High field magnetization of Eu spin clusters, carrier spin polarization and Lattice diamagnetism in p-type Sn1−xEuxTe Diluted Magnetic Semiconductor

We present a theoretical model for the magnetization p-type S n 1 − x E u x T e diluted magnetic semiconductor (DMS), incorporating the contributions from itinerant-localized spin interaction, intrinsic diamagnetism of the lattice, and E u + 2 local moments, as functions of magnetic field at T=4.2K. We evaluate the magnetization contribution from hole spin-polarization using a k → ⋅ π → formalism. The Hamiltonian in this formalism encompasses spin-orbit interaction, the interaction between carrier spins and localized moments in the presence of a magnetic field. Additionally, we include a diamagnetic contribution from the host lattice, originating from interband orbital and spin-orbit effects. Furthermore, the impurity spin magnetization, M E u + 2 , is expressed as the sum of three components: M E u + 2 = M s + M p + M t , where M s represents the principal contribution from a single-ion (isolated spin), and M p and M t arise from correlated spin pairs and triplets, respectively. Our results indicate that M E u + 2 is the dominant contribution to the total magnetization ( M T ) , primarily governed by isolated Eu spins. However, the contributions from spin clusters M p and M t become increasingly significant with higher Eu concentration. The magnetization due to carrier spin polarization ( M c ) is approximately two orders of magnitude smaller than the local moment contribution, even under magnetic fields up to 30 T. Nevertheless, this term is of fundamental interest due to its potential relevance in spintronic applications. The lattice diamagnetic contribution ( M d ) is found to be nearly isotropic. The total magnetization is derived by integrating the effects of all three contributions: M T = M E u + 2 + M c + M d . Our model works well for H > 5T. The theoretical predictions are compared with available experimental data and show reasonable agreement. • Magnetization of S n 1 − x E u x T e is calculated at T=4.2K for x ≤ 0 . 06 up to 30T using k → ⋅ π → theory. • The s/p-f interaction induced magnetization is two orders of magnitude smaller than that from localized spin. • The lattice susceptibility is small, negative and temperature independent. • Magnetization from a multi-spin E u + 2 cluster is described by the modified Brillouin function. • The local Momentum magnetization dominates contributing 90% of the total magnetization.