Spin and Orbital Rashba response in ferroelectric polarized PtSe$_2$/MoSe$_2$/LiNbO$_3$ heterostructures

This study employs first-principles simulations to quantify the spin and orbital Rashba effects at the PtSe$_2$/MoSe$_2$/LiNbO$_3$ interface, revealing how the ferroelectric polarization of LiNbO$_3$ controls THz emission through angular momentum-to-charge conversion mechanisms.

The Gist

The Big Picture: A Traffic Jam of Tiny Particles

Imagine you have a highway made of ultra-thin, two-dimensional materials (like sheets of graphene or platinum diselenide). On this highway, tiny particles called electrons are zooming around. Usually, these electrons are just "cars" carrying energy. But in the world of spintronics, these cars also have a hidden feature: they have a spin (like a spinning top) and an orbit (like a planet circling a sun).

The goal of this research is to understand how to turn the "spinning" or "orbiting" of these electrons into an electrical current that can send out a signal called Terahertz (THz) radiation. Think of THz radiation as a super-fast, invisible radio wave used for high-speed communication and imaging.

The Setup: The "Magnetic Switch" and the "Ferroelectric Battery"

The researchers built a sandwich-like structure:

1. The Road: Layers of PtSe2 and MoSe2 (the 2D materials where the electrons travel).
2. The Battery: A layer of LiNbO3 (Lithium Niobate). This is a "ferroelectric" material.

The Analogy: Think of the LiNbO3 layer as a reversible battery or a magnetic switch.

• Normally, this battery has a "polarity" (a positive and negative side).
• You can flip this battery so the positive side faces up or down.
• When you flip it, it creates an invisible electric wind (an electric field) that blows through the 2D layers above it.

The researchers wanted to see: What happens to the electrons on the road when we flip this electric wind switch?

The Discovery: Two Types of "Spin"

In the past, scientists mostly looked at the Spin of the electron (the spinning top). They knew that if you hit these materials with a laser, the spinning electrons would get pushed sideways, creating an electrical current. This is called the Rashba-Edelstein Effect.

However, this paper introduces a new character: the Orbital motion (the planet circling the sun).

The Creative Metaphor:
Imagine a crowd of people (electrons) running on a track.

• Spin is like everyone spinning their own bodies while running.
• Orbit is like everyone running in a circle around a central pole while running forward.

The researchers used powerful computer simulations (like a high-tech flight simulator for atoms) to see what happens when the "electric wind" from the LiNbO3 battery blows on this crowd.

Key Findings

1. The Wind Changes the Crowd's Shape
When the electric wind blows in one direction (Polarization Up), the "spinning" and "orbiting" patterns of the electrons look one way. When they flip the wind (Polarization Down), the patterns twist and distort.

• The Result: The "orbiting" pattern is actually very sensitive to this wind. It changes shape significantly, almost like a hexagon turning into a triangle.

2. The "Opposite" Reaction
Here is the most interesting part. The researchers found that the Spin and the Orbit react in opposite ways.

• Analogy: Imagine two people pushing a heavy box. If the "Spin" person pushes to the Left, the "Orbit" person pushes to the Right.
• In the computer simulation, when the electric field was flipped, the spin current went one way, but the orbital current went the other way. They are "negatives" of each other.

3. The "Sweet Spot" for Signals
The researchers found a specific energy level (a specific speed of the electrons) where they could flip the direction of the signal just by changing the battery's polarity.

• The Result: By tuning the "wind" (the electric field), they could make the THz signal (the radio wave) stronger or even reverse its direction. They calculated that flipping the battery could boost the signal strength by about 30% for spin, and even 100% for the orbital effect in certain conditions.

Why This Matters (According to the Paper)

The paper claims that for a long time, scientists ignored the "Orbital" part of the electron, focusing only on "Spin." This study shows that the Orbital part is just as important, if not more sensitive, to these electric fields.

• The Takeaway: If we want to build better, faster, and more controllable THz devices (for future wireless tech), we can't just look at the spinning electrons. We have to understand how they "orbit" too.
• The Control: By using the ferroelectric "battery" (LiNbO3), we can act as a remote control, turning the signal up, down, or flipping it, simply by changing the direction of the electric wind.

Summary in One Sentence

This paper uses computer simulations to show that by flipping an electric switch in a layered material, we can control not just the "spin" but also the "orbit" of electrons, creating a powerful and tunable signal for future high-speed technology.

Technical Summary

Technical Summary: Spin and Orbital Rashba Response in Ferroelectric Polarized PtSe2/MoSe2/LiNbO3 Heterostructures

Problem Statement
Recent advances in spintronic terahertz (THz) emitters have demonstrated that ultrafast optical pulses can generate THz radiation via spin-to-charge conversion (SCC) in ferromagnetic/non-magnetic (FM/NM) heterostructures. While mechanisms such as the Inverse Spin Hall Effect (ISHE) and the Inverse Rashba-Edelstein Effect (IREE) are well-established, the role of the orbital degree of freedom in these processes remains underexplored in literature, particularly within van der Waals (vdW) heterostructures. Furthermore, while ferroelectric substrates like LiNbO3 have been shown to modulate THz emission via polarization-dependent electric fields, a first-principles quantification of how these fields influence both spin and orbital Rashba textures—and the resulting SCC efficiency—is lacking. This work addresses the need to quantify the Rashba effect at PtSe2/MoSe2 interfaces, incorporating orbital dynamics to explain experimental THz signatures and the modulation of emission by ferroelectric polarization.

Methodology
The authors employed a multi-stage first-principles approach combining Density Functional Theory (DFT) and linear response theory:

1. Structural Relaxation and Field Extraction: Using DFT-PBE within the VASP code (plane-wave basis, 500 eV cutoff, D2 vdW correction), the authors modeled a PtSe2/MoSe2/LiNbO3 heterostructure. They simulated two configurations: 2D layers placed above and below a Z-cut LiNbO3 slab to represent opposite polarization directions ($\hat{P}_{\uparrow}$ and $\hat{P}_{\downarrow}$). By comparing the electrostatic potential of the full heterostructure against an isolated PtSe2/MoSe2 bilayer, they extracted the effective out-of-plane electric field ($E_{eff}$) generated by the ferroelectric substrate at the 2D interface.
2. Transport and Response Calculations: Utilizing the SIESTA code (localized DZP basis sets) and the Kubo formalism, the authors performed non-equilibrium transport calculations. An artificial electric field, derived from the extracted $E_{eff}$ values, was applied to a pure PtSe2/MoSe2 trilayer system to emulate the ferroelectric environment.
3. Linear Response Analysis: The authors calculated the spin and orbital accumulations (densities) induced by an in-plane electric field ($E_x$) using linear response theory. This involved integrating the Kubo formula over a $200 \times 200$ k-point mesh to determine the out-of-equilibrium spin ($\langle \delta \hat{s}_y \rangle$) and orbital ($\langle \delta \hat{l}_y \rangle$) densities. The study focused on the energy window relevant to experimental optical excitation (approximately -2 eV to +2 eV relative to the Fermi level).

Key Contributions and Results

• Quantification of Effective Electric Fields: The study successfully quantified the effective electric fields acting on the 2D layers due to the LiNbO3 substrate. For the configuration with MoSe2 closer to the LiNbO3 surface, the field was calculated at approximately 0.115 V/Å, while the configuration with PtSe2 closer yielded ~0.047 V/Å. These values were used to simulate the polarization-dependent modulation of the 2D system.
• Orbital Rashba Textures: The authors mapped the orbital textures of the PtSe2/MoSe2 system. They observed that while the chirality near the $\Gamma$ point remained relatively stable, significant distortions occurred near the $K$ and $K'$ points depending on the polarization direction. Notably, the orbital texture exhibited a more hexagonal shape compared to the spin texture, with counter-clockwise chirality at $K/K'$ and clockwise at $\Gamma$.
• Spin vs. Orbital Accumulation:
  • Spin: The simulations revealed a large energy window (approx. -1.75 to -1.0 eV) where the spin accumulation is enhanced by the polarization direction pointing toward the interface ($\hat{P}_{\uparrow}$). This enhancement aligns with experimental observations of a ~30% increase in THz electric field amplitude.
  • Orbital: The orbital accumulation displayed an opposite sign to the spin accumulation within the [-1, 0] eV window. This opposition is attributed to a negative spin-to-orbit correlation ($\langle \hat{l} \cdot \hat{s} \rangle$) across the energy window.
• Modulation and Sign Reversal: The study identified specific energy levels where the accumulation signs reverse. For spin, a sign change occurs around 0.9 eV, while for orbital density, it occurs around -1.5 eV. This suggests that the sign of the THz signal could theoretically be tuned by adjusting the photon energy of the excitation pulse or the chemical potential via gating.
• Rashba Coupling Strength: The estimated Rashba coupling constant ($\alpha_R$) for the PtSe2/MoSe2 interface is approximately -300 meV·Å, driven primarily by Se-p states at the interface. This is higher than the value found in PtSe2/Graphene systems (-195 meV·Å).
• Orbital Contribution to THz Emission: The authors calculated the percentage gain in the inverse Rashba-Edelstein length ($\Lambda_{REE}$) between polarization states. While the spin contribution showed a gain of <30%, the orbital contribution demonstrated a significantly higher sensitivity, reaching an enhancement of ~100% in specific energy windows. This indicates that the orbital degree of freedom is highly susceptible to ferroelectric polarization.

Significance and Claims
The paper claims that incorporating the orbital degree of freedom is crucial for a deeper understanding of angular momentum-to-charge conversion and THz emission in vdW heterostructures. The authors assert that their first-principles simulations provide a quantitative explanation for experimental THz-TDS results, specifically the modulation of emission by ferroelectric polarization.

Key claims include:

1. Complementary Mechanisms: The spin and orbital responses, while having opposite signs in certain energy ranges due to negative spin-orbit correlation, balance each other to produce a net positive accumulation that aligns with experimental THz signals.
2. Orbital Sensitivity: The orbital contribution to the Rashba-Edelstein effect is shown to be more sensitive to polarization fields than the spin contribution, offering a potential pathway for enhancing or tuning THz emission efficiency.
3. Methodological Framework: The work establishes a methodology to calculate out-of-equilibrium spin and orbital densities in the presence of ferroelectric fields, which can be adapted to engineer material properties in vdW heterostructures.
4. Future Directions: The authors modestly note that while the electrical driven response is quantified, the exact amount of orbital polarization injected from the ferromagnetic side remains an unknown quantity dependent on interface details. They suggest that future material engineering (e.g., using elements like Ni) could maximize the orbital contribution, potentially leading to spintronic samples where the orbital response is predominant.

The study concludes that understanding the dynamics of both spin and orbital degrees of freedom is essential for developing next-generation THz technologies and spin-orbit torque devices, particularly in centrosymmetric materials like PtSe2 where lifting spin degeneracy can yield significant efficiencies.