Spin caloritronics in collinear ferromagnetic helical structures under irradiation

This study demonstrates that irradiating collinear ferromagnetic helical structures with polarized light induces spin-split transmission and suppresses thermal conductance, thereby significantly enhancing spin thermoelectric performance and the figure of merit, particularly when combined with long-range hopping.

The Gist

Imagine you have a tiny, twisted staircase made of magnetic atoms. This isn't just any staircase; it's a ferromagnetic helix, meaning every step on the stairs has a tiny magnetic compass needle pointing in the same direction. In the world of physics, this structure is like a specialized filter for electrons, the tiny particles that carry electricity.

The researchers in this paper wanted to see how this magnetic staircase handles heat and electricity, but with a twist: they shined a special kind of light on it. They weren't just looking at how much electricity flows (charge); they were also looking at the "spin" of the electrons. Think of electron spin like a tiny top spinning either clockwise or counter-clockwise.

Here is the story of what they found, broken down into simple concepts:

1. The Problem: Heat vs. Electricity

Usually, when you try to turn waste heat into electricity (a process called thermoelectricity), you run into a traffic jam. In most materials, if electricity flows easily, heat flows easily too. This is bad because you want to stop the heat from leaking away while letting the electricity pass. The paper suggests that by using these magnetic staircases and shining light on them, we can uncouple these two flows.

2. The Magic Light (Floquet Engineering)

The team didn't just turn on a lamp; they used a mathematical trick called "Floquet-Bloch formalism." Imagine the light as a rhythmic drumbeat shaking the staircase.

• Without light: The magnetic staircase already separates electrons based on their spin (like a bouncer letting only people with red hats in, but not blue hats).
• With light: The rhythmic shaking of the light changes the rules of the staircase. It creates a "spin-dependent gap." Imagine the bouncer suddenly deciding that at a specific moment, the door for "blue hat" electrons slams shut, while the "red hat" door stays open or even swings wider. This creates a sharp difference between the two types of electrons.

3. The Result: A Super-Filter for Spin

When they measured the results, they found three major things happened under the light:

• The "Spin" Power Went Up: The ability to generate electricity specifically from the difference in electron spins (called spin thermopower) skyrocketed. In fact, it became much stronger than the ability to generate electricity from the total flow of electrons.
• The Heat Leak Stopped: The light actually suppressed the flow of heat through the electrons. It's like putting a thermal blanket over the staircase, keeping the heat from escaping while still allowing the "spin" electricity to flow.
• The "Figure of Merit" (FOM) Improved: Scientists use a score called the Figure of Merit (FOM) to rate how good a material is at turning heat into power. The paper found that the Spin FOM (the score for spin-based energy) was consistently higher than the Charge FOM (the score for regular electricity). In some cases, the spin score was nearly 2.5, which is considered excellent for these types of materials.

4. The Shape Matters: Short vs. Long Steps

The researchers also played with the geometry of the staircase.

• Short-range: If the electrons can only jump to the very next step, the system isn't very efficient.
• Long-range: If the electrons can "hop" over several steps at once (long-range hopping), the system becomes a much better energy converter. The paper shows that by tuning how far the electrons can jump, you can maximize the efficiency of the spin-based energy conversion.

5. The Materials Used

To make sure their math matched reality, they modeled the staircase as being made of carbon (like organic molecules) and connected to wires made of silicon and germanium. They found that using germanium wires resulted in less heat leaking through the vibrations of the atoms (phonons), which helped keep the efficiency score high.

The Bottom Line

This paper is a theoretical blueprint. It suggests that if you take a magnetic, spiral-shaped structure and shine the right kind of polarized light on it, you can create a device that is incredibly good at harvesting energy from heat, specifically by using the "spin" of electrons rather than just their charge. The light acts as a tuning knob, allowing you to switch on a high-performance "spin engine" that outperforms traditional electrical engines in this specific setup.

Technical Summary

Technical Summary: Spin Caloritronics in Collinear Ferromagnetic Helical Structures under Irradiation

Problem Statement
Thermoelectric (TE) efficiency is traditionally limited in bulk materials by the Wiedemann-Franz law, which couples electrical and thermal conductivities. While low-dimensional systems offer a route to decouple these quantities, achieving high dimensionless figures of merit (FOM, $ZT$) remains challenging. Spin caloritronics proposes utilizing the electron spin degree of freedom to enhance TE performance, potentially yielding high spin-dependent FOMs even when charge-based FOMs are low. However, generating robust spin-polarized currents typically requires ferromagnetic contacts, spin-orbit coupling (often weak in molecular systems), or external magnetic fields. Recent interest in chiral-induced spin selectivity (CISS) suggests helical geometries can act as spin filters, but conventional CISS often relies on spin-orbit coupling and dephasing. This paper investigates whether a ferromagnetic helical system, irradiated by arbitrarily polarized light, can serve as a robust platform for efficient spin-dependent thermoelectric energy conversion, leveraging light-matter interaction to modulate spin polarization without relying solely on intrinsic spin-orbit coupling.

Methodology
The authors employ a theoretical framework combining a tight-binding model with the Floquet-Bloch formalism and non-equilibrium Green's function (NEGF) techniques.

• System Model: A right-handed ferromagnetic helix with collinear magnetic moments aligned along the $z$-axis is modeled. The system is connected to semi-infinite 1D non-magnetic metallic leads.
• Light-Matter Interaction: The effect of arbitrarily polarized light (linear, circular, or elliptical) is incorporated via the minimal coupling scheme. The time-periodic Hamiltonian is transformed into an effective time-independent Hamiltonian using the Floquet-Bloch ansatz, resulting in modified hopping integrals that depend on Bessel functions of the light's vector potential and polarization parameters.
• Transport Calculations: Spin-resolved electrical conductance ($G_\sigma$), Seebeck coefficient ($S_\sigma$), and electronic thermal conductance ($\kappa_{el}$) are calculated using Landauer-Büttiker formalism and NEGF.
• Phonon Transport: To evaluate the total FOM accurately, phonon thermal conductance ($\kappa_{ph}$) is computed using a mass-spring model within the NEGF framework. The central helix is modeled as carbon-based, while leads are modeled as silicon or germanium to account for material-specific vibrational properties.
• Parameters: Simulations are performed at room temperature ($T=300$ K) with high-frequency radiation ($\omega \approx 10^{16}$ Hz) to ensure the validity of the high-frequency Floquet approximation and to avoid significant lattice heating effects.

Key Contributions and Results
The study reveals several critical findings regarding the interplay of helical geometry, ferromagnetism, and light irradiation:

1. Light-Induced Spin Splitting and Gaps: Light irradiation induces spin-split transmission features. Specifically, it opens a light-induced spin-dependent gap near zero energy, significantly suppressing the transmission of the down-spin channel while maintaining finite up-spin transmission.
2. Enhancement of Spin Thermopower: The most significant finding is the dramatic enhancement of spin thermopower ($S_s$) under light irradiation. This arises from the crossing of spin-up and spin-down transmission channels near the Fermi energy. These crossings create sharp energy gradients and opposite slopes in the transmission functions for the two spin channels, leading to large, opposite-sign contributions to the Seebeck coefficient. Consequently, the spin thermopower can reach values as high as $600 \, \mu\text{V/K}$, significantly outperforming the charge thermopower.
3. Suppression of Thermal Conductance: Light irradiation suppresses both electrical and electronic thermal conductances. The reduction in electronic thermal conductance ($\kappa_{el}$) is particularly pronounced, dropping to a few pW/K in certain energy windows.
4. Superior Spin FOM: The spin figure of merit ($Z_sT$) consistently outperforms the charge figure of merit ($Z_cT$). Under optimal conditions (e.g., germanium leads, specific light polarization), $Z_sT$ reaches values close to 2.5 in the absence of light and can exceed 7 under specific polarization angles ($\theta = \pi/2$). The study demonstrates that favorable spin TE performance ($Z_sT > 1$) is achievable across a wide range of light polarizations.
5. Role of Long-Range Hopping: The decay constant ($l_c$) governing the range of electron hopping is identified as a critical tuning parameter. Systems exhibiting long-range hopping (larger $l_c$) demonstrate significantly enhanced spin TE performance compared to short-range (nearest-neighbor only) helices. The spin FOM can be effectively tuned by adjusting $l_c$, with optimal values observed around $l_c \approx 0.7$ Å for certain light configurations.
6. Lead Material Dependence: The choice of lead material affects the total FOM primarily through phonon thermal conductance. Germanium leads, having a lower phonon thermal conductance than silicon leads at room temperature, yield higher overall FOMs.

Significance and Claims
The paper claims to be the first to address spin-dependent TE effects in ferromagnetic helical systems under arbitrarily polarized light. The authors assert that their generalized formalism, which accommodates arbitrary polarization states, offers deeper insight into the influence of light polarization on spin-resolved transport compared to previous studies limited to circular polarization.

The work suggests that combining intrinsic structural chirality, collinear magnetic ordering, and light-induced modulation provides a robust platform for spin-selective TE behavior. The findings indicate that light irradiation is a viable strategy to optimize TE performance in ferromagnetic systems, particularly by enhancing the spin FOM while suppressing thermal losses. The study concludes that long-range hopping processes are essential for maximizing spin thermoelectric efficiency, offering a promising theoretical direction for designing efficient energy conversion devices in related ferromagnetic systems. The authors maintain a modest stance, noting that while the parameters used are physically viable, the model assumes ideal conditions (e.g., neglecting photo-induced structural distortions) and that experimental realization would require engineered systems to mitigate heating effects.