GdAlSi: Magnetic Weyl Semimetal & Altermagnetism

• GdAlSi single crystals are noncentrosymmetric tetragonal intermetallic compounds known for complex magnetic phases and Weyl semimetal behavior.
• They are synthesized via a self-flux method, with detailed structural and transport studies revealing cascaded AFM transitions and significant Berry-curvature responses.
• DFT calculations and ARPES confirm multiple Weyl nodes and momentum-dependent altermagnetic spin splitting, positioning GdAlSi as a promising platform for next-generation topotronics.

GdAlSi single crystals are noncentrosymmetric tetragonal intermetallic compounds that crystallize in the LaPtSi-type (space group $I4_1md$, No. 109). They are distinguished by the interplay of large Gd$^{3+}$ local moments, strong electron correlations, broken inversion symmetry, and the emergence of magnetic Weyl semimetal states. GdAlSi exhibits a rich cascade of antiferromagnetic (AFM) and field-induced magnetic phases, complex transport anomalies, sizable Berry-curvature–driven responses, and unconventional momentum-dependent spin splitting. These combined properties make GdAlSi a benchmark system for the study of correlated topological phases, magnetic symmetry manipulation, and altermagnetic spintronics.

1. Crystal Growth, Structure, and Composition

GdAlSi single crystals are synthesized via a self-flux method. Gd, Al, and Si are combined in the molar ratio 1:10–15:1, sealed in evacuated quartz or under partial Ar, heated to 1000–1423 K, and cooled slowly (2–3 K/h) to ~1073–700 K before decanting to remove excess Al flux. Residual Al is eliminated by centrifugation or NaOH treatment. Resulting crystals are typically plate-like, with millimeter-scale lateral dimensions and thicknesses of 0.1–0.3 mm, with the $ab$-plane as the plate surface (Li et al., 12 Jan 2026, Laha et al., 2023, Nag et al., 2023).

Structural characterization by powder X-ray diffraction (XRD) and Rietveld refinement establishes the noncentrosymmetric tetragonal space group $I4_1md$. Typical lattice parameters are:

• $a = b ≈ 4.12$–$4.13$ Å
• $c ≈ 14.42$–$14.43$ Å

Site occupancy for Gd, Al, and Si is full, with atomic ratios from EDS or XPS consistent with 1:1:1 stoichiometry. Optical second-harmonic generation confirms the point group $4mm$ and the absence of inversion symmetry (Nag et al., 2023). The idealized structure has Gd, Al, Si all at $4a$ Wyckoff positions with $z_{\rm Gd} ≈ 0.374$, $z_{\rm Si} ≈ 0.793$, $z_{\rm Al} ≈ 0.958$.

2. Magnetic Ordering and Phase Transitions

GdAlSi displays complex magnetic behavior as a function of temperature and applied magnetic field. Key properties are summarized in the table below.

Parameter	Value (typical)
$T_{N1}$*	31.9 K
$T_{N2}$*	31.1 K
$T_N$	32 K
$\mu_{\rm eff}$	7.95–8.3 $\mu_B$/Gd
$\theta_P$	–103 to –116 K

*In some studies, two closely spaced zero-field AFM transitions are observed; others report a single sharp Néel temperature.

Susceptibility measurements for $B\parallel c$ reveal antiferromagnetic transitions at $T_{N1} ≈ 31.9$ K and $T_{N2} ≈ 31.1$ K, with features in resistivity and specific heat corroborating these events. The Curie–Weiss effective moment is close to the Gd$^{3+}$ free-ion value (7.94 $\mu_B$), and a large negative Weiss temperature indicates strong AFM exchange (Li et al., 12 Jan 2026, Nag et al., 2023).

Application of a magnetic field ($B\parallel c$) beyond $\mu_0 H ≳ 8$ T induces a third transition ($T_{N3}$), moving to higher temperatures with increasing field, consistent with a linear phase boundary $T_{N3}(H) ≈ T_{N2} + 0.3$ K/T·$(H-8\,{\rm T})$ up to $T ≈ 34$ K at 14 T. Isothermal magnetization in $ab$-plane shows metamagnetic jumps, forming narrow hysteretic regions with low coercivity and remanence.

First-principles calculations favor type-I collinear AFM as the ground state (Gd moments aligned ferromagnetically within each layer, antiferromagnetically stacked along $c$), but spiral orders are close in energy, likely due to weak magnetocrystalline anisotropy ($<1$ meV/Gd). Dzyaloshinskii–Moriya interactions are symmetry-allowed and implicated—REXS confirms cycloidal spin textures in zero field with $|{\bf D}|\sim 0.1$–$1$ meV, underpinning the cascade of field-induced metamagnetic states (Li et al., 12 Jan 2026, Laha et al., 2023).

3. Magnetotransport and Anomalous Hall Effect

Longitudinal resistivity $\rho_{xx}(T)$ is metallic, with a residual resistivity ratio $RRR\approx3$. At $T_N$, $\rho_{xx}(T)$ exhibits sharp kinks; above 40 K, the temperature dependence follows a Fermi-liquid-like power law ($\rho_{xx}(T) = \rho_0 + AT^n$, $n≈1.8$). Field-dependent magnetoresistance is strongly positive, reaching up to 53% at 2 K and 14 T ($B\parallel c$) (Laha et al., 2023), and displays stepwise anomalies and hysteresis coincident with metamagnetic transitions at critical fields ($B_1$, $B_2$).

Hall resistivity is dominated by holes, with the carrier density $n\sim 3\times 10^{20}$ cm$^{-3}$ and mobility $\mu$ ranging from 2000 cm$^2$/Vs (2 K) to 200 cm$^2$/Vs (300 K). In the magnetically ordered phase, the anomalous Hall conductivity (AHC) is exceptionally large: $\sigma_{xy}^A≈1310$ $\Omega^{-1}$cm$^{-1}$ at 2 K, and remains significant at room temperature ($\sim$155 $\Omega^{-1}$cm$^{-1}$). The AHC shows a pronounced field dependence, peaking near 7.5 T, and is attributed primarily to Berry curvature near the multiple Weyl nodes rather than to topological Hall effects from spin chirality (Laha et al., 2023).

4. Electronic Structure and Topological Properties

First-principles density functional theory (DFT+$U$) calculations (with $U_{eff}=6$–$7$ eV for Gd $4f$) confirm GdAlSi as a magnetic Weyl semimetal. In the AFM phase, there are 16–18 pairs of bulk Weyl nodes with Chern number $\pm1$, typically $+24$ to $+100$ meV above the Fermi energy, distributed across trivial and symmetry-related $k$-points (Nag et al., 2023, Laha et al., 2023). Spin-orbit coupling is present but only weakly modifies the band structure due to Gd$^{3+}$’s half-filled $4f$ shell.

Electronic states near $E_F$ show linearly dispersing Gd $5d$ bands hybridized with Al/Si $p$ states. The theoretically calculated Berry curvature hot spots are associated with Weyl nodes, and the expression for intrinsic anomalous Hall conductivity is given by

$$\sigma_{xy}^A = -\frac{e^2}{\hbar}\sum_n \int_{BZ} \frac{d^3k}{(2\pi)^3} f_{n,k} \Omega_{n,z}({\bf k})$$

Angle-resolved photoemission spectroscopy (ARPES) provides experimental evidence for the predicted topology: Fermi surface maps and energy–momentum cuts reveal arc-like surface states connecting bulk electron and hole pockets. Key ARPES features—diamond-shaped BZ, surface state pockets, arc structures—display good qualitative agreement with DFT slab calculations when the theoretical $E_F$ is shifted upward to account for surface effects. Linear dispersing surface bands and Fermi arcs consistent with both type-I and type-II Weyl crossings are observed (Nag et al., 2023).

5. Momentum-Dependent Spin Splitting and Altermagnetic Order

GdAlSi uniquely exhibits large, momentum-dependent non-relativistic spin splitting in its collinear AFM ground state, a phenomenon termed "altermagnetism" (Editor's term). The spin splitting is maximal ($\sim230$ meV) away from symmetry-locked planes and vanishes on high-symmetry lines, reflecting a $d$-wave–like pattern in momentum space. This arises from the material’s non-trivial magnetic symmetry:

$$R_s = [\mathbb{I}||C_{2v}] \cup [C_2||C_{4z}][\mathbb{I}||C_{2v}]$$

where rotation and spin-flip operations ensure that up- and down-spin Fermi surfaces are orthogonally oriented.

Multipole analysis of the DFT density matrix finds that magnetic octupole moments on Gd (even parity) and magnetoelectric quadrupoles (odd parity, only with SOC) drive the splitting. The lowest-order $k$-space term allowed by symmetry is

$$H_{\text{oct}}({\bf k}) = \alpha (k_x^2 - k_y^2) m_z \sigma_z$$

This term enables tunable spin splitting that flips under domain reversal or crystallographic axes exchange—e.g., by swapping Al/Si positions to form GdSiAl. Such symmetry-governed splitting produces alternating, 90-degree-rotated spin polarisations in reciprocal space, and is fundamentally non-relativistic in origin (Nag et al., 2023).

6. Metamagnetism, Transport Anomalies, and Phase Diagram

GdAlSi’s magnetic phase diagram in the $B$–$T$ plane shows four principal regions, defined by the antiferromagnetic transitions ($T_{N1}$, $T_{N2}$), field-induced ($T_{N3}$), and a sequence of metamagnetic steps at critical fields ($B_1$–$B_4$). Magnetization and magnetoresistance measurements reveal stepwise anomalies, pronounced hysteresis, and sharp peaks in $dM/dH$—these are attributed to metamagnetic moment flopping between competing spin structures, enabled by finite Dzyaloshinskii–Moriya interaction and a multi-$\mathbf{Q}$ spin landscape.

In transport, magnetoresistance $MR(H)$ exhibits abrupt jumps and loops at the aforementioned critical fields, combined with smaller intermediate anomalies. These signatures are consistent with first-order transitions between complex AFM, cycloidal, and possibly fan-type or field-polarized magnetic structures as revealed by resonant elastic X-ray scattering and comparison to DFT quasi-degenerate states. The dendritic topology of the phase diagram points to the delicacy of the balance between localized moments, DMI, and itinerant electrons (Li et al., 12 Jan 2026).

7. Implications for Topotronics and Device Concepts

The coexistence of non-centrosymmetric collinear AFM order, topologically protected Weyl nodes, sizeable Berry curvature, and electrically tunable altermagnetic spin splitting renders GdAlSi a model platform for next-generation topological spintronics ("topotronics"). Device concepts harnessing these phenomena have been proposed:

• Spin-Twister Valve (STV): A stack comprising GdAlSi (spin-split AFM), a spin buffer/barrier (TI surface, tunneling oxide), and inverted GdSiAl. The relative orientation of the altermagnetic axes acts as a gate for spin-based current flow.
• Spin-Junction Transistor (SJT): A three-terminal device using GdAlSi and inverted GdSiAl as emitter, base, and collector; operation involves spin-channel depletion and current amplification via Fermi-arc-mediated surface states.

A plausible implication is that magnetic domain engineering and chemical substitution (e.g., GdAlSi ↔ GdSiAl) enable tailored spin textures and topological transitions for customizable device architectures (Nag et al., 2023).

---

References:

• (Li et al., 12 Jan 2026)
• (Laha et al., 2023)
• (Nag et al., 2023)