  Measurements of magnetic torque are most commonly preformed about a single
axis or component of torque. Such measurements are very useful for hysteresis
measurements of thin film structures in particular, where high shape anisotropy
yields a near-proportionality of in-plane magnetic moment and the magnetic
torque along the perpendicular in-plane axis. A technique to measure the full
magnetic torque vector (three orthogonal torque components) on micro- and
nano-scale magnetic materials is introduced. The method is demonstrated using a
modified, single-paddle silicon-on-insulator resonant torque sensor. The
mechanical compliances to all three orthogonal torque components are maximized
by clamping the sensor at a single point. Mechanically-resonant AC torques are
driven by an RF field containing a frequency component for each fundamental
torsional mode of the device, and the resulting displacements read out through
optical position-sensitive detection. The measurements are compared with
micromagnetic simulations of the mechanical torque to augment the
interpretation of the signals. As an application example, simultaneous
observations of hysteresis in the net magnetization along with the
field-dependent in-plane anisotropy is highly beneficial for studies of
exchange bias.
