Observation of current-induced orbital quadrupole accumulation

Abstract: Spintronics and orbitronics rely on current-induced accumulations of magnetic dipoles: spin and orbital angular momentum. However, electronic orbitals inherently carry multipoles beyond the dipole, with the rank-2 orbital quadrupole as the leading term. Here we use polarization-resolved Kerr microscopy to observe current-induced orbital-quadrupole accumulation at the surfaces of Ti and Pt, metals with markedly different spin--orbit-coupling strengths. By separating the symmetric and antisymmetric components of the off-diagonal optical conductivity, we isolate the time-reversal-even quadrupolar response from the conventional time-reversal-odd magnetic-dipolar one, and find that the quadrupolar optical response exceeds the dipolar one in both metals. First-principles analysis of the measured responses indicates that the quadrupole accumulations are of the same order of magnitude in the two metals despite their widely different spin--orbit-coupling strengths, consistent with a previously unidentified channel of charge-to-orbital conversion that does not require spin--orbit coupling. Our findings establish that current-induced orbital polarization is fundamentally multipolar, expanding current-induced phenomena from the dipolar to the multipolar regime and opening a route to electrical control of orbital-ordered phases.