  The paper aims to apply the octonions to explore the contribution of some
influence factors to magnetic moments, revealing the connection among the
influence factors and spin texture. J. C. Maxwell was the first to introduce
the quaternions to describe the electromagnetic theory. The subsequent scholars
utilize the quaternions and octonions to study the gravitational and
electromagnetic theories and so forth. The paper adopts the octonions to
research the gravitational and electromagnetic fields, including the octonion
angular momentum, torque, and force and so on. When the octonion force is equal
to zero under some circumstances, it is able to achieve eight equations
independent of each other. In particular, one of eight independent equations
reveals the interrelation between the second-torque and the divergence of
magnetic moments. One of its deductions is that the directions, magnitudes and
frequencies of some terms are capable of impacting the orientation and vortex
of magnetic moments, altering the frequency of magnetic vortex clusters. It
means that the spin textures are relevant to some external influence factors.
Some terms may have an influence on the arrangements of spin textures. The
study will be helpful for understanding the physical properties of magnetic
skyrmions and merons.
