Emergence of ferromagnetic state due to structural disorder in pseudo-binary Ce(Fe0.9Co0.1)2 compound

This study demonstrates that introducing structural disorder through rapid quenching and severe plastic deformation in the pseudo-binary Ce(Fe0.9Co0.1)2 compound stabilizes a low-temperature ferromagnetic state by suppressing the first-order transition to the antiferromagnetic phase, a mechanism attributed to topological disorder rather than simple structural distortions, which consequently significantly reduces the material's magnetocaloric entropy change.

The Gist

Imagine a material called Ce(Fe0.9Co0.1)2 as a bustling city made of atoms. In this city, the residents (atoms) have a very specific way of organizing themselves, which determines how the city behaves—specifically, whether it acts like a magnet (ferromagnetic) or not (antiferromagnetic).

This paper is a story about how messing up the city's layout (introducing disorder) changes its behavior, and why the scientists were surprised by what they found.

Here is the breakdown of the research using simple analogies:

1. The Perfect City vs. The Messy City

Normally, this material is like a perfectly planned city with a neat, cubic grid (the C15 Laves phase). In this perfect state, at low temperatures, the residents decide to organize themselves into opposing teams. Half the team faces one way, and the other half faces the opposite way. This is called an Antiferromagnetic (AFM) state. Because they cancel each other out, the city acts like it has no overall magnetic pull.

However, the scientists wanted to see what happens if they scramble the city. They did this in two ways:

• Rapid Quenching: Like pouring molten metal into ice water, they froze the atoms so fast they couldn't arrange themselves perfectly. This created a "frozen chaos" or a slightly messy city.
• Severe Plastic Deformation (HPT): They took the already messy city and crushed it under immense pressure (6 GPa, which is like the pressure at the bottom of the ocean, but much higher!). This made the city even more distorted and disordered.

2. The Big Surprise: The "Rebel" Magnet

The scientists expected that making the city messier would just make the opposing teams (AFM state) even more confused or weaker. Instead, something magical happened: The city started acting like a giant magnet (Ferromagnetic state) at low temperatures.

Think of it like a dance floor.

• The Perfect City: Everyone is dancing in pairs, facing opposite directions. The room looks still.
• The Messy City: When the floor gets bumpy and the dancers stumble, they stop dancing in pairs and start all facing the same direction to keep their balance. Suddenly, the whole room has a strong, unified energy.

The paper reveals that this "rebel magnetism" wasn't caused by the atoms simply shifting a little bit (small distortions). The scientists used supercomputers to simulate these small shifts and found that even with small bumps, the "opposing teams" (AFM) would still win.

The Real Culprit: The ferromagnetism only appeared when the structure became topologically disordered. Imagine a neighborhood where the streets are so broken and the houses are so jumbled that the "opposing teams" can't find each other to cancel out. Instead, small pockets of "unified dancers" (ferromagnetic clusters) form in the cracks and defects of the structure. These pockets are so strong they take over the whole city.

3. The Trade-Off: Magnetism vs. Cooling Power

The researchers were also interested in the Magnetocaloric Effect. This is a fancy way of saying: Can this material be used as a super-efficient refrigerator?

• How it works: When you apply a magnetic field to a material, it heats up. When you remove the field, it cools down. The bigger the change in heat (entropy), the better the fridge.
• The Perfect City: Had a strong "heat swap." It could absorb and release a lot of energy, making it a good candidate for cooling.
• The Messy City: When they crushed the material (HPT), the "heat swap" got much weaker.

The Analogy: Imagine a door that swings wide open to let air in (the phase transition).

• In the perfect city, the door swings wide, letting a huge gust of wind through (high cooling power).
• In the messy city, the door is jammed by debris (structural disorder). It barely opens. Even though the room is full of "magnetic rebels," the door can't swing open to let the energy flow.

The study found that while the disorder made the material more magnetic at low temperatures, it ruined its ability to be used as a cooling device. The "jamming" of the structural transition meant the material couldn't release as much heat energy as before.

Summary of Findings

1. Disorder creates Magnetism: By smashing and scrambling the atomic structure, the scientists forced a material that usually cancels itself out to become a strong magnet.
2. It's not just a small shift: This wasn't caused by tiny atomic wiggles. It required a "topological mess"—a fundamental breakdown of the structure's order.
3. The Cost: While the material became more magnetic, it lost its superpower as a cooling agent. The structural damage prevented the efficient energy exchange needed for refrigeration.

In a nutshell: The scientists broke the material to see what would happen. They found that breaking the order turned a "silent" material into a "loud" magnet, but in doing so, they broke the mechanism that made it useful for cooling. It's a classic case of gaining one superpower but losing another.

Technical Summary

1. Problem Statement

The study investigates the magnetic and magnetocaloric properties of the pseudo-binary Laves phase compound Ce(Fe$_{0.9}$Co$_{0.1}$)$_2$.

• Background: CeFe$_2$-based alloys typically exhibit a first-order magnetostructural phase transition from a high-temperature ferromagnetic (FM) cubic phase (MgCu$_2$-type, space group $Fd\bar{3}m$) to a low-temperature antiferromagnetic (AFM) rhombohedral phase (space group $R\bar{3}m$).
• The Issue: While chemical substitution (e.g., with Co) is known to induce this FM-AFM transition, the specific role of topological structural disorder (non-equilibrium defects) in stabilizing the ferromagnetic state at low temperatures remains unclear.
• Objective: The authors aim to determine if increasing structural disorder (via rapid quenching and severe plastic deformation) can suppress the AFM state and stabilize a ferromagnetic ground state, and to quantify the impact of this disorder on magnetocaloric performance.

2. Methodology

The research combines experimental synthesis, characterization, and first-principles calculations:

• Sample Preparation:
  • Synthesis: Ce(Fe$_{0.9}$Co$_{0.1}$)$_2$ ingots were prepared by arc-melting high-purity elements.
  • Disorder Induction:
    1. Rapid Quenching: Melt-spinning technique (30 m/s wheel velocity) to introduce initial disorder.
    2. Severe Plastic Deformation (SPD): High-Pressure Torsion (HPT) applied at 6 GPa for one revolution at room temperature to significantly increase topological disorder and refine grain size.
• Characterization:
  • Structural: X-ray Diffraction (XRD) to analyze phase purity, lattice parameters, and peak broadening (indicative of microstrain and nanograins).
  • Magnetic: Vibrating Sample Magnetometer (VSM) measurements (2–320 K) under fields up to 6 T. Measurements included Zero-Field Cooled (ZFC), Field-Cooled (FC), and Field-Cooled Heating (FCH) protocols to identify transition temperatures and hysteresis.
  • Thermodynamic: Calculation of isothermal entropy change ($\Delta S$) and Relative Cooling Power (RCP) from magnetization isotherms.
• Theoretical Calculations:
  • Ab Initio Simulations: Density Functional Theory (DFT) using VASP with GGA-PBE pseudopotentials.
  • Modeling: Supercells (8 formula units) were constructed to simulate Co substitution on Fe sites in various configurations (nearest neighbors, next-nearest, etc.) to test the stability of FM vs. AFM states in distorted cubic structures.

3. Key Results

Structural Analysis

• Both as-quenched and HPT-treated samples retained the dominant MgCu$_2$-type cubic structure.
• Lattice Parameters: The as-quenched sample had a lattice parameter of $a = 7.313$ Å, while the HPT-treated sample showed a reduced parameter of $a = 7.300$ Å.
• Disorder Evidence: Significant peak broadening in the HPT sample indicated severe microstrain, nanometric grain sizes, and topological disorder. XRD could not definitively distinguish between cubic and rhombohedral phases due to this broadening.

Magnetic Properties

• As-Quenched Sample:
  • Exhibited a Curie temperature ($T_C$) of ~182 K (PM-FM transition).
  • Showed a first-order FM-AFM transition at 90 K with thermal hysteresis (10 K).
  • Crucial Finding: Despite the AFM transition, a significant ferromagnetic fraction persisted down to 2 K (ZFC magnetization did not drop to zero), suggesting the disorder stabilized some FM regions.
• HPT-Treated Sample (High Disorder):
  • The AFM phase was almost completely suppressed.
  • The sample behaved predominantly as a ferromagnet down to 2 K, with FC/ZFC curves nearly overlapping.
  • The Curie temperature remained stable (~186 K), but the phase transition range broadened significantly.
  • Conclusion: The "quenched-in" topological disorder (defects, grain boundaries, amorphous regions) forces the stabilization of the FM state, preventing the transition to the AFM state.

Theoretical Insights (DFT)

• Calculations on supercells with Co substitutions showed that simple structural distortions (cubic to orthorhombic/monoclinic due to Co placement) still resulted in a stable Antiferromagnetic (AFM) ground state.
• The energy difference between various supercell arrangements was negligible (<3 meV/f.u.), but the FM state was never the lowest energy state in these ordered models.
• Implication: The emergence of ferromagnetism in the experiment is not caused by simple lattice distortions or specific Co-arrangements within the ordered lattice. Instead, it is attributed to strongly defective structures (topologically disordered volumes) that cannot be modeled by simple supercell substitutions.

Magnetocaloric Properties

• Entropy Change ($\Delta S$):
  • As-Quenched: $\Delta S$ peaks were 1.94 J kg$^{-1}$K$^{-1}$ (AFM-FM) and -1.43 J kg$^{-1}$K$^{-1}$ (FM-PM) at 4 T.
  • HPT-Treated: $\Delta S$ dropped drastically to 0.30 J kg$^{-1}$K$^{-1}$ (AFM-FM) and -0.96 J kg$^{-1}$K$^{-1}$ (FM-PM).
• Mechanism: The reduction in $\Delta S$ (approx. 85% for the AFM-FM transition) is due to the suppression of the structural transformation volume fraction. The material no longer undergoes a complete FM-to-AFM transition because the FM state is stabilized by disorder.
• Cooling Power: The Relative Cooling Power (RCP) was not improved; the broadening of the transition peak did not compensate for the loss in peak magnitude.

4. Key Contributions

1. Decoupling Disorder from Distortion: The study demonstrates that the stabilization of the ferromagnetic state in Ce(Fe,Co)$_2$ is driven by topological disorder (defects, amorphous regions) rather than simple lattice distortions or specific chemical ordering.
2. Validation via DFT: By proving via ab initio calculations that distorted ordered supercells remain AFM, the authors rule out simple structural motifs as the source of ferromagnetism, pointing instead to "strongly defective" volumes.
3. Magnetocaloric Trade-off: The paper highlights a critical trade-off: while structural disorder can tune magnetic ground states (stabilizing FM), it severely degrades magnetocaloric performance by suppressing the first-order phase transition volume fraction.

5. Significance

• Fundamental Physics: The work provides insight into the competition between FM and AFM states in itinerant electron systems near a phase boundary. It confirms that Ce(Fe,Co)$_2$ is "on the verge" of ferromagnetism, where small perturbations like disorder can tip the balance.
• Material Design: For applications requiring large magnetocaloric effects (e.g., magnetic refrigeration), this study suggests that minimizing structural disorder is crucial to maintain the sharp first-order transitions necessary for high entropy changes. Conversely, if stabilizing a ferromagnetic state at low temperatures is the goal (regardless of cooling power), severe plastic deformation is an effective tool.
• Generalizability: The findings parallel previous work on YCo$_2$, suggesting a general mechanism where quenched disorder stabilizes ferromagnetism in exchange-enhanced paramagnets or near-magnetic Laves phases.