Perfect Triangular Lattice Research Articles

Superconductivity in a Layered Cobalt Oxychalcogenide Na2CoSe2O with a Triangular Lattice.

Unconventional superconductivity in bulk materials under ambient pressure is extremely rare among the 3d transition metal compounds outside the layered cuprates and iron-based family. It is predominantly linked to highly anisotropic electronic properties and quasi-two-dimensional (2D) Fermi surfaces. To date, the only known example of a Co-based exotic superconductor is the hydrated layered cobaltate, NaxCoO2·yH2O, and its superconductivity is realized in the vicinity of a spin-1/2 Mott state. However, the nature of the superconductivity in these materials is still a subject of intense debate, and therefore, finding a new class of superconductors will help unravel the mysteries of their unconventional superconductivity. Here, we report the discovery of superconductivity at ∼6.3 K in our newly synthesized layered compound Na2CoSe2O, in which the edge-shared CoSe6 octahedra form [CoSe2] layers with a perfect triangular lattice of Co ions. It is the first 3d transition metal oxychalcogenide superconductor with distinct structural and chemical characteristics. Despite its relatively low TC, this material exhibits very high superconducting upper critical fields, μ0HC2(0), which far exceeds the Pauli paramagnetic limit by a factor of 3-4. First-principles calculations show that Na2CoSe2O is a rare example of a negative charge transfer superconductor. This cobalt oxychalcogenide with a geometrical frustration among Co spins shows great potential as a highly appealing candidate for the realization of unconventional and/or high-TC superconductivity beyond the well-established Cu- and Fe-based superconductor families and opens a new field in the physics and chemistry of low-dimensional superconductors.

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly fluctuating and highly entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultralow-temperature specific heat, muon spin relaxation (μSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, μSR, and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

Synthesis, structure and magnetism of RTa7O19 (R = Pr, Sm, Eu, Gd, Dy, Ho) with perfect triangular lattice

We present the synthesis, structure and magnetic properties of a hitherto unstudied family of rare-earth based RTa7O19 (R = Pr, Sm, Eu, Gd, Dy, Ho) compounds with space groupP6¯2c. The structural analysis reveals that magnetic R ions form layers of ideal two-dimensional triangular lattices in the ab-plane separated by several nonmagnetic polyhedra layers along the c-axis. The magnetic susceptibility and magnetization measurements indicate the absence of long-range magnetic order and field-induced magnetic transitions in all the studied compounds. The details about the magnetism strongly depend on the type of R ions. The presence of geometrical frustration is discussed. Thus, RTa7O19 provides a new platform for exploring the frustrated magnetism.

Magnetic field effects on the quantum spin liquid behaviors of NaYbS2

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between and ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

Magnetic properties of the triangular-lattice antiferromagnets Ba3RB9O18 (R=Yb, Er)

Frustration, spin correlations and interplay between competing degrees of freedom are some of the key ingredients that underlie exotic states with fractional excitations in quantum materials. Rare-earth based two dimensional magnetic lattice wherein crystal electric field, spin-orbit coupling, anisotropy and electron correlation between rare-earth moments offer a new paradigm in this context. Herein, we present crystal structure, magnetic susceptibility and specific heat accompanied by crystal electric field calculations on the polycrystalline sample of Ba3RB9O18 (R = Yb, Er) in which R3+ ions form a perfect triangular lattice without anti-site disorder. The localized R3+ spins show neither long-range order nor spin-glass state down to 1.9 K in Ba3RB9O18. Magnetization data reveal a pseudospin Jeff = 1/2 ( Yb3+) in the Kramers doublet state and a weak antiferromagnetic interaction between Jeff = 1/2 moments in the Yb variant. On the other hand, the effective moment {\mu}eff = 8.8 {\mu}B was obtained from the Curie-Weiss fit of the low-temperature susceptibility data of Er variant suggests the admixture of higher crystal electric field states with the ground state. The Curie-Weiss fit of low-temperature susceptibility data for Er system unveils the presence of a relatively strong antiferromagnetic interaction between Er3+ moments compared to its Yb3+ analog. Ba3ErB9O18 does not show long-range magnetic ordering down to 500 mK. Furthermore, our crystal electric field calculations based on magnetization data of Ba3ErB9O18 suggest the presence of a small gap between the ground and first excited Kramers doublets. The broad maximum around 4 K in magnetic specific heat in zero-field is attributed to the thermal population of the first CEF excited state in Ba3ErB9O18, which is consistent with our CEF calculations.

LiYbSe2: Frustrated Magnetism in the Pyrochlore Lattice.

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. 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 Fd3m (No. 227). The Yb3+ ions in LiYbSe2 are arranged on a network of corner-sharing tetrahedra, which is particularly susceptible to geometrical frustration. According to our temperature-dependent magnetic susceptibility measurements, the dominant antiferromagnetic interaction in LiYbSe2 is expected to appear around 8 K. However, no long-range magnetic order is detected in thermomagnetic measurements above 70 mK. Specific heat measurements also show magnetic correlations shifting with applied magnetic field with a degree of missing entropy that may be related to the slight mixture of Yb3+ on the Li site. Such magnetic frustration of Yb3+ is rare in pyrochlore structures. Thus, LiYbSe2 shows promise in intrinsically realizing disordered quantum states like QSL in pyrochlore structures.

Diluting a triangular-lattice spin liquid: Synthesis and characterization of NaYb1−xLuxS2 single crystals

Yb-based magnets, with a perfect triangular lattice of pseudospin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{\mathrm{Yb}}^{3+}$ ions, have emerged as candidates for realizing a quantum spin-liquid state, with ${\mathrm{NaYbS}}_{2}$ being a prominent example. Here, we present the solid-solution series ${\mathrm{NaYb}}_{1\ensuremath{-}x}{\mathrm{Lu}}_{x}{\mathrm{S}}_{2}$ with well-defined single crystals over the entire substitution range $0\ensuremath{\le}x\ensuremath{\le}1$. Chemical and structural analysis indicate a statistically homogeneous replacement of ${\mathrm{Yb}}^{3+}$ by ${\mathrm{Lu}}^{3+}$ ions. We magnetically characterize the relatively small single crystals using electron spin resonance (ESR). Below $30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the ESR intensity can be well described by a Curie-Weiss function for all $x$, with a decreasing Weiss temperature with increasing Lu content. This reduction of the average magnetic interaction upon Lu substitution is also supported by magnetization measurements. Importantly, no signs of magnetic or spin-glass order are detected down to $2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for any $x$. For $x>0.5$, the ESR linewidth strongly increases, indicating the breakup of the magnetic system into disconnected clusters, as expected from percolation physics. The experimental magnetization data are found to be in good agreement for all $x$ with results of classical Monte Carlo simulations for a triangular-lattice Heisenberg model, amended with a small second-neighbor interaction. Taken together, our results establish ${\mathrm{NaYb}}_{1\ensuremath{-}x}{\mathrm{Lu}}_{x}{\mathrm{S}}_{2}$ as a family of diluted triangular-lattice spin liquids.

Doping-induced structural transformation in the spin-1/2 triangular-lattice antiferromagnet Na2Ba1-xSrxCo(PO4)2

The effects of Sr doping on the structural properties of Na2BaCo(PO4)2, a spin-1/2 triangular-lattice antiferromagnet as a quantum spin liquid candidate, are investigated by complementary x-ray and neutron powder diffraction measurements. It is found that in Na2Ba1−xSrxCo(PO4)2 (NBSCPO), the trigonal phase (space group P3̅m1) with a perfect triangular lattice of Co2+ ions is structurally stable when the doping level of Sr is below 30% (x≤ 0.3), while a pure monoclinic phase (space group P21/a) with slight rotations of CoO6 octahedra and displacements of Ba2+/Sr2+ ions will be established when the Sr doping level is above 60% (x≥ 0.6). Such a doping-induced structural transformation in NBSCPO is supported by first-principles calculations and Raman spectroscopy. Na2SrCo(PO4)2, a novel spin-1/2 antiferromagnet with glaserite-type structure, although monoclinically distorted, exhibits no long-range magnetic order down to 2 K and a similar negative Curie-Weiss temperature as Na2BaCo(PO4)2 with a perfect triangular lattice, suggesting the robustness of magnetic exchange interaction against the Ba/Sr substitutions.

Synthesis, crystal structure and magnetic properties of KLnSe2 (Ln = La, Ce, Pr, Nd) structures: A family of 2D triangular lattice frustrated magnets

We report the detail synthesis, single crystal structure characterization and magnetic properties of KLnSe2 series obtained via solid state molten flux growth method. The crystal structures were characterized using single crystal x-ray diffraction. The KLnSe2 (Ln ​= ​La, Ce, Pr and Nd) series crystallizes in the trigonal crystal system with the space group of R-3m (No. 166). The overall structure contains two-dimensional (2D) layers made from edged shared LnSe6-octahedra. Ln3+ ions form a perfect triangular magnetic lattice which propagates along ab-plane. These triangular lattices are separated by the K+ ions. The magnetic properties confirm that, Ce, Pr and Nd do not show any long-range ordering down to 0.4 ​K indicating frustrated magnetism in the KLnSe2 series.

Synthesis, Structure and Magnetism of Rta7o19 (R = Pr, Sm, EU, Gd, Dy, Ho) with Perfect Triangular Lattice

Synthesis, Structure and Magnetism of Rta7o19 (R = Pr, Sm, EU, Gd, Dy, Ho) with Perfect Triangular Lattice

Crystal growth and magnetic properties of quantum spin liquid candidate KErTe2 * *Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300504), the National Natural Science Foundation of China (Grant Nos. U1932215 and 11774419), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100), and Postdoctoral Science Foundation of

Recently rare-earth chalcogenides have been revealed as a family of quantum spin liquid (QSL) candidates hosting a large number of members. In this paper we report the crystal growth and magnetic measurements of KErTe2, which is the first member of telluride in the family. Compared to its cousins of oxides, sulfides and selenides, KErTe2 retains the high symmetry of and Er3+ ions still sit on a perfect triangular lattice. The separation between adjacent magnetic layers is expectedly increased, which further enhances the two dimensionality of the spin system. Specific heat and magnetic susceptibility measurements on KErTe2 single crystals reveal no structural and magnetic transition down to 1.8 K. Most interestingly, the absorption spectrum shows that the charge gap of KErTe2 is roughly 0.93±0.35 eV, which is the smallest among all the reported members in the family. This immediately invokes the interest towards metallization even superconductivity using the compound.

Spinon Fermi Surface Spin Liquid in a Triangular Lattice Antiferromagnet NaYbSe2

Triangular lattice of rare-earth ions with interacting effective spin-$1/2$ local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh$_2$ (Ch=O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and muon spin rotation measurements on NaYbCh$_2$ have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystalline NaYbSe$_2$ samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe$_2$ is a QSL with a spinon Fermi surface.

Development of short and long-range magnetic order in the double perovskite based frustrated triangular lattice antiferromagnet Ba_{2}MnTeO_{6}

Frustrated magnets based on oxide double perovskites offer a viable ground wherein competing magnetic interactions, macroscopic ground state degeneracy and complex interplay between emergent degrees of freedom can lead to correlated quantum phenomena with exotic excitations highly relevant for potential technological applications. By local-probe muon spin relaxation (muSR) and complementary thermodynamic measurements accompanied by first-principles calculations, we here demonstrate novel electronic structure and magnetic phases of Ba_{2}MnTeO_{6}, where Mn^{2+} ions with S = 5/2 spins constitute a perfect triangular lattice. Magnetization results evidence the presence of strong antiferromagnetic interactions between Mn^{2+} spins and a phase transition at T_{N} = 20 K. Below T_{N}, the specific heat data show antiferromagnetic magnon excitations with a gap of 1.4 K, which is due to magnetic anisotropy. muSR reveals the presence of static internal fields in the ordered state and short-range spin correlations high above T_{N}. It further unveils critical slowing-down of spin dynamics at T_{N} and the persistence of spin dynamics even in the magnetically ordered state. Theoretical studies infer that Heisenberg interactions govern the inter- and intra-layer spin-frustration in this compound. Our results establish that the combined effect of a weak third-nearest-neighbour ferromagnetic inter-layer interaction (owing to double-exchange) and intra-layer interactions stabilizes a three-dimensional magnetic ordering in this frustrated magnet.

Magnetic structure of undistorted hexagonal ferrites, Lu0.2In0.8FeO3

We report on the crystal and magnetic structure of bulk hexagonal (Lu,In)FeO3. Neutron powder diffraction revealed that Lu0.2In0.8FeO3 has a single-phase P63/mmc structure down to T ≈ 3 K and shows an antiferromagnetic transition at TN ≈ 164 K. Unlike the distorted hexagonal LuFeO3 family with an A2(Γ2)-type spin configuration, undistorted hexagonal Lu0.2In0.8FeO3 shows either an A1(Γ1) or a B1(Γ3)-type spin configuration below TN, which does not produce the c-directional canted ferromagnetic moment. A significant reduction in the ordered magnetic moment was observed at 3 K without trimerization, and hints of a magnetic cluster state were observed in the paramagnetic phase near room temperature. Therefore, the system presents a rare example to study the geometrically frustrated magnetism in the undistorted hexagonal magnet that has a perfect triangular lattice below room temperature.

Partial Up-Up-Down Order with the Continuously Distributed Order Parameter in the Triangular Antiferromagnet TmMgGaO4

Frustrated quasidoublets without time-reversal symmetry can host highly unconventional magnetic structures with continuously distributed order parameters even in a single-phase crystal. Here, we report the comprehensive thermodynamic and neutron diffraction investigation on the single crystal of TmMgGaO$_4$, which entails non-Kramers Tm$^{3+}$ ions arranged on a geometrically perfect triangular lattice. The crystal electric field (CEF) randomness caused by the site-mixing disorder of the nonmagnetic Mg$^{2+}$ and Ga$^{3+}$ ions, merges two lowest-lying CEF singlets of Tm$^{3+}$ into a ground-state (GS) quasidoublet. Well below $T_c$ $\sim$ 0.7 K, a small fraction of the antiferromagnetically coupled Tm$^{3+}$ Ising quasidoublets with small inner gaps condense into two-dimensional (2D) up-up-down magnetic structures with continuously distributed order parameters, and give rise to the \emph{columnar} magnetic neutron reflections below $\mu_0H_c$ $\sim$ 2.6 T, with highly anisotropic correlation lengths, $\xi_{ab}$ $\geq$ 250$a$ in the triangular plane and $\xi_c$ $<$ $c$/12 between the planes. The remaining fraction of the Tm$^{3+}$ ions remain nonmagnetic at 0 T and become uniformly polarized by the applied longitudinal field at low temperatures. We argue that the similar model can be generally applied to other compounds of non-Kramers rare-earth ions with correlated GS quasidoublets.

Synthesis, magnetization, and heat capacity of triangular lattice materials NaErSe2 and KErSe2

In this paper we report the synthesis, magnetization and heat capacity of the frustrated magnets \emph{A}ErSe$_2$(\emph{A}=Na,K) which contain perfect triangular lattices of Er$^{3+}$. The magnetization data suggests no long-range magnetic order exists in \emph{A}ErSe$_2$(\emph{A}=Na,K), which is consistent with the heat capacity measurements. Large anisotropy is observed between the magnetization within the \emph{ab} plane and along the \emph{c} axis of both compounds. When the magnetic field is applied along \emph{ab} plane, anomalies are observed at 1.8 $\mu_B$ in NaErSe$_2$ at 0.2 T and 2.1 $\mu_B$ in KErSe$_2$ at 0.18 T. Unlike NaErSe$_2$, a plateau-like field-induced metamagnetic transition is observed for H$\|$\emph{c} below 1 K in KErSe$_2$. Two broad peaks are observed in the heat capacity below 10 K indicating possible crystal electric field(CEF) effects and magnetic entropy released under different magnetic fields. All results indicate that \emph{A}ErSe$_2$ are strongly anisotropic, frustrated magnets with field-induced transition at low temperature. The lack of signatures for long-range magnetic order implies that these materials are candidates for hosting a quantum spin liquid ground state.

NaBaR(BO3)2 (R = Dy, Ho, Er and Tm): structurally perfect triangular lattice materials with two rare earth layers

We report the crystal growth of NaBaR(BO3)2 (R = Dy, Ho, Er and Tm) by the flux method. In the rhombohedral crystal structures, [RO6] octahedra and planar [BO3] units connect by bridging O atoms, forming triangular layers in the ab plane that are evenly spaced along c. Two perfectly triangular rare earth layers of identical dimension are found. Anisotropic magnetic susceptibility is observed for all; NaBaEr(BO3)2 is nearly isotropic while NaBaTm(BO3)2 is the most anisotropic. Heat capacity measurements reveal no long-range magnetic ordering down to 0.35 K for R = Dy or Er, while the Ho material displays a significant entropy loss. All the magnetic entropy appears to be absent in the Tm case by low temperature, suggesting that a singlet ground state may have formed.

Spin dynamics in the distorted triangular lattice antiferromagnet α−SrCr2O4

The spin dynamics in the distorted triangular lattice antiferromagnet $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$ has been investigated by inelastic neutron scattering on a single crystal. The spin wave dispersion has been mapped out in the $(0\phantom{\rule{4pt}{0ex}}k\phantom{\rule{4pt}{0ex}}l)$ and $(h\phantom{\rule{4pt}{0ex}}k\phantom{\rule{4pt}{0ex}}0)$ planes, and modeled by spin wave calculations, in order to determine the intraplane and interplane exchange couplings. Comparison with $\ensuremath{\alpha}\ensuremath{-}{\mathrm{CaCr}}_{2}{\mathrm{O}}_{4}$ shows that, despite the smaller lattice distortion of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$, the deviation from a perfect triangular lattice still affects the spin dynamics of the Sr compound, with a soft mode, similar to the one observed in the Ca counterpart, being observed in (020). Although $\ensuremath{\alpha}\ensuremath{-}{\mathrm{SrCr}}_{2}{\mathrm{O}}_{4}$ is further away from a magnetic phase boundary than its Ca counterpart, its dynamic magnetic properties still show intriguing features, which are discussed as quantum fluctuations arising from a two-magnon continuum.

Condensed-matter physics: Quantum mechanics in a spin.

Quantum spin liquids are exotic states of matter first predicted more than 40 years ago. An inorganic material has properties consistent with these predictions, revealing details about the nature of quantum matter. See Letter p.559 There are only a handful of candidate quantum spin liquids—exotic states of matter that are ideal for the study of the fundamental nature of quantum matter—so experimental observations of quantum spin liquid behaviour are scarce. Jun Zhao and colleagues use inelastic neutron scattering to study a single crystal of YbMgGaO4, which has a perfect triangular lattice. They find a spin excitation continuum across a large region of the Brillouin zone that persists at near-zero temperatures, providing evidence for a quantum spin liquid state with a spinon Fermi surface. The authors suggest that YbMgGaO4 fits the criteria for a perfect spin-1/2 triangular lattice antiferromagnet, as originally proposed by Philip Anderson in 1973.

Large systems with Coulomb interactions: Variational study and statistical mechanics

Systems with Coulomb and logarithmic interactions arise in various settings: an instance is the classical Coulomb gas which in some cases happens to be a random matrix ensemble, another is vortices in the Ginzburg-Landau model of superconductivity, where one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular lattice patterns named Abrikosov lattices, a third is the study of Fekete points which arise in approximation theory. In this review, we describe tools to study such systems and derive a next order (beyond mean field limit) ‘‘renormalized energy’’ that governs microscopic patterns of points. We present the derivation of the limiting problem and the question of its minimization and its link with the Abrikosov lattice and crystallization questions. We also discuss generalizations to Riesz interaction energies and the statistical mechanics of such systems. This is based on joint works with Etienne Sandier, Nicolas Rougerie, Simona Rota Nodari, Mircea Petrache, and Thomas Leblé.