Vladimir E. Dmitrienko (A.V. Shubnikov Institute of Crystallography, FSRC “Crystallography and Photonics” RAS, Russia)

For more than 30 years, there were tremendous research efforts  to understand the mysterious Hidden Order (HO) in the heavy-fermion compound URu2Si2 [1].

To solve this enigma, we suppose that there is  no spatial symmetry breaking at the HO transition temperature and solely the time-reversal symmetry breaking emerges owing to unusual magnetic ordering [2]. As a result of its high 4/mmm symmetry, each uranium atom is a three-dimensional magnetic vortex; its intra-atomic magnetization M(r) is intrinsically noncollinear, so that its dipole, quadrupole, and toroidal magnetic moments vanish, thus  making the vortex “hidden”. The first nonzero magnetic multipole of the uranium atom is the toroidal quadrupole. In the unit cell, two uranium atoms can have either the same or opposite signs of their vortex magnetization M(r); this corresponds to either ferrovortex or antiferrovortex structures with I4/mmm or PI4/mmm magnetic space groups, respectively.

Our first-principles calculations (DFT with the spin-orbit interaction) show that the vortex magnetic order of URu2Si2 is rather strong [2]: the total absolute magnetization |M(r)| is about 0.9 Bohr magneton per U atom. The vortex structure provides a very unusual form factor of magnetic neutron scattering, calculated both for ferrovortex and antiferrovortex structures [2]. We will also discuss other systems with similar unusual vortex order.

This work was supported RFBR Project No.19-52-12029.

J.A.Mydosh, P.M.Oppeneer, Rev. Mod. Phys. 83, 1301(2011).

V.E.Dmitrienko, V.A.Chizhikov, Phys. Rev. B98, 165118(2018).