🔬 mesoscale physics

Ferroelectric switching control of spin current in graphene proximitized by In $_2$ Se $_3$

This study demonstrates that ferroelectric polarization switching in an In $_2$ Se $_3$ /graphene heterostructure can reversibly control the sign of charge-to-spin conversion coefficients and manipulate in-plane spin textures, offering a promising platform for advanced spintronic devices.

Original authors: Marko Milivojević, Juraj Mnich, Paulina Jureczko, Marcin Kurpas, Martin Gmitra

Published 2026-02-24

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CC BY 4.0

Original authors: Marko Milivojević, Juraj Mnich, Paulina Jureczko, Marcin Kurpas, Martin Gmitra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a super-highway made of graphene (a material as thin as a single atom of carbon) where tiny cars called electrons zoom around at incredible speeds. Usually, these cars don't care about their "spin" (a quantum property that makes them act like tiny spinning tops). But in this paper, the researchers show how to make these cars spin in a specific direction, creating a spin current, which is the holy grail for future, ultra-fast, and energy-efficient computers.

Here is the simple story of how they did it, using some everyday analogies:

1. The Setup: The "Smart Floor" and the "Highway"

Think of the graphene as a smooth, frictionless highway. Now, imagine placing a special, magical floor underneath it called In₂Se₃ (Indium Selenide). This floor is ferroelectric, which is a fancy way of saying it has a built-in "mood" or polarization that can be flipped like a light switch.

The Switch: You can flip this floor's "mood" up (positive) or down (negative) just by applying a tiny electric voltage. It's like flipping a switch on a smart floor that instantly changes the rules of the road above it.

2. The Magic Trick: The "Proximity Effect"

The researchers didn't touch the graphene directly. Instead, they relied on the proximity effect. Think of it like standing next to a very loud person; even if they don't touch you, their voice affects you.

Because the graphene is sitting right on top of the "smart floor" (In₂Se₃), the floor's electric field leaks up and changes how the electrons in the graphene behave. It forces the electrons to start spinning in a coordinated way, creating a spin current.

3. The Two Scenarios: The "Straight Road" vs. The "Twisted Road"

The researchers tested two different ways to stack these materials:

Scenario A: The Straight Road (0° Twist)
Imagine the graphene and the floor are perfectly aligned, like two sheets of paper stacked exactly on top of each other.
- What happens: When you flip the floor's switch (polarization), the direction of the electron spin flips completely.
- The Analogy: Imagine a river flowing North. If you flip the switch, the river instantly reverses and flows South. This is a "chirality switch." It's a perfect way to turn a signal on or off, or change its direction, just by flipping a switch.
Scenario B: The Twisted Road (17.5° Twist)
Now, imagine twisting the top sheet of paper slightly before stacking it. This creates a "twistronics" effect.
- What happens: This twist changes the rules entirely. Depending on which way the floor's switch is flipped, the electrons don't just flow North or South.
  - Switch Up: The electrons spin mostly sideways (perpendicular to their movement).
  - Switch Down: The electrons spin almost with their movement (parallel).
- The Analogy: Imagine a dancer.
  - In the first case, the dancer spins while moving forward.
  - In the second case (with the specific twist and switch), the dancer spins in a perfect circle around their own axis as they move forward, creating a radial pattern. The researchers call this an "Unconventional Rashba-Edelstein Effect." It's like discovering a new dance move that was previously thought impossible.

4. Why This Matters: The "Traffic Controller"

Why do we care about making electrons spin?

Current Computers: Use the charge of electrons (how many are flowing). This generates heat and uses a lot of energy.
Future Computers (Spintronics): Use the spin of electrons. This is faster and uses almost no energy.

This paper shows that by using a ferroelectric switch (the In₂Se₃ floor), we can control the spin of electrons in graphene without needing complex magnetic fields or high temperatures. It's like having a remote control for the direction of traffic on a quantum highway.

The Big Takeaway

The researchers discovered that:

Flipping a switch on a special material can instantly reverse the direction of electron spin in graphene.
Twisting the materials slightly allows for even more exotic control, creating a "radial" spin pattern that could be used for advanced sensors and memory devices.
They found a simple way to measure this: by comparing two different types of spin currents, they can "read" the angle of the spin, like reading a compass.

In a nutshell: They built a tiny, ultra-fast traffic controller for electrons using a stack of two special materials. By simply flipping an electric switch, they can make the electrons spin in any direction they want, paving the way for computers that are faster, smaller, and don't get hot.

1. Problem Statement

The field of spintronics seeks to manipulate electron spin for information processing, often relying on spin-orbit coupling (SOC) to convert charge currents into spin currents. While 2D ferroelectric materials offer a promising route for non-volatile control of electronic properties via electric fields, integrating them with graphene to achieve tunable spin textures remains a challenge. Specifically, there is a need to understand how the ferroelectric polarization direction and the twist angle between graphene and a ferroelectric substrate (In2Se3) influence:

The symmetry of the induced SOC.
The chirality of the in-plane spin texture.
The efficiency and direction of charge-to-spin conversion (Rashba-Edelstein Effect).

The authors aim to demonstrate a platform where the spin current in graphene can be electrically switched and modulated by the ferroelectric state of an adjacent In2Se3 monolayer.

2. Methodology

The study employs a multi-scale computational approach combining First-Principles Calculations and Effective Tight-Binding Modeling:

System Configuration: Graphene/In2Se3 van der Waals heterostructures were modeled with two specific twist angles:
- $\Theta = 0^\circ$ (Aligned).
- $\Theta = 17.5^\circ$ (Twisted).
- Both ferroelectric polarization states of In2Se3 were considered: Positive ( $P_\uparrow$ , +z direction) and Negative ( $P_\downarrow$ , -z direction).
First-Principles (DFT):
- Performed using Quantum ESPRESSO with the PBE functional and Grimme-D2 corrections for van der Waals interactions.
- Fully relativistic pseudopotentials were used to include Spin-Orbit Coupling (SOC).
- Dipole corrections were applied to account for the electric field offset between layers.
- Lattice parameters were adjusted via compressive strain to create commensurate supercells.
Effective Model Hamiltonian:
- A tight-binding Hamiltonian was constructed to describe low-energy dispersion, including terms for:
  - Orbital hopping ( $H_0$ ).
  - Intrinsic SOC ( $H_I$ ).
  - Pseudospin Inversion Asymmetry ( $H_{PIA}$ ).
  - Rashba SOC ( $H_R$ ), which includes a twist-angle-dependent phase $\phi_R$ .
- Parameters were extracted by fitting the DFT band structures.
Charge-to-Spin Conversion:
- The Rashba-Edelstein Effect (REE) and Unconventional Rashba-Edelstein Effect (UREE) efficiencies ( $\alpha_{REE}$ and $\alpha_{UREE}$ ) were calculated using the Kubo formula within the Smrčka-Středa formulation.
- These coefficients quantify the generation of non-equilibrium spin density ( $\delta S$ ) perpendicular or parallel to the applied charge current ( $J_0$ ).

3. Key Contributions

Ferroelectric Control of Spin Chirality: The paper establishes that reversing the ferroelectric polarization of In2Se3 acts as a "chirality switch" for the in-plane spin texture in graphene, directly reversing the sign of the charge-to-spin conversion coefficient.
Discovery of Unconventional Rashba Regime: For the twisted heterostructure ( $\Theta = 17.5^\circ$ ) with negative polarization ( $P_\downarrow$ ), the authors identify the emergence of an almost perfect radial Rashba field. This realizes the Unconventional Rashba-Edelstein Effect (UREE), where the induced spin density is nearly parallel to the charge current.
Quantitative Extraction of Rashba Phase: The authors derive an empirical relationship showing that the Rashba phase angle ( $\phi_R$ ) can be directly extracted from the ratio of conversion coefficients:
$\frac{\alpha_{UREE}}{\alpha_{REE}} \approx \tan(\phi_R)$
This provides a straightforward experimental method to characterize spin textures without complex imaging.

4. Key Results

A. Zero Twist Angle ( $\Theta = 0^\circ$ )

Symmetry: The system possesses $C_{3v}$ symmetry.
Effect: Only the conventional Rashba-Edelstein Effect (REE) is observed, where spin density is perpendicular to the charge current.
Polarization Switching: Switching from $P_\uparrow$ to $P_\downarrow$ reverses the sign of the Rashba parameter ( $\lambda_R$ ). Consequently, the direction of the generated spin current flips (e.g., from $+y$ to $-y$ for a current in $+x$ ).
Mechanism: The reversal is driven by the polarization-induced electric field, which dominates the proximity-induced field, effectively reversing the total out-of-plane electric field governing the Rashba effect.

B. Twisted Heterostructure ( $\Theta = 17.5^\circ$ )

Symmetry: The system symmetry reduces to $C_3$ , breaking vertical mirror symmetry. This allows for both perpendicular ( $\alpha_{REE}$ ) and parallel ( $\alpha_{UREE}$ ) spin current components.
Polarization Dependence:
- $P_\uparrow$ (Positive): The Rashba phase $\phi_R \approx 19.5^\circ$ . The spin current is predominantly orthogonal to the charge current (conventional behavior).
- $P_\downarrow$ (Negative): The Rashba phase shifts drastically to $\phi_R \approx 87.0^\circ$ . This results in an unconventional radial Rashba field where the spin texture is almost entirely radial, and the spin current aligns nearly parallel to the charge current.
Parameter Extraction: The ratio $\alpha_{UREE}/\alpha_{REE}$ remains nearly independent of doping and accurately reflects the Rashba phase angle predicted by the tight-binding model.

C. Electronic Structure

The chemical potential ( $\mu$ ) shifts significantly with polarization (from electron doping in $P_\uparrow$ to heavy hole doping in $P_\downarrow$ ) due to the large out-of-plane polarization of In2Se3.
The intrinsic SOC ( $\lambda_I$ ) is weak compared to the Rashba SOC ( $\lambda_R$ ), making the Rashba term the dominant factor in spin texture manipulation.

5. Significance and Implications

Non-Volatile Spintronics: The study demonstrates a mechanism for non-volatile, electrically controlled switching of spin current direction in graphene without external magnetic fields. This is crucial for low-power memory and logic devices.
Twistronics and Ferroelectricity: The work introduces a new degree of freedom in "twistronics," showing that ferroelectric polarization can act as a control knob for the Rashba phase, complementing the twist angle itself.
Radial Rashba Fields: The realization of a near-perfect radial Rashba field in a 2D heterostructure is significant for applications requiring specific spin textures, such as enhanced spin-orbit torque (SOT) efficiency and the manipulation of correlated phases or superconductivity.
Experimental Feasibility: The authors emphasize that all predicted features (sign switching, radial texture, and coefficient ratios) are experimentally detectable using standard charge-to-spin conversion measurements (e.g., inverse Edelstein effect), offering a practical roadmap for developing advanced graphene-based spintronic devices.