Frustration-induced highly anisotropic magnetic patterns in the classical XY model on the kagome lattice

We predict and observe numerically highly anisotropic magnetic patterns in the classical frustrated model of planar XY spins on the regular kagome lattice. Frustration is introduced by a specific spatial arrangement of both ferromagnetic and antiferromagnetic bonds between adjacent magnetic moments on the lattice vertices. Defining a quantitative measure of frustration, we find that at a critical value of frustration, f = f(c) = 3/4, the system displays a phase transition from an ordered ferromagnetic state to a frustrated regime featuring a highly degenerate ground state. In this frustrated regime, which extends for a finite range of frustrations f(c) < f <= 1, we obtain an unexpected scaling of a spatially averaged magnetization <<(M)over right arrow>> with the total number of nodes N: <(M) over right arrow > similar or equal to N-1/4. This scaling results from highly anisotropic magnetic patterns displaying perfect ferromagnetic ordering along the y-direction, and short-range correlations of magnetic moments along the x-direction. We show that all these features are explained by the presence of the doubly degenerate ground state in the basic cell, i.e., a single triangle, of the kagome lattice combined with an extensive number of intrinsic constraints on the spins. This model represents an interesting class of frustrated magnetic systems, which might be present in other lattice geometries.