The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling

Abstract

While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC $J_{\perp }$, where we study ferro- as well as antiferromagnetic $J_{\perp }$. We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only if the strength of the ILC exceeds about 15\% of the intralayer coupling the spin-liquid phase gives way for $q=0$ magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, $|J_{\perp }^c|$, is almost independent of the sign of $J_{\perp }$. Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin $s$, the ILC leads first to a selection of the $q=0$ GS. Only at larger $|J_{\perp }|$ the ILC drives a first-order transition to the $\sqrt{3}\times \sqrt{3}$ long-range ordered GS. As a result, the stacked spin-1/2 KHAF exhibits a rich GS phase diagram with two continuous and two discontinuous transitions driven by the ILC.

7 pages, 3 figures, version as accepted in Europhys. Lett. (EPL), one formula and a few typos corrected

References in corpus (41)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu${}_3$(OH)${}_6$Cl${}_2$
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Nature of chiral spin liquids on the kagome lattice
• Barlowite: A Spin-1/2 Antiferromagnet with a Geometrically Perfect Kagome Motif
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Constraints on topological order in Mott Insulators
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Spin dynamics and disorder effects in the S=1/2 kagome Heisenberg spin liquid phase of kapellasite
• Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the $s=1/2$ kagome system ZnCu_3(OH)_6Cl_2
• Variational study of J1-J2 Heisenberg model on Kagome lattice using projected Schwinger boson wave functions
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Haydeeite: a spin-1/2 kagome ferromagnet
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Order and excitations in large-$S$ kagomé-lattice antiferromagnets
• Barlowite as a canted antiferromagnet: theory and experiment
• Chiral spin liquids on the kagome Lattice
• A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• Analytical and numerical studies of the one-dimensional sawtooth chain
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 Kagomé antiferromagnet
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations

Cited by in corpus (13)

• Origin of Magnetic Ordering in a Structurally-Perfect Quantum Kagome Antiferromagnet
• Weyl magnons in noncoplanar stacked kagome antiferromagnets
• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Reduction of magnetic interlayer coupling in barlowite through isoelectronic substitution
• Effect of perturbations on the kagome $S=1/2$ antiferromagnet at all temperatures
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Magnetically ordered and kagome quantum spin liquid states in the Zn-doped claringbullite series
• Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method
• Combinatorial exploration of quantum spin liquid candidates in the herbertsmithite material family
• Absence of long-range order in a three-dimensional stacked Ising antiferromagnet on kagome lattice
• Orthorhombic and triclinic modifications of the arsenate Cu4O(AsO4)2 and isotypic phosphates Cu4O(PO4)2: strongly frustrated antiferromagnetics
• Crystal chemistry criteria of the existence of spin liquids on the kagome lattice
• Emergence of magnetic long-range order in kagome quantum antiferromagnets