Crystal Field Symmetry Research Articles

Highly Efficient Novel Garnet‐Structured Yellow Emitting Phosphor for High Power Laser‐Driven Lighting

AbstractA novel blue light excitable yellow emitting phosphor, BaLu2(Mg0.6Al2.8Si1.6)O12:Ce3+, with an external quantum efficiency (EQE) of 66.2%, is developed by substituting Al3+‐Al3+ pairs in BaLu2Al4SiO12:Ce3+ with Mg2+‐Si4+ pairs. Alongside the redshift of Ce3+ emission, this substitution also broadened Ce3+ emission and reduced its thermal stability. The spectral changes are found to result from variations in the local crystal field and site symmetry of Ce3+ due to Mg2+‐Si4+ substitution. To assess the feasibility of the newly developed yellow‐emitting phosphor for high‐power laser lighting, it is constructed into a phosphor wheel. Owing to the efficient heat dissipation via high speed rotation of phosphor wheel, the yellow phosphor exhibit a luminous flux of 3894 lm and shows no obvious emission saturation even excited by blue laser light with a power density of 90.7 W mm−2. Exciting the yellow phosphor wheel with a blue laser diode (LDs) at a power density of 25.2 W mm−2 resulted in bright white light with a luminous of 1718.1 lm, a correlated color temperature of 5983 K, a color rendering index of 65.0, and chromatic coordinates of (0.3203, 0.3631). These results suggest that the newly synthesized yellow‐emitting phosphor holds significant potential for high‐power laser‐driven lighting applications.

Dirac-Like Fermions Anomalous Magneto-Transport in a Spin-Polarized Oxide 2D Electron System.

In a 2D electron system (2DES) the breaking of the inversion, time-reversal and bulk crystal-field symmetries is interlaced with the effects of spin-orbit coupling (SOC) triggering exotic quantum phenomena. Here, epitaxial engineering is used to design and realize a 2DES characterized simultaneously by ferromagnetic order, large Rashba SOC and hexagonal band warping at the (111) interfaces between LaAlO3, EuTiO3, and SrTiO3 insulators. The 2DES displays anomalous quantum corrections to the magneto-conductance driven by the time-reversal-symmetry breaking occurring below the magnetic transition temperature. The results are explained by the emergence of a non-trivial Berry phase and competing weak anti-localization/weak localization back-scattering of Dirac-like fermions, mimicking the phenomenology of gapped topological insulators. These findings open perspectives for the engineering of novel spin-polarized functional 2DES holding promises in spin-orbitronics and topologicalelectronics.

Regulating Spin Polarization via Axial Nitrogen Traction at Fe−N5 Sites Enhanced Electrocatalytic CO2 Reduction for Zn−CO2 Batteries

AbstractSingle Fe sites have been explored as promising catalysts for the CO2 reduction reaction to value‐added CO. Herein, we introduce a novel molten salt synthesis strategy for developing axial nitrogen‐coordinated Fe‐N5 sites on ultrathin defect‐rich carbon nanosheets, aiming to modulate the reaction pathway precisely. This distinctive architecture weakens the spin polarization at the Fe sites, promoting a dynamic equilibrium of activated intermediates and facilitating the balance between *COOH formation and *CO desorption at the active Fe site. Notably, the synthesized FeN5, supported on defect‐rich in nitrogen‐doped carbon (FeN5@DNC), exhibits superior performance in CO2RR, achieving a Faraday efficiency of 99 % for CO production (−0.4 V vs. RHE) in an H‐cell, and maintaining a Faraday efficiency of 98 % at a current density of 270 mA cm−2 (−1.0 V vs. RHE) in the flow cell. Furthermore, the FeN5@DNC catalyst is assembled as a reversible Zn−CO2 battery with a cycle durability of 24 hours. In situ IR spectroscopy and density functional theory (DFT) calculations reveal that the axial N coordination traction induces a transformation in the crystal field and local symmetry, therefore weakening the spin polarization of the central Fe atom and lowering the energy barrier for *CO desorption.

Regulating Spin Polarization via Axial Nitrogen Traction at Fe-N5 Sites Enhanced Electrocatalytic CO2 Reduction for Zn-CO2 Batteries.

Single Fe sites have been explored as promising catalysts for the CO2 reduction reaction to value-added CO. Herein, we introduce a novel molten salt synthesis strategy for developing axial nitrogen-coordinated Fe-N5 sites on ultrathin defect-rich carbon nanosheets, aiming to modulate the reaction pathway precisely. This distinctive architecture weakens the spin polarization at the Fe sites, promoting a dynamic equilibrium of activated intermediates and facilitating the balance between *COOH formation and *CO desorption at the active Fe site. Notably, the synthesized FeN5, supported on defect-rich in nitrogen-doped carbon (FeN5@DNC), exhibits superior performance in CO2RR, achieving a Faraday efficiency of 99 % for CO production (-0.4 V vs. RHE) in an H-cell, and maintaining a Faraday efficiency of 98 % at a current density of 270 mA cm-2 (-1.0 V vs. RHE) in the flow cell. Furthermore, the FeN5@DNC catalyst is assembled as a reversible Zn-CO2 battery with a cycle durability of 24 hours. In situ IR spectroscopy and density functional theory (DFT) calculations reveal that the axial N coordination traction induces a transformation in the crystal field and local symmetry, therefore weakening the spin polarization of the central Fe atom and lowering the energy barrier for *CO desorption.

Record Quantum Tunneling Time in an Air-Stable Exchange-Bias Dysprosium Macrocycle.

In recent years, dysprosium macrocycle single-molecule magnets (SMMs) have received increasing attention due to their excellent air/thermal stability, strong magnetic anisotropy, and rigid molecular skeleton. However, they usually display fast zero-field quantum tunneling of the magnetization (QTM) rate, severely hindering their data storage applications. Herein, we report the design, synthesis, and characterization of an air-stable monodecker didysprosium macrocycle integrating strong single-ion anisotropy, near-perfect local crystal field (CF) symmetry, and efficient exchange bias. These indispensable features enable clear-cut elucidation of the crucial role of very weak antiferromagnetic coupling on magnetization dynamics, creating a prominent SMM with a large effective energy barrier (Ueff) of 670 cm-1, open hysteresis loops at zero field up to 14.9 K, and a record relaxation time of QTM (τQTM), 24281 s, for all known nonradical-bridged lanthanide SMMs.

Luminescence enhancement effects of CaxSr2‒xNb2O7:Er3+,Tm3+ phosphors for temperature sensing and anti-counterfeiting applications

Er3+- and Tm3+-doped CaxSr2‒xNb2O7 (CxS2‒xN, x = 0.6, 0.8, 1.0, 1.2, 1.4) phosphors with layered perovskite structure were designed. These phosphors exhibit a dominant emission peak at 549 nm under 980 nm laser excitation, attributed to the 4S3/2→4I15/2 transition. By increasing the content of Ca2+, the crystal field regulation of rare earth ions is realized and the luminescence enhancement is induced, which is manifested by the increase of 2H11/2,4S3/2→4I15/2 emission. Furthermore, the temperature sensing sensitivities of C0.6S1.4N:Er,Tm and C0.6S1.4N:Er,Tm based on non-thermally coupled energy levels were studied. Finally, an anti-counterfeiting imprint was prepared using phosphors, which have high brightness and excellent photothermal stability. This work not only confirms that closer ionic radii substitution enables to increase the electronic density of states, improve the crystal field symmetry and enhance the luminescence, but also provides a promising phosphor system for temperature sensing and anti-counterfeiting applications, opening up new prospects in the optimization of the optical properties of phosphors.

First-Principles Study of Ti-Doping Effects on Hard Magnetic Properties of RFe11Ti Magnets

Due to the rare earth supply shortage, ThMn12-type RFe12-based (R is the rare earth element) magnets with lean rare earth content are gaining more concern. Most ThMn12-type RFe12 structures are thermodynamically metastable and require doping of the stabilizing element Ti. However, the Ti-doping effects on the hard magnetic properties of RFe11Ti have not been thoroughly investigated. Herein, based on density functional theory calculations, we report the Ti-doping effects on the phase stability, intrinsic hard magnetic properties and electronic structures of RFe11Ti (R = La, Ce, Pr, Nd, Sm, Y, Zr). Our results indicate that Ti-doping not only increases their phase stability, but also enhances the magnetic hardness of ground-state RFe12 phases. Particularly, it leads to the transition of CeFe11Ti and PrFe11Ti from easy-plane to easy-axis anisotropy. Charge density distributions demonstrate that Ti-doping breaks the original symmetry of the R-site crystal field, which alters the magnetic anisotropy of RFe11Ti. Projected densities of states reveal that the addition of Ti results in the shift of occupied and unoccupied f-electron energy levels of rare earth elements, affecting their magnetic exchange. This study provides an insight into regulating the hard magnetic properties of RFe12-based magnets by Ti-doping.

Modulation of the magnetic properties of mononuclear Dy(III) complexes by tuning the coordination geometry and local symmetry.

Precise control of the crystal field and local symmetry around the paramagnetic spin center is crucial for the design and synthesis of single-molecule magnets (SMMs). Herein, three mononuclear Dy(III)-based complexes, [Dy(LN6)(CH3COO)2](BPh4)(CH2Cl2) (1), [Dy(LN6)(2,6-Cl-4-NO2-PhO)(H2O)2]2(PF6)2(H2O)(2,6-Cl-4-NO2-PhO)2 (2) and [Dy(LN6)(2,6-Cl-4-NO2-PhO)2](BPh4)(CH2Cl2)2 (3) (LN6 = N6-hexagonal plane accomplished by a neutral Schiff base ligand formed from 2,6-diacetylpyridine and ethylenediamine), are successfully isolated. In these complexes, the Dy(III) centers are coordinated with six neutral N atoms from a nonrigid equatorial ligand, while different oxygen-bearing ligands are arranged at the axial positions of the central ions by gradual regularization of the axial ligands. As a result, Dy(III) ions in the three complexes exhibit various coordination geometries, forming a ten-coordinate tetradecahedron for 1, a nine-coordinate muffin configuration for 2 and a distorted eight-coordinate hexagonal bipyramid for 3. Magnetic studies reveal that all complexes exhibit no SIM behaviour under zero dc field, due to the predominant quantum tunneling of magnetization (QTM), which can be effectively suppressed by additional dc fields. Experiments, coupled with theoretical calculations, demonstrate that varying local symmetries and coordination geometries are synergistically responsible for the disparities of QTM and uniaxial anisotropy, resulting in notably different magnetic properties.

Co-doped NaYF4:Yb/Er/Tm upconversion luminescent coating to enhance the efficiency of photovoltaic cells.

The use of upconversion luminescent materials to broaden the utilization range of the solar spectrum to enhance the efficiency of photovoltaic cells offers a promising and sustainable approach. However, the low luminescence intensity and easy quenching of upconversion luminescent materials bring serious challenges to the practical application. Herein, a novel method using Co2+ ion doping to regulate the luminescence properties of NaYF4:Yb/Er/Tm is proposed. NaYF4:Yb/Er/Tm microcrystals doped with different proportions of Co2+ ions are prepared and used as coatings on the surface of photovoltaic cells. Co2+ ions regulate the crystallinity and size of the NaYF4:Yb/Er/Tm microcrystals and reduce the crystal field symmetry of the activator (Er3+ and Tm3+) ions. The results show that the emission intensity of green and red light is 18.19% and 83.24% times higher than that of undoped Co2+ ion materials, respectively. Besides, the efficiency of photovoltaic cells after coating Co2+ ion doped NaYF4:Yb/Er/Tm is 2.08% higher than that of the uncoated one. This work underscores the importance of Co2+ ion doping to improve and enhance the luminescence properties of NaYF4:Yb/Er/Tm, to further enhance the efficiency of photovoltaic cells.

Optical Lines in Europium and Terbium-Activated Yttrium Tantalate Phosphor: Combined Experimental and Group-Theoretical Analysis

The rare-earth ions in crystals such as terbium (YTaO4:Tb3+) and europium (YTaO4:Eu3+)-activated yttrium tantalate phosphors have a number of attractive features that predetermine their crucial role in practical application in contemporary optoelectronic devices. In this article, we employ the group-theoretical arguments aimed to reveal the group-theoretical classification of the crystal field levels and selection rules for the allowed optical transition between the crystal field components of Tb3+ and Eu3+ of the low symmetry crystal field in the activated yttrium tantalate phosphors. We also establish possible polarization rules for the lines corresponding to the allowed transitions. We deduce the symmetry-assisted results for the selection rules in the optical transitions accompanied by the absorption/emission of the vibrational quanta. The selection rules for the vibronic satellites of the zero-phonon lines are expected to be useful for the identification of the lines in the spectra of rare-earth ions with a weak vibronic coupling. The results of the low-temperature measurements of photoluminescence under the 325 nm excitation are in compliance with the group-theoretical analysis. The aim of the paper is to establish symmetry-assisted results that are the background of the quantitative crystal field theory based on the quantum-mechanical consideration.

Suppression of intervalley scattering and enhanced phonon anharmonic interactions in 2D Bi2TeSe2: Crystal-field symmetry and band convergence

The electron-phonon (el-ph) and phonon-phonon interactions play a key role in determining electronic and thermal transport properties, respectively, in promising two-dimensional (2D) semiconductor devices. In this study, we investigated el-ph interactions using Wannier-Fourier interpolation method and renormalized phonon scattering considering finite-temperature effects in Bi2TeSe2 monolayer. The results show that the optical phonon modes dominate the carrier scattering, where level repulsion induced by crystal field splitting and spin-orbit coupling (SOC) effect effectively suppresses intervalley scattering, leading to high hole mobility. Moreover, the strong anharmonicity in Bi2TeSe2 monolayer results in the temperature-dependent softening of its optical phonons, along with a corresponding variation in interatomic force constants (IFCs). As a result, the lattice thermal conductivity is remarkably low and exhibits weak temperature dependence. Finally, the predicted dimensionless thermoelectric figure of merit exceeds unity in the range of 200–800 K, indicating the potential of Bi2TeSe2 monolayer for thermoelectric applications. This work provides new insights into the elimination of intervalley scattering by crystal field splitting and SOC effects, and paves the way for the evaluation of thermoelectric properties of materials with complex scattering mechanisms and strong anharmonicity.

Curvature-dependent strain-induced photoluminescence modulations in flexible Er-doped Pb0.98La0.02Zr0.95Ti0.05O3 antiferroelectric thin films prepared by the sol-gel method

Tunable photoluminescence (PL) has wide applications in optical waveguides and communication. Since the PL intensity is strongly dependent on the crystal field symmetry, curvature-dependent strain-induced PL modulation is expected in flexible antiferroelectric (AFE) thin film materials. Here, flexible Er-doped Pb0.98La0.02Zr0.95Ti0.05O3 (PLZT) AFE thin films were prepared via the sol-gel method. A giant and reversible PL intensity modulation (482%) was achieved during the bending process. Based on density functional theory (DFT) calculations and Raman spectra measurements, the relationship amongst the curvature-dependent strains, crystal structure, and PL modulation was discussed. The induced strain leads to lattice distortion and even a phase transition, both of which contribute to the reduction in crystal symmetry and thus significantly enhance the PL intensity.

Enhanced X-ray-induced luminescence and afterglow of NaLuF4:Gd3+/Tb3+ nanoparticles with Ca2+ doping

The synthesis of efficient nano-scintillators is of great significance for the development of X-ray imaging and other applications. Here, X-ray excited afterglow rare earth nanoparticles β-NaLuF4:Gd3+/Tb3+ are investigated. The X-ray-induced luminescence intensity and afterglow duration of NaLuF4:Gd3+/Tb3+ nanoparticles are effectively improved by Ca2+ doping. The optimal luminescence and afterglow performance are achieved when Ca2+ doping ratio reaches 10%. The change of crystal field symmetry is the main reason for the improvement of luminescence performance. According to the thermoluminescence curve, it is proved that Ca2+ doping increases the trap concentration and further enhances the afterglow. This study provides the research basis for the application of persistent luminescence materials in biomedical and other fields.

Effective enhancement of ∼2.86 µm mid-infrared emission of Na5Y9F32 single crystal co-doped Ho3+/Pr3+ introduced by Gd3+ ions

The optical spectral properties of high-quality Na5Y9F32 single crystals triply incorporated Ho3+/Pr3+/Gd3+ ions prepared successfully via a Bridgman technique were characterized with the help of their absorption spectra, emission spectra, and fluorescence lifetimes. It was discovered that the emission intensity at ∼2.86 µm of Na5Y9F32 co-doped Pr3+/Ho3+ single crystal was boosted obviously by introducing of Gd3+ ions, and it reached its maximum when the concentration of Gd3+ ion dopant was ∼0.7 mol%. The release of more luminescent centers due to the destruction of [Ho3+-Ho3+] ion quenching clusters and variation of the symmetry of crystal field around Ho3+ ions are responsible for the augmentation of ∼2.86 µm fluorescence emission. In addition, the introduction of Gd3+ ion reduced the fluorescence lifetime of Ho3+: 5I7 level, while the Ho3+:5I6 level remained slightly changed, which is beneficial to improve the particle inversion of Ho3+ ion between the 5I6 and 5I7 energy levels to enhance the ∼2.86 µm emission. The results showed that the triply doped fluoride single crystal can become a potentially prospective material for ∼2.86 µm mid-infrared lasers.

Effect of annealing temperature on the structural, electronic and magnetic properties of Co doped TiO2 nanoparticles: An investigation by synchrotron-based experimental techniques

The present study examines the effect of annealing temperature on the structural, electronic and magnetic properties of Co-doped TiO2 (TCO) nanoparticles (NPs) synthesized by the sol-gel method. X-ray powder diffractograms of TCO NPs annealed at 400, 600 and 800 °C exhibited the monophasic anatase, diphase (anatase and rutile) and monophasic rutile structures respectively. A morphological investigation using high-resolution scanning electron microscopy (HR-SEM) reveals the presence of nanoparticles with diameters ranging from ∼11 to ∼51 nm. The widening and shifting of the most intense Eg peak in Raman studies and SEM images of TCO NPs suggest Co incorporation in the TiO2 matrix and the formation of oxygen vacancies. Magnetic measurements of TCO at room temperature demonstrate ferromagnetic behaviour which is caused by the existence of oxygen vacancies and the doped Co content. Element specific technique, soft X-ray magnetic circular dichroism (XMCD) was used to study the magnetism in Co doped TiO2 samples. The estimated total magnetic moment by XMCD was in the range of ∼1.3 ± 0.1–2.3 ± 0.2 μB/Co. This huge magnetization was first time observed by the surface-sensitive Total Electron Yield (TEY) mode. The estimated saturation magnetic moment is in the range of 1.0–1.5 μB/Co, also consistent with XMCD analysis and cluster model calculation. The results obtained by XMCD recommend an intrinsic behaviour of ferromagnetism. The X-ray absorption spectra (XAS) of Co-doped TiO2 nanoparticles at Ti L2,3 and Co L2,3 -edge in TEY mode concludes that the valence states of Co and Ti ions are in 2 + and 4 + respectively. Cluster model calculation also confirmed that Co ions are in a 2 + valence state with D2 h high spin crystal-field symmetry at the surface while a random crystal field symmetry in bulk has been observed which is well consistent with experimental data.

Enhanced X-ray-induced luminescence and persistent luminescence of NaLuF4:Tb3+ nanoparticles with Li+ and Gd3+ co-doped

X-ray excitation photodynamic therapy is a new photodynamic therapy mode that induces tumor cell apoptosis by indirectly stimulating photosensitizer on nanoparticles with X-ray as excitation light source and generating singlet oxygen. It solves the problem of light penetration in traditional photodynamic therapy and realizes the treatment of deep tumors. At present, the weak X-ray-induced luminescence restricts further development of X-ray photodynamic therapy. NaLuF4:Li+/Gd3+/Tb3+ rare-earth nanoparticles with uniform size and regular morphology were synthesized by solvothermal method. The X-ray-induced luminescence intensity of NaLuF4:Li+/Gd3+/Tb3+ NPs was improved by Li+ and Gd3+ ions co-doping. The light yield of NaLuF4:Li+/Gd3+/Tb3+ NPs with 5% Li+ ions doping was 1.4 times than that of reference sample due to the change of crystal field symmetry. Furthermore, the effective lifetime of persistent luminescence increased from 221.5 s to 251.9 s after 15% Li+ ions doping. The thermoluminescence curves confirmed that the trap concentration was increased after Li+ ions doping, which was responsible for enhancing persistent luminescence lifetime. Long persistent luminescence emission laid a foundation for further application in photodynamic therapy.

Supercooled Jahn-Teller ice

When the spins on the frustrated pyrochlore lattice obey the celebrated 2-$in$-2-$out$ ice rule, they stay in a correlated disordered phase and break the third law of thermodynamics. Similarly, if the atomic ions on the pyrochlore lattice move in and outward of the tetrahedra, they may obey a constraint resembling the ice rule. We discover that a model for pyrochlore molybdates $A_2$Mo$_2$O$_7$ ($A=$Y, Dy, Tb) exhibits a "supercooled ice" state of the displacement degrees of freedom of Mo$^{4+}$ ions, when we take account of the Jahn-Teller (JT) effect. The JT effect occurs when the lattice distortions reduce the symmetry of the local crystal field, resulting in the orbital-energy-splitting that causes the local energy gain. Unlike the standard JT effect that leads to periodic long range ordering, the displacements of Mo$^{4+}$ ions are disordered following the ice-like rule. We microscopically derive a model that describes this situation by having the 2nd and 3rd neighbor interactions between in-out lattice displacements comparably as strong as the nearest neighbor interactions of standard ice. There, the well-known nearly flat energy landscape of the ice state is altered to a metastable highly quasi-degenerate ice-like liquid state coexisting with a crystalline-like ground state. Our Monte Carlo simulations show that this liquid remains remarkably stable down to low temperatures by avoiding the putative first order transition. The relaxation in the supercooled JT ice state exhibits glassy dynamics with a plateau structure. They fit the feature of a "good glassformer" very often found in molecular liquids, but that has never been observed in material solids. The high glass-forming ability of the interacting lattice degrees of freedom will play a key role in the spin-glass transition of the material.

Complex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics.

Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature’s surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.

Effectively enhanced photoluminescence of CePO4:Tb3+ nanorods combined with carbon dots

CePO4:Tb3+ nanorods were successfully obtained via a simple hydrothermal method and combined with carbon dots (CDs) to obtain CDs@CePO4:Tb3+ nanorods. Due to the combination of CDs, the emission intensity of CDs@CePO4:Tb3+ nanorods increases about 92 times, compared with that of CePO4:Tb3+ nanorods. The combination of CDs and CePO4:Tb3+ nanorods was confirmed by Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS) and so on. The mechanism of luminescence enhancement may be attributed to some aspects: the formation of hexagonal phase results in the increase of crystal field symmetry, and the energy transfer among CDs, Ce3+ and Tb3+ ions, which causes the Tb3+ ions in CDs@CePO4:Tb3+ nanorods to obtain more excited energy and less non-radiative attenuation compared to CePO4: Tb3+ nanorods. The luminescence enhancement strategy through combination of CDs would provide a simple and effective approach for other rare earth ions doped luminescent materials.

Nontrivial fixed points and truncated SU(4) Kondo models in a quasi-quartet multipolar quantum impurity problem

The multipolar Kondo problem, wherein the quantum impurity carries higher-rank multipolar moments, has seen recent theoretical and experimental interest due to proposals of novel non-Fermi liquid states and the availability of a variety of material platforms. The multipolar nature of local moments, in conjunction with constraining crystal field symmetries, leads to a vast array of possible interactions and resulting non-Fermi liquid ground states. Previous works on Kondo physics have typically focused on impurities that have two degenerate internal states. In this work, inspired by recent experiments on the tetragonal material ${\mathrm{YbRu}}_{2}{\mathrm{Ge}}_{2}$, which has been shown to exhibit a local moment with a quasi-fourfold degenerate ground state, we consider the Kondo effect for such a quasi-quartet multipolar impurity. In the tetragonal crystal field environment, the local moment supports dipolar, quadrupolar, and octupolar moments, which interact with conduction electrons in entangled spin and orbital states. Using renormalization group analysis, we uncover a number of emergent quantum ground states characterized by nontrivial fixed points. It is shown that these previously unidentified fixed points are described by truncated SU(4) Kondo models, where only some of the SU(4) generators (representing the impurity degrees of freedom) are coupled to conduction electrons. Such novel nontrivial fixed points are unique to the quasi-quartet multipolar impurity, reinforcing the idea that an unexplored rich diversity of phenomena may be produced by multipolar quantum impurity systems.