Disentangling spin polarization from driven circular ionic motion in EuTiO$_3$
Coherently driven circular ionic motion has been reported to produce large helicity-dependent optical responses attributed to transient magnetization. However, the microscopic nature and magnitude of this phenomenon, sometimes referred to as dynamical multiferroicity, remain strongly debated. Here, we directly study the connection between ionic circulation induced by a high-field circular terahertz (THz) drive and its effect on the spin system of EuTiO$_3$ using X-rays. This material exhibits an optical response consistent with the putative magnetic signal observed in related non-magnetic materials. Furthermore, the presence of Eu$^{2+}$ ions enables the use of X-ray magnetic circular dichroism (XMCD) to test for the creation of transient spin polarization. Simultaneously, ultrafast X-ray diffraction (XRD) measures the circular ionic motion from which we determine the mechanical angular momentum. We find a classical ionic contribution of $3\times10^{-8}~μ_B$ from XRD and upper limits of $0.03~μ_B$ and $0.11~μ_B$ from the sensitivity of XMCD at the europium $M_5$ and $L_2$ edges, probing the $4f$ and $5d$ shells of Eu$^{2+}$, respectively. These observations show that large-amplitude circular ionic motion in this system is not accompanied by a detectable spin polarization despite the clear signature in the optical data, with the XMCD upper bounds and classical contribution differing by many orders of magnitude.