Loop currents in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:msub><mml:mi mathvariant="normal">V</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Sb</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:math> kagome metals: Multipolar and toroidal magnetic orders

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a ``real'' charge density wave (rCDW), but also time-reversal symmetry breaking, typical loop currents described by an ``imaginary'' (iCDW). Here, we combine density-functional theory, group and phenomenological modeling to investigate complex states arise from interactions between low-energy van Hove singularities present electronic structure $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$. We find two broad classes mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, rCDW order, dubbed $3\mathbf{Q}\text{\ensuremath{-}}3\mathbf{Q}$, double-$\mathbf{Q}$ single-$\mathbf{Q}$ $2\mathbf{Q}\text{\ensuremath{-}}1\mathbf{Q}$. Moreover, identify seven different types iCDW stemming vanadium-orbital kagome-sublattice structures pairs above below Fermi level. While $2\mathbf{Q}\text{\ensuremath{-}}1\mathbf{Q}$ trigger orthorhombic distortion breaks threefold rotational lattice, $3\mathbf{Q}\text{\ensuremath{-}}3\mathbf{Q}$ induce various subsidiary uniform magnetic orders, conventional ferromagnetism octupolar, toroidal, even monopolar order. show these exotic orders display unique magnetostriction, magnetoelectric, magnetoelectrostriction properties can be probed experimentally which is realized compounds. briefly discuss impact out-of-plane modulation order interplay superconductivity.