  We present a novel method for measuring the modulation of magnetic anisotropy
and the strength of spin-orbit interaction by an electrical current in
nanomagnets. Our systematic study explores the current dependencies of these
properties across a variety of nanomagnets with different structures,
compositions, and sizes, providing unprecedented insights into the complex
physical origins of this effect. We identified two distinct contributions to
the observed current modulation: one proportional to the current and the other
to the square of the current. The squared-current contribution, originating
from the Spin Hall effect, uniquely accumulates strength with an increasing
number of interfaces, resulting in exceptionally large current modulation of
magnetic anisotropy and spin-orbit interaction in multi-layer nanomagnets.
Conversely, the linear-current contribution stems from the Ordinary and
Anomalous Hall effects and exhibits opposite polarity at different interfaces,
making it significant only in asymmetrical single-layer nanomagnets. The
squared-current contribution induces substantial anisotropy field changes, up
to 30-50$\%$ at typical MRAM recording currents, leading to thermally-activated
magnetization reversal and data recording. The linear-current contribution,
while smaller, is effective for parametric magnetization reversal, providing
sufficient modulation for efficient data recording through resonance
mechanisms. This finding highlights the complex nature of spin accumulation and
spin dynamics at the nanoscale, presenting an opportunity for further
optimization of data recording in MRAM technology.
