Inhomogeneity in the ground state is an intriguing, emergent phenomenon in magnetism. Recently, it has been observed in the magnetostructural channel of the geometrically frustrated $α$-NaMnO$_2$, for the first time in the absence of active charge degrees of freedom. Here we report an in-depth numerical and local-probe experimental study of the isostructural sister compound CuMnO$_2$ that emphasizes and provides an explanation for the crucial differences between the two systems. The experimentally verified, much more homogeneous, ground state of the stoichiometric CuMnO$_2$ is attributed to the reduced magnetoelastic competition between the counteracting magnetic-exchange and elastic-energy contributions. The comparison of the two systems additionally highlights the role of disorder and allows an understanding of the puzzling phenomenon of phase separation in uniform antiferromagnets.
Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-$T_c$ superconductivity in cuprates, colossal magnetoresistance in manganites, and giant electrostriction in relaxors. In these materials distinct phases compete and can coexist due to intertwined ordered parameters. Charge degrees of freedom play a fundamental role, although phase-separated ground states have been envisioned theoretically also for pure spin systems with geometrical frustration that serves as a source of phase competiti…
Epitaxial La3/4Ca1/4MnO3/MgO(100) (LCMO) thin films show unusual rhombohedral (R-3c) structure with a new perovskite superstructure due to unique ordering of La and Ca at the A-site positions. Very sharp insulator-metal and para-ferromagnetic phase transitions at temperatures up to TMI ~ TC=295 K were observed. The ordered films were electronically homogeneous down to 1 nm scale as revealed by scanning tunnelling microscopy/spectroscopy. In contrast, orthorhombic and A-site disordered LCMO demonstrate broadened phase transitions as well as mesoscopic phase separation for T<<TC. The unique La/C…
In this paper, we explore the relationship between strong spin-orbit coupling and spin liquid physics. We study a very general model on the triangular lattice where spin-orbit coupling leads to the presence of highly anisotropic interactions. We use variational Monte Carlo to study both $U(1)$ quantum spin liquid states and ordered ones, via the Gutzwiller projected fermion construction. We thereby obtain the ground state phase diagram in this phase space. We furthermore consider effects beyond the Gutzwiller wavefunctions for the spinon Fermi surface quantum spin liquid, which are of particul…
We report an excellent realization of the highly non-classical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs$_2$CoBr$_4$. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad $m = 1/3$ magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of long-sought SDW-UUD transition in triangular-t…
We investigated the inhomogeneous electronic properties at the surface and interior of VO_{2} thin films that exhibit a strong first-order metal-insulator transition (MIT). Using the crystal structural change that accompanies a VO_{2} MIT, we used bulk-sensitive X-ray diffraction (XRD) measurements to estimate the fraction of metallic volume p^{XRD} in our VO_{2} film. The temperature dependence of the p$^{XRD}$ was very closely correlated with the dc conductivity near the MIT temperature, and fit the percolation theory predictions quite well: $σ$ $\sim$ (p - p_{c})^{t} with t = 2.0$\pm$0.1 an…
High-temperature bad-metal transport has been recently studied both theoretically and in experiments as one of the key signatures of strong electronic correlations. Here we use the dynamical mean field theory (DMFT) and its cluster extensions, as well as the finite-temperature Lanczos method (FTLM) to explore the influence of lattice frustration on the thermodynamic and transport properties of the Hubbard model at high temperatures. We consider the triangular and the square lattice at half-filling and at 15\% hole-doping. We find that for $T \gtrsim 1.5t$ the self-energy becomes practically lo…
We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters t and t' in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly-correlated regime and close to the isotropic limit t'/t=1. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) Néel and the (coplanar) 120° phases. …
In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet $κ$-(ET)$_2$Cu$_2$(CN)$_3$ has been extensively discussed as a quantum spin liquid (QSL) candidate. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Through microscopic analysis of all anisotropic contributions, including Dzyaloshinskii-Moriya and multi-spin scalar chiral interactions, we highlight significant deviations of the experimental observations from a quantum critical scenario. Instead, we show that disorder-ind…
Spin-1/2 antiferromagnetic triangular lattice models are paradigms of geometrical frustration, revealing very different ground states and quantum effects depending on the nature of anisotropies in the model. Due to strong spin orbit coupling and crystal field effects, rare-earth ions can form pseudo-spin-1/2 magnetic moments with anisotropic single-ion and exchange properties. Thus, rare-earth based triangular lattices enable the exploration of this interplay between frustration and anisotropy. Here we study one such case, the rare-earth double vanadate glaserite material K$_3$Er(VO$_4$)$_2$, …
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
A Hubbard model at half-filling on an anisotropic triangular lattice has been proposed as the minimal model to describe conducting layers of $κ-(BEDT-TTF)_2X$ organic materials. The model interpolates between the square lattice and decoupled chains. The $κ-(BEDT-TTF)_2X$ materials present many similarities with cuprates, such as the presence of unconventional metallic properties and the close proximity of superconducting and antiferromagnetic phases. As in the cuprates, spin fluctuations are expected to play a crucial role in the onset of superconductivity. We perform a weak-coupling renormali…
The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of Na$_x$CoO$_2$ at $x=0.5$. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at $x=1/3$ and $x=0.5$ where antiferromagnetic (AF) frustration is alleviated via weak charge inhomogeneity. At $x=0.5$, we show that the $\sqrt{3}a\times2a$ off-plane Na dopant order induces weak $\sqrt{3}a\times1a$ charge order in the Co layer.…
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
The ground state of the stacked triangular antiferromagnet CsFeBr$_3$ is a spin singlet due to the large single ion anisotropy $D(S^z)^2$. The field-induced magnetic ordering in this compound was investigated by the magnetic susceptibility, the magnetization process and specific heat measurements for an external field parallel to the $c$-axis. Unexpectedly, two phase transitions were observed in the magnetic field $H$ higher than 3 T. The phase diagram for temperature versus magnetic field was obtained. The mechanism leading to the successive phase transitions is discussed.
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…
We report results of muon spin relaxation and rotation ($μ$SR) experiments on the spin-liquid candidate~YbMgGaO$_{4}$. No static magnetism $\gtrsim 0.003μ_B$ per Yb ion, ordered or disordered, is observed down to 22~mK, a factor of two lower in temperature than previous measurements. Persistent (temperature-independent) spin dynamics are observed up to 0.20~K and at least 1~kOe, thus extending previous zero-field $μ$SR results over a substantial region of the $H$-$T$ phase diagram. Knight shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes. Inhomogeneo…
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…
We have performed a comparative study of the electronic structures of the spin-Peierls systems TiOCl and TiOBr by means of photoemission spectroscopy and density functional calculations. While the overall electronic structure of these isostructural compounds is qualitatively similar, the bromide appears to be less one-dimensional. We present a quantitative analysis of the experimental dispersions in terms of exchange constant J and hopping integral t as well as a discussion of the qualitative spectral features. From that we conclude that despite the one-dimensional physics triggering the groun…
A magnetic skyrmion crystal (SkX) with a swirling spin configuration, which is one of topological spin crystals as a consequence of an interference between multiple spin density waves, shows a variety of noncoplanar spin patterns depending on a way of superposing the waves. By focusing on a phase degree of freedom among the constituent waves in the SkX, we theoretically investigate a position of the skyrmion core on a discrete lattice, which is relevant with the symmetry of the SkX. The results are obtained for the double exchange (classical Kondo lattice) model on a discrete triangular lattic…
The behavior in magnetic field of a paramagnetic center is characterized by its $g$ tensor. An anisotropic form of the latter implies different kind of response along different crystallographic directions. Here we shed light on the anisotropy of the $g$ tensor of Yb$^{3+}$ 4$f^{13}$ ions in NaYbS$_2$ and NaYbO$_2$, layered triangular-lattice materials suggested to host spin-liquid ground states. Using quantum chemical calculations we show that, even if the ligand-cage trigonal distortions are significant in these compounds, the crucial role in realizing strongly anisotropic, `noncubic' $g$ fac…
We report discovery of a new iridate family K$_x$Ir$_y$O$_2$ with depleted triangular lattice planes made up of edge sharing IrO$_6$ octahedra separated by K planes. Such a material interpolates between the triangular and honeycomb lattices and is a new playground for Kitaev physics. The materials are Mott insulators with $y = 1 - x/4$. Physical property measurements for the $x \approx 0.85$ material are reported. Using magnetic susceptibility $χ$ versus temperature $T$ measurements we find $S_{eff} = 1/2$ moments interacting strongly with a Weiss temperature $θ\approx - 180$~K and no magnetic…
We present a scenario for the peculiar coexistence of charge fluctuations observed in quasi-2D 1/4-filled organic conductors $θ$-(BEDT-TTF)$_2X$ in the quantum critical regime where the charge ordering is suppressed down to zero temperature. The scenario is explored in the extended Hubbard model including electron-phonon couplings on an anisotropic triangular lattice. We find that the coexisting fluctuations emerge from two different instabilities, the ``Wigner crystallization on lattice'' driven by the off-site Coulomb repulsion and the charge-density-wave formation due to the nesting of the …
The magnetic and dielectric properties of the multiferroic triangular lattice magnet compound alpha-NaFeO2 were studied by magnetization, specific heat, dielectric permittivity, and pyroelectric current measurements and by neutron diffraction experiments using single crystals grown by a hydrothermal synthesis method. This work produced magnetic field (in the monoclinic ab-plane, B_ab, and along the c*-axis, B_c) versus temperature magnetic phase diagrams, including five and six magnetically ordered phases in B_ab and along B_c, respectively. Comparing the polarization direction to the magnetic…
We consider a finite two-dimensional Heisenberg triangular spin lattice at different degrees of anisotropy coupled to a dissipative Lindblad environment obeying the Born-Markovian constrain at finite temperature. We show how applying an inhomogeneous magnetic field to the system may significantly affect the entanglement distribution and properties among the spins in the asymptotic steady state of the system. Particularly, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustnes…
A study of spinless matter fermions coupled to a constrained $\mathbb{Z}_{2}$ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared to previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (…
Motivated by the research interests on realizing flat bands and magnetization plateaus in kagome lattices, we study the electronic properties and magnetic interactions in both zero- and one-dimensional triangular Kagome lattice (1D-TKL) models, by using the real-space Greens function approach in tight-binding model. We firstly study the electronic properties of both 0D and 1D-TKL in the presence of staggered sublattice potential, then, by analyzing the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in these lattice structures, the magnetic ground states of both 0D and 1D-TKL in the presence…
$^{13}$C NMR observation of a nonmagnetic charge-ordered state in the organic conductor $κ$-(ET)$_{2}$Hg(SCN)$_{2}$Cl
University of Tokyo（东京大学）；The Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Institute of Problems of Chemical Physics RAS（俄罗斯科学院化学物理问题研究所）；The Institute for Quantum Matter and the Department of Physics and Astronomy, The Johns Hopkins University（约翰斯·霍普金斯大学量子物质研究所及物理与天文学系）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；University of Stuttgart（斯图加特大学）；Department of Advanced Materials Science, University of Tokyo（东京大学先进材料科学系）
Parent compounds AFe2As2 (A=Ca, Ba, Eu) of the 122 family of the iron-based superconductors have been studied by 57Fe Moessbauer spectroscopy in the temperature range 4.2 K - ~300 K. Spin density waves (SDW) have been found with some confidence. They are either incommensurate with the lattice period or the ratio of the respective periods is far away from ratio of small integers. SDW shape is very unconventional i.e. differs from the sinusoidal shape. Magnetic order starts with lowered temperature as narrow sheets of the significant electron spin density separated by areas with very small spin …
We investigate the ground-state and finite-temperature properties of the bond-random $s=1/2$ Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, $J_1$ and $J_2$, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration ($J_2/J_1$) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)…
Sr_4Cr_3O_9 is the n = 2 member of a family of quasi-one-dimensional compounds A_{n+2}T_{n+1}O_{3n+3} (A = Ca, Sr, or Ba, T = transition metal, and n = 1 to \infty) having a crystal structure which consists of chains of n TO_6 octahedra alternated by one TO_6 trigonal prism running along the c-axis. The chains are arranged on a triangular lattice in the ab-plane. We report the synthesis, structure, magnetization M versus magnetic field H, magnetic susceptibility χversus temperature T and specific heat C versus T measurements on sintered and arc-melted polycrystalline samples of Sr_4Cr_3O_9. Th…
