An indispensable step to understand collective magnetic phenomena in rare-earth compounds is the determination of spatially-anisotropic single-ion properties resulting from spin-orbit coupling and crystal field (CF). The CF Hamiltonian has a discrete energy spectrum -- accessible to spectroscopic probes such as neutron scattering -- controlled by a number of independent parameters reflecting the point-symmetry of the magnetic sites. Determining these parameters in low-symmetry systems is often challenging. Here, we describe a general method to analyze CF excitation spectra using adjustable effective point-charges. We benchmark our method to existing neutron-scattering measurements on pyrochlore rare-earth oxides and obtain a universal point-charge model that describes a large family of related materials. We adapt this model to the newly discovered tripod Kagome magnets ($R_{3}$Mg$_2$Sb$_{3}$O$_{14}$, $R$ = Tb, Ho, Er, Yb) for which we report broadband inelastic neutron-scattering spectra. Analysis of these data using adjustable point-charges yields the CF wave-functions for each compound. From this, we calculate thermomagnetic properties that accurately reflect our measurements on powder samples, and predict the effective gyromagnetic tensor for pseudo-spin degrees of freedom -- a crucial step to understand the exotic collective properties of these kagome magnets at low temperature. We present further applications of our method to other tripod kagome materials and triangular rare-earth compounds $R$MgGaO$_4$ ($R$ =Yb, Tm). Overall, this study establishes a widely applicable methodology to predict CF and single-ion properties of rare-earth compounds based on interpretable and adjustable models of effective point-charges.
We present the structural and magnetic properties of a new compound family, Mg$_2$RE$_3$Sb$_3$O$_{14}$ (RE = Gd, Dy, Er), with a hitherto unstudied frustrating lattice, the "tripod kagome" structure. Susceptibility (ac, dc) and specific heat exhibit features that are understood within a simple Luttinger-Tisza type theory. For RE = Gd, we found long ranged order (LRO) at 1.65 K, which is consistent with a 120 $^{\circ}$ structure, demonstrating the importance of diople interactions for this 2D Heisenberg system. For RE = Dy, LRO at 0.37 K is related to the "kagome spin ice (KSI)" physics for a …
We report an experimental study of the static magnetization $M(H,T)$ and high-field electron spin resonance (ESR) of polycrystalline \MgGd, a representative member of the newly discovered class of the so-called tripod-kagome antiferromagnets where the isotropic Gd$^{3+}$ spins ($S = 7/2$) form a two-dimensional kagome spin-frustrated lattice. It follows from the analysis of the low-$T$ $M(H)$-curves that the Gd$^{3+}$ spins are coupled by a small isotropic antiferromagnetic (AFM) exchange interaction $|J| \approx$ 0.3\,K. The $M(H,T)$-dependences measured down to 0.5\,K evidence a long-range A…
A second-order topological insulator in $d$ dimensions is an insulator which has no $d-1$ dimensional topological boundary states but has $d-2$ dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this paper, we generalize them to breathing Kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lattice. Three topological boundary states emerge at the corner of the triangle, realizing a 1/3 f…
The results of magnetic investigations on a new series of compounds, Mn2R3Sb3O14, containing 2-dimensional Kagome lattice of R ions and belonging to pyrochlore series, are presented. Crystallographic features of light R members (R= La, Pr and Nd) of this family, as established in the recent literature, have been reported to be novel in many respects, in particular, the rhomohedral nature of the structure which is rare among pyrochlores. It was also reported that, as the R becomes heavier, beyond R= Sm, the fraction of well-known cubic pyrochlore phase tends to gradually dominate. Here, we repo…
Quantum spin ice, modeled for magnetic rare-earth pyrochlores, has attracted great interest for hosting a U(1) quantum spin liquid, which involves spin-ice monopoles as gapped deconfined spinons, as well as gapless excitations analogous to photons. However, the global phase diagram under a [111] magnetic field remains open. Here we uncover by means of unbiased quantum Monte-Carlo simulations that a supersolid of monopoles, showing both a superfluidity and a partial ionization, intervenes the kagomé spin ice and a fully ionized monopole insulator, in contrast to classical spin ice where a direc…
Two Dimensional Kagome Correlations and Field Induced Order in the Ferromagnetic XY Pyrochlore Yb2Ti2O7
中子散射测量表明，铁磁XY烧绿石Yb 2 Ti 2 O 7在低温下表现出很强的准二维（2D）自旋关联，在适当的磁场作用下，这种关联让位于长程序（LRO）.由于< 111 >这些2D自旋相关性沿方向的散射棒意味着立方烧绿石系统的磁分解成解耦的可果美平面。沿[1-10]方向施加约0.5 T的磁场，诱导向3D LRO状态的转变，其特征在于长寿命的色散自旋波。我们的测量绘制出一个复杂的低温场相图，这种异国情调的烧绿石磁铁。
We present a systematic study of the structural and magnetic properties of two branches of the rare earth Tripod Kagome Lattice (TKL) family A$_{2}$RE$_{3}$Sb$_{3}$O$_{14}$ (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb; here, we use abbreviation \textit{A-RE}, as in \textit{MgPr} for Mg$_{2}$Pr$_{3}$Sb$_{3}$O$_{14}$), which complements our previously reported work on \textit{MgDy}, \textit{MgGd}, and \textit{MgEr} \cite{TKL}. The present susceptibility ($χ_{dc}$, $χ_{ac}$) and specific heat measurements reveal various magnetic ground states, including the non-magnetic singlet state for \tex…
Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets
The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determ…
We study the $S=1/2$ pyrochlore Heisenberg antiferromagnet in a magnetic field. Using large scale density-matrix renormalization group (DMRG) calculations for clusters up to $128$ spins, we find indications for a finite triplet gap, causing a threshold field to nonzero magnetization in the magnetization curve. We obtain a robust saturation field consistent with a magnon crystal, although the corresponding $5/6$ magnetization plateau is very slim and possibly unstable. Most remarkably, there is a pronounced and apparently robust $\frac 1 2$ magnetization plateau where the groundstate breaks (re…
Topological phases in layered pyrochlore oxide thin films along the [111] direction
本文从理论上研究了烧绿石氧化物A $_2$ B $_2$ O $_7$的多带哈伯德模型，其中B是具有强自旋轨道耦合的重过渡金属离子，在沿[111]方向取向的薄膜几何结构中.沿着这个方向，烧绿石晶格由B离子的交替的kagome和三角形晶格平面组成。我们考虑一个单一的可果美层，双层，和两个不同的三层。作为一个函数的自旋-轨道耦合，直接和间接的$d$ -轨道跳跃，和频带填充的强度，我们确定了一些情况下，一个非相互作用的时间反演不变的Z $_2$拓扑相位是预期的，我们建议一些候选材料。我们在Hatree-Fock理论下研究了半填充$d$壳层中的相互作用，并确定了可以找到零磁场Chern绝缘体的参数区域，其中Chern数为$\pm1$.最有希望的拓扑相的几何结构似乎是既支持Z $_2$拓扑绝缘体又支持Chern绝缘体的双层结构，以及三角形-kagome-三角形三层，其支持相对稳健的Chern绝缘体相。
Quite recently, magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. Thermal Hall conductivity $κ^{xy}$, changes sign as a function of magnetic field or temperature on the kagome lattice, and $κ^{xy}$ changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the brea…
Signatures of field-induced multi-color kagome spin liquids in the dipole-octupole pyrochlore $\mathrm{Ce_2Hf_2O_7}$
Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides（巴黎萨克雷大学，法国国家科学研究中心，固体物理实验室）；The Institute for Solid State Physics, The University of Tokyo（东京大学固体物质研究所）；Institut für Theoretische Physik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Technische Universität Dresden（德累斯顿工业大学理论物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat）；Department of Physics, The University of Tennessee（田纳西大学物理系）；Institute for Advanced Study, Chengdu University（成都大学高等研究院）；Department of Physics and Astronomy, McMaster University（麦克马斯特大学物理与天文学系）；Brockhouse Institute for Materials Research, McMaster University（麦克马斯特大学布罗克豪斯材料研究所）；Département de Physique, Université（大学物理系）
We investigate the electronic and magnetic properties of the kagome mineral averievite (CsCl)Cu$_5$V$_2$O$_{10}$ and its phosphate analog (CsCl)Cu$_5$P$_2$O$_{10}$ using first-principles calculations. The crystal structure of these compounds features Cu$^{2+}$ kagome layers sandwiched between Cu$^{2+}$-P$^{5+}$/Cu$^{2+}$-V$^{5+}$ honeycomb planes, with pyrochlore slabs made of corner-sharing Cu-tetrahedra being formed. The induced chemical pressure effect upon substitution of V by P causes significant changes in the structure and magnetic properties. Even though the in-plane antiferromagnetic …
We investigate analytically and numerically the classical ground states of frustrated Heisenberg models on pyrochlore and kagome lattices in zero and finite magnetic fields. Each model has a wide region in the microscopic parameter space, where the propagation vector is turned to a commensurate position equal to a half of the reciprocal lattice vector with a nontrivial star. Within these regions the zero-field ground states for both models correspond to noncoplanar triple-k spin configurations. A universal appearance of the 3-k states can be related to the spin-space dimensionality. A strong m…
Transverse field Ising model is a common model in quantum magnetism and is often illustrated as an example for quantum phase transition. Its physical origin in quantum magnets, however, is actually not quite well-understood. The quantum mechanical properties of this model on frustrated systems are not well-understood either. We here clarify the physical origin, both extrinsic one and intrinsic one, for the transverse field of the quantum Ising model, and then explain the quantum effects in the Kagome system. We discuss the quantum plaquette order and the quantum phase transition out of this or…
We report on the epitaxial growth, structural and electrical properties of metallic pyrochlore bismuth ruthenate heterostructures grown along both the [001] and [111] directions. Ordered pyrochlore thin films were obtained with highly oriented texture along the [001] and [111] crystallographic directions. Density functional theory calculations of the electronic band structure and density of states indicated that Bi$_2$Ru$_2$O$_7$ is semimetallic and that hybridization of the Ru 4$d$ and Bi 6$p$ orbitals via the anion network at the Fermi energy was responsible for the metallicity. Electrical c…
We present the crystal structures and magnetic properties of RE3Sb3Mg2O14 (La3Sb3Mg2O14, Pr3Sb3Mg2O14, Sm3Sb3Mg2O14, Eu3Sb3Mg2O14, Tb3Sb3Mg2O14, and Ho3Sb3Mg2O14), a family of novel materials based on a perfect geometry 2D rare earth Kagome lattice. Structure refinements were performed by the Rietveld method using X-ray diffraction data, indicating that the layered compounds are fully structurally ordered. The compounds crystallize in a rhombohedral supercell of the cubic pyrochlore structure, in the space group R-3m. As indicated by magnetic susceptibility measurements, they exhibit predomina…
A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod kagome lattice material Ho${_3}$Mg${_2}$Sb${_3}$O${_{14}}$ unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho$^{3+}$ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodyna…
In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy. These flat bands can coexist with Dirac nodes …
We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local $\langle 111 \rangle$ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable $\textit{"snake"}$ domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field…
Neutron scattering measurements have been performed on deuterated powder samples of claringbullite and Zn-doped claringbullite (Zn$_x$Cu$_{4-x}$(OD)$_{6}$FCl). At low temperatures, claringbullite Cu$_4$(OD)$_{6}$FCl forms a distorted pyrochlore lattice with long-range magnetic order and spin-wave-like magnetic excitations. Partial Zn doping leads to the nominal ZnCu$_3$(OD)$_{6}$FCl compound, a geometrically frustrated spin-1/2 kagome antiferromagnet that shows no transition to magnetic order down to 1.5 K. The magnetic excitations form a gapless continuum, a signature of fractional excitation…
The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction is shown to possess Weyl points, i.\,e., pairs of topological nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions of the Weyl points in reciprocal space can be tuned widely by an external magnetic field: rotated within the surface plane, the Weyl points and magn…
We have studied long range orders of electric quadrupole moments described by an effective pseudospin-$\frac{1}{2}$ Hamiltonian representing pyrochlore magnets with non-Kramers ions under [111] magnetic field, in relevance to Tb$_{2}$Ti$_{2}$O$_{7}$. Order parameters and phase transitions of this frustrated system are investigated using classical Monte-Carlo simulations. In zero field, the model undergoes a first-order phase transition from a paramagnetic state to an ordered state with an antiparallel arrangement of pseudospins. This pseudospin order is characterized by the wavevector $\boldsy…
There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor coupling parameters allowed. In this Article, we ask what kinds of classical, ordered, ground states can be expected to occur in these materials, assuming generic (i.e. non-fine-tuned) sets of exchange parameters. We use symmetry analysis to show that there are only five distinct classical ground state phases occurring for generic parameters. The five…
Anomalous Hall Effect due to Non-collinearily in Pyrochlore Compounds: Role of Orbital Aharonov-Bohm Effect
为了阐明烧绿石化合物中自旋结构驱动的反常霍尔效应（AHE）的起源，我们构建了$t_{2g}$ -轨道kagome晶格模型，并分析了反常霍尔电导（AHC）.我们发现，一个传导电子获得一个Berry相位由于复杂的d-轨道波函数的存在下的自旋轨道相互作用。这种“轨道Aharonov-Bohm（AB）效应”产生了在非共线自旋结构存在下急剧变化的AHC。在铁磁化合物Nd $_2$ Mo $_2$ O $_7$和顺磁化合物Pr $_2$ Ir $_2$ O $_7$中，由轨道AB效应产生的AHC完全支配自旋手征机制，并成功地解释了自旋结构与AHC之间的实验关系。特别地，在Pr $_2$ Ir $_2$ O $_7$中观察到的“在没有磁化的情况下的有限AHC”可以通过假设Ir 5d电子的小磁序而用轨道机制来解释。
As materials with suppressed ordering temperatures and enhanced ground state entropies, frustrated magnetic oxides are ideal candidates for cryogenic magnetocaloric refrigeration. While previous materials design has focused on tuning the magnetic moments, their interactions, and density of moments on the lattice, there has been relatively little attention to frustrated lattices. Prior theoretical work has shown that the magnetocaloric cooling rate at the saturation field is proportional to a macroscopic number of soft mode excitations that arise due to the classical ground state degeneracy. Th…
A quantum spin liquid (QSL) is a state of matter where unpaired electrons' spins in a solid are quantum entangled, but do not show magnetic order in the zero-temperature limit. Because such a state may be important to the microscopic origin of high-transition temperature superconductivity and useful for quantum computation, the experimental realization of QSL is a long-sought goal in condensed matter physics. Although neutron scattering experiments on the two-dimensional (2D) spin-1/2 kagome-lattice ZnCu3(OD)6Cl2 and effective spin-1/2 triangular lattice YbMgGaO4 have found evidence for a cont…
Frustrated three dimensional quantum magnets are notoriously impervious to theoretical analysis. Here we use a combination of three computational methods to investigate the three dimensional pyrochlore $S=1/2$ quantum antiferromagnet, an archetypical frustrated magnet, at finite temperature, $T$: canonical typicality for a finite cluster of $2\times 2 \times 2$ unit cells (i.e. $32$ sites), a finite-$T$ matrix product state method on a larger cluster with $48$ sites, and the numerical linked cluster expansion (NLCE) using clusters up to $25$ lattice sites, which include non-trivial hexagonal a…
Exact eigenstates of highly frustrated spin lattices probed in high fields
强阻挫反铁磁体如磁性分子{Mo 72 Fe 30}、kagome或烧绿石晶格表现出各种迷人的性质，如低位单线态、磁化平台以及磁化跳变。在最近几年中，精确的多体本征态可以为这些自旋系统中的几个构建。这些态在高磁场中成为基态，并且它们也导致奇异行为。理解这些性质的一个关键概念是由独立的定域磁振子提供的。这些n-磁振子态的能量本征值与独立磁振子的数目n成线性比例，因此与总磁量子数M=Ns-n成线性比例。在外加磁场中，这导致了一个巨大的磁化跳变，构成了一个新的宏观量子效应。它将被证明，这种行为是伴随着一个大规模的简并，广泛的（T=0）熵，从而在饱和磁场的大磁热效应。将概述与平带铁磁性的联系。
We study the formation of magnetic clusters in frustrated magnets in their cooperative paramagnetic regime. For this purpose, we consider the $J_1$-$J_2$-$J_3$ classical Heisenberg model on kagome and pyrochlore lattices with $J_2 = J_3=J$. In the absence of farther-neighbor couplings, $J=0$, the system is in the Coulomb phase with magnetic correlations well characterized by pinch-point singularities. Farther-neighbor couplings lead to the formation of magnetic clusters, which can be interpreted as a counterpart of topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C.…
Critical behavior of 2 and 3 dimensional ferro- and antiferromagnetic spin ice systems in the framework of the Effective Field Renormalization Group technique
