Identifying the origin of out-of-plane spin polarization in the noncollinear antiferromagnet Mn$_3$Ge

This study resolves the debate regarding the origin of out-of-plane spin polarization in noncollinear antiferromagnet Mn$_3$Ge by demonstrating that it arises from the coexistence of bulk magnetic spin Hall effect and interfacial spin swapping, distinguished through angular-dependent spin-torque measurements in Mn$_3$Ge/Py bilayers.

The Gist

Imagine you are trying to push a heavy shopping cart (the magnet) to make it turn around. Usually, to get it to turn smoothly without an external helper (like a magnetic field), you need to push it from a very specific angle. If you push from the wrong angle, the cart just wobbles or stops.

For a long time, scientists knew that certain materials called antiferromagnets (specifically a crystal called Mn3Ge) could act like a super-efficient "spin factory." When you run electricity through them, they shoot out a stream of tiny spinning particles (electrons) that can push that shopping cart around without needing any extra help. This is great for making faster, more energy-efficient computer memory.

However, there was a big mystery: Where exactly does this "push" come from?

Scientists knew the material produced a "push" that was tilted out of the flat surface (out-of-plane), which is the magic ingredient needed to flip the cart. But they had two competing theories about the source of this push:

1. The "Internal Engine" Theory (MSHE): The material itself has a special internal magnetic structure (like a tiny, hidden engine) that generates this push. If you flip the internal structure, the push flips direction too.
2. The "Bumper Car" Theory (SSW): The push happens because the spinning particles crash into the wall where the two materials meet (the interface). It's like bumper cars: when they hit the wall, they bounce off in a new direction. This theory says the push doesn't care about the internal engine; it only cares about the crash at the wall.

The Experiment: The "Twist" Test

To solve this mystery, the researchers built two different versions of their "spin factory" using a single crystal of Mn3Ge:

• Device A (The Flexible One): They oriented the crystal so that its internal magnetic structure could easily rotate and follow the direction of an external magnetic field.
• Device B (The Stiff One): They oriented the crystal so that its internal magnetic structure was "pinned" or stuck in place and couldn't move, even when they tried to rotate the magnetic field.

They then ran electricity through both devices and measured the "push" (spin torque) they generated.

The Discovery: It's Both!

Here is what they found, explained simply:

• In the Flexible Device (A): When they changed the direction of the magnetic field, the "push" changed direction. This proved that the Internal Engine (MSHE) was real. The material's own magnetic structure was actively contributing to the push.
• In the Stiff Device (B): Even though the internal engine was stuck and couldn't move, the device still produced a significant "push." This proved that the Bumper Car effect (SSW) was also happening at the interface.

The Verdict: The "magic push" isn't just one thing. It's a team effort.

• About half the push comes from the material's internal magnetic engine (MSHE).
• The other half comes from the particles bouncing off the interface (SSW).

They are like two people pushing a car together. One person is pushing from the inside (the engine), and the other is pushing from the outside (the bumper). Even if you tie up the person inside, the person outside can still move the car, but you get the best results when both are working together.

Why Does This Matter?

Think of this like figuring out how a car engine works. Before, engineers were arguing: "Is the speed coming from the fuel combustion (MSHE) or the wind pushing the car (SSW)?"

This paper says: "It's both!"

By understanding that both mechanisms are working together and are roughly equal in strength, engineers can now design better computer chips. They know they need to optimize both the internal crystal structure and the quality of the interface between layers to get the maximum performance. This brings us one step closer to ultra-fast, low-power computers that don't need bulky magnets to work.

In a nutshell: The scientists solved a debate by building two different versions of a crystal, proving that the "spin push" comes from a combination of the material's internal magic and the friction at its surface.

Technical Summary

1. Problem Statement

Noncollinear antiferromagnets (AFMs) like Mn3Sn and Mn3Ge are promising candidates for spintronic applications due to their ability to generate spin currents with both in-plane and out-of-plane polarizations. This unique capability enables field-free magnetization switching in adjacent ferromagnetic layers, a critical requirement for low-power memory devices.

However, the microscopic origin of the out-of-plane spin polarization in these materials has been a subject of intense debate. Two competing mechanisms have been proposed:

• Magnetic Spin Hall Effect (MSHE): A bulk effect driven by the magnetic octupole order of the AFM. It is odd under magnetization reversal (changes sign when the magnetic octupole flips).
• Spin Swapping (SSW): An interfacial effect where the flow direction and spin polarization of a spin current are interchanged due to spin-orbit scattering at the interface. It is independent of the magnetic octupole configuration.

Distinguishing between these two mechanisms is essential for understanding the fundamental physics of spin-torque generation and optimizing device performance. Previous studies struggled to separate them because they often exhibited similar angular dependencies in standard device geometries.

2. Methodology

The authors employed Spin-Torque Ferromagnetic Resonance (ST-FMR) to quantitatively evaluate spin torques in single-crystal Mn3Ge/Py (Permalloy) bilayers. The core innovation of their approach was the comparative analysis of devices with different crystallographic orientations:

• Device Fabrication: Single-crystal Mn3Ge strips were fabricated using Focused Ion Beam (FIB) milling from bulk crystals grown via the Bismuth flux method. These were transferred to coplanar waveguides and capped with a 20 nm Py layer.
• Geometries:
  1. In-plane Device: The Mn3Ge c-axis is perpendicular to the film plane ($z$-direction). In this geometry, the magnetic octupole moments are free to rotate and follow the applied in-plane magnetic field.
  2. Out-of-plane Device: The Mn3Ge c-axis lies within the film plane ($y$-direction). In this geometry, the magnetic octupole moments are pinned within the kagome plane and do not follow the rotation of the applied in-plane magnetic field.
• Measurement: An RF current was applied along the a-axis. The resulting spin currents injected into the Py layer generated spin torques, detected via the mixing voltage ($V_{mix}$) arising from Anisotropic Magnetoresistance (AMR). The symmetric ($V_S$) and antisymmetric ($V_A$) components of the voltage were analyzed to extract in-plane (anti-damping-like) and out-of-plane (field-like) torque magnitudes.
• Structural Characterization: Scanning Transmission Electron Microscopy (STEM) and Energy Dispersive X-ray (EDX) mapping were used to verify interface quality and rule out compositional gradients as a source of symmetry breaking.

3. Key Contributions

• Experimental Decoupling: The study provides the first experimental method to unambiguously separate MSHE and SSW contributions by exploiting the distinct magnetic responses of Mn3Ge in different crystallographic orientations.
• Quantitative Separation: By fitting the angular dependence of the ST-FMR signals to theoretical models derived for both geometries, the authors successfully isolated the magnitudes of the MSHE and SSW components.
• Interface Quality Verification: The authors confirmed that the observed SSW is intrinsic to the high-quality crystalline interface rather than an artifact of fabrication-induced compositional gradients.

4. Key Results

• Distinct Angular Dependences:
  • In the in-plane device, the magnetic octupole reverses with the field, causing the MSHE contribution to change sign. The ST-FMR signals showed specific angular dependencies consistent with a superposition of SHE, MSHE, and SSW.
  • In the out-of-plane device, the magnetic octupole remains pinned. Consequently, the MSHE contribution remains constant regardless of the field direction, while the SSW contribution remains unchanged in both geometries.
• Coexistence of Mechanisms: The analysis revealed that both MSHE and SSW coexist and contribute significantly to the out-of-plane spin polarization.
  • MSHE: Confirmed as a bulk effect dependent on the magnetic octupole order. It generates a field-like torque that partially compensates for the conventional SHE torque.
  • SSW: Identified as a significant interfacial effect generating a "giant" in-plane field-like torque. It is independent of the magnetic octupole order.
• Quantitative Ratios: The extracted spin-torque ratios (normalized to the SHE reference) showed that the MSHE and SSW contributions are comparable in magnitude to the conventional SHE.
  • $\xi_{FL}^{z}[MSHE] \approx -0.014$
  • $\xi_{FL}^{z}[SSW] \approx -0.077$
  • The combined effect explains the large out-of-plane spin polarization observed in these systems.
• Interface Analysis: STEM-EDX mapping showed a homogeneous elemental distribution with no compositional gradients, ruling out gradient-induced symmetry breaking as the source of the octupole-independent signal. This confirms SSW as the dominant origin of the non-magnetic-order-dependent component.

5. Significance

• Resolution of Scientific Debate: This work definitively resolves the controversy regarding the origin of out-of-plane spin polarization in Mn3Ge, proving it is not solely MSHE or SSW, but a synergistic combination of both.
• Design Guidelines for Spintronics: The findings suggest that optimizing spintronic devices based on noncollinear AFMs requires simultaneous control of:
  1. Bulk Magnetic Order: To maximize the MSHE contribution.
  2. Interface Quality: To enhance the SSW contribution (which relies on weak spin-orbit coupling and low interfacial disorder).
• Future Applications: Understanding these dual mechanisms provides a roadmap for engineering more efficient field-free magnetization switching and domain-wall motion devices, potentially leading to next-generation low-power, high-speed magnetic memory and logic technologies.