Magnetic Field and Ferromagnetic Proximity Effects
The chapter examines various magnetic gaps in the Dirac spectrum and proximity-induced surface Hall conductivity. Topological phase transitions in a parallel magnetic field, the current-induced torque, and possible device applications are discussed.
- PDF / 934,882 Bytes
- 23 Pages / 439.37 x 666.142 pts Page_size
- 99 Downloads / 267 Views
Magnetic Field and Ferromagnetic Proximity Effects
The device applications of topological insulators, let’s say transistors, require a gapped electron spectrum. The gap also provides the conditions for the quantum anomalous Hall effect [1] and topological magnetoelectric effects [2, 3]. The surface energy spectrum of a TI film, discussed in Chap. 1, is gapped as long as the states on opposite surfaces overlap. The overlap opens the tunneling gap in the otherwise massless electron spectrum when the Bi2Se3 film thickness becomes less than six quintuple layers [4]. If the thickness increases, the gap tends to zero and each surface independently carries 2D gapless Dirac fermions. In a thick film, the tunneling gap is negligibly small, and the energy gap on the surface can be created by breaking the time reversal symmetry with an out-of-plane magnetic field. This setting induces Landau levels and creates conditions for the QHE. Without an external magnetic field the loss of the time reversal symmetry in TI might be caused by magnetic doping with transition metal atoms (Fe, Mn, Cr, V) to the extent that the surface becomes ferromagnetic [5–9]. Also, the proximity effect from the ferromagnetic insulator (FM) creates out-of-plane magnetization of surface electrons in TI, thus creating conditions for the QAHE [10–12]. The experimental observation of the QAHE in an FM/TI bilayer is considered proof of the proximity ferromagnetism. For example, the Bi2Se3/EuS heterostructure reveals proximity-induced high temperature magnetization in the Bi2Se3 in a 20 A_ -deep near-interface region. What is essential for the development of TI-based spintronic devices is that the surface helical electrons affect the magnetization dynamics in an adjacent ferromagnet by the spin-transfer torque, that is, the transfer of spin angular momentum between surface electrons and the magnetization in the ferromagnetic layer [13–15]. In this chapter, we consider the exchange field-induced gapped spectrum in 2Dand 3D- TI and discuss the role of in-plane and out-of-plane magnetic fields on the topological properties of the surface.
© Springer Nature Switzerland AG 2020 V. Litvinov, Magnetism in Topological Insulators, https://doi.org/10.1007/978-3-030-12053-5_3
55
56
3 Magnetic Field and Ferromagnetic Proximity Effects
3.1
Magnetic Energy Gap
We start with the Hamiltonian of the surface states (Chap. 1, (1.38)) which includes Zeeman energy, mz ¼ JMz, originating from out-of-plane proximity magnetization in an adjacent ferromagnetic (FM) layer, J is the exchange interaction constant: 0
ΔS Bk2 þ mz B 2 B B V~ AS B ~ ¼B H B B 0 B @ iA~2 kþ
V~ AS
0
iA~2 k
ΔS þ Bk 2 þ mz 2 iA~2 kþ
iA~2 k
0
0
ΔS Bk2 mz 2 V~ AS
1 C C C C C, C C C A
V~ AS
ΔS þ Bk 2 mz 2 ð3:1Þ
Both parameters ΔS and B originate from the quantum tunneling between electron states residing on opposite surfaces and tend to zero if the film thickness exceeds six quintuple layers. All three components of magnetization are needed to describe the magnetic anisotropy in a ferro
Data Loading...
