The frustrated isotropic $J_1-J_2$ model with ferromagnetic $J_1$ and anti-ferromagnetic $J_2$ interactions in presence of an axial magnetic field shows many exotic phases, such as vector chiral and multipolar phases. The existing studies of the phase boundaries of these systems are based on the indirect evidences such as correlation functions {\it etc}. In this paper, the phase boundaries of these exotic phases are calculated based on order parameters and jumps in the magnetization. In the strong magnetic field, $Z_2$ symmetry is broken, therefore, order parameter of the vector chiral phase is calculated using the broken symmetry states. Our results obtained using the modified density matrix renormalization group and exact diagonalization methods, suggest that the vector chiral phase exist only in narrow range of parameter space $J_2/J_1$.
Competing interactions in Quantum Materials induce novel states of matter such as frustrated magnets, an extensive field of research both from the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block-magnetism (magnetic order of the form $\uparrow\uparrow\downarrow\downarrow$). Now…
7Li NMR spectra were measured in a magnetic field up to 17 T at temperatures 5-30 K on single crystalline LiCu2O2. Earlier reported anomalies on magnetization curves correspond to magnetic field values where we observe changes of the NMR spectral shape. For the interpretation of the field and temperature evolutions of our NMR spectra, the magnetic structures were analyzed in the frame of the phenomenological theoretical approach of the Dzyaloshinskii-Landau theory. A set of possible planar and collinear structures was obtained. Most of these structures have an unusual configuration; they are c…
A number of topological nodes including Dirac, quadratic and triple band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock spac…
Fracton Spin Liquid and Exotic Frustrated Phases in Ising-like Octochlore Magnets
University of California, Irvine（加州大学尔湾分校）；University of Waterloo（滑铁卢大学）；Waterloo Institute for Nanotechnology, University of Waterloo（滑铁卢大学滑铁卢纳米技术研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Rice University（莱斯大学）
Frustrated magnets can host numerous exotic many-body quantum and topological phenomena. GeNi$_2$O$_4$ is a three dimensional $S=1$ frustrated magnet with an unusual two-stage transition to the two-dimensional antiferromagnetic ground state, while GeCu$_2$O$_4$ is a high-pressure phase with a strongly tetragonally elongated spinel structure and magnetic lattice formed by $S=1/2$ CuO$_2$ linear chains with frustrated exchange interactions and exotic magnetic behavior. Here we report on the first thin-film epitaxial stabilization of these two compounds. Developed growth mode, surface morphology,…
Featureless quantum spin liquid, 1/3-magnetization plateau state and exotic thermodynamic properties of spin-1/2 frustrated Heisenberg antiferromagnet on an infinite Husimi lattice
The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange $J_2 > 0$ between first neighbors in the legs, variable isotropic AF exchange $J_1$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when $J_1 \gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F…
To establish the microscopic model of the compound BiCu$_2$PO$_6$ is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is non-degenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu$_2$PO$_6$ on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the m…
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo si…
Exotic magnetism and persistent spin dynamics in a frustrated Jeff = 1/2 triangular lattice antiferromagnet
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；ISIS facility, Rutherford Appleton Laboratory（鲁瑟福阿普尔顿实验室ISIS设施）
Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$\frac{1}{2}$ isotropic ($XXX$) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.
We present a numerical study of the magnetization process of frustrated quantum spin-S chains with S=1, 3/2, 2 as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-S chains with S>1/2. Similar to the case of S=1/2, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this…
Theory of the field-induced BEC in the frustrated spin-1/2 dimer compound BaCuSi2O6
最近的中子和NMR实验的基础上，我们调查的领域引起的外来临界观察到的挫折自旋1/2二聚体化合物BaCuSi 2 O 6使用挫折模型与两种类型的双层。有效的硬核玻色子模型的半经典处理表明，完美的层间挫折导致一个2D的临界指数φ =1，没有对数校正和3D低温相不同，但非零三重态人口在两种类型的双层。这些结果进一步表明，一个简单的现象，在一个依赖于场的横向耦合的上下文中，我们重现整个场-温度相图与量子蒙特卡罗模拟。
We study the ground-state phase diagram of a spin-$\frac{1}{2}$ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, $J_\perp$ and $J_\times$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime $J_\perp\approx 2J_\times$, especially for ferromagnetic $J_{\perp, \times}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and obtain a …
Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin-$\frac{1}{2}$ ferromagnetic ($J_1$) Heisenberg chain with next-nearest-neighbor antiferromagnetic ($J_2$) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at $J_2/|J_1|>1/4$ and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous …
The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter- and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out…
A geometrically frustrated lattice may host frustrated electron spin or charge states that spawn exotic quantum phases. We show that a newly synthesized metal-organic framework of Cu-Hexaaminobenzene [Cu$_3$(HAB)$_2$] exhibits a multi spectra of unusual quantum phases long sought after in condensed matter physics. On one hand, the Cu$^{2+}$ ions form an ideal $S$-1/2 antiferromagnetic kagome lattice. On the other hand, the conjugated-electrons from the organic ligands give rise to completely dispersionless energy bands around the Fermi level, reproducing a frustrated $π_x$-$π_y$ hopping model …
Emergence of highly degenerate excited states in frustrated magnet MgCr$_2$O$_4$
基态的高简并导致奇异零能模的产生，其中一个代表性的例子是在受抑磁体中形成分子自旋类液体涨落。在这里，我们提出了单晶非弹性中子散射的结果为阻挫磁体MgCr $_2$ O $_4$，这表明，一组共同的有限能量分子自旋激发模式是持续在液体状顺磁相和磁有序相具有极其复杂的结构。基于这一发现，我们提出了激发态高简并度的概念，它促进了局域共振元激发。这一概念有望对我们理解许多复杂系统中的激发产生影响，这些系统不仅包括自旋，而且包括原子液体、复杂有序系统和无定形系统。
Finite-${\mathbf Q}$ magnetic instabilities are rather common in frustrated magnets. When the magnetic susceptibility is maximized at multiple-${\mathbf Q}$ vectors related through lattice symmetry operations, exotic magnetic orderings such as vortex and skyrmion crystals may follow. Here we show that a periodic array of nonmagnetic impurities, which can be realized through charge density wave ordering, leads to a rich phase diagram featuring a plethora of chiral magnetic phases, especially when there is a simple relation between the reciprocal vectors of the impurity superlattice and the magn…
Frustrated rare-earth pyrochlore titanates, Yb$_2$Ti$_2$O$_7$, and Tb$_2$Ti$_2$O$_7$ have been proposed as promising candidates to realize quantum spin ice (QSI). Multiple exotic quantum phases, including Coulombic ferromagnet, quantum valence-bond solid, and quadrupolar ordering, have been predicted to emerge in the QSI state upon application of a (111)-oriented external magnetic field. Here, we report on the primal successful layer-by-layer growth of ultra-thin films of frustrated quantum pyrochlores, R$_2$Ti$_2$O$_7$ (R = Er, Yb, and Tb), along the (111) direction. We confirm their high cry…
While geometrically frustrated quantum magnets are known for a variety of exotic spin states that are of great interests of understanding emergent phenomena as well as enabling revolutionary quantum technologies, most of them are necessarily good insulators which are difficult to be integrated with modern electrical circuit that relies on moving charge carriers. The grand challenge of converting fluctuations and excitations of frustrated moments into electronic responses is finding ways to introduce charge carriers that interact with the localized spins without destroying the spin states. Here…
Geometric magnetic frustration (GMF) has attracted substantial interest due to the exotic physics and rich phase diagrams revealed by the cancellation of normally-dominant magnetic interactions, giving impetus for the search for novel frustrated systems, most often based on antiferromagnetic correlations between magnetic ions decorating triangular or tetrahedral lattices. We report here low-temperature magnetic susceptibility and muon spin relaxation results on Li4MgOsO6 and Li3Mg2OsO6, members of the A5BO6 "rock salt ordered" family of frustrated materials. In Li3Mg2OsO6 we find spin freezing…
From the electrical resistivity and ac susceptibility measurements down to $T$ = 40 mK, a rich temperature-field phase diagram has been constructed for the geometrically frustrated heavy-fermion compound CePdAl. In the limit of zero temperature, the field-induced suppression of the antiferromagnetism in this compound results in a sequence of phase transitions/corssovers, rather than a single critical point, in a critical region of field 3$-$5 T. In the lowest temperature region, a power-law description of the temperature-dependent resistivity yields $A$$\cdot$$T^n$ with $n$$>$2 for all applied…
We use a semiclassical large-$S$ expansion to study a plateau at $1/3$ saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagomé lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating next-nearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exoti…
The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction ($J_2 = 1$) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction ($J_1$) along the rungs. As a function of $J_1$, the system shows many interesting ground states (gs) which vary from different types of …
The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio $t'/t$. Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell $\sqrt{12} \times \sqrt{12}$…
$β$-TeVO$_4$ is a frustrated spin 1/2 zig-zag chain system,where spin-density-wave (SDW), vector chiral (VC)and an exotic dynamic spin-stripe phase compete at low temperatures. Here we use torque magnetometry to study the anisotropy of these phases in magnetic fields of up to 5 T. Our results show that the magnetic-field-induced spin reorientation occurs in the SDW and in the spin stripe phases for $μ_0 H \geq 2$~T. The observed spin reorientation is a new element of the anisotropic phase diagram for the field directions in the $ac$ and $a^*b$ crystallographic planes. The presented results sho…
We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets ($S=1/2$) with square, rectangular and triangular structure. Our discussion is based on the $J_1$-$J_2$ type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in …
Collective behaviour of electrons, frustration induced quantum fluctuations and entanglement in quantum materials underlie some of the emergent quantum phenomena with exotic quasi-particle excitations that are highly relevant for technological applications. Herein, we present our thermodynamic and muon spin relaxation measurements, complemented by ab initio density functional theory and exact diagonalization results, on the recently synthesized frustrated antiferromagnet Li4CuTeO6, in which Cu2+ ions (S = 1/2) constitute disordered spin chains and ladders along the crystallographic [101] direc…
CoAl2O4 spinel with magnetic Co2+ ions on the diamond A-lattice is known to be magnetically frustrated. We compare neutron single crystal diffraction patterns measured in zero and applied magnetic fields with the ones obtained from classical Monte-Carlo models. In simulations we test the influence of various parameters on diffraction patterns: the ratio of nearest-, J1, and next-nearest, J2, neighbor interactions, magnetic field applied along the principal crystallographic directions, and random disorder on the A(Co2+)- and B(Al3+)- sites. We conclude that the models considered so far explain …
We report the synthesis and characterization of a new quantum magnet [2-[Bis(2-hydroxybenzyl)aminomethyl]pyridine]Ni(II)-trimer (BHAP-Ni3) in single-crystalline form. Our combined experimental and theoretical investigations reveal an exotic spin state that stabilizes a robust 2/3 magnetization plateau between 7 and 20 T in an external magnetic field. AC-susceptibility measurements show the absence of any magnetic order/glassy state down to 60 mK. The magnetic ground state is disordered and specific-heat measurements reveal the gapped nature of the spin excitations. Most interestingly, our theo…
