Inductive detection of inverse spin-orbit torques in magnetic heterostructures

This study demonstrates that ferromagnetic [Co/Ni] and [Co/Pt] multilayers with perpendicular magnetic anisotropy can effectively generate spin-orbit torques comparable to platinum to drive magnetization dynamics in CoFeB layers, while also revealing a significant correlation between torque strength and the CoFeB layer thickness through inductive detection.

The Gist

The Big Idea: Turning Spin into Electricity (and Back Again)

Imagine you have a tiny, invisible river flowing inside a piece of metal. In the world of spintronics (a type of electronics that uses the "spin" of electrons instead of just their charge), this river is made of electrons spinning like tiny tops.

Usually, scientists use heavy metals (like Platinum) to turn an electrical current into a flow of these spinning tops, which then pushes on a magnet to move it. This is like using a water wheel to turn a gear.

This paper asks a bold question: What if we don't need the heavy metal? What if the magnet itself can do the heavy lifting?

The researchers discovered that certain magnetic "sandwiches" (layers of Cobalt and Nickel, or Cobalt and Platinum) are actually just as good at generating this spinning force as the traditional heavy metals. Even better, they found a way to "listen" to the magnet to see how hard it's being pushed, without needing to touch it with wires.

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The Experiment: The "Magnetic Dance Floor"

To test this, the team built a special "dance floor" made of layers:

1. The DJ Booth (The Torque Generator): This is the top layer, made of magnetic materials like [Co/Ni] or [Co/Pt]. Think of this as the DJ who controls the beat.
2. The Dance Floor (The Magnet): Below the DJ is a layer of CoFeB (a magnetic metal). This is the magnet that needs to be moved.
3. The Buffer Zone: A thin layer of Copper separates them so they don't get too close, but they can still "talk" to each other.

The Setup:
They placed this stack on a special antenna (a waveguide) and zapped it with microwaves. This made the magnet on the dance floor wobble (precess) like a spinning top that is about to fall over.

The Magic Trick: "Listening" to the Spin

Here is the clever part. When the magnet wobbles, it doesn't just sit there. Because of a quantum effect called Spin-Orbit Torque, the wobble generates a tiny, invisible electrical current inside the magnet itself.

Usually, to measure this, you'd have to stick wires on the sample, which is messy and can mess up the experiment.

The Analogy:
Imagine the magnet is a spinning top on a table. As it spins, it creates a tiny whirlpool in the air around it.

• Old Method: You stick a wind sensor (a wire) right next to the top to feel the wind.
• This Paper's Method: They used a "super-sensitive microphone" (a Vector Network Analyzer) to listen to the sound of the whirlpool from a distance.

By measuring the tiny electrical signal picked up by the antenna, they could calculate exactly how much "spin force" the top layer (the DJ) was giving to the bottom layer (the dancer).

The Findings: The Underdogs Win!

The researchers expected the traditional heavy metals (like Platinum) to be the champions. Instead, they found:

1. The New Champions: The [Co/Ni] (Cobalt/Nickel) layers were just as powerful as Platinum. In fact, in some cases, they were even stronger!
2. The Thickness Surprise: They noticed that the thicker the bottom magnet layer was, the stronger the force became.
   • The Analogy: Usually, if you have a thick blanket, it absorbs the wind. But here, it was like the blanket was generating its own wind as it got thicker. This suggests the magnet is helping to push itself, a phenomenon called "self-induced torque."
3. The Math Check: They used super-computers to simulate the atoms. The computer said, "Yes, theoretically, these Cobalt/Nickel layers should be strong." The experiment confirmed the computer was right.

Why Does This Matter?

Think of current hard drives and memory chips. They use electricity to move magnets, which takes a lot of energy and creates heat.

• Efficiency: If we can use these new magnetic layers instead of heavy metals, we might be able to build faster, cooler, and more energy-efficient computer chips.
• Simplicity: Since the magnetic layer itself generates the force, we might be able to design simpler devices with fewer layers.

Summary in One Sentence

The researchers discovered that certain magnetic "sandwiches" can generate powerful forces to move magnets just as well as heavy metals, and they used a clever "listening" technique to prove it without needing to touch the sample with wires.

Technical Summary

1. Problem Statement

Spin-orbit torques (SOTs) are critical for the efficient manipulation of magnetization in spintronic devices. Conventionally, heavy metals (HMs) with strong spin-orbit coupling (SOC), such as Platinum (Pt), Tantalum (Ta), and Tungsten (W), are used to generate SOTs via the Spin Hall Effect (SHE) or Rashba-Edelstein effect.

• The Gap: While HM-based SOTs are well-studied, there is a need to explore SOT generation within all-ferromagnetic heterostructures containing layers with large spin-orbit interactions (e.g., [Co/Ni] or [Co/Pt] multilayers).
• The Challenge: Distinguishing the contributions of different mechanisms (SHE, orbital Hall effect, self-induced torques) and quantifying the efficiency of spin-to-charge conversion in these complex multilayer systems requires precise measurement techniques that can separate even and odd symmetry torques.

2. Methodology

The authors employed a combination of sample fabrication, advanced inductive measurement techniques, and first-principles calculations.

• Sample Design:

  • Target Structures: Ferromagnetic heterostructures consisting of a Perpendicular Magnetic Anisotropy (PMA) layer acting as the torque generator and an In-Plane Magnetic Anisotropy (IMA) layer acting as the detector.
  • Specific Stacks:
    • PMA Layers: [Co(0.2)/Ni(0.6)]$_6$ and [Co(0.5)/Pt(0.5)]$_5$ (thicknesses in nm).
    • IMA Detector: Co$_{20}$Fe$_{60}$B$_{20}$ (CoFeB) with varying thicknesses ($d_{CoFeB}$ from 2 to 15 nm).
    • Spacer: Non-magnetic Copper (Cu) separates the PMA and IMA layers to prevent direct exchange coupling.
    • Controls: Bilayer Pt/CoFeB and Trilayer Pt/Cu/CoFeB samples were fabricated for comparison.
  • Substrate: SiO$_2$/Ta(3)/Cu(3) seed layers.

• Experimental Technique (VNA-FMR):

  • Method: Vector Network Analyzer Ferromagnetic Resonance (VNA-FMR) using an inductive detection scheme.
  • Mechanism: An AC magnetic field excites the CoFeB layer into precession (FMR). This dynamic magnetization pumps an AC spin current into the adjacent PMA layer.
  • Inverse SOT (iSOT): The spin current is converted back into an AC charge current within the PMA layer via inverse spin-orbit processes (inverse SHE, inverse Rashba-Edelstein).
  • Detection: The resulting AC current generates a magnetic field detected by the coplanar waveguide (CPW) as a change in the complex transmission parameter ($S_{21}$).
  • Analysis: The complex inductance ($L$) is extracted from the $S_{21}$ data. By analyzing the real and imaginary parts of the normalized inductance ($\tilde{L}$) as a function of frequency, the authors separated the even symmetry ($\sigma_e^{SOT}$) and odd symmetry ($\sigma_o^{SOT}$) spin-orbit torque conductivities.

• Theoretical Support:

  • First-Principles Calculations: Density Functional Theory (DFT) was used to calculate the intrinsic Spin Hall Conductivity (SHC) of bulk [Co/Ni] and [Co/Pt] multilayers to compare with experimental findings.

3. Key Contributions

1. Demonstration of All-Ferromagnetic SOT Generation: The study successfully demonstrates that ferromagnetic multilayers with PMA ([Co/Ni] and [Co/Pt]) can act as efficient torque-generating layers, rivaling traditional heavy metals.
2. Inductive Separation of Torque Symmetries: The authors utilized a phase-sensitive inductive technique to quantitatively separate odd-symmetry (damping-like) and even-symmetry (field-like) torques in these complex trilayer systems.
3. Discovery of Thickness-Dependent Enhancement: A significant finding is the linear increase of odd-symmetry SOT conductivity with the thickness of the CoFeB layer, a behavior not explained by standard SHE models alone.
4. Validation via DFT: The experimental results are corroborated by DFT calculations showing that [Co/Ni] and [Co/Pt] possess intrinsic spin Hall conductivities comparable to Pt.

4. Results

• Magnitude of SOTs:
  • The [Co/Ni]/Cu/CoFeB samples exhibited the highest odd-symmetry SOT conductivity ($\sigma_o^{SOT}$).
  • For a CoFeB thickness of 5 nm, $\sigma_o^{SOT} \approx 4.19 \times 10^5 (\Omega \cdot m)^{-1}$.
  • This value is comparable to, and in some cases exceeds, values reported for Pt-based systems (typically $2.1 - 5.5 \times 10^5 (\Omega \cdot m)^{-1}$).
• Symmetry Analysis:
  • Odd Symmetry ($\sigma_o^{SOT}$): Dominated the signal in all samples. The [Co/Ni] multilayer showed the strongest effect.
  • Even Symmetry ($\sigma_e^{SOT}$): Values were negligible across all samples, suggesting that field-like torques (e.g., from Oersted fields or inverse Rashba-Edelstein) are minimal in this configuration.
• Thickness Dependence:
  • Unlike standard SHE where conductivity saturates with thickness, $\sigma_o^{SOT}$ in the [Co/Ni] and [Co/Pt] systems increased linearly with CoFeB thickness up to 15 nm.
  • Interpretation: This suggests a self-induced SOT mechanism within the CoFeB layer or a non-local spin current generation mechanism facilitated by the interfaces, rather than a simple bulk SHE effect.
• Trilayer vs. Bilayer:
  • Trilayer structures (HM/Spacer/FM) showed higher torques than bilayers (HM/FM), attributed to non-local spin current generation and interface effects (Cu/[Co/Ni] and Cu/[Co/Pt] interfaces).
• DFT Correlation:
  • Calculated SHE conductivities for [Co/Ni] and [Co/Pt] were found to be $4.55 \times 10^5$ and $4.19 \times 10^5 (\Omega \cdot m)^{-1}$ respectively, closely matching the experimental data and confirming their potential as efficient spin sources.

5. Significance

• Material Innovation: This work establishes that ferromagnetic multilayers (specifically [Co/Ni]) are viable, high-performance alternatives to heavy metals for generating spin-orbit torques. This opens avenues for designing all-ferromagnetic spintronic devices with reduced material costs and potentially lower damping.
• Mechanism Insight: The observation of linearly increasing torque with ferromagnet thickness challenges the conventional understanding of SHE in thin films and points toward complex interfacial and self-induced mechanisms that require further theoretical development.
• Device Optimization: The high efficiency of [Co/Ni] multilayers suggests they are excellent candidates for next-generation magnetic memory (MRAM) and logic devices, where efficient magnetization switching with low current density is paramount.
• Methodological Advancement: The successful application of VNA-FMR inductive detection to separate torque symmetries in all-ferromagnetic stacks provides a robust tool for characterizing future spintronic materials.