CePdIn: Geometric Frustration in ZrNiAl-type Lattice

• CePdIn is a heavy-fermion antiferromagnet defined by its hexagonal ZrNiAl-type structure, where a distorted kagome lattice induces near-degenerate RKKY exchange paths and geometric frustration.
• Experimental techniques including Czochralski crystal growth and combined magnetization, heat capacity, and resistivity measurements under extreme temperature and pressure reveal distinct magnetic transitions (AF₁ and AF₂).
• Increasing pressure enhances Kondo coupling and electron itinerancy, resulting in a non-monotonic quantum phase diagram where localized and itinerant magnetic behaviors compete.

CePdIn is a prototypical heavy-fermion antiferromagnet exhibiting geometric frustration and pressure-tunable electronic ground states. Crystallizing in the hexagonal ZrNiAl-type structure (space group P-6 2 m), CePdIn features Ce ions arranged on a two-dimensional kagome lattice in the basal plane, leading to near-degenerate nearest- and next-nearest-neighbor Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange paths and substantial magnetic frustration. The onsite Kondo screening, arising from coupling between Ce 4f moments and conduction electrons, competes with these frustrated interactions, giving rise to complex phase behavior under applied magnetic fields and hydrostatic pressure. Two distinct antiferromagnetic phases, denoted AF₁ and AF₂, are observed, separated by an abrupt transition at moderate pressures. The quantum phase diagram of CePdIn is characterized by non-monotonic evolution of Néel temperatures, field-induced suppression of magnetic order, and the interplay between localized and itinerant f-electrons, making it an ideal platform for studying frustrated Kondo lattices (Shen et al., 27 Dec 2025).

1. Crystal Structure and Magnetic Frustration

CePdIn adopts the ZrNiAl-type lattice, where Ce atoms occupy the vertices of a slightly distorted kagome net in the ab-plane. Each Ce ion is surrounded by six nearest Ce neighbors within the plane and three along the c-axis, yielding triangular motifs (Ce–Ce ≈ 4.45 Å) and a near-three-dimensional connectivity (c ≈ 4.08 Å). Compared to its structurally related compound CePdAl, CePdIn is more three-dimensional due to its larger ratio of lattice parameters. The presence of alternating triangular motifs and hexagonal voids frustrates conventional Néel order, suppressing the ordered moment and amplifying quantum fluctuations. The competing RKKY exchange pathways and moderate frustration from kagome geometry are directly responsible for the rich low-temperature magnetism observed.

Parameter	Value/Notes	Comparison
Space group	P-6 2 m (ZrNiAl-type)	Hexagonal lattice
Ce–Ce in-plane	∼4.45 Å (kagome net)	Triangular motifs
Ce–Ce along c-axis	∼4.08 Å	Near 3D coupling
c/a ratio	Larger than CePdAl (c/a ≈ 0.59)	Weaker frustration

2. Experimental Synthesis and Measurement Protocols

Single crystals of CePdIn are grown using the Czochralski technique in a tetra-arc furnace. Magnetization, heat capacity, and electrical resistivity measurements are performed across a range of temperatures (down to 0.1 K) in Quantum Design MPMS and PPMS systems equipped with ^3He inserts and dilution refrigerators. High-pressure environments, reaching up to 6.3 GPa, are achieved using piston-cylinder cells and diamond anvil cells (DAC), with pressure calibration through ruby fluorescence. Resistivity is explored using standard four-probe techniques, enabling simultaneous field (up to 9 T) and pressure tuning.

Measurement	Instrument/Method	Range
Magnetization	MPMS (^3He, dilution fr.)	0.1–300 K, H up to 9 T
Heat capacity	PPMS, ac-calorimetry (DAC)	0.3–10 K, P up to 5 GPa
Resistivity	Four-probe, Oxford ^3He	0.3–300 K, P up to 6.3 GPa

3. Magnetic Transitions: $T_{\rm{N}}$ and $T_{\rm{M}}$

At ambient pressure, CePdIn displays two successive antiferromagnetic transitions identified via anomalies in heat capacity and resistivity: $T_{\rm N}(0) \simeq 1.65\,\rm K$ and $T_{\rm M}(0) \simeq 1.15\,\rm K$. Both transitions are suppressed monotonically by c-axis magnetic fields, vanishing at $\mu_0 H_c \simeq 6\,\rm T$. The heat capacity shows no divergence at $H_c$, but instead a Schottky-like feature attributed to Zeeman splitting of the crystal electric field (CEF) doublet appears. Application of hydrostatic pressure reveals a non-monotonic pressure dependence for $T_{\rm N}(P)$: it decreases to 0.8 K by 2.3 GPa, jumps to 1.5 K at $P_c \simeq 2.6$ GPa, and remains weakly pressure dependent until it vanishes near 5 GPa. The lower transition $T_{\rm M}$ broadens under pressure and becomes indistinguishable, likely due to enhanced quantum fluctuations.

$$T_{\rm N}(P)\approx\begin{cases} 1.65-0.35\,P\,(\rm K/GPa), & P<2.3\,\rm GPa \ 1.5\,\rm K, & 2.6 < P < 4.7\,\rm GPa \ 0, & P>5\,\rm GPa \end{cases}$$

A plausible implication is that the non-monotonicity signals a pressure-induced rearrangement of the magnetic ground state associated with changing f-electron hybridization.

4. Field- and Pressure-Induced Phases: AF₁ and AF₂

CePdIn hosts two antiferromagnetic ground states distinguished by their pressure and field responses. For $P < 2.6$ GPa (AF₁ phase), $T_{\rm N}$ is rapidly suppressed by c-axis fields and disappears by $\mu_0H\sim6$ T. Magnetoresistance in AF₁ is weakly negative at low temperatures with a metamagnetic kink near 4 T. These are hallmarks of a localized-moment antiferromagnet with weaker Kondo screening.

For $P > 2.6$ GPa (AF₂ phase), $T_{\rm N}$ is robust against magnetic field (remaining visible up to 8 T), and low-temperature resistivity increases below $T_{\rm N}$. This suggests the generation of a partial spin-density-wave gap and a more itinerant character of the f-electrons, with magnetoresistance now positive over the studied field range. The boundary between AF₁ and AF₂ is tracked experimentally via sharp jumps in $d\rho/dT(T)$ and ac-calorimetry at $T_{\rm N}(P)$.

Microscopically, increasing pressure enhances the Kondo coupling $J_K(P)$, driving the single-ion Kondo scale:

$$T_K(P) \sim D\,\exp\Bigl[-\frac{1}{J_K(P)\,N_0}\Bigr]$$

where $N_0$ is conduction-electron density of states and $D$ the bandwidth. As $P \to P_c$, $T_K$ approaches the CEF splitting ($\sim$70 K), leading to the merging of two resistivity maxima ($T_\text{max1}$ and $T_\text{max2}$) above 6 GPa—a signature of enhanced hybridization and itinerant magnetism.

5. Phase Diagrams: Field–Temperature and Pressure–Temperature Relations

The $H$–$T$ phase diagram for $H \parallel c$ demonstrates linear suppression of $T_{\rm N}(H)$ and $T_{\rm M}(H)$ with increasing field, both vanishing at $\sim$6 T, beyond which a polarized paramagnetic Fermi-liquid state emerges ($\rho = \rho_0 + AT^2$).

In the $P$–$T$ diagram:

• AF₁ exists for $P < 2.6$ GPa with decreasing $T_{\rm N}(P)$.
• AF₂ appears abruptly at $P_c \simeq 2.6$ GPa and persists up to 5 GPa with $T_{\rm N} \simeq 1.5$ K.
• Beyond 5 GPa, antiferromagnetism collapses rapidly.
• Above ∼6.3 GPa, merging of $T_\text{max1}$ and $T_\text{max2}$ marks the Kondo crossover to a fully itinerant ground state.

A plausible implication is that pressure and field tuning provide a powerful means to control the balance between localized and itinerant magnetism in heavy-fermion systems.

6. Specific Heat and Electronic Mass Renormalization

At zero field and ambient pressure, the specific heat coefficient follows $C/T = \gamma + \beta T^2$, with $$\gamma \simeq 121\,\text{mJ}\,\text{mol}^{-1}\,\text{K}^{-2}$$, confirming moderately heavy quasiparticle masses (cf. LaPdIn: $$\gamma \approx 11\,\text{mJ}\,\text{mol}^{-1}\,\text{K}^{-2}$$). Just above $T_{\rm N}$, $C_m/T$ reaches $\sim 1.4\,\text{J}\,\text{mol}^{-1}\,\text{K}^{-2}$ as $T \to 0$, reflecting strong spin fluctuations. For $H > H_c$, $\gamma$ is reduced and no divergence is observed. Although explicit $\gamma(P)$ was not reported, merging of coherence peaks and increased field robustness in AF₂ suggest increased f-electron itinerancy and reduced low-temperature effective mass compared to AF₁.

7. Quantum Criticality and Frustration: Comparative Perspective

Unlike more strongly frustrated ZrNiAl-type compounds such as CePdAl, which show stepwise metamagnetism, partial moment order, and an extended quantum-critical regime, CePdIn exhibits only two antiferromagnetic phases separated by a sharp, likely first-order, transition, with no clear non-Fermi-liquid behavior at either $H_c$ or $P_c$. This suggests significantly weaker geometric frustration in CePdIn, in line with its more three-dimensional structure. The competition between RKKY exchange and Kondo screening in CePdIn is consistent with a modified Doniach scenario: pressure-enhanced hybridization suppresses local AF₁ order, induces AF₂ with more itinerant f-electrons, and ultimately yields a paramagnetic heavy-Fermi-liquid for $P \sim 5$ GPa. The absence of continuous quantum critical points (marked by lack of divergent $C/T$ or subquadratic resistivity) indicates weakly first-order transitions that preempt critical fluctuations.

CePdIn thus serves as a model system for unraveling the interplay between anisotropic frustration, Kondo physics, and pressure-tuned ground states in heavy-fermion magnets (Shen et al., 27 Dec 2025).