisotropy. These two mechanisms induce a difference in the magnetic field depen…
In this work, we argue that an anisotropic interaction potential may stabilize anisotropic liquid phases of electrons even in a strong magnetic field regime where normally one expects to see only isotropic quantum Hall or isotropic Fermi liquid states. We use this approach to support a theoretical framework that envisions the possibility of an anisotropic liquid crystalline state of electrons in the lowest Landau level. In particular, we argue that an anisotropic liquid state of electrons may stabilize in the lowest Landau level close to the liquid-solid transition region at filling factor $ν=…
CsYbSe$_2$, a recently identified quantum spin liquid (QSL) candidate, exhibits strong crystal electric field (CEF) excitations. Here, we identify phonon and CEF modes with Raman spectroscopy and observe strong CEF-phonon mixing resulting in a vibronic bound state. Complex, mesoscale interplay between phonon modes and CEF modes is observed in real space, and an unexpected nearly resonant condition is satisfied, yielding up to fifth-order combination modes, with a total of 17 modes identified in the spectra. This study paves the way to coherent control of possible QSL ground states with optical…
We have measured the electrical resistivity of a single strand of a ferromagnetic Ni nanowire of diameter 55 nm using a 4-probe method in the temperature range 3 K-300 K. The wire used is chemically pure and is a high quality oriented single crystalline sample in which the temperature independent residual resistivity is determined predominantly by surface scattering. Precise evaluation of the temperature dependent resistivity ($ρ$) allowed us to identify quantitatively the electron-phonon contribution (characterized by a Debye temperature $θ_R$) as well as the spin-wave contribution which is s…
Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this paper, by directly studying the physical bulk properties of several band-theory-based nontrivial TCIs that are conceptually interesting and/or experimentally feasible, we show they are stable under interactions. These TCIs include (1) a weak topological insulator, (2) a TCI with a mirror symmetry and its time-reversal symmetric generalizations, (3…
A new kind of phase transition is proposed for lattice fermion systems with simplified f^2 configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contra…
Our ultrasound results obtained in pulsed magnetic fields show that the filled-skutterudite compound SmOs$_4$Sb$_{12}$ has the $Γ_{67}$ quartet crystalline-electric-field ground state. This fact suggests that the multipolar degrees of freedom of the $Γ_{67}$ quartet play an important role in the unusual physical properties of this material. On the other hand, the elastic response below $\approx$ 20 T cannot be explained using the localized 4$f$-electron model, which does not take into account the Kondo effect or ferromagnetic ordering. The analysis result suggests the presence of a Kondo-like …
It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realisation of this soft quantum matter physics in an ultra-cold gas. It uses optical lattices and dipolar interactions to realise a particularly simple model. Our analysis reveals a rich phase diagram featuring a meta-nematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes); and a crystalline, `checkerboard' phase.
Novel electronic order is found theoretically for a system where even number of localized electrons per site are coupled with conduction electrons. For precise quantitative study, a variant of the Kondo lattice model is taken with crystalline electric field (CEF) singlet and triplet states for each site. Using the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method, a staggered order with alternating Kondo and CEF singlets is identified for a case with one conduction electron per site being distributed in two conduction bands each of which is quarter-filled…
Chiral spin liquids (CSLs) are time-reversal symmetry breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering, but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal symmetry breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model,…
The effective mass probed by the de Haas-van Alphen oscillations is studied for a model Ce system under magnetic field higher than the Kondo energy. In the mean-field theory, the mass enhancement per Ce ion in the periodic system is identical with that in the dilute system. With decreasing magnetic field, the effective mass tends to diverge corresponding to a formation of the Kondo ground state. The effective mass can be very different between up and down spins depending on the nature of the 4f wave functions.
We investigate the temperature ($T$)-evolution of orbital anisotropy and its effect on spectral function and optical conductivity in Ce$_{2}$IrIn$_{8}$, using a first principles dynamical mean field theory combined with density functional theory. The orbital anisotropy develops by lowering $T$ and it is intensified below a temperature corresponding to the crystalline-electric field (CEF) splitting size. Interestingly, the depopulation of CEF excited states leaves a spectroscopic signature, "shoulder", in the $T$-dependent spectral function at the Fermi level. From the two-orbital Anderson impu…
We have measured crystalline electric field (CEF) excitations of Nd3+ ions in the two-channel Kondo lattice candidates NdT2Zn20 (T = Co, Rh, and Ir) by means of inelastic neutron scattering (INS). In the INS measurements at 5 K, dispersionless excitations were observed at 3.8 and 7.2 meV for T = Co, 3.1 and 5.8 meV for T = Rh, and 3.0 and 5.3 meV for T = Ir. Analyses of the temperature dependence of the INS spectra confirm that the CEF ground states are the Gamma 6 doublet, that is a requisite for manifestation of the magnetic two-channel Kondo effect. For T = Co, a shoulder was observed at 7.…
We discuss deformation of quasi 1-dimensional conductors with charge-density wave (CDW) under the electric field deforming the CDW. In case of ``strong'' CDW-lattice interaction the effect can be treated in terms of the converse piezoelectric effect with enormous piezomodulus, $\sim L_c/λ$ times larger than that in ionic crystals ($λ$ is the CDW wavelength, $L_c$ is the CDW coherence length, mm scale in the sliding state). The CDW-lattice interaction is likely to be defined by the interband charge transfer (rearrangement of the covalent bonds) with lattice deformation, possible in a number of …
We investigated electron phases in the $f^2$-configuration system with the $Γ_1$ crystalline-electric-field (CEF) ground state in cubic symmetry. An extended three-orbital periodic Anderson model, which consists of $j=5/2$ states, is evaluated by using the rotationally invariant slave boson formalism. As a result, we found three phases at zero temperature: the $Γ_1$ CEF singlet phase, and two kinds of Fermi liquid (FL). One of the FL arises owing to the presence of the $Γ_5$ CEF state, while the other forms a quasi-degenerated CEF state. All these phases are separated by first-order transition…
