Robust Triple-q Magnetic Order with Trainable Spin Vorticity in Na_{2}Co_{2}TeO_{6}

Recent studies suggest that the candidate Kitaev magnet Na_{2}Co_{2}TeO_{6} possesses novel triple-q magnetic order instead of conventional single-q zigzag order. Here we present dedicated experiments in a search for distinct properties expected of the triple-q order, namely, insensitivity of the magnetic Bragg intensities to weak C_{3} symmetry-breaking fields and fictitious magnetic fields generated by the spin vorticity. In structurally pristine single crystals, we show that C_{3} symmetry-breaking in-plane uniaxial strains do not affect the order's magnetic neutron diffraction signals. We further show that c-axis propagating light exhibits large Faraday rotations in the ordered state due to the spin vorticity, the sign of which can be trained via the system's ferrimagnetic moment. These results favor the triple-q order in Na_{2}Co_{2}TeO_{6} and reveal its unique emerging behavior.