Minimum Anisotropy of a Magnetic Nanoparticle out of Equilibrium

TL;DR

This study investigates the minimum magnetic anisotropy necessary for hysteresis in nanoparticles, linking it to residual magnetization noise caused by spin-orbit torques during electron tunneling.

Contribution

It introduces the concept of a minimum anisotropy threshold for magnetic hysteresis in nanoparticles, explained by spin-orbit torque-induced noise, and correlates hysteresis abundance with material anisotropy.

Findings

Hysteresis abundance varies significantly among different metals.

A minimum anisotropy of approximately 13 meV is required for hysteresis.

Hysteresis abundance is weakly affected by tunneling current, indicating current-dependent damping.

Abstract

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.