Compensation engineering via a direct skip bond in a transverse-field mixed-spin (2, 1, 1/2) triangular-prism...

We introduce and solve a transverse-field mixed-spin Ising model on a triangular-prism nanotube, in which three parallel strands of spins S_A = 2, S_B = 1 and S_C = 1/2 are coupled around each triangular cross-section by sequential bonds J_1 (A-B) and J_2 (B-C), closed by a direct A-C bond J_3 (the skip bond, absent from the corresponding open chain), with an axial coupling J_0, single-ion anisotropies D_A and D_B, and a transverse field Gamma. The cross-section is uniform, so the three sublattices are equally populated, r_A = r_B = r_C = 1/3. The model is treated within the variational mean-field (Bogoliubov-Peierls) approximation applied to the full quantum single-site Hamiltonian, giving the sublattice magnetizations, thermodynamics, hysteresis loops and magnetocaloric response self-consistently. For antiferromagnetic A-B coupling the ground state is the collinear ferrimagnet (+2, -1, -1/2). Because the spin-2 strand alone outweighs the other two at saturation, compensation cannot arise from stoichiometry; it arises from the crystal field. A planar anisotropy on the spin-2 strand makes that sublattice soften faster, so the net moment crosses zero at a finite compensation temperature. Within the physically realistic window |J_3| <= 0.5|J_1| the skip bond raises the compensation temperature by 49% while raising the Curie temperature by only 12%, so the two can be engineered almost independently. The planar anisotropy and the axial coupling each confine compensation to a finite window, and the transverse field destroys compensation at Gamma_comp = 0.40, far below the mean-field quantum critical field Gamma_c = 1.75. Hysteresis loops are multi-step, with plateaux assigned to successive strand reversal, and the magnetocaloric response changes sign. Benchmarking against an exact transfer-matrix solution and Monte Carlo simulation of the same classical Hamiltonian quantifies how far the mean-field ordering temperature is overestimated; all transverse-field results are mean-field predictions.