Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.
We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks do…
Tunable quantum spin liquidity in the 1/6th-filled breathing kagome lattice
我们提出了一系列材料，Li $_2$ In $_{1-x}$ Sc $_x$ Mo $_3$ O $_8$，可以被描述为1/6填充呼吸戈薇晶格的测量。用Sc代替In产生化学压力，其非单调地改变呼吸参数。$μ$ SR实验表明，该化学压力将系统从反铁长程序调谐到量子自旋液体相。与呼吸参数的强相关性意味着它是控制磁挫挫水平的主导参数，增加的kagome对称性产生量子自旋液体相。磁化率测量表明，这与晶格对称性变化引起的不同类型的电荷有序有关，符合Chen等人的理论[Phys. Rev. B 93，245134（2016）]。在中等Sc浓度和最小呼吸参数下，样品的比热与预测的$U(1)$量子自旋液体一致。
High-pressure modulation of breathing kagome lattice: Cascade of Lifshitz transitions and evolution of the electronic structure
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿罗森多夫赫尔姆霍兹中心）；TUD Dresden University of Technology（德累斯顿工业大学）；Universität Stuttgart（斯图加特大学）；Synchrotron SOLEIL（索雷尔同步辐射中心）；ESRF（欧洲同步辐射装置）；ShanghaiTech University（上海科技大学）；Renmin University of China（中国人民大学）
We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our …
Motivated by recent experiments in Gd$_3$Ru$_4$Al$_{12}$, we demonstrate the emergence of atomic scale Skyrmions in interacting spins on a breathing kagome lattice with competing nearest neighbor ferromagnetic and next nearest neighbor antiferromagnetic exchange interactions. In the presence of an applied longitudinal magnetic field, the ground state magnetic order evolves from a helical phase at low fields to a Skyrmion phase at intermediate fields before finally entering a polarized phase at high fields. The size of each Skyrmion spans only two unit cells of the lattice, in contrast to tens …
We show that classical Heisenberg antiferromagnets on the breathing kagome lattice can be a platform to realize a zero-field topological order of the scalar spin chirality which can be viewed as a miniature skyrmion crystal (SkX) of discrete form with a small number of spins in its magnetic unit cell. In the model, a third nearest-neighbor (NN) antiferromagnetic interaction along the bond direction $J_3$ and the breathing bond-alternation characterized by the ratio of the NN interaction for large triangles to that for small ones, $J_1'/J_1$, are essential. It is found by means of Monte Carlo s…
Precompression engineering of metal-insulator transition and magnetism in designed breathing kagome systems
School of Physics and Astronomy, and Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学物理与天文学院，多尺度自旋物理教育部重点实验室）；College of Physics, Hebei Normal University, and Hebei Advanced Thin Films Laboratory（河北师范大学物理学院，河北省先进薄膜实验室）
The stability of a miniature skyrmion crystal (SkX) with only a small number of spins in the magnetic unit cell has been theoretically investigated in $J_1$-$J_3$ antiferromagnets on the breathing kagome lattice with a single-ion anisotropy $D$ at zero field. It is found by means of Monte Carlo simulations that due to the breathing bond-alternation, a zero-field triple-${\bf Q}$ miniature SkX can be stabilized not only in the specific case of $D=0$ [K. Aoyama and H. Kawamura, Phys. Rev. B 105, L100407 (2022)] but also in more general situations with easy-axis ($D<0$) and easy-plane ($D>0$) ani…
Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice
基于团簇Mott绝缘材料LiZn $_2$ Mo $_3$ O $_8$的最新进展，我们考虑了呼吸Kagome晶格上扩展哈伯德模型的强元胞电荷有序区，揭示了团簇Mottness的性质.格点电荷序是由格点间电荷相互作用和六边形格点上三个局域电子的集体运动引起的。该模型自然导致局部矩减少2/3，如在LiZn $_2$ Mo $_3$ O $_8$中所观察到的。此外，在低温下，每个六边形元格除了剩余的1/2自旋外，还包含额外的类轨道自由度。我们探讨的后果，这紧急轨道自由度。我们指出，局域矩之间的相互作用是自然描述的Kugel-Khomskii自旋轨道模型。我们发展了一个部分子方法，并提出了一个自旋液体基态与自旋费米表面的模型。我们进一步预测了当系统处于强磁场下时，系统会出现一个新的轨道序。讨论了LiZn $_2$ Mo $_3$ O $_8$的各种实验结果，包括一个论点，即如果每个Mo的电荷稍微偏离化学计量，则电荷排序会很短。
Magnetic Anisotropies and Skyrmion Lattice Related to Magnetic Quadrupole Interactions of the RKKY Mechanism in Frustrated Spin-Trimer System Gd$_{3}$Ru$_{4}$Al$_{12}$ with a Breathing Kagome Structure
Anomalous Hall Response Induced by Correlated Disorder in the Breathing Kagome Lattice Mn$_{3}$Sn
Oak Ridge National Laboratory（橡树岭国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Brigham Young University（杨百翰大学）；Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）
From strong to weak correlations in breathing-mode kagome van der Waals materials: Nb$_3$(F,Cl,Br,I)$_8$ as a robust and versatile platform for many-body engineering
Radboud University（拉德堡德大学）；University of Groningen（格罗宁根大学）；Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam（阿姆斯特丹大学物理学院范德瓦尔斯-泽曼研究所）；Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University（奥胡斯大学跨学科纳米科学中心（iNANO）物理与天文学系）
We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down t…
Kagome Chern Magnets are lattices which host a Chern state when they are non-magnetic and a Chern Gap when they become magnetic. These Chern gaps can host fractional Chern Fermions. There has been extensive research in the RMn$_6$Sn$_6$ system which hosts a small Chern gap with many trivial bands surrounding them. RMn$_6$Ge$_6$ is studied theoretically in order to find a more insulating Kagome magnetic with fewer bands near the Chern gap.
Magnetic Transitions under Ultrahigh Magnetic Fields of up to 130 T in the Breathing Pyrochlore Antiferromagnet LiInCr4O8
利用脉冲磁场研究了自旋为3/2的反铁磁体LiInCr 4 O 8在高达130 T的交变磁场下的磁化过程.在90 T ~ 130 T范围内，LiInCr_4 O_8具有较强的自旋-晶格耦合，与传统的铬尖晶石氧化物相似. LiGa 0.125 In 0.875 Cr 4 O 8的磁化强度在低温下的结构和磁转变被完全抑制，在13 T以上突然增加，表明在四聚体单重基态和总自旋为1的激发态之间存在2.2 meV的自旋间隙，后者通过施加磁场而稳定。呼吸烧绿石反铁磁体是一个独特的阻挫系统，具有很强的自旋-晶格耦合和键的交替。
We theoretically investigate spin-lattice coupling (SLC) effects on the in-field ordering properties of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. Here, we use the two possible simplified models describing the effect of local lattice distortions on the spin ordering via the SLC, the bond-phonon and site-phonon models. It is found by means of Monte Carlo simulations that in both models, the $\frac{1}{2}$ plateau shows up in the magnetization curve being relatively robust against the breathing bond-alternation, although magnetic long-range orders (LRO's) are reali…
Magnetic phase diagrams and magnetization plateaus of the spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice with three nonequivalent exchange interactions
Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using th…
Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge order, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to non-kagome surface layers. Here we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifes a 2x2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin-mapping across steps of unit-cell-height demonstrates that this charge order emerges from spin-polarized electrons with an antiferr…
Kagome magnet usually hosts nontrivial electronic or magnetic states drawing great interests in condensed matter physics. In this paper, we report a systematic study on transport properties of kagome magnet TmMn$_6$Sn$_6$. The prominent topological Hall effect (THE) has been observed in a wide temperature region spanning over several magnetic phases and exhibits strong temperature and field dependence. This novel phenomenon due to non-zero spin chirality indicates possible appearance of nontrival magnetic states accompanying with strong fluctuations. The planar applied field drives planar Hall…
The spin-1/2 kagome antiferromagnets are key prototype materials for studying frustrated magnetism. Three isostructural kagome antiferromagnets LnCu$_3$(OH)$_6$Cl$_3$ (Ln = Gd, Tb, Dy) have been successfully synthesized by the hydrothermal method. LnCu$_3$(OH)$_6$Cl$_3$ adopts space group $P\overline{3}m1$ and features the layered Cu-kagome lattice with lanthanide Ln$^{3+}$ cations sitting at the center of the hexagons. Although heavy lanthanides (Ln = Gd, Tb, Dy) in LnCu$_3$(OH)$_6$Cl$_3$ provide a large effective magnetic moment and ferromagnetic-like spin correlations compared to light-lant…
Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena. Here, utilizing angle-resolved photoemission spectroscopy, we demonstrate Weyl lines with strong out-of-plane dispersion in an A-A stacked kagome magnet TbxGd1-xMn6Sn6. On the Gd rich side, the Weyl line remains nearly spin-orbit-gapless due to a remarkable cooperative interplay between Kane-Mele spin-orbit-coupling, low site symmetry and in-plane magnetic order. Under Tb substitution, the kagome Weyl line gaps due to a magnetic reorientation to out-of-plane order. Our results illustrate the magnetic…
The ground state of the simple Heisenberg nearest-neighbor quantum kagome antiferromagnetic model is a magnetically disordered spin liquid, yet various perturbations may lead to fundamentally different states. Here we disclose the origin of magnetic ordering in the structurally-perfect kagome material YCu$_3$(OH)$_6$Cl$_3$, which is free of the widespread impurity problem. {\it Ab-initio} calculations and modeling of its magnetic susceptibility reveal that, similar to the archetypal case of herbertsmithite, the nearest-neighbor exchange is by far the dominant isotropic interaction. Dzyaloshins…
Singlet Ground State and Spin Gap in S=1/2 Kagome Antiferromagnet Rb$_2$Cu$_3$SnF$_{12}$
本文研究了Rb $_2$ Cu $_3$ SnF $_{12}$的晶体结构和磁性。该化合物由角共享的CuF $_{6}$八面体的可果美层组成，与适当的可果美层相比，具有2a x 2a的放大单元。Rb $_2$ Cu $_3$ SnF $_{12}$在磁性上被描述为具有四种相邻交换作用的$S$ =1/2修正的可果美反铁磁体。从磁化率和高场磁化强度测量，它被发现，基态是一个无序的单重态与自旋间隙，从最近的理论预测。精确对角化的12个站点的可果美集群进行分析的磁化率，和个人的交换相互作用进行了评估。
