Session L2: Focus Session: Beyond Graphene - Spin and Magnetic Properties

Indirect exchange interaction in 3D Dirac semimetals

3D Dirac semimetals are new three-dimensional materials with linear band crossings --Dirac points-- at distinctive locations in the Brillouin zone. They are predicted to have fascinating properties such as the chiral anomaly and surface Fermi arcs. Na$_3$Bi and Cd$_3$As$_2$ are two prototypical examples that have been characterized experimentally [1]. Breaking of time reversal symmetry splits the Dirac points into Weyl points, which are protected by the underlying crystal symmetry. We study the indirect exchange interaction, between two magnetic impurities in these materials. We present results on the behavior of the interaction as a function of the inter-impurity separation in the Dirac phase. We also analyze the transition into the Weyl phase, by introducing perturbations that can be induced by external fields. [1] Science 343, 864; arXiv:1312.7624; Nat. Commun. 5, 3786; PRL 113, 027603.   

First-principles study of magnetic properties of two-dimensional semi conductors ABX$_3$

We investigate the magnetic properties of monolayers of van der Waals semiconductors ABX$_3$ theoretically. Our density functional theory (DFT) calculations show that these materials display rich magnetic phases. We use wannier analysis to study the competition between the antiferromagnetic direct exchange and the ferromagnetic superexchange, which governs the magnetic ground state. Using the low-energy effective models derived from our DFT results, we discuss the origin of rich magnetic behavior and phase transitions at finite temperature of these materials. We conclude that monolayers ABX$_3$ are suitable candidates for two-dimensional magnetic semiconductors, which have immense applications in next generation spintronics.   

Structure and magnetism of the van der Waals bonded ferromagnet CrI$_{3}$

Chromium triiodide is an easily cleavable, semiconducting ferromagnet which has received relatively little attention to date. Here we report results of our experimental investigations of the crystallographic and magnetic properties of CrI$_{3}$ single crystals. We find a first order structural phase transition at T$_{\mathrm{S}} = $ 210 K and strong magnetic anisotropy below the Curie temperature T$_{\mathrm{C}} = $ 61 K. Our findings demonstrate the interaction between structure and magnetism manifested as a magnetic anomaly at T$_{\mathrm{S}}$ and structural anomaly at T$_{\mathrm{C}}$. Our first principles calculations incorporating the van der Waals interactions reproduce the high and low temperature structures accurately, and indicate cleavage energies comparable to materials of interest for post-silicon electronics like graphite and molybdenum dichalcogenides. Theoretical investigations of the magnetic ordering suggest ferromagnetism may persist in monolayer structures. Overall our results motivate further study of CrI$_{3}$ in few- or single-layer-thick samples.   

Topological Spintronics: Materials, Phenomena and Devices

The two-dimensional surface states of three-dimensional topological insulators such as Bi$_2$Se$_3$ and (Bi,Sb)$_2$Te$_3$ possess a spin texture that can potentially be exploited for spintronics applications. We provide a perspective on the emergence of ``topological spintronics,'' demonstrating how this spin texture can be engineered using either quantum tunneling between surfaces [1] or by breaking time-reversal symmetry [2]. We then discuss recent experiments that show striking spintronic phenomena useful for proof-of-concept devices, including a spin-orbit torque of record efficiency at room temperature [3] and an electrically-gated ``giant anisotropic magnetoresistance'' at low temperature [4].\\[4pt] This work was carried out in collaboration with A. Richardella, S.-Y. Xu, M. Neupane, A. Mellnik, A. Kandala, J. S. Lee, D. M. Zhang, M. Z. Hasan and D. C. Ralph. We acknowledge funding from the DARPA Meso program, ONR and C-SPIN (under sponsorship of MARCO and DARPA). \\[4pt] [1] M. Neupane, A. Richardella {\it et al.}, Nature Communications {\bf 5}, 3841 (2014).\\[0pt] [2] S.-Y. Xu {\it et al.}, Nature Physics {\bf 8}, 616 (2012).\\[0pt] [3] A. Mellnik, J. S. Lee, A. Richardella {\it et al.}, Nature {\bf 511}, 449 (2014).\\[0pt] [4] A. Kandala, A. Richardella, {\it et al.}, submitted.   

Thermodynamic Stability of Topological Insulators

Well known three-dimensional TIs such as Bi$_2$Te$_3$, Bi$_2$Se$_3$, Bi$_2$Te$_2$Se, Sb$_2$Te$_2$Se, have been the subject of research due to potential application for spintronic devices. TIs have large bulk band gap and metallic surface states at the special time-reversal-invariant momentum (TRIM) points of the Brillouin zone. These fascinating properties constitute the current carry along the surface and not conduct current through the bulk. Creating heterostructures of TIs has recently been demonstrated to be advantageous for controlling electronic properties. In addition to the importance of the electronic properties of materials, thermodynamic stability is the key for manufacturability of materials. Guided by cluster expansion, we have investigated the thermodynamic stability of TI interfaces.   

A Field-effect Transistor based on Two-dimensional Topological Insulators

Monolayer tin functionalized with iodine (iodostannanane) is a two-dimensional topological insulator and iodostannanane ribbons have a very high mobility when the Fermi level is in the bandgap. For wide ribbons, the mobility and the conductivity decrease by several orders of magnitude when the Fermi level is in the conduction or valence band[1]. We show how this property can be exploited to make a topological-insulator field-effect transistor (TIFET) by gating the iodostannanane. We simulate the TIFETs electrical characteristics invoking a drift-diffusion like approximation and introducing a simplified model for the conductivity of the topological insulator. The TIFET is shown to have input and output characteristics similar to those of conventional field-effect transistors with an on/off ratio exceeding three orders of magnitude. Furthermore, the on-current is very high enabling high-speed operation and the amount charge in the channel is small making TIFETs interesting for low-power applications.\\[4pt] [1] W. G. Vandenberghe and M. V. Fischetti, Journal of Applied Physics 116, 173707 (2014).   

Magneto-optical studies of MoS$_{2}$

We report infrared and visible (0.100 -- 2.75 eV) magneto-optical measurements on high quality monolayer MoS$_{2}$ prepared by sulfurizing MoO$_{3}$ films. Reflection, photoluminescence, and magneto-optical Kerr spectra of MoS$_{2}$ on different substrates are measured at magnetic fields up to 7 T and temperatures down to 10 K. In the visible reflection spectrum we observe the A1 and B1 excitonic transitions. While the A1 strength is independent of magnetic field, the B1 amplitude increases by a factor of 1.5 at 5 T. This work is supported by NSF-DMR1006078.   

Valley contrasting chiral phonons in monolayer hexagonal systems

In monolayer haxagonal lattice systems, two inequivalent valleys appear in the reciprocal lattice space. With inversion symmetry breaking, we find valley dependent chiral phonons which are circularly polarized with carrying spin angular momentum and ionic magnetic moment. At valleys, light and heavy phonons are found and evolve in intervalley electronic scattering. Under three-fold rotation operation, phonons have pseudo angular momentum, which include spin and orbital parts. From conservation of pseudo angular momentum, momentum and energy, the selection rules in valleytronics are obtained. Due to chiral valley phonons, one can observe polarized infrared photoluminescence and phonon valley coherence by infrared excitation. There is also a valley dependent phonon Berry curvature which can result a valley phonon Hall effect. The valley-dependent chiral phonon, together with its spin angular momentum, pseudo angular momentum, infrared polarized photoluminescence, phonon valley coherence and valley Hall effect, will form a basis for valley-based phononics applications.   

Thickness dependence of spin polarization and electronic structure of ultra-thin films of MoS$_2$ and related transition-metal dichalcogenides

Thickness dependence of electronic structures of transition-metal dichalcogenides (TMDs) MX$_2$ (M=Mo or W; X=S, Se or Te) is investigated using first-principles calculations. When spin-orbit coupling (SOC) is included in the computations, the electronic structure of monolayer MX$_2$ films exhibits significant band splittings due to the breaking of spatial inversion symmetry. In particular, spin-split states appear around the valence band maximum with nearly 100\% out-of-the-plane spin polarization with the spin oriented oppositely at the K and K$'$ symmetry points in the Brillouin zone. For bilayer films, the spin-polarization can be tuned by an out-of-the-plane electric field, and the spin-polarized states are weakly coupled between the layers with small $k_z$ dispersion. We confirm a transition from an indirect to a direct band gap as the thickness is reduced to a monolayer in MoX$_2$, in agreement with recent experimental findings. Our study provides insight into the thickness dependence of electronic structure and the degree of spin polarization of the valence bands in ultra-thin TMD films and their viability for spintronics applications. \\[4pt] [1] T.-R. Chang, H. Lin, H.-T. Jeng, and A. Bansil, Sci. Rep. {\bf 4}, 6270 (2014).   

RKKY interaction in transition-metal dichalcogenide nanoflakes

Transition metal dichalcogenides (TMDs) are layered crystals with unique electronic and optical properties, and are promising candidates for a new generation of semiconductor-based devices, mainly when exfoliated to one or a few layers. The process of exfoliation often produces nanoscale samples --flakes-- with different shapes and boundaries. These flakes might have applications as quantum dots with novel characteristics. One interesting topic relates to the presence of magnetic impurities and their interaction. In combination with strong spin-orbit coupling and valley degrees of freedom, TMDs might have a great impact in the field of spintronics. Using an effective low-energy two-orbital tight-binding model, we study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in 2D TMD nanoflakes. We consider different geometries and terminations, analyzing the effect of the sample size. Our results show the behavior of the interaction for impurities sitting at different positions in the flake, and its possible tunability with the electron/hole concentration. The magnetic impurities can be intrinsic to the sample production process or can be introduced extrinsically. Our results can be tested with local probes, such as spin-polarized STM.   

Two-dimensional Mineral [Pb2BiS3][AuTe2]: High mobility Charge Carriers in Single-atom-thick Layers

We report that [Pb2BiS3][AuTe2], known as a naturally occurring mineral buckhornite, hosts 2D carriers in single-atom-thick layers. The structure is composed of stacking layers of weakly coupled [Pb2BiS3] and [AuTe2] sheets. The insulating [Pb2BiS3] sheet inhibits interlayer charge hopping and confines the carriers in the basal plane of the single-atom-thick [AuTe2] layer. Magneto-transport measurements and theoretical calculations show a property of multiband semimetal with compensated density of electrons and holes, which exhibit high hole carrier mobility of 1360 cm$^2$/Vs. This material possesses an extremely large anisotropy 10$^4$, comparable to benchmark materials graphite. The electronic structure features linear band dispersion at the Fermi level and ultrahigh Fermi velocities of 10$^6$ m/s which are virtually identical to that of graphene. The weak interlayer coupling gives rise to the highly cleavable property of single crystal specimens, indicating a prospect for monolayer system.   

Giant spin-splitting and orbital angular momentum in triangular lattice

We study the spin-splitting in triangular-lattice materials including Au (111) surface and transition-metal dichalcogenides quantitatively as well as qualitatively using tight-binding calculations and first-principles calculations. To analyze the spin-splitting of the bands, we calculate the orbital angular momentum (OAM) and consider the symmetry of the system. We confirm that the giant spin-splitting results from the presence of significant local OAMs and strong spin-orbit interactions in the vicinity of high-atomic number elements. This work was supported by NRF of KOREA (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2013-C3-062).   

Excitonic and marginal Fermi liquid instabilities in 2D and 3D Dirac semimetals

We study the quantum electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb interaction and the number N of Dirac fermions. In this framework, 2D Dirac semimetals have just a strong-coupling instability characterized by exciton condensation (and dynamical generation of mass) that we find at a critical coupling well above the estimates made with RPA screening (large-N approximation), thus explaining the absence of that instability in free-standing graphene samples. On the other hand, we show that 3D Dirac semimetals have a richer phase diagram, with a strong-coupling instability leading to dynamical mass generation up to N = 4 and a line of critical points for larger values of N characterized by the vanishing of the electron quasiparticle weight in the low-energy limit. Such a marginal Fermi liquid boundary marks the transition to a kind of strange metal that can still be defined in terms of electron quasiparticles, but with parameters that have large imaginary parts implying an increasing deviation at strong coupling from the conventional Fermi liquid picture.