Griffiths-like phase, spin-phonon coupling, and exchange-bias in the disordered double perovskite GdSrCoMnO$_{6}$

This study reveals that structural disorder in the double perovskite GdSrCoMnO$_6$ drives complex magnetic behaviors, including a Griffiths-like phase, spin-phonon coupling, slow magnetic dynamics, and a significant low-temperature exchange-bias effect, all stemming from the competition between ferromagnetic and antiferromagnetic interactions caused by the random distribution of mixed-valence Co and Mn ions.

The Gist

Imagine a crowded dance floor where two different groups of dancers are trying to move in sync, but they keep tripping over each other. This is essentially what happens inside a special crystal called GdSrCoMnO6 (let's call it GSCM for short).

Scientists studied this material to understand how its atoms behave, how they "talk" to each other, and how they react to magnets. Here is the story of their findings, broken down into simple concepts.

1. The Setting: A Chaotic Dance Floor

In a perfect crystal, atoms line up in neat, orderly rows. But in GSCM, it's a bit messy. The crystal is a "double perovskite," which is like a complex building made of two types of bricks.

• The Mess: The "bricks" (atoms of Cobalt and Manganese) are mixed up randomly. Some are in one spot, some in another, and they have different electrical charges (valences).
• The Result: This disorder creates a chaotic environment where the atoms can't agree on how to dance. Some want to hold hands and spin one way (Ferromagnetic), while others want to spin the opposite way (Antiferromagnetic). This constant arguing creates a state of magnetic frustration.

2. The Big Freeze: When the Dance Starts (153 K)

As the scientists cooled the material down, something interesting happened around -120°C (153 Kelvin).

• The Transition: Suddenly, the majority of the dancers stopped arguing and started moving in the same direction. This is called a Ferromagnetic transition. The material became magnetic, like a fridge magnet.
• The "Ghost" Clusters (Griffiths Phase): But here's the twist. Even before the whole floor froze into sync (at temperatures slightly higher than -120°C), small groups of dancers started forming little circles and dancing together, even though the rest of the crowd was still chaotic.
  • Analogy: Imagine a huge party where most people are just chatting randomly. But before the music really starts, you see small groups of friends huddled together, dancing in a circle. These "huddles" are called Griffiths-like clusters. They are short-lived and local, but they show that the material is trying to organize itself early.

3. The Whispering Floor: Spin-Phonon Coupling

The scientists also listened to the crystal using a technique called Raman spectroscopy (which is like shining a laser to hear how the atoms vibrate).

• The Connection: They found that the "music" (the vibration of the atoms) changed exactly when the magnetic "dance" started.
• Analogy: Imagine a floor that creaks differently when people walk on it in a specific pattern. In this material, the magnetic spins (the dancers) and the atomic vibrations (the floorboards) are holding hands. When the dancers change their steps, the floorboards change their creak. This is called spin-phonon coupling. It proves that the magnetism and the physical structure of the crystal are deeply linked.

4. The Glassy Trap: Getting Stuck at -243°C (30 K)

When the scientists cooled the material even further, down to about -243°C (30 Kelvin), the dance floor turned into a glass.

• The Slow Down: The dancers didn't stop moving, but they got stuck. They couldn't find a perfect rhythm anymore. They were frozen in place, but in a messy, random way. This is called a Cluster-Glass state.
• The Evidence: When they tried to shake the floor (using an alternating magnetic field), the dancers responded very slowly, like honey dripping. This "slow motion" behavior confirmed that the magnetic clusters were trapped in a disordered state.

5. The One-Way Street: Exchange Bias

This is perhaps the most fascinating part. When the scientists cooled the material while applying a strong magnetic field, they noticed something strange: the material's memory became biased.

• The Hysteresis Loop: Usually, if you push a magnet one way and then the other, it behaves symmetrically. But here, the material "remembered" the direction it was pushed first. It was harder to push it back the other way.
• Analogy: Imagine a door with a heavy spring. If you push it open, it swings back easily. But if you push it open while someone is holding the doorframe, the door gets stuck slightly off-center. Now, it's harder to push it back the other way. This "off-center" memory is called Exchange Bias.
• Why it matters: This effect lasted up to -223°C (50 K), which is surprisingly high for such a messy material. It suggests that the "frozen" clusters act like anchors, holding the magnetic direction in place.

6. The "Training" Effect

The scientists noticed that if they kept flipping the magnet back and forth (cycling the field), the "bias" (the memory) got weaker.

• Analogy: Think of a new employee who is very strict about how they do a task. If you ask them to do it the same way ten times in a row, they might get tired or realize there's a better way, and their strictness fades.
• In the crystal, the "strict" magnetic boundaries (the interface between the ordered and disordered parts) get rearranged and relaxed after repeated cycles, causing the memory effect to fade.

The Big Picture

The paper concludes that disorder is actually a superpower in this material.

• The random mixing of atoms creates a chaotic environment.
• This chaos forces the material to form small, competing groups (clusters).
• These clusters create a unique state where the material is part-magnet, part-glass, and part-crystal.
• This messy state allows for cool effects like Exchange Bias (magnetic memory) and strong connections between magnetism and heat (spin-phonon coupling).

In short: By making the crystal messy, the scientists accidentally created a material that acts like a complex, memory-having magnetic sponge, which could be very useful for future computer memory or sensors.

Technical Summary

1. Problem Statement and Motivation

Double perovskites ($R_2B'B''O_6$) are a rich platform for studying coupled spin, charge, orbital, and lattice degrees of freedom. However, crystallographic disorder, particularly antisite disorder (ASD) and mixed valency, often leads to complex magnetic ground states characterized by competing ferromagnetic (FM) and antiferromagnetic (AFM) interactions.

• The Gap: While rare-earth double perovskites like $Gd_2CoMnO_6$ are well-studied, the specific effects of Sr substitution (replacing $Gd^{3+}$ with $Sr^{2+}$) on the lattice geometry, valence balance, and resulting magnetic inhomogeneity in the $GdSrCoMnO_6$ (GSCM) system remain under-explored.
• Objective: To investigate how structural disorder and mixed valence in GSCM influence magnetic ordering, the emergence of Griffiths-like phases, spin-lattice coupling, and exchange-bias phenomena.

2. Methodology

The authors synthesized and characterized single-phase polycrystalline GSCM using the following techniques:

• Synthesis: Conventional solid-state reaction method using high-purity oxides/carbonates ($Gd_2O_3$, $Co_3O_4$, $SrCO_3$, $MnO_2$) sintered at 1350°C.
• Structural Characterization:
  • X-ray Diffraction (XRD): Confirmed phase purity and orthorhombic $Pnma$ structure.
  • Electron Microscopy (TEM/SAED/HRTEM): Verified single-crystalline nature of particles (~250 nm) and local structural features.
• Magnetic Measurements:
  • DC Magnetization: Zero-field-cooled (ZFC) and field-cooled (FC) measurements (5–300 K) to determine transition temperatures and hysteresis.
  • AC Susceptibility: Frequency-dependent measurements (399–799 Hz) to probe glassy dynamics and freezing temperatures.
  • Exchange Bias Analysis: Hysteresis loops ($M$-$H$) measured under cooling fields ($H_{CF} = \pm 3$ T) to quantify exchange bias ($H_{EB}$) and training effects.
• Spectroscopic Analysis:
  • Raman Spectroscopy: Temperature-dependent measurements (100–273 K) to analyze phonon modes and detect spin-phonon coupling.

3. Key Contributions and Results

A. Structural and Magnetic Ordering

• Structure: GSCM adopts a disordered orthorhombic structure.
• Ferromagnetic Transition: DC magnetization reveals a sharp ferromagnetic transition at $T_C \approx 153$ K, which is higher than the parent compound $Gd_2CoMnO_6$ ($T_C = 123$ K). This enhancement is attributed to mixed-valence states ($Co^{2+/3+}$, $Mn^{3+/4+}$) and Sr-induced lattice modifications favoring FM exchange paths.
• Griffiths-like Phase: The inverse magnetic susceptibility ($\chi^{-1}$) exhibits a downturn above $T_C$, deviating from Curie-Weiss behavior. This indicates the formation of short-range FM clusters within a paramagnetic matrix, defining a Griffiths-like regime extending up to $T_G \approx 172$ K.
  • Analysis using the power-law expression $\chi^{-1} \propto (T/T_C^R - 1)^{1-\lambda}$ yielded $T_C^R \approx 158.9$ K and $\lambda \approx 0.42$ (DC) / $0.66$ (AC), confirming the Griffiths phase.

B. Low-Temperature Glassy Dynamics

• Freezing Temperature: AC susceptibility shows a frequency-dependent anomaly near $T_f \approx 30$ K, indicating a glassy freezing process.
• Cluster-Glass Behavior: The Mydosh parameter ($\Phi_f = 0.09$) and fitting to the Vogel-Fulcher law ($T_{VF} \approx 27.45$ K) and critical slowing-down model suggest the system is an interacting cluster glass rather than a canonical spin glass. This arises from the competition between FM and AFM interactions driven by disorder.

C. Spin-Phonon Coupling

• Raman Analysis: Two active modes were observed: an $A_g$ stretching mode (675 cm$^{-1}$) and a $B_g$ bending mode (561 cm$^{-1}$).
• Coupling Evidence: The phonon frequency deviated from the expected anharmonic background (Balkanski model) near $T_C$. This deviation correlates with the square of the magnetization ($M^2$), confirming spin-phonon coupling.
• Coupling Constant: The spin-phonon coupling constant was estimated as $\lambda_{sp} \approx 0.13$ cm$^{-1}$.

D. Exchange Bias and Training Effect

• Exchange Bias (EB): A significant exchange bias was observed in field-cooled hysteresis loops below 50 K. At 5 K, the exchange bias field is $|H_{EB}| = 379$ Oe with a coercive field of 1897 Oe.
• Training Effect: Repeated field cycling caused a decay in $H_{EB}$, described well by the Binek recursive model and a frozen/rotatable spin relaxation model. This indicates a rearrangement of interfacial spins between FM clusters and the AFM/frustrated matrix.
• Cluster Size: Modeling the cooling-field dependence of $H_{EB}$ suggests the presence of finite FM clusters with an estimated size of $D \approx 6.31$ nm.

4. Significance and Conclusion

This work provides a comprehensive framework for understanding the interplay between structural disorder, mixed valency, and magnetic correlations in Sr-substituted Gd-based double perovskites.

• Disorder as a Tuning Knob: The study demonstrates that Sr substitution enhances disorder (estimated ~25% antisite disorder), which stabilizes ferromagnetic order at higher temperatures while simultaneously inducing a Griffiths phase and cluster-glass behavior at lower temperatures.
• Coupled Phenomena: It establishes a direct link between the magnetic ground state and lattice dynamics (spin-phonon coupling) in disordered systems.
• Exchange Bias Mechanism: The observation of exchange bias up to 50 K, driven by the interface between FM clusters and a magnetically frustrated matrix, highlights the potential of disordered double perovskites for spintronic applications where tunable exchange bias is required.

In summary, GdSrCoMnO6 serves as a model system where structural disorder does not merely degrade magnetic properties but creates a complex, inhomogeneous magnetic landscape rich in Griffiths phases, glassy dynamics, and robust exchange bias.