Session A7: Focus Session: Magnetism & Topological Insulators

Realization of high-precision and more robust quantum anomalous Hall state in a hard ferromagnetic topological insulator

The discovery of the integer quantum Hall (QH)~effect in 1980 led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic field. The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon as the QH effect, whereas its physical origin is a result of intrinsic spin-orbit coupling of the topological insulator (TI) and when it is in ferromagnetic state. Since the QAH effect does not require an external field and the associated Landau levels, it is believed that this effect has unique potential for applications in electronic devices with low-power consumption. In this talk, we shall describe the experimental observation of the QAH state in V-doped (Bi,Sb)$_{2}$Te$_{3}$ TI films. We find that in zero-field longitudinal resistance decreases to 0.00013 $\pm$ 0.00007 $h/e^{2}$ $\sim$ 3.35 $\pm$ 1.76$\Omega )$, Hall conductance reaches 0.9998 $\pm$ 0.0006 $e^{2}/h$ and the Hall angle becoming as high as 89.993 $\pm$ 0.004$^{\circ}$ at $T=$25mK, thus realizing the anomalous Hall transport with negligible dissipation in the absence of any initial magnetic field. The advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field ($H_{c}$\textgreater 1.0T) and a relative high Curie temperature. These results were unexpected from the theoretical calculations. This high-precision realization of a more robust QAH state in hard FMTIs is a major step towards dissipationless electronic applications without external applied fields. \\[4pt] Work done in collaboration with W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S. C. Zhang, C. Liu, M. H. W. Chan, and J. S. Moodera. \\[4pt] Supported by funding from NSF (DMR-1207469), NSF (DMR-0907007), ONR (N00014-13-1-0301), NSF (DMR-0820404, Penn State MRSEC), and the STC Center for Integrated Quantum Materials under~NSF grant DMR-1231319.   

Transport studies on Cr-doped (Bi,Sb)2Te3 thin films with nearly quantized anomalous Hall effect

We describe measurements of the quantum anomalous Hall effect in ferromagnetic Cr-doped (Bi,Sb)$_{2}$Te$_{3}$ thin films (6-8 QL thickness) grown on (111) SrTiO$_{3}$ (STO) substrates by molecular beam epitaxy. The Fermi level is tuned close to the neutral point by tuning the growth flux ratios of Cr, Bi and Sb. Transport measurements were carried out in a dilution fridge at a base temperature of 20 mK. By tuning the chemical potential with a back gate on the STO substrate, we observed an anomalous Hall effect as high as 0.95h/e$^{2}$, with a coercive field $\sim$ 0.15 T and a narrow transition between positive/negative Hall plateaus. Transport measurements in a non-local configuration showed a Hall-effect-like non-local resistance with a systematic dependence on the back gate voltage and with pronounced peaks which resembled the non-local resistance of the quantum Hall effect. The non-local signal has a maximum that coincides with the maximum in Hall conductivity, indicating the edge channel as its origin. Our results show that the edge channel manifests itself in various transport properties even though the Hall resistance is not perfectly quantized.   

Spin-Orbital texture and magnetic proximity effect of Bi$_2$Se$_3$/EuS heterostructure

A topological insulator Bi$_2$Se$_3$ has gapless Dirac surface states topologically protected by time reversal symmetry with the helical spin texture. The spin texture has a unique orbital dependence and it allows topological insulator hybrid structures to be used for spintronics or spin transfer torque devices. Recently, an interface between a topological insulator Bi$_2$Se$_3$ and a ferromagnetic insulator EuS, has been experimentally realized, which provides an opportunity to study effects of magnetic interface on Dirac surface states of Bi$_2$Se$_3$. In this talk, we present our study of magnetic proximity effects and spin-orbital texture of the topological surface states of Bi$_2$Se$_3$ at the Bi$_2$Se$_3$/EuS interface, by using first-principles calculations and an low-energy effective model [A. T. Lee et al., Phys. Rev. B. 90, 155103 (2014)]. We discuss an energy gap opening due to the out-of-plane magnetic moment induced by the EuS, and a new Dirac cone occurring for thick Bi$_2$Se$_3$ slabs. Furthermore, we show an interesting coupling between the out-of-plane spin moment and the orbitals caused by broken time reversal symmetry.   

Giant anisotropic magneto-resistance in the magnetic topological insulator Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$

We demonstrate magnetization control of edge state transport and report the observation of a gate-tunable giant anisotropic magneto-resistance (GAMR) effect in the magnetic topological insulator Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$ as an external field (and the magnetization $M$) is rotated from out-of-plane (polar angle $\theta = 0^{\circ}$) to in-plane ($\theta = 90^{\circ}$). The angular dependence of the GAMR deviates from the standard $\cos^2\phi$ form (where $\phi$ is the angle between $M$ and the current density $J$), and is instead explained by a Landauer-Buttiker formalism that accounts for bulk-edge mixing. However, the rotation of the magnetization in-plane produces a weak, conventional AMR. These results serve as evidence for a field tilt-tuned crossover between an ``imperfect'' quantum anomalous Hall insulator (QAH) and a gapless, ferromagnetic topological insulator. We expect the GAMR to become stronger in the ideal QAH regime where edge state conduction dominates over bulk conduction, thus providing a route toward proof-of-concept ferromagnetic topological insulator transistors and magnetic field sensors. Funded by DARPA.   

Magnetization in Intrinsic Topological Insulators Induced by Exchange Interaction with Ferromagnetic Insulator

We examine the magnetic proximity-induced symmetry breaking via the exchange interaction in heterostructures of the topological insulator (TI) Bi$_{2}$Se$_{3}$ and the ferromagnetic insulator (FMI) EuS [1]. We observed the emergence of a ferromagnetic phase in TI with the excess of magnetic moment at the interface using depth and element sensitive Polarized Neutron Reflectometry (PNR). We find that the magnetization, penetrating into the TI originates through exchange interaction, without structural perturbation at the interface. Due to the different interlayer exchange coupling as well as the properties of the bulk and surface magnetizations, we investigated several different heterostructures after cooling in zero field (ZFC) and in an external magnetic field (FC). The significantly enhanced magnetic properties of the heterostructures as revealed by the PNR studies, as well as the temperature and external magnetic field dependence will be presented.\\[4pt] [1] P. Wei, et al Phys. Rev. Lett. 110, 186807 (2013)   

Observation of ferromagnetic domains in magnetic topological insulator

The breaking of time reversal symmetries in a topological insulator can lead to exotic quantum effects, such as magnetic monopoles, quantum anomalous hall effect(QAHE), and so on. Recently QAHE has been experimentally observed in a ferromagnetic topological insulator Cr doped Bi$_x$Sb$_{2-x}$Te$_3$[1]. Although a lot of studies have conducted on characterizing the ferromagnetic properties in these fascinating materials, direct observation of ferromagnetic domains is still lacking. Here we report variable temperature magnetic force microscopy (VT-MFM) studies on thin film of Cr doped Bi$_x$Sb$_{2-x}$Te$_3$ synthesized by molecular beam epitaxy (MBE). Small bubble-like ferromagnetic domains were observed below T$_C\approx$ 30 K. The evolution of these domains at various temperatures and magnetic fields will be presented.\\[4pt] [1] C.-Z. Chang et al., Science 340, 167 (2013).   

Study of magnetism in Cr doped (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$

The quantum anomalous Hall (QAH) effect was first observed in Cr doped films of the topological insulator (TI) (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$. This ferromagnetic TI opens a gap at the Dirac point and, when the Fermi energy lies inside this gap, a quantized QAH conductance can be observed. The origin of ferromagnetism in this material is still not well understood with the mechanism typically attributed to either a high van-Vleck susceptibility or a carrier mediated RKKY like interaction. To elucidate this we have studied Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$ thin films grown by MBE on SrTiO$_3$ (STO) substrates using polarized neutron reflectivity (PNR) while in-situ backgating the film to change the position of the Fermi energy. The films are also characterized by XRD, AFM, TEM and low temperature transport measurements. PNR measurements provide a direct measure of the depth dependent magnetization of a sample. We use this to study how the magnetization changes as the Fermi energy is moved towards the Dirac point. Funded by DARPA and ARO-MURI.   

Electrical Transport Properties of Mn doped Bi$_{2}$Se$_{3}$ Thin Films

Magnetic impurity doping in topological insulators manifest itself with a gap opening in the Dirac cone as a result of breaking the time reversal symmetry. Moreover, the magnetic impurities affect the structural and quantum transport properties of topological insulators by increasing the disorder and by changing the bulk charge carrier type, charge carrier density and Hall mobility. Here, we investigated the effect of Mn doping on the structural and electrical transport properties of Bi2-xMnxSe3 thin films which are 12 quintuple layers thick and grown on Al2O3 (0001) single crystal substrates via molecular beam epitaxy (MBE). Hikami-Larkin-Nagaoka (HLN) formalism was used to study the weak antilocalization (WAL). Increasing Mn doping concentration was found to increase the bulk charge carrier density and to decrease the Hall mobility. A decrease was also observed in the phase coherence length related to WAL as a function of Mn content x. Values of another WAL parameter, the pre-factor alpha, showed that the top and bottom surfaces were coupled through the bulk conducting channels. The temperature dependence of phase coherence length indicated the electrical transport was dominated by 2D electron-electron scattering for the undoped, and by bulk weak localization effects for the Mn doped samples, respectively.   

Probing interface ferromagnetism of EuS/Bi$_{2}$Se$_{3}$ heterostructures with magnetic second harmonic generation

Ferromagnet / topological insulator interfaces are novel heterostructures that can host various interesting physical phenomena, such as massive Dirac fermions, the quantum anomalous hall effect, and the topological magnetoelectric effect. By using magnetic second harmonic generation (MSHG), we separately measure the in-plane and the out-of-plane magnetization at the interface between a ferromagnetic insulator EuS and Bi$_{2}$Se$_{3}$. In contrast to bulk-sensitive linear magneto-optics, such as the Faraday and Kerr effects, MSHG allows a selective measurement of ferromagnetism and crystal symmetry of the interface, at which inversion symmetry is broken. Our technique can thus be used to study magnetism and crystal structure of such ``buried'' interfaces to which other conventional probes do not have direct access.   

Investigation of the structural and magnetic properties of MBE-grown Cr-doped Bi$_2$Se$_3$ thin films

We report a study of the structural and magnetic properties of Cr-doped Bi$_2$Se$_3$ thin films grown by MBE. We will present a thorough exposition of the electronic character of the magnetic ground state of this material as determined by x-ray magnetic circular dichroism (XMCD) as well as complementary measurements by polarised neutron reflectometry, X-ray diffraction and SQUID magnetometry. We observe the formation of a ferromagnetic ground state (via SQUID), below a measured $T_c \sim 8.5$~K with a saturation magnetization of $2.1$~$\mu_{\mathrm{B}}$/Cr. By XRD we observe a reduction in $c$-axis lattice parameter with increasing Cr concentration up to 12~at.\% of dopant. XMCD and EXAFS studies indicate that, contrary to expectations, the Cr dopes into the system as Cr$^{2+}$ due to covalency between the Cr-$d$ and Se-$p$ orbitals. We will demonstrate that no evidence is found of surface enhancement of the magnetic order and present recent work on the effect of ferromagnetic proximity coupling.   

Critical Mechanism of Magnetic Doped Cr$_{x}$Bi$_{2-x}$Te$_{3}$ Topological Insulator Thin Films

Introducing magnetic dopants into topological insulators can lead to the opening of the surface band gap which can induce interesting phenomena such as the quantized anomalous Hall effect (QAH) and magnetoelectric effect. However, the critical properties of ferromagnetism in magnetic doped TIs are not well studied. In this work, we investigated the effect of magnetic doping on magnetic and transport response in Bi$_{2}$Te$_{3}$ thin films. Cr$_{x}$Bi$_{2-x}$Te$_{3}$ thin films with x $=$ 0.03, 0.14, and 0.29 were grown with low surface roughness ($\sim$ 0.4 nm). It is found that Cr is an n-type doping element, which reduces the carrier density of p-type Bi$_{2}$Te$_{3}$. Moreover, doping Cr induces long range ferromagnetism when x$=$0.14 and 0.29, where anomalous Hall effect and weak localization of magnetoconductance were observed. The Arrott-Noakes plot for Cr$_{x}$Bi$_{2-x}$Te$_{3}$ demonstrates that the critical mechanism of the ferromagnetism can be described well with 3D-Heisenberg model. Our work may benefit for the practical applications of ferromagnetic TIs with opened surface band gap in spintronics and magnetoelectric devices.   

Electrostatic control of spin polarization in a quantum Hall ferromagnet: a new platform to realize non-Abelian excitations

Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor $\nu=2$, and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.