Minimum Anisotropy of a Magnetic Nanoparticle out of Equilibrium

In this article we study magnetotransport in single nanoparticles of Ni, Py=Ni$_{0.8}$Fe$_{0.2}$, Co, and Fe, with volumes $15\pm 6$nm$^3$, using sequential electron tunneling at 4.2K temperature. We measure current versus magnetic field in the ensembles of nominally the same samples, and obtain the abundances of magnetic hysteresis. The hysteresis abundance varies among the metals as Ni:Py:Co:Fe=4\,:50\,:100\,:100(\%), in good correlation with the magnetostatic and magnetocrystalline anisotropy. The abrupt change in the hysteresis abundance among these metals suggests a concept of minimum magnetic anisotropy required for magnetic hysteresis, which is found to be $\approx 13$meV. The minimum anisotropy is explained in terms of the residual magnetization noise arising from the spin-orbit torques generated by sequential electron tunneling. The magnetic hysteresis abundances are weakly dependent on the tunneling current through the nanoparticle, which we attribute to current dependent damping.