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

We introduce and solve a transverse-field mixed-spin Ising model on a triangular-prism nanotube, in which three parallel strands of spins= 2,= 1 and= 1/2 are coupled around each triangular cross-section by sequential bonds(A-B) and(B-C), closed by a direct bond,(A-C), which closes the triangular plaquette and has no counterpart in the corresponding open chain, and which we call the skip bond throughout, with an axial backbone coupling, single-ion anisotropiesand, and a transverse fieldacting on every site. The cross-section is uniform, so the three sublattices are equally populated and enter every macroscopic average with the same weight,=== 1/3. The model is treated within the variational mean-field (Bogoliubov-Peierls) approximation extended to the full quantum single-site Hamiltonian, from which the sublattice magnetizations, total magnetization, free energy, entropy, specific heat, longitudinal susceptibility, hysteresis loops and magnetocaloric response are obtained self-consistently. For antiferromagneticA-Bcoupling the ground state is the collinear ferrimagnet (+2, -1, -1/2). Because the spin-2 strand alone outweighs the other two at saturation, compensation in a uniformly populated prism cannot arise from stoichiometry; it arises instead from the crystal field. A planar anisotropy on the spin-2 strand makes that sublattice soften faster than the other two, so the net moment crosses zero at a finite compensation temperature. Within the physically realistic windowthe skip bond then raises the compensation temperature by 49% while raising the Curie temperature by only 12%, so the temperature of zero net moment can be engineered nearly independently of the ordering temperature. The planar anisotropy and the axial coupling each confine compensation to a finite window, and the transverse field acts as a second, independent control: it destroys compensation at≈ 0.40, far below the mean-field quantum critical field≈ 1.75 at which the longitudinal order itself vanishes. Hysteresis loops are multi-step, with plateaux that we assign to the successive reversal of the three strands, and the loop area and coercive field are themselves tuned by the skip bond. The magnetocaloric response changes sign, giving an inverse regime whose boundary shifts with. Finally, we benchmark the approximation against an exact transfer-matrix solution and Monte Carlo simulation of the same classical Hamiltonian, which quantify by how much the mean-field ordering temperature is overestimated for a quasi-one-dimensional tube. The transfer-matrix and Monte Carlo benchmarks are performed in the classical limit, so all transverse-field results reported here are mean-field predictions.