Magnetism is an important problem in many areas of science including biology, physics and material science. For example, many migratory animals (birds, whales and sea turtles) use magnetism to sense direction for their migrations; computer hard drives store information via magnetism; and so forth. Quantum magnetism in low-dimensional systems plays a particularly important role in biophysical systems within which magnetic moments of different sizes might be useful for different purposes. In this perspective, the role of magnetism with higher magnetic moments is relatively less understood.

To gain a better understanding for magnetism encompassing low and high moments, we studied a quantum mechanical spin lattice system consisting of one-dimensional anti-ferromagnetic Heisenberg chain of spin s embedded in a three dimensional lattice. We solved the system numerically in a one-dimensional lattice of finite size for different spin values of s. By replacing each of the spin n/2 ions in the lattice with n spin 1/2 ions we also studied the low excitation spectrums and compared the results with the exact spin n/2 systems. Such procedures may shed light on how the Halden-gap appear when the total spin of the ion changes from half-integer to integer, a spin-chain behavior that has been conjectured almost thirty-five years ago but has not yet been solved analytically.