  In the brain, the membrane potential of many neurons oscillates in a
subthreshold damped fashion and fire when excited by an input frequency that
nearly equals their eigen frequency. In this work, we investigate theoretically
the artificial implementation of such "resonate-and-fire" neurons by utilizing
the magnetization dynamics of a fixed magnetic skyrmion in the free layer of a
magnetic tunnel junction (MTJ). To realize firing of this nanomagnetic
implementation of an artificial neuron, we propose to employ voltage control of
magnetic anisotropy or voltage generated strain as an input (spike or
sinusoidal) signal, which modulates the perpendicular magnetic anisotropy
(PMA). This results in continual expansion and shrinking (i.e. breathing) of a
skyrmion core that mimics the subthreshold oscillation. Any subsequent input
pulse having an interval close to the breathing period or a sinusoidal input
close to the eigen frequency drives the magnetization dynamics of the fixed
skyrmion in a resonant manner. The time varying electrical resistance of the
MTJ layer due to this resonant oscillation of the skyrmion core is used to
drive a Complementary Metal Oxide Semiconductor (CMOS) buffer circuit, which
produces spike outputs. By rigorous micromagnetic simulation, we investigate
the interspike timing dependence and response to different excitatory and
inhibitory incoming input pulses. Finally, we show that such resonate and fire
neurons have potential application in coupled nanomagnetic oscillator based
associative memory arrays.
