Generic nearest-neighbor kagome model: XYZ and Dzyaloshinskii-Moriya couplings with comparison to the pyrochlore-lattice case

Abstract

The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids. 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 arising from nearest neighbour exchange anisotropy on the kagome lattice. We determine a generic anisotropic exchange Hamiltonian from symmetry arguments. In the high-symmetry case where reflection in the kagome plane is a symmetry of the system, the generic nearest-neighbour Hamiltonian can be locally defined as a XYZ model with out-of-plane Dzyaloshinskii-Moriya interactions. We proceed to study its phase diagram in the classical limit, making use of an exact reformulation of the Hamiltonian in terms of irreducible representations (irreps) of the lattice symmetry group. This reformulation in terms of irreps naturally explains the three-fold mapping between spin liquids recently studied on kagome by the present authors [Nature Communications 7, 10297 (2016)]. In addition, a number of unusual states are stabilised in the regions where different forms of ground-state order compete, including a stripy phase with a local Z8 symmetry and a classical analogue of a chiral spin liquid. This generic Hamiltonian also turns out to be a fruitful hunting ground for coexistence of different forms of magnetic order, or of order and disorder, which we find is a particular property of the kagome lattice arising from the odd number of spins per frustrated unit. These results are compared and contrasted with those obtained on the pyrochlore lattice, and connection is made with recent progress in understanding quantum models with S = 1/2. arXiv:1706.09101v1 [cond-mat.str-el] 28 Jun 2017 where the Greek and Latin indices respectively label the spin components and the sublattices of a triangle [see Figs. 1 and 2 for the labelling convention]. Alternatively, H ∆ can be written in the form of a 9 × 9 coupling matrix J H ∆ = 1 2S   0Ĵ 01Ĵ02 J 10 0Ĵ 12 J 20Ĵ21 0  S = 1 2SĴS ,

Negative-vector-chirality 120∘ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu3(OH)6ClZorko1, Pregelj2, Gomilšek3 et al. 2019Phys. Rev. B376400View full textAdd to dashboardCite

“…Firstly, it can be due to strong quantum renormalization effects, as theoretical predictions suggest that the ordered magnetic moments should be strongly reduced close to the quantum critical point at D z /J 1 ∼ 0.1 [18,23]. Alternatively, the observed reduction of the average ordered magnetic moment can occur even for classical spins, because some of the order parameters described by the irreps of the kagome lattice correspond to configurations in which spins are not of unit length [25]. Consequently, there exist extended regions in parameter space where either multiple types of order have to coexist, or partial order that coexists with a magnetically disordered phase is established.…”

“…Moreover, persistent spin dynamics was detected by µSR at temperatures as low as T /T N = 1/300 [35]. This might have various origins, including emergent spin excitations of correlated spin-loop structures [37], or fragmentation of magnetic moments into an ordered and a fluctuating part, e.g, as proposed for some partially ordered magnetic states on the kagome lattice [25] and for incommensurate ordered states [38].…”

“…3. For Γ 5 where the basis vectors are complex and three pairs related by complex conjugation can be formed, we rather show their six linear combinationsψ j 5 = k a k ψ k 5 that constitute an equivalent real basis of this irrep [25]. The spins on each site are normalized for all basis vectors, except for the antiferromagnetic vectorsψ 3 5 andψ 6 5 , because it is impossible to form a net zero-magnetization state for three normalized collinear spins.…”

“…which represent a real basis of Γ5 [25]. The chosen assignation of the three magnetically nonequivalent sites in Eq.…”

Ordering phenomena of spin trimers accompanied by a large geometrical Hall effect

“…This is partly due to the difficulty in stabilizing commensurate non-coplanar magnetic structures on twodimensional lattices [15]. For example, on the prototypical kagomé lattice, Heisenberg spins normally prefer to order in a coplanar structure due to its amenability to fluctuations [21][22][23], and the coplanarity is maintained even in a magnetic field [24].…”