Ytterbium-based delafossites with effective S=1/2 moments are investigated intensively as candidates for quantum spin-liquid ground states. While the synthesis of related cerium compounds has also been reported,many important details concerning their crystal, electronic, and magnetic structures are unclear. Here we analyze the S=1/2 system KCeO2, combining complementary theoretical methods. The lattice geometry was optimized and the band structure investigated using density functional theory extended to the level of a GGA+U calculation in order to reproduce the correct insulating behavior. The Ce 4f1 states were then analyzed in more detail with the help of ab initio wave-function-based computations. Unusually large effective crystal-field splittings of up to 320 meV are predicted, which puts KCeO2 in the strong field coupling regime. Our results reveal a subtle interplay between ligand-cage electrostatics and the trigonal field generated by the extended crystalline surroundings, relevant in the context of recent studies on tuning the nature of the ground-state wave function in 4f triangular-lattice and pyrochlore compounds. It also makes KCeO2 an interesting model system in relation to the effect of large crystal-field splittings on the anisotropy of intersite exchange in spin-orbit coupled quantum magnets.
The electronic and magnetic properties of the delafossite CuFeO2 are investigated by means of electronic structure calculations. They are performed using density functional theory in the generalized gradient approximation as well as the new full-potential augmented spherical wave method. The calculations reveal three different spin states at the iron sites. Taking into account the correct crystal structure, we find long-range antiferromagnetic ordering in agreement with experiment. Contrasting previous work, our calculations show that non-local exchange interactions lead to a semiconducting gr…
We report quantum oscillation data on the metallic triangular antiferromagnet PdCrO$_2$. We find that, to very high accuracy, the observed frequencies of PdCrO$_2$ can be reproduced by reconstruction of the (nonmagnetic) PdCoO$_2$ Fermi surface into a reduced zone. The reduced zone corresponds to a magnetic cell containing six chromium sites, giving a $\sqrt{3} \times \sqrt{3}$ in-plane reconstruction, and $\times 2$ interplane reconstruction. The interplane ordering represents a reduction in lattice symmetry, possibly to monoclinic, and an associated lattice distortion is expected. In additio…
We predict that the anti-ferromagnetic (AFM) magnetic structure of delafossite PdCrO$_2$ has a staggered chirality with the double-layer periodicity along the $z$-axis with intriguing magnetic anisotropy. We study the electronic and magnetic structures of PdCrO$_2$ by carrying out density functional theory (DFT) calculation. The calculated ground state turns out to exhibit a 120$^\circ$ AFM ordering with staggered chirality. The result is consistent with the previous neutron experiments, but our calculations determine and provide more detailed information on the high symmetric easy-plane and l…
While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of 4f magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic Yb$^{3+}$ triangular lattice planes with pseudospin $s=1/2$ at low temperatures, are an ideal platform to study these new phenomena. Competing frustrated interactions …
We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with Néel temperature TN ~ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-flop type) transition below TN in moderate magnetic fields. The GGA+U calculations show the importance of the orbital degrees of freedom, which maintain a hierarchy of exchange interaction in the system.…
In this work, we study the doping effects on the magnetic states of CuCrO2 based on the classical frustrated spin model [Lin et al., Phys. Rev. B 89, 220405(R) (2014)]. Several experimental observations can be well reproduced by the Monte Carlo simulations of the modified spin models. Our work suggests that the disorder induced by V/Al doping cooperated with the frustration in the system may contribute to the emergence of the spin glass state. Furthermore, the hole-doping by Mg2+ substituting Cr3+ enhances the quantum fluctuations and bond disorder which modulate the biquadratic exchanges, and…
Layered rare-earth delafossites $ARX_2$ with $R$ = Yb(III) or Ce(III) have received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest measured temperatures, such as NaYbO$_2$, NaYbS$_2$, and NaYbSe$_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS$_2$ exhibits stripe-$yz$ magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigat…
We report single crystal growth of the delafossite oxide PtCoO$_2$, and basic transport measurements on single crystals etched to well-defined geometries using focused ion beam techniques. The room temperature resistivity is 2.1 $μΩ$ cm, and the Hall coefficient is consistent with the existence of one free electron per Pt. Although the residual resistivity ratio is greater than fifty, a slight upturn of resistivity is seen below 15 K. The angle dependence of the in-plane magnetoresistance is also reported.
Recently, several putative quantum spin liquid (QSL) states were discovered in ${\tilde S} = 1/2$ rare-earth based triangular-lattice antiferromagnets (TLAF) with the delafossite structure. A way to clarify the origin of the QSL state in these systems is to identify ways to tune them from the putative QSL state towards long-range magnetic order. Here, we introduce the Ce-based TLAF KCeS$_2$ and show via low-temperature specific heat and $μ$SR investigations that it yields magnetic order below $T_{\mathrm N} = 0.38$ K despite the same delafossite structure. We identify a well separated ${\tilde…
Finite Spinon Density-of-States in Triangular-Lattice Delafossite TlYbSe$_2$
Purdue University（普渡大学）；Indian Institute of Science（印度科学学院）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；National High Magnetic Field Laboratory（国家高磁场实验室）；Imperial College London（伦敦帝国理工学院）
We investigated the spin dynamics by electron spin resonance (ESR) of the Yb-based, effective spin-1/2 delafossites NaYbO$_{2}$, AgYbO$_{2}$, LiYbS$_{2}$, NaYbS$_{2}$, and NaYbSe$_{2}$ which all show an absence of magnetic order down to lowest reachable temperatures and thus are prime candidates to host a quantum spin-liquid ground state in the vicinity of long range magnetic order. Clearly resolved ESR spectra allow to obtain well-defined $g$ values which are determined by the crystal field of the distorted octahedral surrounding of the Yb-ions in trigonal symmetry. This local crystal field i…
Rare-earth delafossites were recently proposed as promising candidates for the realization of an effective $S$=1/2 quantum spin liquid (QSL) on the triangular lattice. In contrast to the most actively studied triangular-lattice antiferromagnet YbMgGaO$_4$, which is known for considerable structural disorder due to site intermixing, NaYbS$_2$ delafossite realizes structurally ideal triangular layers. We present detailed $μ$SR studies on this regular (undistorted) triangular Yb sublattice based system with effective spin $J_{\mathrm{eff}}=1/2$ in the temperature range 0.05 - 40 K. Zero-field (ZF…
The delafossite structure of NaYbS2 contains a planar spin-1/2 triangular lattice of Yb3+ ions and features a possible realisation of a quantum spin-liquid state. We investigated the Yb3+ spin dynamics by Electron Spin Resonance (ESR) in single-crystalline samples of NaYbS2. Very clear spectra with a well-resolved and large anisotropy could be observed down to the lowest accessible temperature of 2.7 K. In contrast to the ESR properties of other known spin-liquid candidate systems, the resonance seen in NaYbS2 is accessible at low fields (< 1T) and is narrow enough for accurate characterisatio…
Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields - crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fer…
The transport properties of a magnetic two dimensional electron gas consisting of a modulation doped n type HgMnTe/HgCdTe quantum well, QW, have been investigated. By analyzing the Shubnikov-de Haas oscillations and the node positions of their beating patterns, we have been able to separate the gate voltage dependent Rashba spin-orbit splitting from the temperature dependent giant Zeeman splitting. It has been experimentally demonstrated that the Rashba spin-orbit splitting is larger than or comparable to the $sp-d$ exchange interaction induced giant Zeeman splitting in this magnetic 2DEG even…
Detailed far-infrared spectra of the optical phonons are reported for antiferromagnetic MnO. Eigenfrequencies, phonon damping and effective plasma frequencies are studied as a function of temperature. Special attention is paid to the phonon splitting at the antiferromagnetic phase transition. The results are compared to recent experimental and theoretical studies of the spin-phonon coupling in frustrated magnets, which are explained in terms of a spin-driven Jahn-Teller effect, and to ab initio and model calculations, which predict phonon splitting induced by magnetic order.
Near itinerancy and slow singlet formation in the triangular lattice NaRuO2
University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Leibniz IFW Dresden（莱布尼茨德累斯顿研究所）；Argonne National Laboratory（阿贡国家实验室）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究中心）
The splitting of the Kondo resonance in the density of states of an Anderson impurity in finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for nonzero magnetic field and Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulae are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large-N appro…
Using the numerical renormalization group method, we study the splitting of the Kondo resonance by a magnetic field applied in different directions in the Kondo model for anisotropic magnetic impurities. Several types of magnetic anisotropy are considered: the XXZ exchange coupling anisotropy J_perp J_z, the longitudinal magnetic anisotropy DS_z^2, and the transverse magnetic anisotropy E(S_x^2-S_y^2). In the spin-1/2 model with the XXZ exchange coupling anisotropy we find very small direction dependence in the magnitude of the splitting. In the spin-3/2 model with the easy-plane (D>0) anisotr…
We study the magneto-optical (MO) response of polar semiconductor BiTeI with giant bulk Rashba spin splitting at various carrier densities. Despite being non-magnetic, the material is found to yield a huge MO activity in the infrared region under moderate magnetic fields (<3 T). By comparison with first-principles calculations, we show that such an enhanced MO response is mainly due to the intraband transitions between the Rashba-split bulk conduction bands in BiTeI, which give rise to distinct novel features and systematic doping dependence of the MO spectra. We further predict an even more p…
Quantum tunneling of the magnetization is a major obstacle to the use of single-molecule magnets (SMMs) as basic constituents of next-generation storage devices. In this context, phonons are often only considered (perturbatively) as disturbances that promote the spin system to traverse the anisotropy barrier. Here, we demonstrate the ability of phonons to induce a tunnel splitting of the ground doublet which then reduces the required bistability due to Landau-Zener tunneling of the magnetization. Harmful are those phonons that modify the spin Hamiltonian so that its rotational symmetry about t…
A primary goal at the interface of theoretical and experimental quantum magnetism is the investigation of exotic spin states, most notably quantum spin liquids (QSLs). Magnetic rare-earth ions go beyond the straightforward paradigm of geometrical frustration in Heisenberg antiferromagnets by introducing competing energy scales, and in particular their strong spin-orbit coupling creates multiple split crystal electric-field (CEF) levels, leading to anisotropic effective spin models with intrinsic frustration. While rare-earth delafossites have a triangular-lattice geometry, and thus have gained…
We apply the first-principles density functional theory + dynamical mean field theory framework to evaluate the crystal field splitting on rare earth sites in hard magnetic intermetallics. An atomic (Hubbard-I) approximation is employed for local correlations on the rare earth 4$f$ shell and self-consistency in the charge density is implemented. We reduce the density functional theory self-interaction contribution to the crystal field splitting by properly averaging the 4$f$ charge density before recalculating the one-electron Kohn-Sham potential. Our approach is shown to reproduce the experim…
By using the full density matrix approach to spectral functions within the numerical renormalization group method, we present a detailed study of the magnetic field induced splittings in the spin-resolved and the total spectral densities of a Kondo correlated quantum dot described by the single level Anderson impurity model. The universal scaling of the splittings with magnetic field is examined by varying the Kondo scale either by a change of local level position at a fixed tunnel coupling or by a change of the tunnel coupling at a fixed level position. We find that the Kondo-peak splitting $…
Excitonic magnetism involving superpositions of singlet and triplet states is expected to arise for two holes in strongly correlated and spin-orbit coupled $t_{2g}$ orbitals. However, uncontested material examples for its realization are rare. Applying the Variational Cluster Approach to the square lattice, we find conventional spin antiferromagnetism combined with orbital order at weak and excitonic order at strong spin-orbit coupling. We address the specific example of Ca$_2$RuO$_4$ using ab-initio modeling and conclude it to realize excitonic magnetism despite its pronounced orbital polariz…
By measuring the angles at which the Landau levels overlap in tilted magnetic fields (the coincidence method), we determine the splitting of the conduction-band valleys in high-mobility two-dimensional (2D) electrons confined to AlAs quantum wells. The data reveal that, while the valleys are nearly degenerate in the absence of magnetic field, they split as a function of perpendicular magnetic field. The splitting appears to depend primarily on the magnitude of the perpendicular component of the magnetic field, suggesting electron-electron interaction as its origin.
We report novel manifestation of the valley splitting for the two valley electron system in (100) Si-inversion layers at low carrier density. We found that valley splitting causes almost 100% modulation of the Shubnikov de Haas oscillations in very low magnetic fields, almost on the bound of the quantum interference peak of the negative magnetoresistance. From the interference pattern of oscillations we determined the valley splitting in the B=0 limit which appears to vary only within a factor of 1.3 over the density range (3-7)x10^{11}/cm^2. We found also that level broadenings in both electr…
We apply the diagram-technique formalism beyond the Hartree-Fock approximation to a two-dimensional nearly ideal electron gas in a weak perpendicular magnetic field. The case of an almost completely filled upper Landau level (filling factor $ν_0 \lesssim 1$) with a quantum number $N_0 \gg 1$ is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where $N^{1/2}_0(1-ν_0) \ll 1$, these interactions lead to a splitting of the Landau levels. In the second regime, where $N^{1/2}_0(1-ν_0) \gg 1$, apart of the splitting, a renormalization of th…
Rare earth triangular lattice materials have been proposed as a good platform for the investigation of frustrated magnetic ground states. KErSe$_2$ with the delafossite structure, contains perfect two-dimensional Er$^{3+}$ triangular layers separated by potassium ions, realizing this ideal configuration and inviting study. Here we investigate the magnetism of KErSe$_2$ at miliKelvin temperatures by heat capacity and neutron powder diffraction. Heat capacity results reveal a magnetic transition at 0.2 K in zero applied field. This long-range order is suppressed by an applied magnetic field of 0…
A simple consistency check is proposed for the Fermi liquid description of the low-temperature properties of quasi-two-dimensional metals. In a quasi-two-dimensional Fermi liquid the Zeeman splitting of magnetic oscillations can be used to determine g^*, the gyro-magnetic ratio which is renormalised by many-body effects. It is shown that g^*/g is equal to Wilson's ratio R, the dimensionless ratio of the low-temperature spin susceptibility to the specific heat coefficient. Measured values of g^*/g and R are compared for the layered perovskite Sr2RuO4 and for a range of organic metals based on t…
In a recent work Zhang and coworkers (PRB 82, 075111 (2010)) studied the Zeeman splitting of the Kondo resonance for the single impurity Anderson model in a finite magnetic field $B$ with the numerical renormalization group (NRG) method. There, it was found that with increasing magnetic field $B$ the position of the Kondo resonance in the total spectral function \textit{does not} approach its position in the spin resolved spectral function. Additionally, the position of the Kondo maximum exceeded the Zeeman energy for $B/ T_K\gtrsim 5-10$, where $T_K$ is the low energy Kondo scale of the model…
We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.
