We study the consequences of in-plane (D_p) and out-of-plane (D_z) Dzyaloshinsky-Moriya (DM) interactions on the thermodynamic properties of spin-1/2} Heisenberg model on the kagome lattice using numerical linked cluster expansions and exact diagonalization, and contrast them with those of other perturbations such as exchange anisotropy and dilution. We find that different combinations of the DM anisotropies lead to a wide variety of thermodynamic behavior, which are quite distinct from those of most other perturbations. We argue that the sudden upturn seen experimentally in the susceptibility of the material ZnCu3(OH)6Cl2 can be understood in terms of Dzyaloshinsky-Moriya anisotropies with D_p>|D_z|. We also show that the measured specific heat of the material puts further constraints on the allowed DM parameters.
Dzyaloshinsky-Moriya interaction in vesignieite: A route to freezing in a quantum kagome antiferromagnet
本文报道了自旋为1/2的几何阻挫反铁磁玻镁矿BaCu $_3$ V $_2$ O $_8$（OH）$_2$的电子自旋共振研究.的线宽和线位移的分析表明，占主导地位的面内Dzyaloshinsky-Moriya各向异性，提出抑制强烈的量子自旋波动，从而促进长程有序，而不是自旋液体状态。我们还证明了增强的自旋-声子贡献，可能源于晶格不稳定性，并讨论了局部不均匀性方面的内在和体磁化率之间的低温失配的起源。
Dzyaloshinsky-Moriya antisymmetric exchange coupling in cuprates: Oxygen effects
我们重新审视一个问题的Dzyaloshinsky-Moriya反对称交换耦合铜酸盐中的单键指定的本地自旋轨道贡献Dzyaloshinsky矢量专注于氧项。的Dzyaloshinsky矢量和各自的弱铁磁矩被证明是一个叠加的可比性，有时，竞争本地铜和O的贡献。中间态氧的$^{17}$ O Knight位移被证明是一个有效的工具，以检查在外部磁场中的Dzyaloshinsky-Moriya耦合的影响。我们预测了$strong$氧弱反铁磁性的影响，在边缘共享的CuO $_2$链由于未补偿的氧Dzyaloshinsky矢量。最后，我们重新审视对称自旋各向异性的影响，特别是那些直接引起的Dzyaloshinsky-Moriya耦合。
In order to clarify why the experimental magnetization curve of the spherical kagome cluster in {W72V30} at 0.5 K shows no sign of staircase behavior up to 50 T, we study the effects of Dzyaloshinsky-Moriya (DM) interactions and tilts of the g tensors, both of which lead to the breaking of the total-S z conservation, by using the exact diagonalization method. It is found that the D vector component parallel to the radiation direction of the polyhedron cancels out the staircase in a low magnetic field region efficiently. The tilts of the g tensors are inherent to systems defined on the poly- he…
We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of non-collinear magnetic orders of the $J_1$-$J_2$ Heisenberg model ($\mat…
We investigate the antiferromagnetic canting instability of the spin-1/2 kagome ferromagnet, as realized in the layered cuprates Cu$_3$Bi(SeO$_3)_2$O$_2$X (X=Br, Cl, and I). While the local canting can be explained in terms of competing exchange interactions, the direction of the ferrimagnetic order parameter fluctuates strongly even at short distances on account of frustration which gives rise to an infinite ground state degeneracy at the classical level. In analogy with the kagome antiferromagnet, the accidental degeneracy is fully lifted only by non-linear 1/S corrections, rendering the sel…
Pyrochlore oxides show several fascinating phenomena, such as the formation of heavy fermions and the thermal Hall effect. Although a key to understanding some phenomena may be the Dzyaloshinsky-Moriya (DM) interaction, its microscopic origin is unclear. To clarify the microscopic origin, we constructed a $t_{2g}$-orbital model with the kinetic energy, the trigonal-distortion potential, the multiorbital Hubbard interactions, and the $LS$ coupling, and derived the low-energy effective Hamiltonian for a $d^{1}$ Mott insulator with the weak $LS$ coupling. We first show that lack of the inversion …
Quantum-classical crossover in finite spin-1/2 rings with Dzyaloshinsky-Moriya interaction
i Intelligent Insights（4i智能洞察）；Nanjing University of Information Science and Technology（南京信息工程大学）；Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean（江苏省大气与海洋光电探测重点实验室）
We study the modification of low temperature properties of quantum magnets such as magnetization, heat capacity, energy spectrum, and densities of condensed and noncondensed quasiparticles (triplons) due to anisotropies in the framework of mean-field based approach. We show that in contrast to exchange anisotropy (EA) interaction, Dzyaloshinsky-Moriya (DM) interaction modifies the physics dramatically. Particularly, it changes the sign of the anomalous density in the whole range of temperatures. Its critical behavior is slightly modified also by the EA. We have found that the shift of the crit…
A single crystal S=3/2 perfect kagome lattice antiferromagnet $\mathrm{KCr_3(OH)_6(SO_4)_2}$ (Cr-jarosite) has been studied by X-band and high-frequency electron spin resonance (ESR). The g-values perpendicular to the kagome plane (c-axis) and in the plane are determined to be $g_c=1.9704 \pm 0.0002$ and $g_ξ=1.9720 \pm 0.0003$, respectively, by high-frequency ESR observed at 265 K. Antiferromagnetic resonances (AFMR) with the antiferromagnetic gap of 120 GHz are observed at 1.9 K, which is below $T_N$=4.5 K. The analysis of AFMR modes by the conventional molecular field theory shows $d_p=0.27…
We have studied the effect of the Dzyaloshinskii-Moriya interaction on kagome Heisenberg anti-ferromagnet using Schwinger boson mean field theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ansätze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and…
A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J \simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need t…
We apply linked cluster expansion techniques to study the polarized high-field phase of a spin-half antiferromagnet on the Kagome lattice with Heisenberg and Dzyaloshinskii-Moriya interactions (DMI). We find that the Dirac points of the single-magnon spectrum without DMI are robust against arbitrary DMI when the magnetic field lies in the Kagome plane. Unlike the typical case where DMI gaps the spectrum, here we find that varying the DMI merely shifts the location of the Dirac points. In contrast, a magnetic field with a component out of the Kagome plane gaps the spectrum, leading to topologic…
We theoretically study magnetic and topological properties of antiferromagnetic kagome spin systems in the presence of both in- and out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron jarosites, the in-plane interactions stabilize a canted noncollinear "umbrella" magnetic configuration with finite scalar spin chirality. We derive expressions for the canting angle, and use the resulting order as a starting point for a spin-wave analysis. We find topological magnon bands, characterized by non-zero Chern numbers. We calculate the magnon thermal Hall conductivity, and pr…
The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with non-negligible Dzyaloshinskii-Moriya interaction~(DMI). A well established phase transition to the $\mathbf q=0$ long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in inelastic neutron scattering experiment by Han et al (…
The field of frustrated magnetism has been enriched significantly by the discovery of various kagome lattice compounds. These materials exhibit a great variety of macroscopic behaviours ranging from magnetic orders to quantum spin liquids. Using large-scale exact diagonalization, we construct the phase diagram of the $S=1/2$ $J_1$-$J_2$ kagome Heisenberg model with $z$-axis Dzyaloshinskii-Moriya interaction $D_z$. We show that this model can systematically account for many of the experimentally observed phases. Small $J_2$ and $D_z$ can stabilize respectively a gapped and a gapless spin liquid…
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…
For the spin-1/2 spherical kagomé cluster, as well as for the 2D kagomé lattice, many low-energy singlet excitations have been expected to exist in the energy region below the spin gap, which has been actually confirmed by Kihara $et \ al.$ in their specific heat measurements up to 10K in {W$_{72}$V$_{30}$}, for which the exchange interaction was estimated as $J=115$K. However, the experimental result of the specific heat can not be reproduced by the theoretical result in the Heisenberg model. Although the theoretical result has a peak around 2 K, the experimental one does not. To elucidate th…
The finite-temperature magnetism of a monolayer on a bcc (110) surface was examined using a model Hamiltonian containing ferromagnetic or antiferromagnetic exchange interactions, Dzyaloshinsky-Moriya interactions and easy-axis on-site anisotropy. We examined the competition between the collinear ground state parallel to the easy axis and the spin spiral state in the plane perpendicular to this axis preferred by the Dzyaloshinsky-Moriya interaction. Using approximative methods to calculate the magnon spectrum at finite temperatures, it was found that even if the ground state is collinear, incre…
We performed a comprehensive electron spin resonance, magnetization and heat capacity study on the field-induced magnetic phase transitions in the kagome antiferromagnet $α-Cu_3Mg(OH)_6Br_2$. With the successful preparation of single crystals, we mapped out the magnetic phase diagrams under the $c$-axis and $ab$-plane directional magnetic fields $B$. For $B\|c$, the three-dimensional (3D) magnon Bose-Einstein condensation (BEC) is evidenced by the power law scaling of the transition temperature, $T_c\propto (B_c-B)^{2/3}$. For $B\|ab$, the transition from the canted antiferromagetic (CAFM) sta…
We perform a symmetry analysis of the ABC-stacked kagome planes of Mn atoms common to the $L1_2$ Mn$_3$X and antiperovskite Mn$_3$AB alloys. In addition to the single-ion-anisotropy and Kitaev-type anisotropic exchange known to stabilize 120° spin structures in these materials, our analysis results in a staggered Dzyaloshinskii-Moriya interaction and further gamma-type anisotropic exchange between nearest-neighbor spins. The presence of these new terms is shown not to affect the energetics of the 120° ground-states which explains their absence in prior minimal magnetic models. We go on to show…
In this work, topological properties of a ferromagnetic Heisenberg model on a breathing kagome lattice are investigated extensively in the presence of Dzyaloshinskii-Moriya interaction. While the kagome ferromagnet hosts only a single first order topological phase, the breathing kagome system exhibits multiple first and second order topological phases along with their coexistence. Magnon dispersion relation is obtained by using linear spin wave theory. Flat band and Dirac cones are obtained in the absence of Dzyaloshinskii-Moriya interaction. A topological phase diagram is presented where seve…
