PdCrAs: Half-Heusler Ferromagnetic Alloy

• PdCrAs is a half-Heusler alloy in the C1₋b structure that exhibits a ferromagnetic ground state with 100% spin polarization at the Fermi level.
• First-principles studies using WIEN2k and related packages confirm its mechanical, dynamical, and chemical stability, underpinning predicted multifunctionality.
• Detailed transport and thermoelectric analyses predict high Seebeck coefficients, a Curie temperature around 566 K, and a figure of merit (ZT) close to 0.9.

PdCrAs is a ternary Pd–Cr–As compound that, in the current arXiv literature, is primarily treated as a half-Heusler alloy in the C1$_b$ structure and investigated by first-principles methods for its electronic, magnetic, thermodynamic, optical, and transport properties. In that formulation, PdCrAs is predicted to have a ferromagnetic ground state, half-metallic electronic structure, mechanical and dynamical stability, and a thermoelectric figure of merit approaching $0.9$ over $300$–$1500$ K (Singh et al., 7 Sep 2025). The literature also contains a distinct experimentally characterized compound, CrPdAs, which crystallizes in a distorted-kagome structure and exhibits spin-glass behaviour and quasi-linear “non-metallic” resistivity; despite the near-identical elemental composition, it is a different material with different symmetry, disorder phenomenology, and transport signatures (Lau et al., 13 Apr 2026).

1. Crystal structure and energetic stability

PdCrAs crystallizes in the C1$_b$ (half-Heusler) structure, space group $F\overline{4}3m$, with Wyckoff positions Pd at $4a$: $(0,0,0)$, Cr at $4c$: $(\tfrac12,\tfrac12,\tfrac12)$, and As at $0.9$0: $0.9$1. After fitting the energy-versus-volume curve to a Birch–Murnaghan equation of state, the optimized lattice constants are $0.9$2 Å and $0.9$3 Å (Singh et al., 7 Sep 2025).

The ferromagnetic phase is calculated to be energetically preferred. Specifically, ferromagnetic PdCrAs has the lower total energy $0.9$4 than the nonmagnetic phase $0.9$5, so the FM ground state is stable. Chemical stability is further supported by the reported formation energy per atom,

$0.9$6

together with an OQMD value of $0.9$7 (Singh et al., 7 Sep 2025).

These results place PdCrAs within the class of theoretically stable half-Heusler systems. A plausible implication is that its predicted multifunctionality should be interpreted in the context of this specific $0.9$8 phase, not as a property of all Pd–Cr–As stoichiometries.

2. First-principles methodology

The reported study of PdCrAs employs WIEN2k in the all-electron FP-LAPW framework. Structural optimization and total-energy calculations use GGA in the PBE form, while the electronic band structure and DOS are refined with the Tran–Blaha modified Becke–Johnson potential. The muffin-tin radii are $0.9$9 a.u., $300$0 a.u., and $300$1 a.u.; the plane-wave cutoff is $300$2, the valence/core separation is at $300$3 Ry, Brillouin-zone sampling uses a $300$4 Monkhorst–Pack $300$5-mesh, and total-energy convergence is better than $300$6 Ry per unit cell (Singh et al., 7 Sep 2025).

Auxiliary property calculations are distributed across established packages. Phonons are computed with Phonopy using the finite-displacement method, elastic constants with the IRelast module in WIEN2k, thermodynamic quantities over $300$7–$300$8 K with GIBBS2 in the quasi-harmonic Debye model, and transport coefficients with BoltzTraP2 within the rigid-band, constant relaxation time approximation (Singh et al., 7 Sep 2025).

This methodological stack is notable because the principal claims about stability, half-metallicity, and thermoelectric performance are all conditional on these approximations. In particular, the transport analysis explicitly depends on the constant-$300$9 approximation and on assumed lattice thermal conductivity when estimating $1500$0.

3. Electronic structure and ferromagnetism

The calculated spin-polarized band structure and DOS show a metallic majority-spin ($1500$1) channel and a minority-spin ($1500$2) channel with an indirect band gap

$1500$3

The result is $1500$4 spin polarization at $1500$5, which the study identifies as half-metallicity suitable for spintronics (Singh et al., 7 Sep 2025).

The magnetic moment decomposition is reported as follows:

Site or region	Magnetic moment
Cr	$1500$6
Pd	$1500$7
As	$1500$8
Interstitial	$1500$9
Total $_b$0	$_b$1

The total moment follows the Slater–Pauling rule for half-Heuslers,

$_b$2

which gives $_b$3. On that basis, the study states that the magnetic moment aligns with the Slater Pauling rule, indicating robust ferromagnetism. Using the empirical relation

$_b$4

the Curie temperature is estimated as $_b$5 K, implying ferromagnetism well above room temperature (Singh et al., 7 Sep 2025).

The electronic and magnetic description is therefore internally consistent: the integer total moment, minority-spin gap, and fully spin-polarized $_b$6 are the canonical signatures of a half-metallic ferromagnet in this computational framework.

4. Mechanical, dynamical, and thermodynamic properties

For the ferromagnetic state, the elastic constants are $_b$7 GPa, $_b$8 GPa, and $_b$9 GPa. The Voigt–Reuss–Hill averages give $F\overline{4}3m$0 GPa, $F\overline{4}3m$1 GPa, $F\overline{4}3m$2 GPa, and $F\overline{4}3m$3. The ductility indicators are reported as $F\overline{4}3m$4 and Cauchy pressure $F\overline{4}3m$5 GPa, leading to the conclusion that the material is ductile in nature. Phonon dispersion shows no imaginary frequencies across the Brillouin zone, so the phase is dynamically stable (Singh et al., 7 Sep 2025).

Thermodynamic properties are obtained within the quasi-harmonic Debye model over $F\overline{4}3m$6–$F\overline{4}3m$7 K at $F\overline{4}3m$8. The Debye temperature $F\overline{4}3m$9 falls from $4a$0 K at low $4a$1 to $4a$2 K at $4a$3 K. The entropy $4a$4 rises rapidly at low $4a$5 and then more slowly, with $4a$6. The constant-volume heat capacity follows the Debye law,

$4a$7

giving $4a$8 and approaching the Dulong–Petit limit $4a$9 for $(0,0,0)$0. The vibrational free energy decreases with temperature, the vibrational internal energy increases, and the bulk modulus slowly decreases with thermal softening, leveling off above $(0,0,0)$1 K (Singh et al., 7 Sep 2025).

Taken together, these results characterize PdCrAs as a mechanically robust and dynamically stable half-Heusler phase whose finite-temperature response is consistent with ordinary quasi-harmonic phonon softening rather than anomalous lattice instability.

5. Optical response and thermoelectric transport

The optical properties are calculated from the complex dielectric function $(0,0,0)$2 using TB-mBJ. The real part $(0,0,0)$3 becomes negative below $(0,0,0)$4 eV, consistent with Drude-like metallic behavior, and crosses zero at $(0,0,0)$5 eV. The imaginary part $(0,0,0)$6 shows strong interband peaks at $(0,0,0)$7 eV, $(0,0,0)$8 eV, and $(0,0,0)$9 eV. The energy-loss function $4c$0 has a plasmon peak at $4c$1 eV. Reflectivity is $4c$2, drops to $4c$3 at $4c$4 eV, and then exhibits smaller oscillations up to the ultraviolet. The refractive index is $4c$5, the extinction coefficient peaks at $4c$6 eV and remains nonzero through $4c$7–$4c$8 eV, the absorption coefficient is of order $4c$9–$(\tfrac12,\tfrac12,\tfrac12)$0 in the UV–visible region with pronounced maxima at $(\tfrac12,\tfrac12,\tfrac12)$1–$(\tfrac12,\tfrac12,\tfrac12)$2 eV, and the optical conductivity shows a static Drude-like tail up to $(\tfrac12,\tfrac12,\tfrac12)$3 eV and a main peak near $(\tfrac12,\tfrac12,\tfrac12)$4 eV with $(\tfrac12,\tfrac12,\tfrac12)$5 (Singh et al., 7 Sep 2025).

Transport coefficients are evaluated with BoltzTraP2 up to $(\tfrac12,\tfrac12,\tfrac12)$6 K while varying the chemical potential $(\tfrac12,\tfrac12,\tfrac12)$7 around $(\tfrac12,\tfrac12,\tfrac12)$8. At $(\tfrac12,\tfrac12,\tfrac12)$9 K, the maximum $0.9$00 is $0.9$01 at $0.9$02 eV; $0.9$03 decreases with increasing temperature due to enhanced bipolar conduction. The electrical conductivity $0.9$04 increases monotonically with $0.9$05 and is weakly temperature-dependent, while $0.9$06 has a similar $0.9$07-dependence and is smallest near $0.9$08. The power factor $0.9$09 peaks at $0.9$10 eV, with $0.9$11 per $0.9$12. The figure of merit is written as

$0.9$13

and, assuming a typical lattice thermal conductivity $0.9$14, the reported value is $0.9$15–$0.9$16 across $0.9$17–$0.9$18 K, reaching $0.9$19–$0.9$20 at $0.9$21 K (Singh et al., 7 Sep 2025).

The study interprets this combination of large Seebeck coefficient, moderate electrical conductivity, and moderate thermal conductivity as a basis for strong thermoelectric characteristics. Since the calculation uses rigid-band and constant-$0.9$22 transport theory together with an assumed $0.9$23, a plausible implication is that experimental confirmation would be decisive in assessing the quantitative $0.9$24 values.

6. Distinction from the experimentally realized compound CrPdAs

A recurring source of ambiguity is the coexistence of two different materials in the recent literature: the predicted half-Heusler alloy PdCrAs and the experimentally synthesized distorted-kagome compound CrPdAs. The latter crystallizes in space group $0.9$25 (#189) with lattice parameters $0.9$26 Å and $0.9$27 Å; Cr forms edge-linked triangles in the $0.9$28-plane and Pd forms trimers in adjacent layers. Single-phase crystals nevertheless have $0.9$29 anti-site disorder of the Cr and Pd sites, determined by Rietveld refinement of powder neutron diffraction (Lau et al., 13 Apr 2026).

The magnetic and transport phenomenology of CrPdAs is qualitatively different from that predicted for PdCrAs. CrPdAs shows spin-glass freezing at $0.9$30 K in all single-phase crystals, a large linear coefficient of the heat capacity at low temperature $0.9$31, and an in-plane resistivity $0.9$32 that increases monotonically on cooling from $0.9$33 K to $0.9$34 K. Below about $0.9$35 K, this resistivity becomes quasi-linear in $0.9$36, with the fit

$0.9$37

where $0.9$38, $0.9$39, and $0.9$40. The calculated band structure of CrPdAs shows several Dirac-type crossings within $0.9$41 eV of $0.9$42 near the top of the Brillouin zone around $0.9$43, and spin-orbit coupling gaps those crossings, producing a very flat band within a few meV of $0.9$44 (Lau et al., 13 Apr 2026).

These two bodies of work therefore describe different regimes of Pd–Cr–As chemistry. PdCrAs, as treated in the half-Heusler study, is a computationally predicted $0.9$45 ferromagnetic half-metal with optical and thermoelectric functionality. CrPdAs, as experimentally characterized, is a $0.9$46 distorted-kagome metal with anti-site disorder, spin-glass behaviour, and quasi-linear “non-metallic” resistivity. Any direct transfer of conclusions between them would be unwarranted unless the specific crystal structure and stoichiometric ordering are explicitly controlled.