The search for two dimensional quantum spin liquids, exotic magnetic states with an entangled ground state remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism during the last decades. Recently, fractionalized excitations, called spinons, emerging from these states, have been evidenced in kagome and triangular antiferromagnets. In contrast, quantum ferromagnetic spin liquids in two dimensions, namely quantum kagome ices, have been less investigated, yet their classical counterparts exhibit amazing properties, magnetic monopole crystals as well as magnetic fragmentation. Here we show that, by applying a magnetic field on the pyrochlore oxide Nd$_2$Zr$_2$O$_7$, which has been shown to develop three dimensional quantum magnetic fragmentation in zero field, we are able to reduce the dimension of the system and to create a dynamic kagome ice state. Our results open the way to the observation of the quantum kagome ice state which was recently investigated theoretically.
Spin ices are exotic phases of matter characterized by frustrated spins obeying local ice rules, in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole, and can lead to various unique orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e. non-artificial) sys…
Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in charge order.
3D XY Universality and Nonlinear magnetic susceptibility in a kagome ice compound
Beihang University（北京航空航天大学）；University of Augsburg（奥格斯堡大学）；ShanghaiTech University（上海科技大学）；RWTH Aachen University（亚琛工业大学）；Colorado State University（科罗拉多州立大学）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）；Forshungszentrum Jülich GmbH（于利希研究中心有限公司）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The stability of the kagome-ice insulator against the three dimensionality and the canting angle of the spin anisotropy axes is studied numerically using the exact diagonalization method. The kagome-ice insulator, which was recently found at 2/3 electron filling in the double-exchange model on a kagome lattice, is a Chern insulator showing a quantized Hall response despite the absence of magnetic long-range order. We find that this peculiar state remains stable when the lattice is extended to three dimensions in an anisotropic pyrochlore lattice in the weak interlayer coupling region. On the o…
We study the quantum Kagomé ice hardcore bosons, which corresponds to the XY limit of quantum spin ice Hamiltonian. We estimate the values of the zero-temperature thermodynamic quantities using the large-$S$ expansion. We show that our semi-classical analysis is consistent with finite temperature quantum Monte Carlo estimates.
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…
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…
An anomalous Hall insulator without magnetic long-range ordering is theoretically reported in the absence of the relativistic spin-orbit coupling. It is realized in itinerant electrons coupled with the Ising spins on a <111> kagome plane of pyrochlore spin ice in applied magnetic field. We find that the kagome-ice type local spin correlation in the magnetization plateau state opens a charge gap without magnetic ordering, which results in quantization of the Hall conductivity. By Monte Carlo simulation, we identify the anomalous Hall insulating region in the magnetic phase diagram, in addition …
We present the results of first-principle calculations using the Vienna Ab-initio Simulation Package (VASP) for a new class of organometallics labeled TM3C6O6 (TM =Sc, Ti, V, Cr, Fe, Co, Ni and Cu) in the form of planar, two-dimensional, periodic free-standing layers. These materials, which can be produced by on-surface coordination on metallic surfaces, have a kagome lattice of TM ions. Calculating the structural properties, we show that all considered materials have local magnetic moments in the ground state, but four of them (with Fe, Co, Ni and Cu) show spin-crossover behavior by changing …
We study the Renyi mutual information of classical systems characterized by a transfer matrix. We first establish a general relationship between the Renyi mutual information of such classical mixtures of configuration states, and the Renyi entropy of a corresponding Rokhsar-Kivelson--type quantum superposition. We then focus on chiral and nonchiral kagome-ice systems, classical spin liquids on the kagome lattice, which respectively have critical and short-range correlations. Through a mapping of the chiral kagome ice to the quantum Liftshitz critical field theory, we predict a universal sublea…
Dy$_2$Ti$_2$O$_7$ is at present the cleanest example of a spin-ice material. Previous theoretical and experimental work on the first-order transition between the kagome-ice and the fully polarized state has been taken as a validation for the dipolar spin-ice model. Here we investigate in further depth this phase transition using ac-susceptibility and dc-magnetization, and compare this results with Monte-Carlo simulations and previous magnetization and specific heat measurements. We find signatures of an intermediate state between the kagome-ice and full polarization. This signatures are absent…
Low Temperature Specific Heat of Dy$_2$Ti$_2$O$_7$ in the Kagome Ice State
我们报告了在所谓的可果美冰态下，温度低至100 mK时自旋冰化合物Dy $_2$ Ti $_2$ O $_7$单晶的比热。在我们以前的论文中，我们展示了剩余熵在不同磁场方向上的各向异性释放，并报道了在[111]方向上的场在Kagome板中与自旋阻挫相关的新的剩余熵。在本文中，我们确认了一阶相变线的场-温度相图和临界点的存在下（0.98 T，400 mK），以前报道的磁化强度和比热数据。我们在0.3K以下的1.25T处新发现了另一个比热峰。对于1 T和1.25T之间的状态的一个可能的解释是具有不同自旋构型的状态的共存，包括2-in-2-out状态（Kagome冰状态）、1-in-3-out状态（有序状态）和顺磁状态（自由自旋状态）。
Quantum effect is expected to dictate the behaviour of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy (TEE) and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a $Z_2$ topological order down to …
We present a large-$S$ study of a quantum spin ice Hamiltonian, introduced by Huang, et al., [PRL 112, 167203 (2014)], on the kagome lattice. This model involves a competition between the frustrating Ising term of classical kagome ice, a Zeeman magnetic field $h$,and a nearest-neighbor transverse spin-flip term $S^x_iS^x_j - S^y_iS^y_j$. Recent Quantum Monte Carlo (QMC) simulations by Carrasquilla, et al., [Nature Communications, 6, 7421, (2015)], uncovered lobes of a disordered phase for large Ising interaction and $h\neq 0$ -- a putative quantum spin liquid phase. Here, we examine the nature…
We study the effects of lattice deformations on the Kagome spin ice, with Ising spins coupled by nearest neighbor exchange and long range dipolar interactions, in the presence of in-plane magnetic fields. We describe the lattice energy according to the Einstein model, where each site distortion is treated independently. Upon integration of lattice degrees of freedom, effective quadratic spin interactions arise. Classical MonteCarlo simulations are performed on the resulting model, retaining up to third neighbor interactions, under different directions of the magnetic field. We find that, as th…
We show that in colloidal models of artificial kagome and modified square ice systems, a variety of ordering and disordering regimes occur as a function of biasing field, temperature, and colloid-colloid interaction strength, including ordered monopole crystals, biased ice rule states, thermally induced ice rule ground states, biased triple states, and disordered states. We describe the lattice geometries and biasing field protocols that create the different states and explain the formation of the states in terms of sublattice switching thresholds. For a system prepared in a monopole lattice s…
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 Ho3Mg2Sb3O14 unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, realizing a frustrated transverse Ising model. Using neutron scattering and thermodynamic experiments, we observe a…
A theory for frequency-dependent magnetic susceptibility χ(ω) is developed for thermally activated magnetic monopoles in kagome ice. By mapping this system to a two-dimensional (2D) Coulomb gas and then to a sine-Gordon model, we have shown that the susceptibility has a scaling form χ(ω)/χ(0)={\cal F}(ω/ω_1), where the characteristic ω_1 is related to a charge correlation length between diffusively moving monopoles, and to the sine-Gordon principal breather. The dynamical scaling is universal among superfluid and superconducting films, and 2D XY magnets above Kosterlitz-Thouless transitions.
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 …
Actively shought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at extremely low temperatures. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in real materials. Here, we study a theoretical model for a broad class of frustrated magnetic rare-earth pyrochlore materials called "quantum spin ices". When subject to an external magnetic field along the [111] crystallographic direction, the resulting spin i…
Thermodynamic properties of a spin ice model on a Kagomé lattice are obtained from dynamic simulations and compared with properties in square lattice spin ice. The model assumes three-component Heisenberg-like dipoles of an array of planar magnetic islands situated on a Kagomé lattice. Ising variables are avoided. The island dipoles interact via long-range dipolar interactions and are restricted in their motion due to local shape anisotropies. We define various order parameters and obtain them and thermodynamic properties from the dynamics of the system via a Langevin equation, solved by the H…
We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbors, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz-Thouless transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high and low-temperature phase transitions are of the Isin…
A magnetic monopole in spin ice is a novel quasiparticle excitation in condensed matter physics, and we found that the ac frequency dependent magnetic susceptibility $χ(ω)$ in the two-dimensional (2D) spin ice (so-called kagomé ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG) systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge correlation length $ξ(\propto1/\sqrt{ω_1})$, where $ω_{1}$ is a characteristic frequency proportional to the peak position of the imaginary part of $χ(ω)…
We derive an effective $Z_2$ gauge theory to describe the quantum kagome ice (QKI) state that has been observed by Carrasquilla $\textit{et. al.}$ in Monte Carlo studies of the $S = 1/2$ kagome XYZ model in a Zeeman field. The numerical results on QKI are consistent with, but do not confirm or rule out, the hypothesis that it is a $Z_2$ spin liquid. Our effective theory allows us to explore this hypothesis and make a striking prediction for future numerical studies, namely that symmetry-protected vison zero modes arise at lattice disclination defects, leading to a Curie defect term in the spin…
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…
The kagome lattice -- a two-dimensional (2D) arrangement of corner-sharing triangles -- is at the forefront of the search for exotic states generated by magnetic frustration. Such states have been observed experimentally for Heisenberg and planar spins. In contrast, frustration of Ising spins on the kagome lattice has previously been restricted to nano-fabricated systems and spin-ice materials under applied magnetic field. Here, we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scatte…
Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase…
We present numerical studies of dipolar spin ice in the presence of a magnetic field slightly tilted away from the [111] axis. We find a first-order transition from a kagome ice to a $\mathbf{q}=$X state when the external field is tilted toward the $[11\bar{2}]$ direction. This is consistent with the anomalous critical scattering previously observed in the neutron scattering experiment on the spin ice material $\textrm{Ho}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$ in a tilted field [Nat. Phys. 3, 566 (2007)]. We show that this ordering originates from the antiferromagnetic alignment of spin chains on …
We report on the non-equilibrium monopole dynamics in the classical spin ice Dy$_2$Ti$_2$O$_7$ detected by means of high-resolution magnetostriction measurements. Significant lattice changes occur at the transition from the kagome-ice to the saturated-ice phase, visible in the longitudinal and transverse magnetostriction. A hysteresis opening at temperatures below 0.6 K suggests a first-order transition between the kagome and saturated state. Extremely slow lattice relaxations, triggered by changes of the magnetic field, were observed. These lattice-relaxation effects result from non-equilibri…
Magneto-optical signatures of plateau states in the kagome spin-ice HoAgGe
Augsburg University（奥格斯堡大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）；Colorado State University（科罗拉多州立大学）；Beihang University（北京航空航天大学）；Laboratoire National des Champs Magnétiques Intenses, LNCMI-EMFL, CNRS UPR3228, Univ. Grenoble Alpes, Univ. Toulouse, Univ. Toulouse 3, INSA-T（强磁场国家实验室，LNCMI-EMFL，法国国家科学研究中心UPR3228，格勒诺布尔阿尔卑斯大学，图卢兹大学，图卢兹第三大学，国立应用科学学院-图卢兹）；Charles University（查理大学）；National Institute of Chemical Physics（国立化学物理研究所）
Saturation field entropies of antiferromagnetic Ising models on quasi one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give, in Boltzmann's units, S = 0.393589(6). We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound dysprosium titanium oxide.
We study the phase diagram of the extended Hubbard model on the kagome lattice at 1/3 filling. By combining a configuration interaction approach to an unrestricted Hartree-Fock, we construct an effective hamiltonian which takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, in particular, the presence of two original phases. The first one consists of polarized droplets of metal standing on the hexagons of the lattice, and an enlarged kagome charge order, inversely polarized, on the remaining sites. The second, obeying a local ice-rule type constra…
Asymmetric destruction of the one-third magnetization plateau upon heating is found in the spin-1/2 kagome Heisenberg antiferromagnets using the typical pure quantum state approach. The asymmetry originates from larger density of states of low-lying excited sates of $N_{\rm s}$ spin systems with magnetization $(1/3-2/N_{\rm s})$ than that of low-lying sates with magnetization $(1/3+2/N_{\rm s})$. The enhanced specific heat and entropy that reflect the larger density of states in the lower-field side of the plateau are detectable in candidate materials of the kagome antiferromagnets. We discuss…
We show that the chiral kagome ice manifold exhibits an anomalous integer quantum Hall effect (IQHE) when coupled to itinerant electrons. Although electron-mediated interactions select a magnetically ordered ground state, the full ice manifold can coexist with the IQHE over a range of finite temperatures. The degenerate ice states provide a natural realization of power-law correlated flux disorder, for which the spectral gap of the system remains robust. The quantized (up to exponentially small finite-temperature corrections) Hall conductance persists over a wide range of electron densities du…
We have studied the field-dependent ac magnetic susceptibility of single crystals of Dy2Ti2O7 spin ice along the [111] direction in the temperature range 1.8 K - 7 K. Our data reflect the onset of local spin ice order in the appearance of different field regimes. In particular, we observe a prominent feature at approximately 1.0 T that is a precursor of the low-temperature metamagnetic transition out of field-induced kagome ice, below which the kinetic constraints imposed by the ice rules manifest themselves in a substantial frequency-dependence of the susceptibility. Despite the relatively hi…
We study a local ferromagnetic Ising model for classical spins on the trillium lattice. The ground state of this model features two spins out(/in) and one spin in(/out) on each triangle, and leads to a macroscopic ground state degeneracy. Our Monte Carlo simulations find a ground state entropy intermediate to that of spin ice on the kagome and pyrochlore lattices, suggesting that trillium spin ice is highly frustrated. To motivate the search for trillium spin ice, we calculate the magnetic susceptibility and structure factor. We note the qualitative resemblance of the susceptibility to previou…
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…
We treat the ground state, elementary excitations, and neutron scattering cross section for a system of trimers consisting of three tightly bound spins 1/2 on a distorted Kagomé lattice, subject to isotropic nearest neighbor (usually antiferromagnetic) Heisenberg interactions. The interactions between trimers are assumed to be weak compared to the intra trimer interactions. We compare the spin-wave excitation spectrum of trimers with that obtained from standard spin-wave theory and attribute the differences at low energy to the fact that the trimer formulation includes exactly the effects of i…
We study the low-temperature thermal conductivity (κ) of Dy_2Ti_2O_7 along and perpendicular to the (111) plane and under the magnetic field along the [111] direction. Besides the step-like decreases of κat the field-induced transitions from the spin-ice state to the kagomé-ice state and then to the polarized state, an abnormal phenomenon is that the κ(H) isotherms show a clear irreversibility at very low temperatures upon sweeping magnetic field up and down. This phenomenon surprisingly has no correspondence with the well-known magnetization hysteresis. Possible origins for this irreversibili…
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）
