Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature

The Gist

Imagine a magnetic material called GdFeCo not as a solid block, but as a busy dance floor with two distinct groups of dancers: the Gadolinium (Gd) crew and the Iron-Cobalt (FeCo) crew.

Normally, these two groups dance in opposite directions (antiferromagnetically coupled). As you heat up or cool down the dance floor, the energy of the groups changes. At a specific temperature called the compensation temperature, the two groups are dancing with such equal strength in opposite directions that the net movement of the whole floor stops. It looks like the dance has frozen, even though the dancers are still moving furiously.

This paper is about what happens when you run an electric current through this "dance floor" and how it creates a hidden "spin current" (a flow of magnetic momentum) that pushes on a neighboring layer of material (NiFe).

Here is the breakdown of their discovery using simple analogies:

1. The Two Types of "Pushes" (Spin Currents)

When electricity flows through this magnetic material, it generates two different types of "pushes" (torques) on the neighboring layer. Think of these as two different ways to nudge a friend:

• The "Heavy Metal" Push (Spin Hall Effect - SHE): This is like a generic shove that happens because the material is heavy and has strong internal friction (spin-orbit coupling). The paper suggests this push comes specifically from the Gd dancers (the 5d electrons).
• The "Magnetic" Push (Spin Anomalous Hall Effect - SAHE): This is a push that depends entirely on which way the dancers are facing (their magnetization). The paper suggests this push comes specifically from the FeCo dancers (the 3d electrons).

2. The Big Mystery: The "Freeze"

Scientists have long wondered: If the net movement of the dance floor stops at the compensation temperature (because the Gd and FeCo groups cancel each other out), does the "push" they send to the neighbor also stop or flip direction?

To test this, the researchers used a special technique called Spin-Torque Ferromagnetic Resonance (ST-FMR). You can think of this as tapping the neighboring layer (NiFe) with a rhythmic beat (microwaves) and listening to how it wobbles. By changing the temperature, they could watch how the wobble changed as the GdFeCo dance floor went through its "freeze" point.

3. The Surprising Discovery

The researchers found something counter-intuitive: The direction of the push never flipped.

• The Gd Push (SHE): Even when the Gd dancers were dominating the floor or the FeCo dancers were dominating, the "Heavy Metal" push from the Gd side kept pointing in the same direction. It didn't care that the net dance floor stopped moving; it only cared about the Gd dancers.
• The FeCo Push (SAHE): Similarly, the "Magnetic" push from the FeCo side also kept its direction, even when the net magnetization flipped.

The Twist: While neither push flipped direction on its own, they actually push in opposite directions relative to each other.

• The Gd push goes one way.
• The FeCo push goes the other way.
• At most temperatures, the FeCo push is stronger, so the total push looks like it's going the FeCo direction.
• But as they crossed the "freeze" point, the Gd push didn't suddenly reverse; it just stayed steady, while the FeCo push also stayed steady.

4. Why This Matters (The "Who Did It?" Conclusion)

The paper concludes that these two pushes come from completely different electronic "subsystems" within the material.

• The SHE is the signature of the Gd electrons.
• The SAHE is the signature of the FeCo electrons.

Because they are generated by different groups of electrons, the "net" cancellation of the magnetic dance floor doesn't cancel out the source of the push. The Gd electrons keep pushing one way, and the FeCo electrons keep pushing the other way, regardless of who is winning the dance-off at that specific temperature.

Summary

In short, the paper shows that even when a magnetic material's overall magnetism cancels itself out (at the compensation temperature), the hidden "spin currents" it generates do not vanish or flip. Instead, they reveal that different parts of the material (Gd vs. FeCo) are responsible for different types of magnetic pushes, and these parts act independently of the material's overall "net" state.

Technical Summary

Technical Summary: Spin Current Symmetries in GdFeCo Ferrimagnets Across the Magnetisation Compensation Temperature

Problem Statement
Rare-earth transition-metal (RE-TM) ferrimagnets, such as GdFeCo, offer a unique platform for spintronics due to their tunable net magnetisation and angular momentum via temperature. While it is established that heavy metals (HMs) generate spin currents via the Spin Hall Effect (SHE), magnetic materials can also act as sources of spin currents through mechanisms like the Spin Anomalous Hall Effect (SAHE) and self-torques. However, fundamental questions remain regarding the origin of these currents: Are they governed by the net magnetisation or specific magnetic sublattices? Do sign reversals in observed torques across the magnetisation compensation temperature ($T_M$) stem from changes in spin current generation or spin current absorption? Previous studies on single-layer ferrimagnets have yielded conflicting results regarding sign reversals of self-torques, necessitating a clearer disentanglement of the contributions from the SHE and SAHE symmetries.

Methodology
The authors investigated a Gd$_{25}$Fe$_{65.6}$Co$_{9.4}$(10 nm)/Cu(4 nm)/Ni$_{81}$Fe$_{19}$(4 nm)/Al(3 nm) heterostructure deposited on a Si/SiO$_2$ substrate. The Cu spacer magnetically decouples the GdFeCo ferrimagnet from the NiFe ferromagnetic detector layer. The study utilized Spin-Torque Ferromagnetic Resonance (ST-FMR) spectroscopy to probe the spin currents generated by GdFeCo and absorbed by NiFe.

To separate the contributions of different spin current symmetries, the authors employed two complementary techniques across a broad temperature range (15 K to 300 K), covering the magnetisation compensation temperature ($T_M \approx 146$ K):

1. Lineshape (LS) Analysis: This technique isolates the contribution of the SHE. In the specific configurations used (parallel and perpendicular magnetisation alignments), the SAHE contribution to the torque on the NiFe layer vanishes or is suppressed, allowing the extraction of the SHE-induced damping-like (DL) and field-like (FL) torque efficiencies.
2. DC-Bias Measurements: By applying a DC current during ST-FMR, the authors measured the modulation of the resonance linewidth and the shift in the resonance field. This method captures the combined contributions of both SHE and SAHE symmetries.

The experimental setup allowed for two distinct magnetic configurations controlled by temperature:

• Parallel Configuration: At temperatures far from $T_M$ (e.g., 15 K and 300 K), the GdFeCo magnetisation aligns in-plane with the external field, enabling both SHE and SAHE contributions.
• Perpendicular Configuration: Near $T_M$ (e.g., 120–160 K), the high anisotropy field of GdFeCo forces its magnetisation out-of-plane, while the NiFe remains in-plane. In this regime, the SAHE spin current component along the detection axis vanishes, isolating the SHE contribution.

Key Results

• Sign Stability of SHE: The lineshape analysis revealed that the SHE-induced torque efficiencies ($\xi^{SHE}_{DL}$ and $\xi^{SHE}_{FL'}$) remain positive across the entire temperature range, including the magnetisation compensation point. This indicates that the sign of the SHE-driven spin current does not invert when the net magnetisation of the ferrimagnet reverses.
• Sign Stability of SAHE: DC-bias measurements in the parallel configuration showed that the total damping-like torque efficiency ($\xi^{SHE+SAHE}_{DL}$) is negative, while the field-like component is positive. Since the SHE contribution is known to be positive, this implies that the SAHE-driven damping-like torque has the opposite sign (negative) to the SHE term. Crucially, the SAHE contribution also retains its sign across $T_M$ and the angular compensation temperature.
• Sublattice Dominance: The results demonstrate that the SAHE-driven damping-like torque dominates the SHE-induced torque at temperatures far from compensation.
• Electronic Origin: The authors correlate these findings with the electronic structure of the constituent elements. The SHE is attributed to the 5d electrons of the Gd sublattice, while the SAHE arises from the 3d electrons of the FeCo sublattice.

Significance and Claims
The paper claims to clarify the interplay between magnetic sublattices in ferrimagnetic spin transport. By demonstrating that the signs of both SHE and SAHE torques remain invariant across the magnetisation compensation temperature, the authors conclude that these spin current generation mechanisms are governed by specific electronic subsystems (Gd 5d and FeCo 3d) rather than the net magnetisation of the ferrimagnet.

Specifically, the study suggests:

1. The SHE sign is insensitive to the magnetisation state because it originates from the Gd 5d electrons.
2. The SAHE sign does not invert at compensation because it originates from the FeCo 3d electrons.
3. The diverging anisotropy near $T_M$ can be utilized to suppress the SAHE contribution, effectively allowing for the separation and identification of spin currents with different symmetries within a single ferrimagnetic material.

These insights highlight the potential of ferrimagnetic spin currents to generate spin torques in adjacent layers or within the ferrimagnet itself, providing a mechanism to tune spin transport properties by manipulating the magnetic state near compensation without altering the sign of the underlying generation mechanisms.