Magnetic field and pressure tuning of the heavy fermion antiferromagnet CePdIn

This study reveals that applying hydrostatic pressure to the frustrated heavy-fermion antiferromagnet CePdIn induces a non-monotonic evolution of its magnetic transition temperature and a distinct phase transition near 2.6 GPa, suggesting that enhanced Kondo hybridization drives a change in the underlying electronic structure between two different antiferromagnetic phases.

The Gist

Imagine a crowded dance floor where two very different groups of people are trying to decide how to move.

On one side, you have the "Kondo Crowd." These are the energetic, free-moving electrons (the conduction electrons) who want to pair up with the local magnetic spins (the "dancers") and calm them down, effectively hiding their magnetic personality. They want a smooth, non-magnetic flow.

On the other side, you have the "RKKY Gang." These are the magnetic spins who want to link arms with their neighbors and march in a synchronized, ordered line (magnetic order).

In most materials, one group wins. But in a special class of materials called Heavy Fermions, these two groups are locked in a fierce, delicate tug-of-war. The material in this paper, CePdIn, is a perfect arena for this battle, but with a twist: the dance floor itself is shaped like a tricky, triangular pattern (a "frustrated" lattice) that makes it hard for the dancers to agree on a formation.

Here is what the scientists did and what they found, explained simply:

1. The Setup: A Tug-of-War on a Tricky Floor

The researchers studied a crystal called CePdIn. At normal room conditions, this material is a bit of a mess. It has two magnetic "transitions" (moments where the dancers suddenly change their routine) at very cold temperatures (around 1.65 K and 1.15 K).

Think of these transitions as the dancers suddenly deciding to stop dancing randomly and start marching in a specific pattern.

2. Experiment A: Pushing with a Magnet (The "Crowd Control")

The scientists applied a strong magnetic field, like a bouncer trying to force the dancers to face a specific direction.

• What happened: As they increased the magnetic force, the dancers got confused. The two ordered patterns they had formed started to break down.
• The Result: Once the magnetic field got strong enough (above 6 Tesla), the order completely collapsed. The dancers stopped marching and just spun around individually. The material became a "spin-polarized" state, where the magnetic field won the tug-of-war, and the material acted like a normal metal.

3. Experiment B: Squeezing the Crystal (The "Pressure Cooker")

This is where the story gets really interesting. Instead of using a magnet, they squeezed the crystal with hydrostatic pressure (imagine putting the crystal in a hydraulic press).

Usually, when you squeeze these materials, the "Kondo Crowd" gets stronger because the atoms are forced closer together, making it easier for them to pair up and hide the magnetism. You would expect the magnetic order to just slowly fade away as you squeeze harder.

But CePdIn did something weird:

1. Phase 1 (The Slow Fade): At first, squeezing did what we expected. The magnetic order got weaker and the transition temperature dropped.
2. The Plot Twist (The Jump): Suddenly, at a specific pressure (around 2.6 GPa), the magnetic order jumped back up! The dancers suddenly decided to march in a new, different pattern.
3. Phase 2 (The Stronghold): This new pattern (called AF2) was surprisingly tough. Even when they applied the magnetic field again, this new formation held its ground much better than the old one.
4. The End Game: If they squeezed even harder (past 5 GPa), the order finally vanished completely.

The Big Analogy: The "Rehearsal Room"

Imagine the dancers are rehearsing for a play.

• At low pressure: They are practicing a slow, wobbly routine. If you squeeze the room (pressure), they get cramped and the routine gets worse.
• At the "Magic Squeeze" (2.6 GPa): Suddenly, the room gets so small that they are forced to change their choreography entirely. They switch to a brand new, much tighter, and more synchronized routine that is actually harder to break apart.
• At high pressure: Eventually, the room is so small they can't move at all, and the play stops.

Why Does This Matter?

The scientists discovered that CePdIn has two distinct magnetic phases (two different ways the material can order itself) separated by that sudden jump at 2.6 GPa.

• The Old Phase (AF1): Weak and easily broken by magnets.
• The New Phase (AF2): Strong and resilient, likely because the electrons have changed their nature (becoming more "itinerant" or free-moving) due to the pressure.

This is a big deal because it shows that pressure doesn't just slowly kill magnetism; it can fundamentally rewrite the rules of the game, creating a completely new state of matter.

The Takeaway

This paper is like finding out that a material has a "secret mode." By squeezing it just right, you don't just weaken it; you unlock a stronger, more complex version of itself. This helps scientists understand how quantum mechanics works in materials where frustration and competition are the norm, potentially leading to new types of superconductors or quantum computers in the future.

In short: CePdIn is a shape-shifter. Squeeze it, and it doesn't just break; it reinvents itself.

Technical Summary

1. Problem Statement

Heavy fermion compounds are ideal platforms for studying the competition between the Kondo effect (which screens local magnetic moments, favoring a non-magnetic ground state) and the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction (which mediates magnetic exchange, favoring magnetic order).

• Context: Hexagonal ZrNiAl-type structures, such as CePdAl, exhibit geometric frustration (distorted kagome lattice) leading to complex phase diagrams with multiple metamagnetic transitions and potential spin-liquid behaviors.
• Gap: While CePdAl is well-studied, its isostructural counterpart CePdIn (where In replaces Al) has distinct lattice parameters (expanded $a$-axis, compressed $c$-axis) that may alter the balance between frustration and dimensionality. Previous studies on CePdIn showed two magnetic transitions ($T_N \approx 1.7$ K and $T_M \approx 1.0$ K) and non-Fermi liquid behavior under chemical pressure (Ni-doping), but the response to hydrostatic pressure and magnetic fields remained unexplored.
• Objective: To investigate how hydrostatic pressure and magnetic fields tune the magnetic ground state and electronic structure of CePdIn, specifically looking for quantum criticality and the nature of its magnetic phases.

2. Methodology

The study utilized single-crystal samples of CePdIn synthesized via the Czochralski method. The researchers employed a multi-faceted experimental approach:

• Magnetic Measurements:
  • Isothermal magnetization $M(H)$ measured using a Quantum Design MPMS (0.4–1.2 K) and a homemade capacitive Faraday magnetometer (0.1 K).
  • Fields applied parallel and perpendicular to the $c$-axis up to 9 T.
• Thermodynamic Measurements:
  • Specific heat ($C_p$) measured down to 0.4 K using a relaxation method (PPMS) and AC calorimetry under pressure.
  • Magnetic entropy ($S_m$) calculated by subtracting the non-magnetic analog (LaPdIn) data.
• Transport Measurements:
  • Electrical resistivity ($\rho$) measured via the four-probe method from 0.3 K to 300 K.
  • Measurements conducted at ambient pressure and under hydrostatic pressure using:
    • Piston-cylinder cells (up to ~2.3 GPa, Daphne 7373 medium).
    • Diamond Anvil Cells (DAC) (up to ~7.3 GPa, Daphne 7373 medium).
• Pressure Calibration:
  • Superconducting transition of Pb (piston-cylinder).
  • Ruby fluorescence method (DAC).

3. Key Contributions and Results

A. Ambient Pressure Behavior

• Magnetic Transitions: Two distinct transitions were confirmed: an antiferromagnetic transition at $T_N \approx 1.65$ K and a lower-temperature transition at $T_M \approx 1.15$ K.
• Field Response: Both transitions are suppressed by magnetic fields applied along the $c$-axis.
  • $T_N$ vanishes abruptly above 6 T.
  • Unlike CePdAl, CePdIn shows no complex metamagnetic transitions or multiple field-induced phases, suggesting weaker geometric frustration.
  • Above 6 T, the system enters a spin-polarized state exhibiting Fermi liquid behavior.
• Electronic Structure: The specific heat coefficient $\gamma = 121$ mJ/mol K$^2$ indicates moderately heavy quasiparticles. Magnetic entropy analysis shows significant Kondo hybridization even in the ordered phase.

B. Hydrostatic Pressure Evolution

• Non-Monotonic $T_N$: Under pressure, the Néel temperature ($T_N$) exhibits a complex, non-monotonic evolution:
  1. Decrease: $T_N$ drops from 1.65 K to 0.8 K at 2.3 GPa.
  2. Abrupt Increase: At 2.6 GPa, $T_N$ jumps sharply to 1.5 K.
  3. Suppression: Above 2.6 GPa, $T_N$ decreases weakly and vanishes abruptly near 5 GPa.
• Resistivity Maxima: The low-temperature resistivity maximum ($T_{max1}$, associated with coherent Kondo scattering) shifts upward with pressure, merging with the high-temperature maximum ($T_{max2}$, associated with Crystal Electric Field effects) near 6.3 GPa. This indicates an enhancement of the Kondo temperature ($T_K$) due to increased $f$-electron/conduction-electron hybridization.

C. Discovery of Two Distinct Antiferromagnetic Phases (AF1 and AF2)

The non-monotonic behavior of $T_N$ and the abrupt jump at 2.6 GPa signal a first-order phase transition between two distinct antiferromagnetic phases:

• AF1 Phase (0 – 2.6 GPa):
  • $T_N$ is strongly suppressed by magnetic fields.
  • Magnetoresistance (MR) is predominantly negative.
• AF2 Phase (2.6 – 5 GPa):
  • $T_N$ is significantly more robust against magnetic fields compared to AF1 (surviving up to 8 T in some measurements).
  • MR becomes positive across the entire field range.
  • Resistivity shows a slight enhancement upon entering the magnetic phase, suggesting the opening of a gap (possibly spin-density wave type) and more itinerant character.
• Significance of the Transition: The transition at 2.6 GPa is driven by the evolution of the underlying electronic structure (enhanced Kondo hybridization) rather than a simple suppression of magnetic order.

4. Significance and Discussion

• Weaker Frustration: Compared to CePdAl, CePdIn exhibits a simpler field-temperature phase diagram with fewer metamagnetic transitions. This is attributed to its more three-dimensional crystal structure (expanded $a$-axis, compressed $c$-axis), which reduces geometric frustration.
• Beyond the Doniach Picture: The abrupt disappearance of magnetic order at ~5 GPa and the non-monotonic evolution of $T_N$ do not follow the standard Doniach phase diagram (smooth competition between Kondo and RKKY). Instead, they resemble sudden collapses seen in CeOs$_2$Al$_{10}$, suggesting a first-order quantum phase transition.
• Electronic State Evolution: The distinct magnetic and transport properties of AF1 and AF2 imply that pressure induces a fundamental change in the nature of the magnetic order, likely shifting from a more localized moment regime (AF1) to a more itinerant, Kondo-hybridized regime (AF2).
• Chemical vs. Hydrostatic Pressure: While Ni-doping (chemical pressure) suppresses $T_N$ monotonically, hydrostatic pressure induces the AF1 $\to$ AF2 transition. This highlights that chemical and hydrostatic pressures affect the system's electronic and magnetic interactions differently.

Conclusion

The paper establishes that CePdIn is a unique heavy fermion system where geometric frustration is sufficiently reduced to allow for a simpler magnetic ground state than its analog CePdAl, yet complex enough to host two distinct pressure-induced antiferromagnetic phases. The study demonstrates that hydrostatic pressure can drive a first-order transition between these phases by tuning the Kondo hybridization, offering new insights into how frustration and electronic correlations compete in quantum materials.