  The magnetic properties and hysteresis loops for the hexagonal Ising nanowire
(HIN) with a core-shell structure consisting of mixed spins with the core spin
being spin-5/2 and the shell spins being spin-3/2 are studied. The Blume-Capel
model is considered by using the mean-field approximation (MFA) based on the
Gibbs--Bogoliubov inequality for free energy. The impact of different bilinear
interaction parameters ($J_{cc}, J_{ss}, J_{cs}$) between the core, shell, and
core and shell spins, respectively, including the crystal ($D_c, D_s$) and
external magnetic fields ($h=h_c=h_s$) at the core and shell sites, are taken
into consideration. In order to obtain phase diagrams on various planes, the
thermal changes of the net, core, and shell magnetizations are investigated for
various values of our system parameters. It is discovered that the model
exhibits only second-order phase transitions when $h=0.0$ for $D$ greater or
equal to zero, first- and second-order phase transitions for $h\neq0.0$ and
compensation temperatures for all $h$.
