Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally fluctuate cooperatively from a collection of spiral configurations at low temperatures. These spiral propagation wavevectors form a continuous manifold in reciprocal space, \textit{i.e.}, a spiral contour or a spiral surface, that strongly governs the low-temperature thermal fluctuations and magnetic physics. In this paper, the relevant spin models conveying the spiral spin liquid physics are systematically explored and the geometric origin of the spiral manifold is clarified in the model construction. The spiral spin liquids based on the dimension and the codimension of the spiral manifold are further clarified. For each class, the physical properties are studied both generally and for specific examples. The results are relevant to a wide range of frustrated magnets. A survey of materials is given and future experiments are suggested.
Spiral spin-liquids are correlated paramagnetic states with degenerate propagation vectors forming a continuous ring or surface in reciprocal space. On the honeycomb lattice, spiral spin-liquids present a novel route to realize emergent fracton excitations, quantum spin liquids, and topological spin textures, yet experimental realizations remain elusive. Here, using neutron scattering, we show that a spiral spin-liquid is realized in the van der Waals honeycomb magnet FeCl$_3$. A continuous ring of scattering is directly observed, which indicates the emergence of an approximate U(1) symmetry i…
Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by sub-dimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is non-bipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As illustr…
We investigate the stability of the spiral spin liquid phase in MnSc$_2$S$_4$ against thermal and quantum fluctuations as well as against perturbing effects of longer-range interactions. Employing $ab~initio$ density functional theory (DFT) calculations we propose a realistic Hamiltonian for MnSc$_2$S$_4$, featuring second ($J_2$) and third $(J_3)$ neighbor Heisenberg interactions on the diamond lattice that are considerably larger than previously assumed. We argue that the combination of strong $J_2$ and $J_3$ couplings reproduces the correct magnetic Bragg peak position measured experimental…
Quantum spin liquids are long-range entangled phases whose magnetic correlations are determined by strong quantum fluctuations. While an overarching principle specifying the precise microscopic coupling scenarios for which quantum spin-liquid behavior arises is unknown, it is well-established that they are preferably found in spin systems where the corresponding classical limit of spin magnitudes $S\rightarrow\infty$ exhibits a macroscopic ground state degeneracy, so-called classical spin liquids. Spiral spin liquids represent a special family of classical spin liquids where degenerate manifol…
Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc$_2$S$_4$ by directly observing the 'spiral surface' - a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step order…
Like the twisting control in magic angle twisted bilayer graphenes, the stacking control is another mechanical approach to manipulate the fundamental properties of solids, especially the van der Waals materials. We explore the stacking-induced magnetic frustration and the spiral spin liquid on a multilayer triangular lattice antiferromagnet where the system is built from ABC stacking with competing intralayer and interlayers couplings. By combining the nematic bond theory and the self-consistent Gaussian approximation, we establish the phase diagram for this ABC-stacked multilayer magnet. It i…
Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear Néel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the Néel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critica…
Fractional vortices in a spin-isotropic spiral spin liquid
University of Oslo（奥斯陆大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源研究中心）；Freie Universität Berlin（柏林自由大学）；The University of Tokyo（东京大学）
Incommensurate order with translationally invariant projected entangled-pair states: Spiral states and quantum spin liquid on the anisotropic triangular lattice
In this work we identify a previously unexplored type of topological defect in spiral spin liquids -- the momentum vortex -- and reveal its dominant role in shaping the low energy physics of such systems. Spiral spin liquids are a class of classical spin liquids featuring sub-extensively degenerate ground states. They are distinct from spin liquids on geometrically frustrated lattices, in which the ground state degeneracy is extensive and connected by local spin flips. Despite a handful of experimental realizations and many theoretical studies, a concrete physical picture of their spin liquidi…
University of Oxford（牛津大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体的化学物理研究所）；University College Cork（科克大学学院）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Cornell University（康奈尔大学）
We study classical $J_1$-$J_2$ models with distinct spin degrees of freedom on a honeycomb lattice. For the XY and Heisenberg spins, the system develops a spiral spin liquid (SSL) that is a thermal cooperative paramagnetic regime with spins fluctuating around the spiral contours in the momentum space, and at low temperatures supports a vector spin-chirality order despite the absence of long-range magnetic order. In a strong contrast, for the Ising moments, the low-temperature spin correlation forms a reciprocal "kagomé" structure in the momentum space that resembles the SSL behaviors and persi…
By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmet…
We investigated the spiral spin density waves in the monolayer 1T-MnCl$_2$ for a set of spiral vectors based on first-principles calculations. The magnetic ground states were evaluated by means of the generalized Bloch theorem within the linear combination of pseudo-atomic orbitals. To reach our purpose, a flat spiral configuration was constructed for the Mn magnetic atom by fixing the direction of its magnetic moment. We confirmed that the ground state was a spiral ground state. We also clarified that a phase transition from a spiral ground state to the other ground states, such as the ferrom…
Spiral spin liquid resilient to quantization in the frustrated honeycomb antiferromagnet GdZnPO
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院武汉国家磁强场中心）；School of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China（中国人民大学物理学院光电功能材料与微纳器件北京市重点实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Songshan Lake Materials Laboratory（松山湖材料实验室）
The unconventional magnetic orderings found in Kitaev spin liquid candidates suggest frustration of spin interactions, and raise a possibility of nearby spin liquid phases. In particular, counter-rotating spiral ordering in three-dimensional (3D) iridates is striking, and understanding the microscopic mechanism of such ordering may provide routes to 3D Kitaev spin liquids. We study a minimal 3D model including Kitaev $K$ and a symmetric off-diagonal bond-dependent $Γ$ interaction on the hyperhoneycomb lattice using exact diagonalization. We first show that a 12-site unitary transformation unve…
The archetype cubic chiral magnet MnSi is home to some of the most fascinating states in condensed matter such as skyrmions and a non-Fermi liquid behavior in conjunction with a topological Hall effect under hydrostatic pressure. Using small angle neutron scattering, we study the evolution of the helimagnetic, conical and skyrmionic correlations with increasing hydrostatic pressure. We show that the helical propagation vector smoothly reorients from $\langle 111 \rangle$ to $\langle100\rangle$ at intermediate pressures. At higher pressures, above the critical pressure, the long-range helimagne…
We address quantum spin helical states in the strongly frustrated Heisenberg model. Contrary to conventional Dzyaloshinskii-Moriya approach we show that such states appear without central symmetry breaking. As an example, we demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound $\mathrm{(CuBr)Sr_{2}Nb_{3}O_{10}}$ can be interpreted within 2D $S = 1/2$ $J_1-J_2-J_3$ Heisenberg model. In this compound neutron experiment indicates helical spin order while central symmetry does hold.
We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are res…
Electric-dipole active two-magnon excitation in {\textit{ab}} spiral spin phase of a ferroelectric magnet Gd$_{\textbf{0.7}}$Tb$_{\textbf{0.3}}$MnO$_{\textbf 3}$
Massachusetts Institute of Technology（麻省理工学院）；California Institute of Technology（加州理工学院）；Oak Ridge National Laboratory（橡树岭国家实验室）；PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与缪子科学中心）
Collinear-to-Spiral Spin Transformation without Changing Modulation Wavelength upon Ferroelectric Transition in Tb1-xDyxMnO3
用X射线衍射和中子衍射研究了铁电居里温度T_C附近的磁电化合物Tb_（1-x）Dy_xMnO_3的晶格调制和磁结构。对于0.50< x < 0.68的化合物，通过T_C观察到温度无关的调制矢量。这表明，铁电性与极化（P）沿c轴的RMnO 3系列不能归因于这样的ininadenate相称的过渡的反铁磁秩序，如先前预期的。X=0.59的单晶的中子衍射研究表明，FE转变伴随着Mn自旋取向从正弦（共线）反铁磁性到横向螺旋结构的转变。在T_C以下观察到的螺旋结构预期沿c轴产生P，并具有“逆”Dzialoshinski-Moriya相互作用，这与观察一致。
We demonstrate that dynamics of the ab-spiral-spin order in a magnetoelectric multiferroic Eu0.55Y0.45MnO3 can be unambiguously probed through optical second harmonic signals, generated via the spin-induced ferroelectric polarization. In the case of relatively weak photoexcitation,the ferroelectric and the spiral-spin order remains interlocked, both relaxing through spin-lattice relaxation in the non-equilibrium state. When the additional optical pulse illuminating sample is intense enough to induced a local phase transition thermally, the system creates a metastable state of the bc-spiral-spi…
In the present work we address a long standing problem of the magnetic ground state and magnetic excitations in underdoped cuprates. Modelling cuprates by the extended $t-J$ model we show that there is a hidden dimensionless parameter $λ$ which drives magnetic criticality at low doping $x$. Hence we derive the zero temperature $λ-x$ phase diagram of the model. It is argued that all underdoped cuprates are close to the quantum tricritical point $x=0$, $λ=1$. The three phases "meet" at the tricritical point: (i) Néel antiferromagnet, (ii) spin spiral with antinodal direction of the spiral wave v…
We revisit the ground state of the spin-Fermion model within a semiclassical approximation. We demonstrate that antiphase spin spirals, or pi-spirals, whose chirality alternates between consecutive rows (or columns) of local moments, have, for sufficiently high carrier concentration, lower energy than the traditional Shraiman and Siggia spirals. Furthermore, pi-spirals give rise to modulated hopping, anisotropic 1D transport, and charge density wave formation. Finally, we discuss the relevance of pi-spirals to the physics of charge stripe formation in cuprates, such as La(2-x)Sr(x)CuO4.
Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family Li2IrO3 shows an incommensurate order where spirals on neighboring sublattices are counter-rotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: the Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we pro…
Planar Topological Hall effect (PTHE) is known to arise from in-plane skyrmion tubes with an external magnetic field applied in the plane of the charge current. Here, we propose that the PTHE can robustly appear also from an unexpected source, the conical spin spiral, realizable in a variety of materials. We show that for both in-plane skyrmion tubes and conical spin spirals, the PTHE is two-fold symmetric with respect to the magnetic-field angle, while it is four-fold symmetric for 90$^{\circ}$-rotated domains of conical spin spirals. We predict that the symmetry and magnetic-field response o…
