Here, we report the synthesis and magnetic properties of a Yb-based triangular-lattice compound LiYbS$_2$. At low temperatures, it features an effective spin-$\frac{1}{2}$ state due to the combined effect of crystal electric field and spin orbit coupling. Magnetic susceptibility measurements and $^7$Li nuclear magnetic resonance experiments reveal the absence of magnetic long range ordering down to 2~K, which suggests a possible quantum spin liquid ground state. A dominant antiferromagnetic nearest neighbour exchange interaction $J/k_{\rm B}\simeq$ 5.3~K could be extracted form the magnetic susceptibility. The NMR linewidth analysis yields the coupling constant between the Li nuclei and Yb$^{3+}$ ions which was found to be purely dipolar in nature.
Three-dimensionally (3D) frustrated magnets generally exist in the magnetic diamond and pyrochlore lattices, in which quantum fluctuations suppress magnetic orders and generate highly entangled ground states (GS). LiYbSe2 in a previously unreported pyrochlore lattice was discovered from LiCl flux growth. Distinct from the quantum spin liquid (QSL) candidate NaYbSe2 hosting a perfect triangular lattice of Yb3+, LiYbSe2 crystallizes in the cubic pyrochlore structure with space group Fd-3m (No. 227). The Yb3+ ions in LiYbSe2 are arranged on a network of corner-sharing tetrahedra, which is particu…
Insulator to Metal Transition, Spin-Phonon Coupling, and Potential Magnetic Transition Observed in Quantum Spin Liquid Candidate LiYbSe$_2$ under High Pressure
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…
A triangular lattice selenide series of rare earth (RE), CsRESe2, were synthesized as large single crystals using a flux growth method. This series stabilized in either trigonal (R-3m) or hexagonal (P63/mmc) crystal systems. Physical properties of CsRESe2 were explored by magnetic susceptibility and heat capacity measurements down to 0.4 K. Antiferromagnetic interaction was observed in all magnetic compounds, while no long-range magnetic order was found, indicating the frustrated magnetism. CsDySe2 presents spin freezing at 0.7 K, revealing a spin-glass state. CsCeSe2 and CsYbSe2 present broad…
Ab initio spin Hamiltonians and magnetism of Ce and Yb triangular-lattice compounds
École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Collège de France, Université PSL（法兰西公学院，巴黎文理研究大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
We report the synthesis of the entire $Ln$AuAl$_4$Ge$_2$ ($Ln$ = Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) series and focus on the magnetic properties of GdAuAl$_4$Ge$_2$ and TbAuAl$_4$Ge$_2$. Temperature and magnetic field dependent magnetization, heat capacity, and electrical resistivity measurements reveal that both compounds exhibit several magnetically ordered states at low temperatures, with evidence for magnetic fluctuations extending into the paramagnetic temperature region. For magnetic fields applied in the $ab$-plane there are several ordered state regions that are associated with …
The weakly interacting S=1/2 dimers system Sr3Cr2O8 has been investigated by powder neutron diffraction and inelastic neutron scattering. Our data reveal a structural phase transition below room temperature corresponding to an antiferro-orbital ordering with nearly 90 degrees arrangement of the occupied 3z^2-r^2 d-orbital. This configuration leads to a drastic reduction of the inter-dimer exchange energies with respect to the high temperature orbital-disorder state, as shown by a spin-dimer analysis of the super-superexchange interactions performed using the Extended Huckel Tight Binding metho…
Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range magnetic order are found down to 0.3~K, evidencing a highly frustrated spin-liquid-like ground state in zero field. Above 2\,T, signatures of magnetic order are observed in thermodynamic measurements, suggesting the possibility of a field-induced quantum phase transition. The $^{23}$Na NMR relaxation rates reveal the absence of magnetic order and persistent fluctu…
Using magnetic torque measurement on a NaNiO2 single crystal, we have established the magnetic phase diagram of this triangular compound. It presents 5 different phases depending on the temperature (4 K - 300 K) and magnetic field (0 - 22 T) revealing several spin reorientations coupled to different magnetic anisotropies.
We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO$_4$ to be spin glass, including no long-range magnetic order, prominent broad excitation continua, and absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature a.c. susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion to hold also for its sister compound YbMgGaO$_4$, which is confirmed by the observation of spin freezing at low temperatures. We conside…
The origin of the lowest-temperature anomaly reported several years ago using a polycrystalline sample of the spin ice compound Dy2Ti2O7 had remained unresolved. Here we finally clarify its origin by susceptibility measurements down to 65 mK using single crystals under accurate control of the magnetic fields in two independent directions. We demonstrate that the transition is induced under a subtle field combination that precisely cancel the nearest-neighbor spin interactions acting on the spins on the triangular lattice within the pyrochlore structure. Contrary to the other two fieldinduced t…
We report on the emergence of antiferromagnetic spin chains from two-dimensionally aligned spins on the anisotropic triangular lattice (ATL) in the insulating calcium rhenium oxychloride Ca3ReO5Cl2. The compound contains Re6+ ions each with one unpaired electron in the dxy orbital, which are arranged to form a spin-1/2 ATL with J'/J ~ 0.32 and J = 41 K, where J and J' are magnetic interactions in and between the chains, respectively. In spite of the apparent two dimensionality, we observe clear evidence of a gapless spin liquid that is characteristic of the spin-1/2 Heisenberg chain. This one-…
Birnessite compounds are stable across a wide range of compositions that produces a remarkable diversity in their physical, electrochemical and functional properties. These are hydrated analogues of the magnetically frustrated, mixed-valent manganese oxide structures, with general formula, NaxMnO2. Here we demonstrate that the direct hydration of layered rock-salt type a-NaMnO2, with the geometrically frustrated triangular lattice topology, yields the birnessite type oxide, Na0.36MnO2 0.2H2O, transforming its magnetic properties. This compound has a much-expanded interlayer spacing compared to…
A 59Co NMR study of CoO2, the x=0 end member of AxCoO2 (A = Na, Li...) cobaltates, reveals a metallic ground state, though with clear signs of strong electron correlations: low-energy spin fluctuations develop at wave vectors q different from 0 and a crossover to a Fermi-liquid regime occurs below a characteristic temperature T*~7 K. Despite some uncertainty over the exact cobalt oxidation state n this material, the results show that electronic correlations are revealed as x is reduced below 0.3. The data are consistent with NaxCoO2 being close to the Mott transition in the x -> 0 limit.
We present single crystal inelastic neutron scattering measurements of the S=1 dimerized quasi-two-dimensional antiferromagnet Ba$_3$Mn$_2$O$_8$. The singlet-triplet dispersion reveals nearest-neighbor and next-nearest-neighbor ferromagnetic interactions between adjacent bilayers that compete against each other. Although the inter-bilayer exchange is comparable to the intra-bilayer exchange, this additional frustration reduces the effective coupling along the c-axis and leads to a quasi-two dimensional behavior. In addition, the obtained exchange values are able to reproduce the four critical …
Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates, such as $κ$-(ET)$_2$Cu$_2$(CN)$_3$ ($κ$-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring-exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this work, we discuss the properties of the recently synthesized $κ$-(BETS)$_2$Mn[N(CN)$_2$]$_3$ ($κ$-Mn). Based on analysis of specific heat, mag…
We report the first detailed investigation of K$_2$MnS$_2$ and K$_2$MnSe$_2$ from the K$_2$MnS$_2$ structure type and their magnetic solid solution K$_2$MnS$_{2-x}$Se$_x$ and find that compounds of this structure type consist of strongly-coupled pseudo-one-dimensional antiferromagnetic chains that collectively represent a frustrated two-dimensional triangular antiferromagnet. Bulk samples of K$_2$MnS$_{2-x}$Se$_x$ with $0 \leq x \leq 2$ are characterized using X-ray diffraction, neutron diffraction, magnetization and heat capacity measurements. An incommensurate cycloid magnetic structure with…
We report a study of the triangular lattice Heisenberg magnet NiGa2S4 by the positive muon spin rotation and relaxation technique. We unravel three temperature regimes: (i) below T_c = 9.2(2) K a spontaneous static magnetic field at the muon site is observed and the spin dynamics is appreciable: the time scale of the modes we probe is ~ 7 ns; (ii) an unconventional stretched exponential relaxation function is found for T_c < T < T_{cross} where T_{cross} = 12.6 K, which is a signature of a multichannel relaxation for this temperature range; (iii) above T_{cross}, the relaxation is exponential …
We present data on the magnetic properties of two classes of layered spin S=1/2 antiferromagnetic quasi-triangular lattice materials: $Cu_{2(1-x)}Zn_{2x}(OH)_3NO_3$ ($0 < x < 0.65$) and its long chain organic derivatives $Cu_{2(1-x)}Zn_{2x}(OH)_3(C_7H_{15}COO)\cdot mH_2O$ ($0 < x < 0.29$), where non-magnetic Zn substitutes Cu isostructurally. It is found that the long-chain compounds, even in a clean system in the absence of dilution, $x\!=\!0$, show spin-glass behavior, as evidenced by DC and AC susceptibility, and by time dependent magnetization measurements. A striking feature is the observ…
We report the magnetic properties of compounds in the KBaRE(BO3)2 family (RE= Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), materials with a planar triangular lattice composed of rare earth ions. The samples were analyzed by x-ray diffraction and crystallize in the space group R-3m. Physical property measurements indicate the compounds display predominantly antiferromagnetic interactions between spins without any signs of magnetic ordering above 1.8 K. The ideal 2D rare earth triangular layers in this structure type make it a potential model system for investigating magnetic frustration in rare-earth-b…
The triangular lattice compound TlYbS$_2$ was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures less than 2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable lon…
We present our theoretical results on the ground states in layered triangular-lattice compounds ANiO2 (A=Na, Li, Ag). To describe the interplay between charge, spin, orbital, and lattice degrees of freedom in these materials, we study a doubly-degenerate Hubbard model with electron-phonon couplings by the Hartree-Fock approximation combined with the adiabatic approximation. In a weakly-correlated region, we find a metallic state accompanied by \sqroot3x\sqroot3 charge ordering. On the other hand, we obtain an insulating phase with spin-ferro and orbital-ferro ordering in a wide range from inte…
We study spin fluctuation (SF) mediated superconductivity (SC) in a half-filled square lattice Hubbard model with the transfer matrices -t between nearest neighbor sites and -t' between a half of next nearest neighbor sites neighboring along only one of the <1,1> directions, considering application of this model to organic kappa-(BEDT-TTF)2X compounds. Varying the t'/t value from 0 to 1, one can interpolate between a square and an equilateral triangular lattice, the latter giving frustration to antiferromagnetically (AF) coupled spin systems. Within the fluctuation exchange (FLEX) approximatio…
Heat-capacity (C) and ac susceptibility measurements have been performed on the spin-chain compounds, Sr3ZnRhO6 and Ca3NiMnO6, to establish their magnetic behavior and to explore whether there are magnetic frustration effects due to antiferromagnetic coupling of the chains arranged in a triangular fashion. While the paramagnetic Curie temperatures have been known to be large with a negative sign, as though antiferromagnetic interaction is very strong, the results establish that (i) the former apparently undergoes inhomogeneous magnetic ordering only around 15 K, however without spin-glass anom…
We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with spinon Fermi surface as…
We report the synthesis, crystal structure, and magnetic properties of two new quantum antiferromagnets A3ReO5Cl2 (A = Sr and Ba). The crystal structure is isostructural with the mineral pinalite Pb3WO5Cl2, in which the Re6+ ion is square-pyramidally coordinated by five oxide atoms, and forms an anisotropic triangular lattice (ATL) made of S = 1/2 spins. The magnetic interactions J and J' in the ATL are estimated from magnetic susceptibilities to be 19.5 (44.9) and 9.2 (19.3) K, respectively, with J'/J = 0.47 (0.43) for A = Ba (Sr). For each compound, heat capacity at low temperatures shows a …
The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet KCeO$_2$ are investigated. Below $T_N =$ 300 mK, KCeO$_2$ develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent Ce$^{3+}$ ions in the $D_{3d}$ local environment of this compound exhibit large splittings among the lowest three $4f^1$ Kramers doublets defining for the free ion the $J = 5/2$ sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions in M. S. Eldeeb …
CuCrO2 is a manifestation of a two-dimensional triangular antiferromagnet which exhibits an incommensurate noncollinear magnetic structure similar to a classical 120 degree ordering. Using the inelastic neutron scattering technique, direct evidence of a magnon-phonon coupling in CuCrO2 is revealed via the mixed magnon-phonon character of the excitation mode at 12.5 meV as well as a minimum at the zone boundary. A simple model Hamiltonian that incorporates an exchange striction type magnon-phonon coupling reproduces the observed features accurately. Also, continuum excitations originating from …
The interplay of non-local Coulomb repulsion and Hund's coupling in the d-orbital manifold in frustrated triangular lattices is analyzed by a mutliband extended Hubbard model. We find a rich phase diagram with several competing phases, including a robust pinball liquid phase, which is an unconventional metal characterized by threefold charge order, bad metallic behavior and the emergence of high spin local moments. Our results naturally explain the anomalous charge-ordered metallic state observed in the triangular layered compound AgNiO2. The potential relevance to other triangular transition …
We consider the possible charge and orbital ordering in a Hollandite compound Bi_xV_8O_{16}, which is a new one-dimensional triangular-lattice t_{2g}-orbital system. Using the strong-coupling perturbation theory, we derive the effective spin-orbit Hamiltonian in the approximation neglecting the small off-diagonal hopping parameters or orbital fluctuation, whereby we obtain the spin Hamiltonians in the partial space of each orbital-ordering pattern. We then apply an exact-diagonalization technique on small clusters to these spin Hamiltonians and calculate the ground-state phase diagram. We find…
Motivated by recent experimental progress on triangular lattice heavy-fermion compounds, we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo-Heisenberg model on the triangular lattice. In the heavy Fermi liquid state, the introduced Heisenberg antiferromagnetic interaction ($J_H$) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping, respectively. Driven b…
The trigonal compound EuSn2As2 was recently discovered to host Dirac surface states within the bulk band gap and orders antiferromagnetically below the Neel temperature TN = 24 K. Here the magnetic ground state of single-crystal EuSn2As2 and the evolution of its properties versus temperature T and applied magnetic field H are reported. Included are zero-field single-crystal neutron-diffraction measurements versus T, magnetization M(H,T), magnetic susceptibility chi(H,T) = M(T)/H, heat capacity Cp(H,T), and electrical resistivity rho(H,T) measurements. The neutron-diffraction and chi(T) measure…
Correlation between dielectric and magnetic properties was investigated on the triangular lattice antiferromagnets ACrO2 (A= Cu, Ag, Li, or Na) showing 120-degree spiral spin structure with easy-axis anisotropy. For the A= Cu and Ag compounds with delafossite structure, ferroelectric polarization emerges upon the spiral spin order, implying the strong coupling between the ferroelectricity and spiral spin structure. On the other hand, for the A = Li and Na compounds with ordered rock salt structure, no polarization but only clear anomalies in dielectric constant can be observed upon the spiral …
Canted ferromagnetic order in a distorted triangular-lattice magnet Na$_2$SrCo(VO$_4$)$_2$
School of Physics, Beihang University（北京航空航天大学物理学院）；Department of Nuclear Physics, China Institute of Atomic Energy（中国原子能科学研究院核物理研究所）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Spallation Neutron Source Science Center（散裂中子源科学中心）；Songshan Lake Materials Laboratory（松山湖材料实验室）；State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室）
Two$-$dimensional (2D) triangular lattices antiferromagnets (2D$-$TLA) often manifest intriguing physical and technological properties, due to the strong interplay between lattice geometry and electronic properties. The recently synthesized 2$-$dimensional transition metal dichalcogenide LiCrTe$_2$, being a 2D$-$TLA, enriched the range of materials which can present such properties. In this work, muon spin rotation ($μ^+$SR) and neutron powder diffraction (NPD) have been utilized to reveal the true magnetic nature and ground state of LiCrTe$_2$. From high$-$resolution NPD the magnetic spin ord…
The magnetic properties of the high temperature alpha form of the CaCr2O4 compound have been investigated for the first time by magnetic susceptibility, specific heat and powder neutron diffraction. The system undergoes a unique magnetic phase transition at 43K to a long range order incommensurate helical phase with magnetic propagation vector k=(0,0.3317(2),0). The magnetic model proposed from neutron diffraction data shows that the plane of rotation of the spins is perpendicular to the wave-vector, and that the magnetic modulation is consistent with two modes belonging to distinct irreducibl…
Spin-liquid behavior was recently suggested experimentally in the moderately one-dimensional organic compound $κ$-H$_3$(Cat-EDT-TTF)$_2$. This compound can be modeled by the one-band Hubbard model on the anisotropic triangular lattice with $t^\prime/t \simeq 1.5$, where $t'$ is the minority hopping. It thus becomes important to extend previous studies, that were performed in the range $0 \leq t'/t \leq 1.2$, to find out whether there is a regime where Mott insulating behavior can be found without long-range magnetic order. To this end, we study the above model in the range $1.2 \leq t'/t \leq …
Based on density functional theory band structure calculations, quantum Monte-Carlo simulations, and high-field magnetization measurements, we address the microscopic magnetic model of BaAg2Cu[VO4]2 that was recently proposed as a spin-1/2 anisotropic triangular lattice system. We show that the actual physics of this compound is determined by a peculiar superposition of ferromagnetic and antiferromagnetic uniform spin chains with nearest-neighbor exchange couplings of Ja(1) ~ -19 K and Ja(2) ~ 9.5 K, respectively. The two chains featuring different types of the magnetic exchange perfectly mimi…
The magnetic behavior of the Ca3Co2O6 spin chain compound is characterized by a large Ising-like character of its ferromagnetic chains, set on triangular lattice, that are antiferromagnetically coupled. At low temperature, T < 7K, the 3D antiferromagnetic state evolves towards a spin frozen state. In this temperature range, magnetic field driven magnetization of single crystals (H//chains) exhibits stepped variations. The occurrence of these steps at regular intervals of the applied magnetic field, Hstep=1.2T, is reminiscent of the quantum tunneling of the magnetization (QTM) of molecular base…
Crystal structure, thermodynamic properties, and adiabatic demagnetization refrigeration (ADR) effect in the spin-7/2 triangular antiferromagnet KBaGd(BO3)2 are reported. With the average nearest-neighbor exchange coupling of 44 mK, this compound shows magnetic order below $T_N = 263$\,mK in zero field. The ADR tests reach the temperature of $T_{min} = 122$ mK, more than twice lower than $T_N$, along with the entropy storage capacity of 192 mJK$^{-1}$cm$^{-3}$ and the hold time of more than 8 hours in the PPMS setup, both significantly improved compared to the spin-1/2 Yb$^{3+}$ analog. We arg…
We report x-ray diffraction, magnetic susceptibility, heat capacity, $^{1}$H nuclear magnetic resonance (NMR), and muon spin relaxation ($μ$SR) measurements, as well as density-functional band-structure calculations for the frustrated $S=3/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) $α$-HCrO$_{2}$ (trigonal, space group: $R\bar{3}m$). This compound undergoes a clear magnetic transition at $T_{\rm N} \simeq 22.5$~K, as seen from the drop in the muon paramagnetic fraction and concurrent anomalies in the magnetic susceptibility and specific heat. Local probes (NMR and $μ$SR) reveal a…
Ca3Co2O6 is a system exhibiting a series of fascinating properties, including magnetization plateaus and remarkably slow dynamics at low-T. These properties are intimately related to the geometrical frustration, which results from a particular combination of features: (i) the chains are arranged on a triangular lattice; (ii) there is a large uniaxial anisotropy; (iii) the intrachain and interchain couplings are ferromagnetic and antiferromagnetic, respectively. The uniaxial anisotropy is thus an issue of crucial importance for the analysis of the physical properties of Ca3Co2O6. However, it tu…
Emergence of partially disordered antiferromagnetism and isothermal magnetization plateau due to geometrical frustration in a metallic compound, Er2RhSi3
We investigate the thermodynamic properties of the ytterbium-based triangular lattice compound Ba3Yb(BO3)3. The results demonstrate the absence of any long-range ordering down to 56 mK. Analysis of the magnetization, susceptibility and specific heat measurements suggests that Ba3Yb(BO3)3 may realize a S = 1/2 quantum dipole lattice, in which the dominant interaction is the long range dipole-dipole coupling on the geometrically frustrated triangular lattice, and exchange interactions are subdominant or negligible.
A quasi one-dimensional compound, Ca3CuRuO6, has been synthesized by solid-state reaction method and studied using magnetization (M) and heat capacity (C) measurements. This compound undergoes magnetic ordering (T_o) around 40 K, as evidenced by the dc magnetic susceptibility (chi) behavior. However, the magnitude of the paramagnetic Curie temperature (theta_p) obtained from the high temperature linear region is large (-277 K, with the negative sign indicating antiferromagnetic interaction). The reduction of T_o, compared to theta_p, is attributed to geometrical frustration effect arising from…
