Complex spin dynamics induced metamagnetic phase transitions in Dirac semimetal EuAuBi

This study reveals that the Dirac semimetal EuAuBi exhibits complex, field-induced metamagnetic phase transitions and non-trivial spin textures, offering a unique platform to investigate the interplay between momentum-space and real-space Berry curvature effects.

The Gist

Imagine a tiny, magical city built inside a crystal called EuAuBi. In this city, the "citizens" are electrons (the ones carrying electricity) and "spins" (tiny magnetic arrows attached to atoms).

This paper is a detective story about how these citizens behave when the temperature drops and when we apply a magnetic field (like a giant magnet hovering over the city). The researchers found that this crystal is special because it hosts two different kinds of "magic" at the same time: one that happens in the map of the city (momentum space) and one that happens in the streets of the city (real space).

Here is the story of their discovery, broken down into simple parts:

1. The City Layout (The Crystal Structure)

The city is built in a hexagonal pattern, like a honeycomb.

• The Map Magic (Momentum Space): The researchers used computer simulations to look at the "blueprint" of the city. They found a special spot where the roads for electrons cross each other perfectly, like a 3D intersection. In physics, this is called a Dirac Semimetal. It's like a highway where cars (electrons) can zoom without hitting any traffic jams. This is the "momentum space" magic.

2. The Magnetic Arrows (The Spins)

Now, let's look at the "spins"—tiny magnetic arrows on the Europium atoms.

• The Cold Snap: When the city gets very cold (below 4 degrees Kelvin, which is colder than outer space!), these arrows start to organize.
• The Three Transitions: The researchers saw the arrows change their formation three times as it got colder (at 4K, 3.5K, and 2.8K).
  • First, they line up in a neat, opposing pattern (Antiferromagnetic).
  • Then, they tilt slightly, like a crowd of people leaning to one side (Canted Antiferromagnetic).
  • The Mystery: Between these states, something weird happens. The arrows don't just flip; they seem to swirl into a complex, twisted shape.

3. The "Skyrmion" Dance (Real Space Magic)

This is the most exciting part. The researchers suspect that in a specific range of magnetic fields (between 1.5 and 3 Tesla), the magnetic arrows form a Skyrmion.

The Analogy: Imagine a crowd of people holding hands.

• In a normal magnet, everyone points North.
• In a Skyrmion, the people in the center point North, those in the middle point East, and those on the edge point South, creating a perfect, swirling vortex or a whirlpool of magnetic arrows.
• These whirlpools are incredibly stable. You can poke them, and they just wiggle but don't break. They are like "magnetic bubbles" that are topologically protected.

The paper suggests that EuAuBi creates these magnetic whirlpools naturally when you apply a specific magnetic field. This is the "Real Space" magic.

4. The Evidence (How they knew)

How did they know these magnetic whirlpools existed if they couldn't see them directly? They looked for clues:

• The "Tilted Plateau": When they measured the magnetization (how magnetic the crystal is) while turning up the magnetic field, the graph didn't go up smoothly. Instead, it hit a flat, tilted shelf (a plateau) before jumping up again.
  • Analogy: Imagine pushing a heavy box. Usually, it gets harder to push as you go. But here, the box suddenly gets easier to push for a moment (the plateau) before getting hard again. This "easy zone" is where the magnetic whirlpools (Skyrmions) are forming.
• The Slow Dance (Relaxation): When they wiggled the magnetic field back and forth quickly (using AC fields), the magnetic arrows didn't respond instantly. They were "slow."
  • Analogy: It's like trying to spin a heavy merry-go-round. It takes time to get it moving and time to stop. This "sluggishness" is a classic sign of complex, swirling magnetic textures like Skyrmions.
• The Traffic Jam (Resistivity): They measured how hard it is for electricity to flow through the crystal. When the magnetic whirlpools formed, the electricity flowed better (resistance dropped).
  • Analogy: It's as if the swirling magnetic arrows cleared a path for the electrons, acting like a traffic controller that suddenly opens all the green lights.

5. The Big Picture: Why Does This Matter?

Most materials are either a "Map Magician" (good for electronics because of their band structure) OR a "Street Magician" (good for memory storage because of magnetic whirlpools).

EuAuBi is a "Double Agent."
It has the perfect highway for electrons (Dirac Semimetal) AND it creates stable magnetic whirlpools (Skyrmions).

Why is this a big deal?

• Future Computers: Magnetic whirlpools (Skyrmions) are being studied as the next generation of computer memory. They are tiny, stable, and use very little energy.
• The "Berry Curvature": This is a fancy physics term for the "twist" in the fabric of the material. EuAuBi has this twist in both the map (where electrons go) and the streets (how spins arrange).
• The Opportunity: Because this material has both, scientists can use the magnetic fields to control the electron flow in new, exciting ways. It's like having a car that can drive on roads and fly, giving engineers a whole new set of tools to build faster, smaller, and smarter devices.

Summary

The researchers discovered that EuAuBi is a rare crystal where electrons travel on a super-highway, and when you apply a magnetic field, the atoms inside start dancing in a swirling, stable vortex (a Skyrmion). This combination of "highway magic" and "swirling dance" makes it a perfect candidate for building the next generation of ultra-efficient, topological spintronic devices.

Technical Summary

Here is a detailed technical summary of the paper "Complex spin dynamics induced metamagnetic phase transitions in Dirac semimetal EuAuBi."

1. Problem Statement

Quantum materials exhibiting topological states are crucial for next-generation spintronic applications. These states are often characterized by Berry curvature, which can exist in two distinct domains:

• Momentum space (k-space): Associated with band topology (e.g., Dirac/Weyl semimetals).
• Real space: Associated with non-coplanar spin textures (e.g., magnetic skyrmions).

While most research focuses on either momentum-space or real-space effects independently, systems where both coexist are rare. Such systems offer a unique degree of freedom to tune k-space quantum states using real-space magnetic elements. The specific problem addressed in this work is the lack of comprehensive understanding regarding the interplay between the topological electronic structure and complex spin dynamics in the Dirac semimetal EuAuBi. Previous studies hinted at superconductivity in this material, but the intricate spin arrangements and field-induced magnetic textures above 2 K remained unexplored.

2. Methodology

The authors conducted a multi-faceted investigation on high-quality single crystals of EuAuBi grown via the flux method (using Bismuth and Lead fluxes). The study employed the following techniques:

• Structural & Electronic Characterization:
  • X-ray & Laue Diffraction: Confirmed hexagonal crystal structure (Space group $P6_3mc$) and single-crystal quality.
  • Density Functional Theory (DFT): First-principles calculations to map the band structure and identify topological features.
• Magnetic Measurements:
  • DC & AC Magnetization: Measured under varying temperatures (1.8–200 K) and magnetic fields (0–14 T) to detect phase transitions, hysteresis, and anisotropy.
  • AC Susceptibility: Frequency-dependent measurements to probe spin relaxation dynamics and identify glassy or correlated states.
• Neutron Diffraction:
  • Zero-field Powder Neutron Diffraction (PND): Performed at the ISIS facility to resolve magnetic structures and spin alignments at low temperatures (1.5–10 K).
• Thermodynamic & Transport Measurements:
  • Specific Heat ($C_p$): To identify phase transition orders (first-order vs. second-order).
  • Electrical Transport: Longitudinal resistivity ($\rho_{xx}$) and Hall resistivity ($\rho_{xy}$) measurements to study the coupling between charge carriers and spin textures.

3. Key Contributions

• Discovery of a Rare Coexistence: The paper establishes EuAuBi as a rare material system where momentum-space Berry curvature (due to Dirac nodes) and real-space Berry curvature (due to complex spin textures) coexist.
• Resolution of Complex Magnetic Phases: The study identifies three distinct magnetic transitions below 4 K, resolving a complex magnetic phase diagram that includes commensurate and canted antiferromagnetic phases, as well as a field-induced intermediate phase.
• Identification of Non-Trivial Spin Textures: The authors provide strong evidence for a field-induced, topologically protected spin texture (resembling a skyrmion lattice or helical phase) in the intermediate field range (1.5–3 T), characterized by a "tilted plateau" in magnetization.
• Comprehensive Phase Diagram: Construction of a detailed magnetic phase diagram for the $B \perp c$ configuration, mapping the boundaries of the intermediate non-trivial phase.

4. Key Results

A. Structural and Electronic Properties

• Crystal Structure: EuAuBi crystallizes in a hexagonal structure ($P6_3mc$) with a honeycomb-like arrangement of Au and Bi atoms in the $ab$-plane, with Eu atoms occupying interstitial sites.
• Dirac Semimetal Nature: DFT calculations confirm a symmetry-protected Dirac point near the Fermi level ($E_F$) along the $\Gamma-A$ direction, confirming its topological nature in momentum space.

B. Magnetic Phase Transitions

• Zero-Field Transitions: Magnetization and specific heat measurements reveal three distinct transitions at $T_{N1} \approx 4$ K, $T_{N2} \approx 3.5$ K, and $T_{N3} \approx 2.8$ K.
• Neutron Diffraction Findings:
  • At 1.5 K, the system orders into a canted antiferromagnetic (cAFM) phase with a propagation vector $k = (1/3, 0, 0)$.
  • At 4 K, a commensurate antiferromagnetic (coAFM) phase is observed.
  • The intermediate phase between $T_{N2}$ and $T_{N3}$ could not be resolved by neutron diffraction due to strong Eu neutron absorption, but is inferred from other measurements.

C. Field-Induced Non-Trivial Spin Textures

• Metamagnetic Transitions: In the $B \perp c$ configuration, magnetization curves show a tilted plateau between 1.5 T and 3 T. This region is bounded by two distinct hysteresis loops, indicating first-order phase transitions.
• AC Susceptibility & Relaxation:
  • The real part of AC susceptibility ($\chi'$) shows peaks at the boundaries of the plateau, with a plateau region in between.
  • Frequency-dependent measurements reveal a slow relaxation time ($\tau_0 \sim 1.6 \times 10^{-7}$ s), characteristic of correlated spin clusters or glassy dynamics, rather than individual spin flips. This supports the existence of a stable, topologically protected spin texture.
• Specific Heat: A $\delta$-type peak (indicative of a first-order transition) appears in the specific heat data within the 1.5–3 T range, coinciding with the magnetization plateau.

D. Transport Properties

• Resistivity Anomalies: The longitudinal resistivity ($\rho_{xx}$) exhibits a sharp drop and distinct anomalies in the 1.5–3 T range, mirroring the magnetic phase boundaries. This suggests a strong coupling between conduction electrons and the spin texture, reducing spin-dependent scattering.
• Hall Effect: The system shows hole-dominant carriers. While a topological Hall effect was not observed in the specific measurement configuration (likely due to crystal morphology constraints), the resistivity anomalies confirm the interaction between carriers and the complex spin state.

5. Significance

• Model System for Topological Interplay: EuAuBi serves as a critical model system for studying the interplay between k-space topology (Dirac fermions) and real-space topology (complex spin textures). This duality is essential for developing advanced topo-spintronic devices.
• Skyrmion-like Physics in Centrosymmetric Lattices: The observation of a field-induced non-trivial phase in a centrosymmetric hexagonal lattice broadens the scope of candidate materials for skyrmion physics, suggesting mechanisms beyond the Dzyaloshinskii–Moriya interaction (DMI), such as frustrated magnetic interactions.
• Tunability: The ability to tune these spin textures via magnetic fields offers a pathway to control electronic transport properties (magnetoresistance) and potentially manipulate the Berry curvature in both real and momentum spaces.

In conclusion, the paper provides a comprehensive characterization of EuAuBi, revealing a complex landscape of magnetic phases and establishing it as a promising platform for investigating the synergy between electronic topology and magnetic texture.