Transport Modeling Framework

My approach often starts from an atomistic view of materials using tight-binding modeling of band structures. I explore various phenomena using semiclassical Boltzmann and non-equilibrium Green's function-based quantum transport models and connect new materials and phenomena to novel device structures. I developed many physics-based SPICE models for simulations of new devices within conventional electronics, which are available on nanoHUB.org and used by researchers in the field. In addition, I am using existing machine learning models as a supporting tool for my materials and device engineering research.

Figure: My theoretical approach.

Quantum transport model for quantum materials and devices

The physical scaling of devices has brought tremendous improvements in our technology. For example, on the transistor side, IBM recently unveiled a 2 nm chip technology that is projected to achieve 45% higher performance and 75% lower energy use than today's most advanced 7 nm node chips. On the memory side, reliable magnetic tunnel junctions with sub-10nm diameter have been introduced for high-density MRAM applications.

While such a physical scaling of devices has enabled many new functionalities and applications, it imposes daunting challenges in modeling and simulation since various quantum phenomena become prominent in the miniaturized devices that were not important in the previous larger technology nodes. Thus, we need efficient quantum-transport modeling and simulation frameworks that can analyze quantum phenomena in materials and nanostructures and connect them all the way to devices, circuits, and systems.

I have been using the non-equilibrium Green's function (NEGF)-based approaches to understand novel phenomena in materials and quantum effects in nanoscale device structures. The approach starts with a Hamiltonian that describes various materials at the atomic level. Then, I can construct discretized lattices for structures with various materials combinations and analyze various phenomena. The total Hamiltonian H of the structure can be used to calculate Green's function (g) and all associated equilibrium and transport parameters. The framework allows me to construct a simulation exactly equivalent to an experimental setup using relevant contacts and appropriate voltage or current sources, which helps me re-create the exact experimental conditions while looking at the internal parameters to understand the underlying mechanisms better.

The green's function for a structure is calculated as

where E is the energy, I is the identity matrix, Σ₁and Σ₂are self-energy functions of the contacts. One powerful aspect about NEGF-based simulation framework is that it take into account the effects from contacts, especially, because contacts play very important role in experimental realizations of new phenomena.

Understanding quantum phenomena in existing devices

I have analyzed quantum phenomena in magnetic multi-layers, which agree quantitatively with experiments and provided insights on the underlying mechanisms. For example, I have used NEGF to analyze the oscillatory interlayer exchange coupling in magnetic multi-layers. It was observed around the 90s' that two magnets separated by a transition metal-based spacer show a preferential configuration, either parallel or antiparallel. The configuration periodically alternates between parallel and antiparallel as a function of the transition metal thickness. The underlying mechanism relies on a spin-dependent wavefunction-based quantum interference which yields an exchange coupling energy between the magnet. The sign of the exchange coupling energy alternates between constructive and destructive interference, which determines the magnetic configuration and leads to the oscillatory behavior as a function of the transition metal thickness. My NEGF-based model captured this quantum phenomenon and showed that the periodicity of such oscillation relies on the quantum-well-like potential profile formed below the equilibrium Fermi level due to a d-orbital mismatch between the magnetic material and the transition metal.

My model also reproduced the observation of spin-dependent resonant tunneling in magnetic multi-layers that results in a quantum oscillation in the magnetoresistance of the magnetic structure. In addition, I have also analyzed the voltage asymmetry in spin-torques observed in existing magnetic tunnel junctions using my NEGF-based model.

Engineering quantum phenomena in existing devices

I have engineered two established room temperature quantum phenomena observed in magnetic multi-layers: oscillatory interlayer exchange coupling and spin-dependent resonant tunneling, into existing magnetic memory device structure to predict a new voltage-controlled magnetization switching mechanism. it is well known that two magnets sandwiched by a transition metal like Ru shows a preferential configuration (either parallel or antiparallel) depending on the sign of the interlayer exchange coupling between them (negative or positive). The interlayer exchange coupling arises due to a spin-dependent wavefunction-based quantum interference at the magnetic interfaces. If we place an oxide barrier at one of the magnetic interfaces, it prohibits the wavefunction to propagate and thus eliminates the interlayer exchange coupling. If we place two oxide barriers at both of the magnetic interfaces, then we create a quantum-well with discrete energy states above the Fermi level. At equilibrium, the wave function from one magnet cannot reach the other magnetic interfaces, due to the oxide barriers. However, when we apply an electric field across the structure, we can tune the contact Fermi level to align with the discrete energy states within the device, which in turn, enables a spin-dependent resonant tunneling and eventually a spin-dependent quantum interference to induce an resonant exchange coupling. The sign of the resonant exchange coupling can be controlled with the applied voltage and the magnetic configuration will switch to become parallel or antiparallel, depending on the sign. The switched configuration will be nonvolatile as the equilibrium coupling is negligible. This new prediction can have tremendous impact in the emerging magnetic nonvolatile memory technologies.

Understanding quantum phases of materials and phenomena

I have used the NEGF approach to understand the bandstructure of diverse materials, including 2D materials, topological materials, magnetic topological materials, transition metal-based oxides, and halides, etc. For example, I have analyzed the formation of topological surface states and Dirac cone in the presence of time-reversal symmetry. I have also analyzed the effect of a time-reversal symmetry break field in an arbitrary direction and observed that a gap around the Dirac node opens up for a symmetry-breaking field in the out-of-plane direction.

I have also analyzed the bandstructure of emerging transition metal-based oxides and halides that exhibit strong anisotropic exchange interactions. I have studied how the band structure changes in relation to the anisotropic interactions and related phenomena. I have also evaluated the quantum phases of these materials, which arise due to an interplay between anisotropic and isotropic exchange interactions. I have calculated the parameter spaces to observe novel quantum magnetism, especially a stripe and zigzag antiferromagnetic phases. I have also calculated the parameter space to observe an interesting spin liquid quantum phase of these materials where magnetic moments do not settle into an ordered pattern as the temperature approaches absolute zero. This new quantum phase of matter can host unique topological quasiparticle excitations, which are of great interest for a new kind of quantum computation. Topological quantum computations are expected to be significantly robust against environmental noise as compared to conventional quantum computation.

New predictions

I have predicted a new mechanism for chiral edge conduction within such quantum phases of materials, induced by an interplay between the isotropic and the anisotropic interactions. The chirality induced phase cancellation or addition of the edge conduction is solely determined the atomic chains along the transverse direction. I have also identified materials and necessary conditions where these predictions can be observed.

I plan to use and extend my framework to understand the quasiparticle excitations in the spin-liquid phases and explore new device concepts to enable topologically protected qubits and novel quantum devices.

Related manuscript:

S. Sayed, C.-H. Hsu, N. Roschewsky, S.-H. Yang, and S. Salahuddin, "Resonant enhancement of exchange coupling for voltage-controlled magnetic switching", Phys. Rev. Applied 14, 034070, Sep 2020.
S. Sayed, P. Brahma, C.-H. Hsu, and S. Salahuddin, "Chiral edge conduction in materials with anisotropic exchange interactions", 2021. (In preparation).

Figure: Quantum-transport modeling for magnetic multi-layers and comparison with experiments.

Figure: Bandstruture of materials and related quantum phenomena.

Figure: Quantum phases of material.

Semiclassical transport model for diverse spin-orbit materials

Recently, there is an increasing interest in materials exhibiting a relativistic effect called the spin-orbit coupling (SOC), especially because of efficient electrical generation and detection of electron spins due to the unique spin-momentum locking, that could lead to low power consumption in standard electronics. I have developed a semiclassical transport theory starting from the Boltzmann transport equation which unified experiments on a broad classes of materials e.g. topological insulators (TI), transition metals, III-V semiconductors, perovskites oxide, etc.

Based on the theory, I predicted several phenomena, some of which were later experimentally demonstrated up to room temperature. The key results from my theory includes:

Provides an unified explanation of existing experiments.
Provides an analytical guidance for various figure-of-merits for efficient materials and devices.
Identified several scaling trend for efficient device designs.
Predicted new phenomena, some of which later received experimental confirmation.
Identified new time-dependent dynamics of charge and spin in these materials.

New Prediction: Spin-charge separation in spin-orbit materials

The model captures the spin-charge separation that is well-established for materials without SOC. The model suggests that such spin-charge separation persist even in the presence of SOC and predicts a high velocity spin signal in these materials proportional to the degree of spin-momentum locking, which has not been noted before.

Tunable spin-charge interconversion in oxide materials

The theoretical model suggests that the spin-torque efficiency is higher in a SOC material with lower density of states. My collaborators experimentally observed that in strontium iridate both the resistivity and the carrier concentration decreases with sample thickness, however, the spin-torque efficiency increases with the thickness. This trend is opposite to the popular belief based on the observation in metals, that the spin-torque efficiency has an inverse relation to the resistivity. The observation in the spin-orbit torque experiment is in good agreement with my theoretical model when compared in terms of the carrier concentration. Note that carrier concentration is a measure of the density of states in the material. My model suggest further tunability of the density of states in such correlated oxide systems using strain modulation.

Prediction and demonstration of unequal antiparallel states in a multi-terminal spin valve

I have made a surprising prediction that the antiparallel resistances of a multi-terminal lateral spin valve can be unequal where one of the antiparallel resistance is larger than the parallel resistance while the other one is symmetrically smaller. The predicted signal was later observed independently by my collaborators in a semiconductor, InAs, and in a 2D material, PtSe₂, up to room temperature. The signal persisted without any degradation up to 1.62 mm of magnetic contact separation, which is very long range as compared to existing spin related phenomena.

Related manuscript:

S. Sayed, S. Hong, X. Huang, A. S. Everhardt, L. Caretta, R. Ramesh, S. Salahuddin, and S. Datta, "Unified Framework for Charge-Spin Interconversion in Spin-Orbit Materials", Phys. Rev. Applied, 15, 054004, May 2021. (Link).
S. Sayed, S. Hong, and S. Datta, “Transmission-Line Model for Materials with Spin-Momentum Locking”, Phys. Rev. Applied 10, 054044, November 2018. (Link).
X. Huang, S. Sayed, J. Mittelstaedt, S. Susarla, S. Karimeddiny, L. Caretta, H. Zhang, V. A. Stoica, T. Gosavi, F. Mahfouzi, Q. Sun, P. Ercius, N. Kioussis, S. Salahuddin, D. C. Ralph, R. Ramesh, "Novel spin-orbit torque generation at room temperature in an all-oxide epitaxial La_0.7Sr_0.3MnO₃/SrIrO₃system", Advanced Materials, 2008269, May 2021. (Link).
J. Tian, S. Hong, S. Sayed, S. Datta, N. Samarth, and Y. P. Chen, "On the understanding of current-induced spin polarization of 3D topological insulators'', Nature Communications, 10, 1461, April 2019. (Link).
A. S. Everhardt, D. C. Mahendra, X. Huang, S. Sayed, T. Gosavi, Y. Tang, C.-C. Lin, S. Manipatruni, I. Young, S. Datta, J.-P. Wang, R. Ramesh, "Tunable charge to spin conversion in strontium iridate thin films'', Phys. Rev. Materials 3, 051201(R), May 2019. (Link).
J. Kim, C. Jang, X. Wang, J. Paglione , S. Hong, S. Sayed, D. Chun, and D. Kim, "Electrical detection of the inverse Edelstein effect on the surface of SmB6", Phys. Rev. B 102, 054410, August 2020. (Link).
S. Sayed, S. Hong, and S. Datta, “Multi-Terminal Spin Valve on Channels with Spin-Momentum Locking”, Scientific Reports 6, 35658, October 2016. (Link).
J.-H. Lee, H.-J. Kim, J. Chang, S. H. Han, H.-C. Koo, S. Sayed, S. Hong and S. Datta, “Multi-terminal spin valve in a strong Rashba channel exhibiting three resistance states”, Scientific Reports 8, 3397, February 2018. (Link).

Figure: Semiclassical picture of a general spin-momentum locked channel.

Figure: Spin-orbit torque efficiency in SrIrO3.

Figure: New prediction (2016) and experimental demonstration (2018) on InAs quantum well.

SPICE Library for Magnetic and Spintronic Devices

I have converted my semiclassical transport models for various materials into SPICE models for a modular approach to analyze magnetic and spintronics devices. The SPICE models are four-component: one charge component and three (z,x, and y polarized) spin components. The models for different material layers can be added in a modular fashion to analyze the experimental setup or device structure in SPICE. The models have been benchmarked with various existing experiments. Key contributions of my SPICE modeling are:

A transmission line model for spin-orbit materials.
A compact model for 2D spin-orbit channel.
A compact model for the giant spin Hall effect.
A compact model for magnon transport in ferromagnetic insulators.
Hall effect models.
An empirical model for voltage-controlled REC MTJ.
A GUI for distributed approach in SPICE to analyze 2D spin diffusion with spin relaxation mechanisms.

These models are now part of nanoHUB.org and being used by researchers in the field. I have used these models to analyze many new devices integrated within standard CMOS circuits. Recently, I have used my SPICE model to analyze graphene as an efficient spin-interconnect for logic-in-memory architectures. I have modeled a multifunctional majority magnetic logic gate in SPICE and demonstrated experimentally through my collaboration with Chalmers University in Sweden.

Related manuscript:

D. Khokhriakov, S. Sayed, A. M. Hoque, B. Karpiak, B. Zhao, S. Datta, S. P. Dash, "Multifunctional Spin Logic Gates In Graphene Spin Circuits", arXiv:2108.12259 [cond-mat.mes-hall], Aug 2021. (Link).
S. Sayed, C.-H. Hsu, and S. Salahuddin, "A voltage-controlled gain cell magnetic memory", IEEE Electron Device Letters, 42(10), 1452 - 1455, Aug 2021. (Link).
S. Sayed, S. Hong, and S. Datta, “Transmission-Line Model for Materials with Spin-Momentum Locking”, Phys. Rev. Applied 10, 054044, November 2018. (Link).
S. Hong, S. Sayed, and S. Datta, "Spin Circuit Model for 2D Channels with Spin-Orbit Coupling", Scientific Reports 6, 20325, March 2016. (Link).
S. Hong, S. Sayed, and S. Datta, "Spin circuit representation for the spin Hall effect", IEEE Transactions on Nanotechnology 15, 225-236, January 2016. (Link).
S. Sayed, V. Q. Diep, K. Y. Camsari, and S. Datta, “Spin Funneling for Enhanced Spin Injection into Ferromagnets”, Scientific Reports 6, 28868, July 2016. (Link).

Figure: SPICE modeling of magnetic and spintronic devices.

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