We demonstrate that ferromagnetic and antiferromagnetic excitations can be triggered by the dynamical spin accumulations induced by the bulk and surface contributions of the spin Hall effect. Due to the spin-orbit interaction, a time-dependent spin density is generated by an oscillatory electric field applied parallel to the atomic planes of Fe/W(110) multilayers. For symmetric trilayers of Fe/W/Fe in which the Fe layers are ferromagnetically coupled, we demonstrate that only the collective out-of-phase precession mode is excited, while the uniform (in-phase) mode remains silent. When they are antiferromagnetically coupled, the oscillatory electric field sets the Fe magnetizations into elliptical precession motions with opposite angular velocities. The manipulation of different collective spin-wave dynamical modes through the engineering of the multilayers and their thicknesses may be used to develop ultrafast spintronics devices. Our work provides a general framework that probes the realistic responses of materials in the time or frequency domain.The interplay between charge, spin and orbital angular momentum in nano-structured systems is significantly widening the prospects of future technologies [1,2]. Spinorbit coupling (SOC) is responsible for a variety of fascinating phenomena in condensed matter physics. For example, the lack of inversion symmetry activates the Dzyaloshinskii-Moriya interaction which favors the occurrence of non collinear ground-state magnetic configurations [3][4][5]. Combined with time-reversal symmetry, it leads to protected conducting states in the so-called topological insulators [6], where spin injection and spin-tocharge conversion were recently demonstrated with the spin-pumping technique [7]. In fact, the generation of spin currents and spin accumulations by an electric current, in particular, has been a subject of much interest and research recently [8][9][10][11][12][13][14][15][16]. Several groups showed that these non-equilibrium quantities can be used to set a magnetization into precessional motion in metallic systems [17][18][19], including antiferromagnets [20]. Two recent reviews of the major experimental and theoretical results concerning the charge-to-spin conversion are outlined in Refs. [21,22], for both metal and semiconductor devices.So far, theoretical approaches to current-induced spin currents, accumulations and torques in systems with more elaborate electronic structures are restricted to the case in which the applied electric field is static [23][24][25][26][27]. Here, we take it one step further, and investigate the dynamic magnetic response which is driven by a timedependent electric field, as realized in the original experiments reported in Refs. [17][18][19]28]. One advantage of such an electronic-structure-based method is that it naturally includes all surfaces, interfaces, and bulk contributions [10,29,30] to the spin Hall effect, including the coupling between local moments and the currentinduced spin accumulation of conduction electrons [31], the transp...