Band structure control in the altermagnetic candidate MnTe by temperature and strain

This study confirms the altermagnetic nature of hexagonal MnTe by demonstrating that its terahertz optical absorption, arising from spin-split bands, exhibits temperature-dependent behavior consistent with a ferromagnetic-like transition and strain-induced shifts that align with theoretical predictions of decreasing spin-splitting angles.

The Gist

Imagine a dance floor where the dancers are electrons. In most materials, these dancers move in a chaotic, unorganized crowd. In magnets, they all try to spin in the same direction, like a synchronized marching band. But in Manganese Telluride (MnTe), the material studied in this paper, the dancers are doing something very strange and special.

They are an Altermagnet. Think of this as a "ghostly" dance troupe. Half the dancers spin clockwise, and the other half spin counter-clockwise. Because they are perfectly balanced, the whole group looks like it has no spin at all (no net magnetism). However, if you look closely at the individual dancers, they are still spinning in opposite directions, creating a hidden, powerful structure.

This paper is about how scientists learned to control this hidden dance floor using two simple tools: Temperature (heat) and Strain (squeezing).

The Main Discovery: The "Ghost" Energy Gap

The researchers shined a special kind of light (Terahertz light, which is like a super-low-energy flashlight) at the MnTe crystals to see how the electrons reacted. They found three main things happening on the dance floor:

1. The "Invisible" Gap (The Energy Gap)
Imagine the dance floor has a big, empty pit in the middle that electrons usually can't jump into. This is the "energy gap."

• What they found: As the room got colder, this pit got slightly wider.
• The Analogy: It's like a frozen lake. As it gets colder, the ice thickens, making the gap between the surface and the water deeper. This behavior is usually seen in ferromagnets (like fridge magnets), but MnTe isn't a normal magnet. This proved that even though MnTe looks "neutral" from the outside, its internal electronic structure is acting like a ferromagnet.

2. The "Ghost" Dancers (The In-Gap State)
Here is the most exciting part. Inside that empty pit, a new group of "ghost dancers" appeared when the temperature dropped.

• What they found: At high temperatures, the pit was empty. But below a certain temperature (about 307 Kelvin, or a chilly 34°C), a new energy level popped up inside the gap.
• The Analogy: Imagine a stage that is supposed to be empty. Suddenly, when the lights dim (cool down), a spotlight turns on, and a solo dancer appears right in the middle of the empty space. This dancer represents the spin-split bands. Their appearance proves that the "ghostly" altermagnetic structure is real. The dancers are splitting into two groups (spin-up and spin-down), and one group is moving closer to the edge of the stage (the Fermi level).

3. The "Wobbly" Floor (Phonons and Fano Shapes)
The atoms in the crystal are constantly vibrating, like a floor shaking to music. These vibrations are called "phonons."

• What they found: The vibration of the atoms (specifically the stretching of the Manganese-Tellurium bonds) changed shape when the "ghost dancers" appeared. The vibration signal became lopsided, looking like a "Fano" shape (a sharp peak with a weird tail).
• The Analogy: Imagine a drum being hit. Normally, it makes a pure, round sound. But if you put a heavy, wobbly object on the drumhead (the in-gap state), the sound becomes distorted and lopsided. The fact that the "ghost dancers" distorted the drum's sound proves they are interacting directly with the crystal's atoms.

The Squeeze Test: Strain Control

Finally, the researchers didn't just change the temperature; they physically squeezed the crystal (applied negative strain) using a special mechanical cell.

• What they found: When they squeezed the crystal, the "ghost dancer" (the in-gap peak) moved away from the edge of the stage.
• The Analogy: Imagine the dance floor is a trampoline. If you pull the edges of the trampoline tight (strain), the dancers in the middle get pushed further away from the edge.
• Why it matters: This proves that we can control the electronic structure of this material just by squeezing it. This is like having a "volume knob" for the material's magnetic properties, which is a huge deal for future technology.

Why Should We Care?

This isn't just about understanding a weird crystal. Altermagnets are the "holy grail" for the next generation of computers (spintronics).

• Current Tech: Uses electricity to move data. It's fast but generates heat and uses a lot of power.
• Future Tech (Spintronics): Uses the "spin" of electrons (like the dancers spinning) to store and move data. It's faster and cooler.
• The Problem: Normal magnets are too heavy and slow to switch on and off quickly.
• The Solution: Altermagnets like MnTe have the speed of ferromagnets but without the magnetic "weight."

The Bottom Line:
This paper shows that MnTe is a real altermagnet. More importantly, it shows that we can tune its internal "dance floor" by simply heating it up or squeezing it. This opens the door to building ultra-fast, low-power electronic switches that could revolutionize how our computers and phones work in the future.

Technical Summary

1. Problem Statement

Altermagnetism is a recently discovered magnetic phase that combines antiferromagnetism (zero net magnetization) with broken time-reversal symmetry, resulting in spin-split electronic bands similar to ferromagnets. Hexagonal manganese telluride (MnTe) is a primary candidate for an altermagnet with a Néel temperature ($T_N$) of approximately 307 K.

While Angle-Resolved Photoemission Spectroscopy (ARPES) has confirmed spin-splitting in the occupied valence bands of MnTe below $T_N$, a critical gap remains in understanding the unoccupied states and the in-gap states. Previous optical studies focused on the fundamental energy gap but failed to resolve low-energy transitions or the specific behavior of states near the Fermi level ($E_F$) in the terahertz (THz) region. Furthermore, theoretical predictions suggest that the altermagnetic band structure is highly sensitive to strain, but experimental verification of strain-induced control over these spin-split bands in MnTe has been lacking.

2. Methodology

The authors employed a comprehensive optical spectroscopy approach combined with mechanical strain manipulation:

• Sample Preparation: High-quality single-crystalline MnTe samples (thickness $\sim$350 $\mu$m) were synthesized via chemical vapor transport.
• Optical Measurements:
  • Reflectivity ($R(\omega)$): Measured over a wide photon energy range (8 meV to 30 eV) at temperatures from 10 K to 370 K.
  • Interference Removal: Due to the sample's transparency, interference fringes were present. The authors utilized a multireflection function model to extract intrinsic optical constants and remove these artifacts.
  • Optical Conductivity ($\sigma_1(\omega)$): Derived from $R(\omega)$ using Kramers-Kronig analysis (KKA) to map the joint density of states between occupied and unoccupied bands.
• Strain Application: A custom-designed uniaxial negative-strain cell was developed to apply compressive strain (up to $\sim$0.8%) to the sample at cryogenic temperatures (10 K).
• Data Analysis: The low-energy spectra (below 150 meV) were fitted using a combination of Fano functions (for asymmetric phonon peaks) and Lorentzian functions (for symmetric electronic transitions) to deconvolute overlapping features.

3. Key Contributions

• Discovery of THz In-Gap States: The study identifies a distinct absorption peak in the THz region (30–200 meV) attributed to transitions from spin-split valence bands to acceptor levels, a feature previously unobserved in optical studies of MnTe.
• Fano Resonance Observation: The detection of a Fano-like asymmetric line shape in the optical phonon absorption, linking lattice vibrations (Mn-Te stretching) directly to the altermagnetic electronic background.
• Strain Control Demonstration: Experimental proof that negative uniaxial strain can modulate the spin-splitting energy, shifting the in-gap state away from the Fermi level, consistent with theoretical predictions of reduced spin-splitting angles.
• Correlation of Occupied and Unoccupied States: By combining THz optical data with existing ARPES results, the authors constructed a unified model of the electronic structure evolution across $T_N$.

4. Key Results

A. Temperature Dependence

• Energy Gap ($E_g$): The fundamental band gap increases from $\sim$1.35 eV to 1.45 eV as temperature decreases. This shift follows the square of the magnetization ($M^2$), a hallmark of ferromagnetic-like band splitting despite the material being antiferromagnetic.
• In-Gap State (THz Peak): A broad peak appears in the 30–200 meV range at low temperatures, centered around 60 meV at 10 K.
  • Origin: This state corresponds to optical transitions from the shallowest spin-split valence band (which moves closer to $E_F$ below $T_N$) to an acceptor level just above $E_F$.
  • Behavior: The intensity of this state and the effective electron number ($N^*$) scale with $M^2$, confirming its altermagnetic origin.
• Phonon-Electron Coupling: The optical phonon peak at $\sim$17 meV exhibits a Fano asymmetry parameter ($1/q^2$) that increases significantly as temperature drops. This indicates a strengthening interaction between the Mn-Te stretching mode and the emerging in-gap electronic states.
• 20 meV Peak: A secondary broad peak at $\sim$20 meV is observed, likely attributed to a polaron formed by the coupling of the optical phonon and the in-gap state.

B. Strain Dependence

• Under negative uniaxial strain at 10 K, the THz absorption peak (in-gap state) is strongly suppressed and shifts to higher energies (away from $E_F$).
• This behavior mirrors the effect of heating (increasing $T$), suggesting that negative strain reduces the spin-splitting width.
• This experimental observation validates theoretical predictions that the spin-splitting angle ($\theta_{SS}$) decreases under negative strain, offering a mechanism for "band engineering" in altermagnets.

5. Significance

• Confirmation of Altermagnetism: The temperature and strain dependence of the THz absorption provides robust, independent evidence that MnTe possesses an altermagnetic electronic structure, characterized by spin-split bands that behave similarly to ferromagnets despite zero net magnetization.
• Band Engineering Potential: The ability to control the position of spin-split bands relative to the Fermi level via external perturbations (temperature and strain) demonstrates the feasibility of tuning altermagnetic properties for spintronic applications.
• New Spectroscopic Fingerprint: The observation of Fano-resonant phonon coupling with spin-split bands offers a new spectroscopic signature for identifying altermagnetic materials.
• Resolution of Discrepancies: The study clarifies previous contradictions between ARPES (showing bands moving toward $E_F$) and older optical absorption data (showing gaps widening), by distinguishing between the fundamental gap and the specific in-gap transitions involving acceptor levels.

In conclusion, this work establishes MnTe as a controllable platform for altermagnetic research, demonstrating that its unique spin-split electronic structure can be manipulated via temperature and strain, paving the way for advanced spintronic devices.