Quantum and classical magnetic Bloch points

A Bloch point represents a three-dimensional hedgehog singularity of a magnetic vector field in which the magnetization vanishes. However, standard micromagnetic theory, developed for magnetic moments of fixed lengths, lacks full applicability in studying such singularities. To address this gap, we study a Bloch point in a quantum Heisenberg model for the case of spin-1/2 particles. Performing an exact diagonalization of the Hamiltonian as well as using density matrix renormalization group techniques, we obtain the ground state, which can be used to recover the corresponding magnetization profile. Our findings demonstrate a variation of the spin length in the quantum model, leading smoothly to zero magnetization at the Bloch point. Our results indicate the necessity of generalizing the classical micromagnetic model by adding the third degree of freedom of the spins: the ability to change its length. To this end, we introduce the micromagnetic $\mathbb{S}_{3}$-model, which enables the description of magnets with and without Bloch point singularities.