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We predict and observed novel highly anisotropic magnetic patterns obtainedin the model of frustrated planar interacting magnetic moments (the classical$X-Y$ model) on the regular kagome lattice. The frustration is provided by thepresence of both ferromagnetic and anti-ferromagnetic interactions betweenadjacent magnetic moments defined on the lattice nodes. At the critical valueof the frustration $f=f_{cr}=3/4$ such a systems displays the phase transitionfrom the ordered ferromagnetic state to the disordered frustration regimecharacterized by the highly-degenerated ground state. In the frustrated regime,$f_{cr}< f \leq 1$, unexpected scaling of spatially averaged magnetization$\langle \vec{M} \rangle $ on the total number of nodes,$N$, i.e. $\langle\vec{M} \rangle \simeq N^{-1/4}$, has been obtained. Such scaling is providedby highly anisotropic magnetic patterns displaying the ferromagnetic orderingalong the $y$-direction, and short-range correlations of magnetic moments alongthe $x$-direction. We conjecture that all these intriguing features areexplained by the presence of the double-degenerated ground state in the basiccell, i.e. single triangle, of the kagome lattice accompanying a large amountof intrinsic constraints. We anticipate the implementation of the phasetransition and anisotropic magnetic patterns in various systems, e.g. naturalmagnetic molecular clusters, artificially prepared Josephson junctionsnetworks, trapped-ions and/or photonic crystals.

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