Spin dynamics of $3d$ and $4d$ impurities embedded in prototypical topological insulators

Abstract

Topological insulators are insulating bulk materials hosting conducting surface states. Their magnetic doping breaks time-reversal symmetry and generates numerous interesting effects such as dissipationless transport. Nonetheless, their dynamical properties are still poorly understood. Here, we perform a systematic investigation of transverse spin excitations of $3d$ and $4d$ single impurities embedded in two prototypical topological insulators (Bi${}_2$Te${}_3$ and Bi${}_2$Se${}_3$). The impurity-induced states within the bulk gap of the topological insulators are found to have a drastic impact on the spin excitation spectra, resulting in very high lifetimes reaching up to $microseconds$. An intuitive picture of the spin dynamics is obtained by mapping onto a generalized Landau-Lifshitz-Gilbert phenomenological model. The first quantity extracted from this mapping procedure is the magnetic anisotropy energy, which is then compared to the one provided by the magnetic force theorem. This uncovers some difficulties encountered with the latter, which can provide erroneous results for impurities with a high density of states at the Fermi energy. Moreover, the Gilbert damping and nutation tensors are obtained. The nutation effects can lead to a non-negligible shift in the spin excitation resonance in the high-frequency regime. Finally, we study the impact of the surface state on the spin dynamics, which may be severely altered due to the repositioning of the impurity-induced state in comparison to the bulk case. Our systematic investigation of this series of magnetic impurities sheds light on their spin dynamics within topological insulators, with implications for available and future experimental studies as, for instance, on the viability of using such impurities for solid-state qubits.

References in corpus (12)

• Reading and Writing Single-Atom Magnets
• First Principles Studies on 3-Dimentional Strong Topological Insulators: Bi2Te3, Bi2Se3 and Sb2Te3
• Magnetic Anisotropy and Magnetization Dynamics of Individual Atoms and Clusters of Fe and Co on Pt(111)
• Spin Inelastic Electron Tunneling Spectroscopy on Local Spin Adsorbed on Surface
• Bulk Band Structure of Bi${}_2$Te${}_3$
• Dynamical magnetic excitations of nanostructures from first-principles
• Relativistic dynamical spin excitations of magnetic adatoms
• Transverse dynamical magnetic susceptibilities from regular static density functional theory: Evaluation of damping and g-shifts of spin-excitations
• Renormalization of electron self-energies via their interaction with spin excitations: A first-principles investigation
• Zero-point spin-fluctuations of single adatoms
• Longitudinal and transverse spin relaxation times of magnetic single adatoms: an ab initio analysis
• Engineering elliptical spin-excitations by complex anisotropy fields in Fe adatoms and dimers on Cu(111)

Cited by in corpus (1)

• Long-time relaxation dynamics of a spin coupled to a Chern insulator