The wavefuntion of conduction electrons moving in the background of a non-coplanar spin structure can gain a quantal phase - Berry phase - as if the electrons were moving in a strong fictitious magnetic field. Such an emergent magnetic field effect is approximately proportional to the solid angle subtended by the spin moments on three neighbouring spin sites, termed the scalar spin chirality. The entire spin chirality of the crystal, unless macroscopically canceled, causes the geometrical Hall effect of real-space Berry-phase origin, whereas the intrinsic anomalous Hall effect (AHE) in a conventional metallic ferromagnet is of the momentum-space Berry-phase origin induced by relativistic spin-orbit coupling (SOC). Here, we report the ordering phenomena of the spin-trimer scalar spin chirality and the consequent large geometrical Hall effect in the breathing kagomé lattice compound Dy$_3$Ru$_4$Al$_{12}$, where the Dy$^{3+}$ moments form non-coplanar spin trimers with local spin chirality. Using neutron diffraction, we show that the local spin chirality of the spin trimers as well as its ferroic/antiferroic orders can be switched by an external magnetic field, accompanying large changes in the geometrical Hall effect. Our finding reveals that systems composed of tunable spin trimers can be a fertile field to explore large emergent electromagnetic responses arising from real-space topological magnetic orders.
The crystal structure of Ba4NbRu3O12 is based on triangular planes of elongated Ru3O12 trimers oriented perpendicular to the plane. We report that it is semiconducting, that its Weiss temperature and effective magnetic moment are -155 K and 2.59 μB/f.u. respectively, and that magnetic susceptibility and specific heat data indicate that it exhibits magnetic ordering near 4 K. The presence of a high density of low energy states is evidenced by a substantial Sommerfeld-like T-linear term (gamma = 31(2) mJ/mole-K^2) in the specific heat. Electronic structure calculations reveal that the electronic…
The electronic properties and spectroscopic features of a magnetic trimer with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at zero temperature. The substrate density of states is depressed in the trimer neighbourhood, being exactly zero at the substrate chemical potential. The size of the resonance strongly depends on the magnetic state of the trimer, and exhibits a two-state behavior. The geometrical dependence of these results agree qualitatively with recent experiments and could be reproduced in a triangular quantum dot arrangement.
Designing electronic magnetoelectric matter with organic quantum spin trimers
Osaka Metropolitan University（大阪公立大学）；University of Florida（佛罗里达大学）；Shanghai Jiao Tong University（上海交通大学）；Osaka Prefecture University（大阪府立大学）；Florida State University（佛罗里达州立大学）；National High Magnetic Field Laboratory, Florida State University（佛罗里达州立大学国家高磁场实验室）
We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers $s$ and their ground state $Φ$ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to $Φ$ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for $Φ$ being a ground state. The classical case $s\to\infty$ can be completely analyzed. For th…
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$O$_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong run…
We investigate the properties of an effective Hamiltonian with competing interactions involving spin and chirality variables, relevant for the description of the {\it trimerized} version of the spin-1/2 {\it kagome} antiferromagnet. Using classical Monte Carlo simulations, we show that remarkable behaviors develop at very low temperatures. Through an {\it order by disorder} mechanism, the low-energy states are characterized by a dynamical freezing of the chiralities, which decouples the lattice into ``dimers'' and ``triangles'' of antiferromagnetically coupled spins. Under the presence of an e…
Quenched disorder may prevent the formation of the widely sought quantum-spin-liquid states (QSLs) or mask their signatures by inducing a spin-glass state, which is why considerable experimental efforts are directed at purifying materials that may host QSLs. However, in geometrically frustrated (GF) magnets, the largest class of materials in which QSLs are sought, the glass-transition temperature $T_g$ grows with decreasing the density of vacancy defects, accompanied by a simultaneous growth of the magnetic susceptibility. In this paper, we develop a phenomenological theory of glass transition…
The hexagonal RMnO$_3$ (h-RMnO$_3$) are multiferroic materials, which exhibit the coexistence of a magnetic order and ferroelectricity. Their distinction is in their geometry that both results in an unusual mechanism to break inversion symmetry, and also produces a 2D triangular lattice of Mn spins, which is subject to geometrical magnetic frustration due to the antiferromagnetic interactions between nearest neighbour Mn ions. This unique combination makes the h-RMnO$_3$ a model system to test ideas of spin-lattice coupling, particularly when the both the improper ferroelectricity and the Mn t…
We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that in the case of strong leg coupling the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the st…
Ground state of the periodic Anderson model on a cubic lattice is investigated by mean-field calculations, with focusing on the possibility of charge ordering. We show that three different charge-ordered phases appear at 3/2 filling, which are accompanied by ferromagnetic, noncoplanar triple-Q, and ferrimagnetic order, respectively. The triple-Q magnetic order is likely stabilized by emergent geometrical frustration in the charge-ordered phase with the ordering wave vector (pi,pi,pi). We show that the nearest-neighbor hopping between localized electrons stabilizes the triple-Q phase relative t…
Heat capacity measurements were used to investigate the magnetic ordering processes in single crystal samples of SrDy2O4 in a magnetic field applied along the [010] and [001] directions. In zero field this compound appears to be magnetically disordered down to at least 0.39 K. A magnetic field applied along the [010] direction induces a very sharp transition at 20 kOe, seen as a strong peak in the heat capacity versus field, C(H) curves, while for H // [001], the magnetisation process is accompanied by the development of only broad features in the C(H) curves. The process of field induced orde…
Recent neutron scattering measurements on the spinel CdCr2O4 revealed a rare example of helical magnetic order in geometrically frustrated pyrochlore antiferromagnet. The spin spiral characterized by an incommensurate wavevector Q = 2pi (0, delta, 1) with delta ~0.09 is accompanied by a tetragonal distortion. Here we conduct a systematic study on the magnetic ground state resulting from the interplay between the Dzyaloshinskii-Moriya interaction and further neighbor exchange couplings, two of the most important mechanisms for stabilizing incommensurate spin orders. We compute the low-energy sp…
Electric-field-tuned consecutive topological phase transitions between distinct correlated insulators in moire MoTe2/WSe2 heterobilayer
State Key Laboratory of Micro-nano Engineering Science, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院，微纳工程科学国家重点实验室，人工结构与控制教育部重点实验室）；School of Applied and Engineering Physics, Cornell University（康奈尔大学应用与工程物理学院）；Departments of Physics and Applied Physics, Stanford University（斯坦福大学物理与应用物理系）；National Institute for Materials Science（日本物质材料研究机构）；SLAC National Accelerator Laboratory（斯坦福直线加速器国家实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science（康奈尔大学卡弗里纳米科学研究所）；Max Planck Institute for the Structure and Dynamics of Matter（德国马普物质结构与动力学研究所）
Effect of the coupling to mobile carriers on the 120$^\circ$ antiferromagnetic state is investigated in a ferromagnetic Kondo lattice model on a frustrated triangular lattice. Using a variational calculation for various spin orderings up to a four-site unit cell, we identify the ground-state phase diagram with focusing on the lightly-doped region. We find that an electron doping from the band bottom immediately destabilizes a 120$^\circ$ coplanar antiferromagnetic order and induces a noncoplanar three-sublattice ordering accompanied by an intervening phase separation. This noncoplanar phase ha…
Geometrical frustration, quantum entanglement and disorder may prevent long-range order of localized spins with strong exchange interactions, resulting in a novel state of matter. $κ$-(BEDT-TTF)$_2$-Cu$_2$(CN)$_3$ is considered the best approximation of this elusive quantum-spin-liquid state, but its ground-state properties remain puzzling. Here we present a multi-frequency electron-spin resonance study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at $T^*=6\,\mathrm{K}$. This opening of a spin gap, accompanied by structural modifications, suggests the eni…
We present our theoretical results on the mechanism of two transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) in which magnetic V cations constitute a geometrically-frustrated pyrochlore structure. We have derived an effective spin-orbital-lattice coupled model in the strong correlation limit of the multiorbital Hubbard model, and applied Monte Carlo simulation to the model. The results reveal that the higher-temperature transition is a layered antiferro-type orbital ordering accompanied by tetragonal Jahn-Teller distortion, and the lower-temperature transition is an antif…
We report a study on the thermal conductivity of CuFe$_{1-x}$Ga$_x$O$_2$ ($x =$ 0--0.12) single crystals at temperatures down to 0.3 K and in magnetic fields up to 14 T. CuFeO$_2$ is a well-known geometrically frustrated triangular lattice antiferromagnet and can be made to display multiferroicity either by applying magnetic field along the $c$ axis or by doping nonmagnetic impurities, accompanied with rich behaviors of magnetic phase transitions. The main experimental findings of this work are: (i) the thermal conductivities ($κ_a$ and $κ_c$) show drastic anomalies at temperature- or field-in…
Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dim…
We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland (SS) lattice with additional Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We show that several noncollinear and noncoplanar magnetic phases, such as the flux, all-in/all-out, 3in-1out/3out-1in, and canted-flux phases are stabilized over wide ranges of parameters in the presence of the DM interaction. We discuss the role of DM interaction in stabilizing these complex magnetic phases. When coupled to these noncoplanar magnetic phases, itinerant electrons experience …
Numerical studies on Mott transitions caused by the control of the ratio between bandwidth and electron-electron interaction ($U$) are reported. By using the recently proposed path-integral renormalization group(PIRG) algorithm, physical properties near the transitions in the ground state of two-dimensional half-filled models with the nearest and the next-nearest neighbor transfers ($-t$ and $t'$, respectively) are studied as a prototype of geometrically frustrated system. The nature of the bandwidth-control transitions shows sharp contrast with that of the filling-control transitions: First, …
Geometrical frustration among interacting spins combined with strong quantum fluctuations destabilize long-range magnetic order in favour of more exotic states such as spin liquids. By following this guiding principle, a number of spin liquid candidate systems were identified in quasi-two-dimensional (quasi-2D) systems. For 3D, however, the situation is less favourable as quantum fluctuations are reduced and competing states become more relevant. Here we report a comprehensive study of thermodynamic, magnetic and dielectric properties on single crystalline and pressed-powder samples of PbCuTe$…
In condensed matter systems, the formation of long range order (LRO) with broken symmetry is often accompanied by new types of excitations. However, in many magnetic pyrochlore oxides, geometrical frustration suppresses conventional LRO while at the same time non-trivial spin correlations are observed. For such materials, a natural question to ask then is what is the nature of the excitations in this highly correlated state without broken symmetry? Frequently the application of a symmetry breaking field can stabilize excitations whose properties still reflect certain aspects of the anomalous s…
