La₍1-x₎Ce₍x₎FeSiH: Tunable Intermetallic Platform

• La₍1-x₎Ce₍x₎FeSiH is a tunable solid solution of intermetallic hydrides that enables systematic investigation of superconductivity, Kondo physics, heavy-fermion behavior, and magnetic order by varying Ce concentration.
• The structure follows Vegard’s law with minimal distortions, allowing continuous electronic modulation and coexistence of competing phases such as superconductivity and single-ion Kondo behavior.
• At high Ce levels, increased RKKY interactions induce antiferromagnetic order while the emergence of a heavy Fermi liquid is reflected in enhanced electronic specific heat and coherence effects.

La$_{1-x}$Ce$_x$FeSiH is a tunable solid solution series of intermetallic hydrides crystallizing in the ZrCuSiAs-type structure (space group $P4/nmm$), spanning the full range $0 \leq x \leq 1$. It provides a platform for systematic investigation of the interplay between $3d$ correlated electrons (from Fe), $4f$ localized moments (from Ce), superconductivity, Kondo physics, heavy-fermion behavior, and magnetic order. The series can be continuously tuned by varying the Ce concentration $x$, thereby modulating the dimensional interplay of electronic correlations, hybridization, and ordering phenomena in a structurally coherent matrix (Sourd et al., 7 Jan 2026).

1. Crystal Structure and Chemical Trends

All La$_{1-x}$Ce$_x$FeSiH compounds adopt the ZrCuSiAs-type structure with alternating [FeSi] and [R–H] layers (R = La, Ce), where hydrogen fully occupies the rare-earth tetrahedral $2b$ site. The structure persists across the entire series without phase separation. The lattice parameters decrease smoothly as $x$ increases, following Vegard’s law: $a(x)$ contracts from 4.027 Å ($x=0$) to 3.996 Å ($x=1$) and $c(x)$ from 8.039 Å to 7.820 Å. Fe–Fe and Fe–Si bond lengths change by less than 1%, indicating minimal distortion of the FeSi layers upon Ce introduction. This chemical robustness ensures electronic tuning occurs without substantial structural perturbation.

2. Superconductivity at Low Cerium Content ($x \leq 0.20$)

Superconductivity (SC) originates from the correlated $3d$ electrons in the Fe sublattice. The superconducting critical temperature $T_c(x)$ is suppressed quasi-linearly with increasing $x$: $T_c \approx 11$ K for LaFeSiH ($x=0$) and falls to $\sim5.4$ K at $x=0.20$. Measurements via resistivity yield $T^{c}_\rho(0)=9.3$ K and $T^{c}_\rho(0.20)=5.4$ K; magnetization gives $T^{c}_\chi(0)=8.0$ K and $T^{c}_\chi(0.15)=6.0$ K. The upper critical field $H_{c2}(T)$ demonstrates type-II behavior, with an initial slope of $\sim1$ T/K and $H_{c2}(0)$ of several tesla. The Ginzburg–Landau coherence length $\xi_{GL}(0)$ is $10$–$20$ nm. The electronic specific heat coefficient ($\gamma$) for LaFeSiH is $\approx19$ mJ mol$^{-1}$ K$^{-2}$. The superconducting gap is consistent with single-gap $s$-wave pairing: $2\Delta_0/k_B T_c \simeq 3.5$–$4$, indicative of weak to moderate coupling.

3. Single-Ion Kondo Regime ($0.07 \leq x \leq 0.50$)

At intermediate Ce concentrations, Kondo physics emerges due to the interaction between localized Ce $4f^1$ moments and conduction electrons. The onset is detected by a crossover in the resistivity at $T_{\rho}^{min}(x)$ (15–26 K, increasing with $x$), characterized by a $-\ln T$ dependence:

$\rho(T) = \rho_0 + mT^2 + c\ln(T/T_K)$

where $T_K(x) \sim T_{\rho}^{min}(x)$ identifies the single-ion Kondo temperature. Above $T_K$, the susceptibility follows a Curie–Weiss law, $\chi=C/(T+\theta_P)$ with $\mu_{\text{eff}} \approx 2.5\,\mu_B$/Ce and $\theta_P \approx -50$ K. Below $T_K$, gradual Kondo screening of the Ce moment occurs. The $4f$-electronic specific heat contribution displays a logarithmic increase at $T \lesssim T_K$: $C_p(T)/T \sim -R \ln(T/T_K)$.

For $0.07 \leq x \leq 0.20$, both superconductivity and single-ion Kondo behavior coexist at low temperature, demonstrating competition and possible microscopic coexistence between these phases.

4. Kondo Coherence and Heavy Fermi Liquids ($x > 0.50$)

A transition from local Kondo impurity behavior to a coherent Kondo lattice and heavy-fermion regime is observed for $x > 0.50$. The coherence manifests as a low-temperature maximum in resistivity at $T_{\rho}^{max}(x) \approx 2.3$–$2.9$ K, denoting the Kondo coherence temperature $T_{\text{coh}}$. $T_{\text{coh}}$ slightly increases with $x$. The specific-heat coefficient $\gamma$ increases markedly, reaching 500 mJ mol$^{-1}$ K$^{-2}$ for CeFeSiH ($x=1$), signifying an effective mass enhancement $m^*/m_b \sim 25$. This regime is consistent with Kadowaki–Woods scaling $A \sim \gamma^2$, although explicit $A$-values are not tabulated.

5. Antiferromagnetic Ordering at High Ce Concentration ($x \geq 0.85$)

For $x \geq 0.85$, long-range magnetic ordering (MO) emerges, with CeFeSiH ($x=1$) displaying a Néel temperature $T_N \approx 3.5$ K and $x=0.85$ giving $T_N \approx 2.8$–$3.0$ K; the ordering is associated with the Ce $4f$ sublattice, as Mössbauer spectra confirm the absence of a Fe magnetic moment. While prior neutron diffraction data point to antiferromagnetic (AFM) character, a full magnetic structure refinement is absent. The entropy released at $T_N$ is $0.5$–$0.7\,R\ln 2$ per Ce, indicative of partial Kondo screening even within the ordered phase.

6. Temperature–Composition Phase Diagram

The electronic phase diagram of La$_{1-x}$Ce$_x$FeSiH, as a function of Ce concentration $x$ and temperature $T$, reveals four main regimes:

$x$	Regime	Characteristic Temperature(s)
$0 \lesssim x \lesssim 0.2$	Superconducting (SC)	$T_c(x)$, suppressed with $x$
$0.07 \lesssim x \lesssim 0.35$	Kondo-impurity	$T^{min}_\rho(x) \sim T_K(x)$
$0.35 \lesssim x \lesssim 0.85$	Heavy Fermi Liquid (HFL)	$T^{max}_\rho(x) \sim T_{\text{coh}}$
$x \gtrsim 0.85$	Magnetic Order (MO)	$T_N(x)$

A schematic $T$–$x$ plot compiles $T_c$, $T_K \approx T^{min}_\rho$, $T_{\text{coh}}$, and $T_N$ as the salient energy scales and phase boundaries.

7. Microscopic Interplay and Theoretical Context

At $x=0$, the system is an iron-based superconductor ($3d$-driven); upon Ce substitution, local $4f^1$ moments produce Kondo-impurity scattering (logarithmic in $T$) and progressively suppress superconductivity. As $x$ increases past 0.2, $T_c$ falls to zero. In the 0.20 $\lesssim x \lesssim$ 0.50 regime, $4f$ Kondo screening dominates, initially as isolated impurities and, with increased hybridization ($x \gtrsim 0.35$), as a coherent Kondo lattice at sub-3 K temperatures. For $x \gtrsim 0.85$, RKKY interactions overcome Kondo screening, culminating in AFM long-range order of the Ce sublattice.

Across all $x$, $3d$ and $4f$ electrons are in competition and hybridize. Qualitative understanding is achieved in a minimal two-band Anderson/Kondo-lattice framework with an Fe-derived conduction band and localized Ce-$4f$ states, tracking the evolution $SC \rightarrow$ Kondo impurity $\rightarrow$ HFL $\rightarrow$ AFM with increasing $J_K(x)$ (Kondo coupling) (Sourd et al., 7 Jan 2026).

Chemical tuning of La$_{1-x}$Ce$_x$FeSiH thus enables continuous transition between a $3d$ electron-mediated superconductor and a $4f$-driven heavy-fermion Kondo lattice, providing a unique experimental platform to study the entanglement and competition of superconductivity, Kondo physics, heavy-fermion behavior, and magnetic order within a coherent structural matrix.