  Magnetic insulators (MIs) attract tremendous interest for spintronic
applications due to low Gilbert damping and absence of Ohmic loss. Magnetic
order of MIs can be manipulated and even switched by spin-orbit torques (SOTs)
generated through spin Hall effect and Rashba-Edelstein effect in heavy
metal/MI bilayers. SOTs on MIs are more intriguing than magnetic metals since
SOTs cannot be transferred to MIs through direct injection of electron spins.
Understanding of SOTs on MIs remains elusive, especially how SOTs scale with
the film thickness. Here, we observe the critical role of dimensionality on the
SOT efficiency by systematically studying the MI layer thickness dependent SOT
efficiency in tungsten/thulium iron garnet (W/TmIG) bilayers. We first show
that the TmIG thin film evolves from two-dimensional to three-dimensional
magnetic phase transitions as the thickness increases, due to the suppression
of long-wavelength thermal fluctuation. Then, we report the significant
enhancement of the measured SOT efficiency as the thickness increases. We
attribute this effect to the increase of the magnetic moment density in concert
with the suppression of thermal fluctuations. At last, we demonstrate the
current-induced SOT switching in the W/TmIG bilayers with a TmIG thickness up
to 15 nm. The switching current density is comparable with those of heavy
metal/ferromagnetic metal cases. Our findings shed light on the understanding
of SOTs in MIs, which is important for the future development of ultrathin
MI-based low-power spintronics.
