Direct demonstration of time-reversal-symmetry-breaking spin injection from a compensated magnet

Technical Summary: Direct Demonstration of Time-Reversal-Symmetry-Breaking Spin Injection from a Compensated Magnet

Problem and Context
The injection, propagation, and detection of spin currents are foundational to spintronics. Historically, these processes have relied on two primary mechanisms: ferromagnetic spin injection, which breaks time-reversal ($T$) symmetry via net magnetization ($M \neq 0$), and relativistic spin Hall injection, which relies on $T$-symmetric spin-orbit coupling. While recent theoretical and experimental work has established that compensated magnets (with $M=0$) can exhibit $T$-symmetry-breaking responses analogous to ferromagnets (such as the anomalous Hall effect), the direct demonstration of $T$-symmetry-breaking spin injection from such materials into a non-magnetic channel has remained unproven. Specifically, it was unclear if a compensated magnet could generate a spin current that is controlled by its magnetic state and distinct from the relativistic spin Hall effect.

Methodology
The authors employed a lateral spin valve (LSV) geometry to probe non-local spin transport. The device consisted of:

1. Materials: A 15-nm-thick epitaxial $\text{Mn}_5\text{Si}_3$ film (a compensated magnet with a Néel temperature $T_N \approx 240$ K) grown on a Si(111) substrate, serving as the spin injector. A reference device used a ferromagnetic Permalloy ($\text{Ni}_{0.8}\text{Fe}_{0.2}$, Py) injector.
2. Geometry: Both devices featured a transverse non-magnetic Copper (Cu) channel (120 nm wide) connecting the injector and a Py detection electrode. The edge-to-edge separation was 300 nm.
3. Biasing Geometries: The study utilized two distinct electrical biasing configurations to distinguish between injection mechanisms:
   • Geometry 1: Bias applied across the injector/channel interface (longitudinal drift).
   • Geometry 2: Bias applied along the injector electrode (transverse spin Hall-like configuration).
4. Measurements: Non-local resistance ($R_{NL}$) was measured to detect spin accumulation in the Cu channel. The magnetic state of the $\text{Mn}_5\text{Si}_3$ injector was characterized via Anomalous Hall Effect (AHE) measurements on a dedicated Hall cross fabricated on the same chip. First-principles calculations were performed to model the spin-resolved Fermi surfaces and conductivity tensors of the altermagnetic phase.

Key Contributions and Results
The paper presents the first direct observation of $T$-symmetry-breaking spin injection from a compensated magnet ($\text{Mn}_5\text{Si}_3$) with vanishing net magnetization.

• $T$-Symmetry Breaking in Compensated Magnets: Unlike the reference Py injector, where spin injection in the second biasing geometry is $T$-symmetric (relying on the spin Hall effect), the $\text{Mn}_5\text{Si}_3$ injector exhibited $T$-symmetry-breaking behavior in both biasing geometries. Switching the $\text{Mn}_5\text{Si}_3$ between its two time-reversed magnetic states resulted in a reversal of the sign of the detected non-local spin signal ($R_{NL}$).
• Universality Across Biasing Geometries: The spin signal magnitude and switching patterns were similar in both biasing geometries for the $\text{Mn}_5\text{Si}_3$ injector. This contrasts sharply with the ferromagnetic reference, where the signal in the second geometry was significantly weaker and $T$-symmetric. This suggests a common, intrinsic mechanism for spin generation in $\text{Mn}_5\text{Si}_3$ that is independent of the specific biasing direction.
• Microscopic Origin (Altermagnetism): The results are attributed to the collinear altermagnetic order of $\text{Mn}_5\text{Si}_3$. First-principles calculations reveal that the altermagnetic phase possesses a $d$-wave splitting of the Fermi surface into separate, conserved spin-up and spin-down channels. This symmetry breaking allows for spin-dependent conductivity where electrical currents in the two spin channels have different magnitudes and propagation angles.
  • In the first biasing geometry, the injected spin current arises primarily from the longitudinal component of this spin-dependent drift.
  • In the second biasing geometry, the injection arises from the transverse component of the spin current.
  • Calculations predict spin polarizations of $\approx 10\%$ and $\approx 6.5\%$ for the two geometries, consistent with the comparable experimental signal magnitudes.
• Injection Interface: Control experiments with a SiO$_2$ barrier on the top surface of the $\text{Mn}_5\text{Si}_3$ electrode confirmed that spin injection occurs predominantly through the vertical side-edge interface between the $\text{Mn}_5\text{Si}_3$ and the Cu channel, rather than the top interface. This is consistent with the in-plane nature of the altermagnetic order parameter.
• AHE Correlation: Remanent AHE measurements confirmed the switching between time-reversed states of the $\text{Mn}_5\text{Si}_3$ injector, correlating the reversal of the Hall signal with the reversal of the non-local spin signal.

Significance
The paper claims that these results demonstrate a fundamentally distinct spin-injection phenomenology. The observed effect is:

1. Distinct from Ferromagnetic Injection: It occurs in a material with zero net magnetization.
2. Distinct from Relativistic Spin Hall Injection: It is $T$-symmetry-breaking and controlled by the magnetic state of the injector, whereas the spin Hall effect is $T$-symmetric.

The authors conclude that compensated altermagnets can generate and control spin currents via non-relativistic mechanisms, offering a new pathway for spintronic functionalities that are not limited by the constraints of net magnetization. The work validates the theoretical framework of altermagnetism, specifically the existence of conserved, spin-polarized transport channels in a compensated magnetic order.