Chiral Spin Mode on the Surface of a Topological Insulator

Abstract

Using polarization-resolved resonant Raman spectroscopy, we explore collective spin excitations of the chiral surface states in a three dimensional topological insulator, Bi2Se3. We observe a sharp peak at 150 meV in the pseudovector A2 symmetry channel of the Raman spectra. By comparing the data with calculations, we identify this peak as the transverse collective spin mode of surface Dirac fermions. This mode, unlike a Dirac plasmon or a surface plasmon in the charge sector of excitations, is analogous to a spin wave in a partially polarized Fermi liquid, with spin-orbit coupling playing the role of an effective magnetic field.Magnets and partially spin-polarized Fermi liquids support collective spin excitations (spin waves), in which all electron spins respond coherently to external fields, and the "glue" that locks the phases of precessing spins is provided by the exchange interaction. In nonmagnetic materials where inversion symmetry is broken but time-reversal invariance remains intact, strong spin-orbit coupling (SOC) may play the role of an effective magnetic field, which locks electron spins and momenta into textures. This phenomenon is encountered in threedimensional (3D) topological insulators (TIs), which harbor topologically protected surface states [1][2][3][4][5]. These states have been a focus of intense studies, both from the fundamental point-of-view [6][7][8][9][10][11][12] and for potential applications in spintronics devices [13][14][15][16][17][18][19][20]. However, the many-body interactions leading to collective effects in TIs remain largely unexplored. An essential aspect of this physics is an interplay between the Coulomb interaction and SOC, which is expected to give rise to a new type of collective spin excitations -chiral spin waves [21][22][23][24][25][26]. In the long wavelength (q = 0) limit, these modes are completely decoupled from the charge channel and thus distinct from spin-plasmons [27,28], Dirac plasmons [29,30], and surface plasmons in TIs [30,31].In this Letter, we employ polarization-resolved resonant Raman spectroscopy, a technique of choice for probing the collective charge [32,33], spin [34][35][36][37] and orbital excitations [38], to study collective spin excitations of the chiral surface states in Bi 2 Se 3 . To enhance the signal from the surface states, we tune the energy of incoming photons in resonance with a transition between two sets of chiral surface states: near the Fermi energy and about 1.8 eV above it [ Fig. 1(a)] [39]. We observe a long-lived excitation at 150 meV in the pseudovector symmetry channel of the Raman spectra, which is most pronounced at low temperatures but persists up to room temperature. By comparing the data with calculations, we identify this excitation as the transverse collective chiral spin mode supported by spin-polarized surface Dirac fermions. Such collective modes -first predicted for nontopological systems [21][22][23][24][25][26]36] but hitherto unobserved -are "peeled off" from the continuum of particle-hole excitations by t...

Observation of chiral surface excitons in a topological insulator Bi 2 Se 3

“…It is known that non-symmetric surface phonons in Bi 2 Se 3 are weak [35,36], leaving J z approximately conserved during the energy relaxation. It would be interesting to study in the future the interaction between the chiral exciton and other more exotic collective modes, such as the Dirac plasmons and chiral spin modes [28,37,38]. Importantly, the |J z = ±1 exciton states can also be resonantly populated with circularly polarized 2.3 eV excitation [ Fig.…”

“…Due to strong SOC, all the three surface bands exhibit spin-momentum locking, which could lead to optical orientation of single-electron spins and excitons [4]. So far, most of research on TIs have been focused on spin dynamics and collective modes of Dirac fermions in SS1 [26][27][28][29], and far less is known about the properties of RSS and SS2. We excite interband transitions between surface states, RSS and SS2 with circularly polarized light and study polarization of PL emission in the backscattering geometry, with light being incident normally on the crystal surface.…”

Dynamical spin susceptibility of silicene

“…By considering the dynamical spin-susceptibility of SO coupled 2D electron system the existence of spin-collective excitations was established 39 , moreover, the surface states of a 3D topological insulator, described by the Dirac spectrum, have been predicted to host hybridized spin-charge coupled plasmons 5 . Recently, Raman spectroscopy was used to reveal the collective spin-excitations of the chiral surface states of the three dimensional topological insulator Bi 2 Se 3 40 . On the other hand, the modifications to the static spin-susceptibility due to the SO terms yield additional interaction terms like Dzyaloshinskii-Moriya and Ising terms besides the usual isotropic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction term [41][42][43][44] .…”

Spin-helix Larmor mode

“…In the latter case, the precession of the interacting spins, the charge motion, and the spin-orbit coupling (SOC) due to inversion asymmetry are all interrelated and lead to novel phenomena. For example, chiral spin waves have been observed in asymmetric monolayers of iron 5 , 6 and on the surface of topological insulators 7 , helical spin waves have been predicted in a two-dimensional electron gas (2DEG) subject to Rashba SOC 8 , and twisted spin waves have been predicted and observed in magnetized 2DEGs 9 .…”