“…However, since their magnetization is close to zero, standard magnetic characterization precluded their experimental evidence until the advent of more sensitive techniques allowed their observation in individual nanocylinders, nanotubes and dot-shaped elements of different compositions by means of electron holography 35,36 , cantilever-based torque magnetometry [37][38][39][40] , nanoscale torque-SQUID magnetometry 41 , spin-polarized scanning tunneling spectroscopy 42 , X-ray microscopy 43 and MFM 44 . Different theoretical and simulation approaches have been used in order to study the thermodynamic properties of magnetic hollow nanocylinders, including micromagnetic studies 15,45 , scaling techniques 46,47 , many-body Green's functions [48][49][50] , ab-initio calculations [51][52][53] , and Monte Carlo (MC) simulations 54 .…”