  Spintronic nano-oscillators with reduced non-linearity could offer key
benefits for realizing neuromorphic applications such as spike-based neurons
and frequency multiplexing in neural networks. Here, we experimentally
demonstrate the reduction in non-linearity of a spin-Hall nano-oscillator
(SHNO) by compensation of its effective magnetic anisotropy. The study involves
optimization of Co/Ni multilayer growth to achieve the compensation, followed
by spin diode measurements on patterned microstrips to quantify their
anisotropy. The relation between the second ($H_{k2}$ = 0.47 mT) and the first
order ($H_{k1}^{eff}$ = $-$0.8 mT) anisotropy fields reveals the existence of
an easy cone, thereby validating the presence of compensation. Furthermore, we
demonstrate a synapse based on the compensated spin diode which has a fixed
frequency when the input power is varied. We then study the current-induced
auto-oscillation properties of SHNOs on compensated films by patterning
nano-constrictions of widths 200 and 100 nm. The invariance of the resonance
frequency and linewidth of the compensated SHNO with applied dc current
indicates the absence of non-linearity. This independence is maintained
irrespective of the applied external fields and its orientations. The
compensated SHNO obtained has a linewidth of 1.1 MHz and a peak output power of
up to 1 pW/MHz emulating a nano-neuron with a low linewidth and a fixed
frequency.
