---
title: 'EuAgAs: Tunable Magnetic Topological Semimetal'
url: https://www.emergentmind.com/topics/euagas
type: topic
---

# EuAgAs: Tunable Magnetic Topological Semimetal

EuAgAs is a hexagonal rare-earth pnictide in space group $P6_3/mmc$ (No. 194) whose defining feature is the strong dependence of its band topology on magnetic order. Across first-principles, neutron, transport, ARPES, resonant x-ray, and ultrafast optical studies, it has been described as a Dirac semimetal in the paramagnetic or symmetry-protected antiferromagnetic regime, and as a system that can host magnetic triply-degenerate points, mirror-topological semimetal phases, linear and double Weyl points, higher-order topology, and pressure-accessible altermagnetism [2107.13345; 2605.16242; 2106.04710; 2605.23836; 2411.10756; 2605.19347]. Its status as a model magnetic topological semimetal rests not on a single fixed phase, but on a closely competing manifold of magnetic states whose electronic structures are topologically distinct.

## 1. Crystal chemistry and symmetry framework

EuAgAs crystallizes in the hexagonal $P6_3/mmc$ structure with two formula units per cell. The literature assigns related prototype labels including a modified Ni$_2$In–type hexagonal structure, a Ni$_2$In–type hexagonal structure, and a BeZrSi–type structure, while retaining the same space-group description [2107.13345; 2411.10756; 2605.16242]. Reported lattice parameters include $a = 4.516$ Å and $c = 8.107$ Å from experiment, $a = 4.5052(2)$ Å and $c = 8.0929(5)$ Å at $250$ K, and room-temperature values of $a \approx 4.27$ Å, $c \approx 7.10$ Å; other studies quote approximate values $a \approx 4.32$ Å, $c \approx 7.62$ Å or note that this family typically has lattice parameters on the order of $a \approx 4.2$ Å and $c \approx 7.5$ Å [2107.13345; 2605.16242; 2605.19347; 2411.10756; 2106.04710].

All cited studies place Eu on the $2a$ Wyckoff site. For Ag and As, several works use Ag at $2d$ and As at $2c$, whereas one neutron-based refinement reports Ag at $2c$ and As at $2d$ [2107.13345; 2106.04710; 2411.10756; 2605.19347; 2605.16242]. Symmetry generators explicitly invoked in topological analyses include $C_{3z}$, $C_{2y}$, inversion $P$, screw $S_{2z}=\{C_{2z}|00\frac{1}{2}\}$, mirror $M_x$, glide $\tilde M_y$, and mirror $M_z$ [2107.13345]. The structure is nonsymmorphic, with $6_3$ screw axes and glide planes, and these operations are central to the protection or reshaping of magnetic topological states, including altermagnetic symmetry and higher-order Weyl nodes [2605.16242; 2605.19347].

Structurally, EuAgAs may be viewed as stacked Eu layers alternating with $[\mathrm{Ag}\!-\!\mathrm{As}]$ honeycomb nets along $c$ [2605.19347]. This layered arrangement underlies the prominence of interlayer magnetic competition and the repeated appearance of propagation vectors with a substantial $c$-axis component.

## 2. Magnetic order: established phases, competing models, and exchange hierarchy

Eu carries a local moment $\simeq 7.45\,\mu_B$ in DFT-based treatments and an ordered moment $\mu_{\mathrm{ord}} \simeq 7\,\mu_B$ per Eu in neutron diffraction, consistent with Eu$^{2+}$ and $S=7/2$ [2107.13345; 2605.16242]. Magnetic ordering is consistently reported near $12$ K: $T_N \approx 11$ K, $T_N = 12$ K, $T_N \simeq 11.8$ K, or a two-step sequence with $T_{\mathrm{N1}} = 12$ K and $T_{\mathrm{N2}} \approx 8$ K [2107.13345; 2106.04710; 2605.16242; 2605.19347].

Early descriptions emphasized A-type antiferromagnetism: ferromagnetic alignment within each $ab$ plane and antiferromagnetic coupling between adjacent planes along $c$, corresponding to a propagation vector $Q=(0,0,\tfrac{1}{2})$ [2106.04710]. A weak ferromagnetic canting was inferred from the small bifurcation of the ZFC–FC susceptibility below $8$ K and a metamagnetic anomaly in $M(B\parallel ab)$ at $\simeq 0.3$ T [2106.04710]. In that phenomenology, the minimal spin Hamiltonian was written as
$$
H_{\mathrm{mag}} = J \sum_{\langle i,j\rangle} S_i \cdot S_j + D \sum_i (S_i^z)^2 + \sum_{\langle i,j\rangle} \mathbf{D}_{ij}\cdot (S_i \times S_j),
$$
with $J>0$, easy-plane anisotropy $D>0$, and Dzyaloshinskii–Moriya vectors $\mathbf{D}_{ij}$ allowed by the $P6_3/mmc$ symmetry [2106.04710].

Subsequent neutron diffraction refined the bulk ground state as a $\mathbf{q}=(0,0,\tfrac{1}{2})$ AFM structure with in-plane moments along the crystallographic $a$-axis and a ferromagnetic-layer stacking sequence $\uparrow\uparrow\downarrow\downarrow$ along $c$, doubling the primitive cell [2605.16242]. The same work extracted a critical exponent from $I(T)\propto (T_N-T)^{2\beta}$ with $\beta \approx 0.35$, consistent with a $3$D second-order transition [2605.16242].

A further neutron and resonant elastic x-ray study resolved an incommensurate transverse helical state. Below $T_{\mathrm{N1}}$ it found
$$
\mathbf{q}_1=(0,0,0.5+\delta_1),
$$
with $\delta_1$ decreasing from $\sim 0.04$ at $12$ K to $\sim 0.01$ at $2$ K, and below $T_{\mathrm{N2}}$ an additional
$$
\mathbf{q}_2=(0,0,0.5-\delta_2),
$$
with $\delta_2 \simeq 0.01$ nearly temperature-independent down to $2$ K [2605.19347]. Spherical neutron polarimetry identified both as transverse helices with moments in the $ab$ plane rotating about the $c$ axis. The turn angle per Eu–Eu layer was reported as
$$
\phi = \pi q_z \simeq \pi(0.5+\delta) \approx 1.7~\mathrm{rad}\ (\approx 97^\circ),
$$
implying a helix period of $\simeq 3.7$–$4$ layers, or $\simeq 4c$ [2605.19347].

The magnetic competition in EuAgAs is unusually strong. One first-principles study of collinear states considered PM, AFM-$x$, AFM-$y$, AFM-$z$, and FM-$z$ configurations, finding AFM-$x$ as the lowest total energy, AFM-$y$ only $\Delta E \sim 0.02$ meV/f.u. higher, AFM-$z$ $\Delta E \sim 0.1$–$0.2$ meV/f.u. higher, and FM-$z$ $\Delta E \sim 7$–$13$ meV/f.u. higher [2107.13345]. A later DFT study centered on the experimentally refined $(0,0,\tfrac{1}{2})$ AFM ground state found an even tighter hierarchy: FM with moments parallel to the $a$-axis at $\Delta E \approx +0.11$ meV/f.u., AM with $q=(0,0,0)$ at $\Delta E \approx +0.40$ meV/f.u., and FM with moments parallel to the $c$-axis at $\Delta E \approx +1.05$ meV/f.u. [2605.16242].

To reproduce the commensurate $\uparrow\uparrow\downarrow\downarrow$ stacking, that later work introduced the effective one-dimensional model
$$
H_{\mathrm{eff}} = -J_2 \sum_{\langle i,j\rangle} S_i \cdot S_j - J_3 \sum_{\langle\langle i,j\rangle\rangle} S_i \cdot S_j - B_2 \sum_{\langle i,j\rangle}(S_i\cdot S_j)^2,
$$
with
$$
J_2 \simeq +0.10~\mathrm{meV},\qquad
J_3 \simeq -0.051~\mathrm{meV},\qquad
B_2 \simeq -0.078~\mathrm{meV}.
$$
Pure bilinear exchange yields $E(q_z)\propto J_2\cos(q_z c/2)+J_3\cos(q_z c)$ and generally favors an incommensurate spin spiral, whereas the negative biquadratic term penalizes non-collinear alignments and stabilizes the commensurate $\uparrow\uparrow\downarrow\downarrow$ state when sufficiently large [2605.16242].

A recurrent point of interpretation is therefore the magnetic ground state itself. Earlier topological analyses were formulated for A-type AFM and closely related collinear configurations, whereas later diffraction studies reported either a commensurate $(0,0,\tfrac{1}{2})$ $\uparrow\uparrow\downarrow\downarrow$ state or an incommensurate transverse helix with two nearby propagation vectors [2107.13345; 2605.16242; 2605.19347]. This suggests an exceptionally shallow magnetic energy landscape.

## 3. Order-dependent bulk topology

The central theoretical result on EuAgAs is that distinct magnetic orders realize different quasiparticle spectra and bulk invariants [2107.13345]. In the paramagnetic state, with time-reversal and inversion both present, EuAgAs is a Dirac semimetal with two accidental fourfold Dirac points $D$ and $D'$ on $\Gamma$–$A$ at $(0,0,\pm k_D)$, where
$$
k_D = 0.316\cdot \pi/c.
$$
The little co-group is $C_{6v}$, and the two crossing bands transform as the $2$D irreps $\Gamma_9$ and $\Gamma_7$ [2107.13345]. The low-energy $k\cdot p$ Hamiltonian around $D$ is
$$
H_D(q)=a_0 q_z + a_1(\sigma_y\tau_z q_x-\sigma_x q_y)+a_2 \sigma_z q_z,
$$
with $(a_0,a_1,a_2)=(0.49,3.25,2.10)$ eV·Å [2107.13345]. The Dirac points are accidental in the sense that they disappear if the band ordering at $\Gamma$ is reversed, and the band inversion at $\Gamma$ yields $2$D $Z_2=1$ in the $k_z=0$ plane [2107.13345].

Under magnetic ordering, the same parent band structure reorganizes into several distinct topological phases.

| Magnetic state | Symmetry/topology outcome | Representative feature |
|---|---|---|
| PM | Dirac semimetal | Two accidental Dirac points on $\Gamma$–$A$ |
| AFM-$z$ | Magnetic triply-degenerate semimetal | Each Dirac splits into two TDPs |
| AFM-$x$, AFM-$y$ | Topological mirror semimetals | Direct gap with band inversion at $\Gamma$ |
| FM-$z$ | Weyl semimetal | Linear and double Weyl points on $\Gamma$–$A$ |
| Helical phase | Higher-order Weyl state | $C=\pm 2$ Weyl nodes near $A$ |
| AM phase | Altermagnetic Dirac-semimetal regime | Twofold spin-split crossings along $\Gamma$–$A$ |

In AFM-$z$, breaking $T$ but preserving $C_{3v}$ along $\Gamma$–$A$ splits each Dirac point into two magnetic triply-degenerate points. The first, $T_1$, is the crossing of $\Gamma_4$ and $\Gamma_5$ at $k_{T1}\simeq 0.30\cdot \pi/c$; the second, $T_2$, is the crossing of $\Gamma_4$ and $\Gamma_6$ at $k_{T2}\simeq 0.28\cdot \pi/c$ [2107.13345].

In AFM-$x$ and AFM-$y$, the systems are fully gapped throughout the Brillouin zone in the direct-gap sense but retain band inversion at $\Gamma$; their topology is captured by mirror Chern numbers
$$
C_{M_i} = \frac{C_+^{M_i}-C_-^{M_i}}{2},
$$
with DFT yielding nonzero $C_{M_x}$, $C_{M_y}$, and $C_{M_z}$ for AFM-$x$, and nonzero $C_{M_z}$ for AFM-$y$ [2107.13345]. These phases were described as adiabatically connected to topological crystalline insulators. All AFM states in that framework also carry a nontrivial parity-based $Z_4$ index
$$
\kappa = \left[\sum_{i=1}^8 \frac{(n_+^{\Gamma_i}-n_-^{\Gamma_i})}{2}\right]\bmod 4 = 2,
$$
indicating second-order topology and implying hinge modes [2107.13345].

In FM-$z$, exchange splitting breaks all degeneracies and produces multiple twofold Weyl points on $\Gamma$–$A$. Four nodes were explicitly identified:
$$
W_1:\ k_z=0.4112\,\pi/c,\ E=+45.9~\mathrm{meV},\ \chi=-1,
$$
$$
W_2:\ k_z=0.3680\,\pi/c,\ E=+10.6~\mathrm{meV},\ \chi=+2,
$$
$$
W_3:\ k_z=0.3604\,\pi/c,\ E=+4.8~\mathrm{meV},\ \chi=+1,
$$
$$
W_4:\ k_z=0.2392\,\pi/c,\ E=-12.0~\mathrm{meV},\ \chi=-1.
$$
The double Weyl point $W_2$ is stabilized by $C_6$ and disperses linearly along $k_z$ and quadratically in $(k_x,k_y)$ [2107.13345].

The more recent altermagnetic analysis extends this landscape. In the AM phase, bulk Dirac-semimetal crossings along $\Gamma$–$A$ at $k_z\neq 0$ remain, but are twofold split by non-relativistic spin polarization with “g-wave” altermagnetism; splittings up to $\sim 100$ meV were reported in Eu-$d$ bands [2605.16242]. Hydrostatic pressure drives the AFM and AM energies through a crossing at $P_c \simeq 14$ GPa, with the sign change of $J_2$ moving the system across the $(J_2,J_3,B_2)$ phase diagram from the AFM sector into the AM sector [2605.16242].

In the helical phase, the exchange field
$$
\mathbf{M}(z)=M\bigl(\cos(qz),\sin(qz),0\bigr)
$$
folds the band structure in a supercell doubled along $c$, and the combination of broken $\mathcal{P}$ and $\mathcal{T}$ with preserved $C_3$ and $S_{2z}$ produces protected higher-order Weyl nodes with Chern number $C=\pm 2$ along $\Gamma$–$A$ [2605.19347]. DFT places these double-Weyl points at or very near the $A$ point in the unshifted helical band structure [2605.19347].

## 4. Electronic structure in experiment: transport, ARPES, and Fermi-level alignment

Magnetotransport established EuAgAs as an antiferromagnetic Dirac semimetal with additional real-space-topological response [2106.04710]. In the AFM ground state, each band remains twofold degenerate by the combination of inversion $I$ and the effective time-reversal symmetry $S=\Theta\cdot \tau_{1/2}$, and a pair of fourfold-degenerate Dirac points occurs along the $C_{3z}$ axis close to the Fermi energy [2106.04710]. The low-energy Hamiltonian about one node was written as
$$
H_D(q)=\hbar v_\perp (q_x\Gamma_1 + q_y\Gamma_2) + \hbar v_z q_z \Gamma_3.
$$

The Hall resistivity was decomposed as
$$
\rho_{xy}=R_0 B + R_s M + \rho_{xy}^T,
$$
with $R_0\approx -2.51\,\mu\Omega\,\mathrm{cm\,T}^{-1}$ and $R_s=-1.72\times 10^{-3}\,(\mu\Omega\,\mathrm{cm})^{-1}\mu_B^{-1}$ [2106.04710]. The topological Hall component appears only below $T_N$ and in the field window $0.3$–$2$ T where the weak metamagnetic transition occurs. At $2$ K, the maximum amplitude reaches $|\rho_{xy}^T|\approx 7\,\mu\Omega\,\mathrm{cm}$ and the corresponding Hall angle $\Theta_{xy}^T=\sigma_{xy}^T/\sigma_{xx}$ reaches $0.17$ [2106.04710]. This signal was attributed to real-space Berry phases from a noncollinear spin texture with finite scalar spin chirality
$$
Q\equiv \frac{1}{4\pi}\int n\cdot(\partial_x n \times \partial_y n)\,dx\,dy
$$
[2106.04710].

Longitudinal magnetoresistance measurements for $B\parallel I$ found a negative LMR that reaches $-66\%$ at $4$ K and persists up to $100$ K in the paramagnetic regime [2106.04710]. Fits using
$$
\sigma_{xx}(B)=\sigma_{\mathrm{WAL}}(1+C_0B^2)+\sigma_N,
$$
with $\sigma_{\mathrm{WAL}}=\sigma_0+a\sqrt{|B|}$ and $\sigma_N=(\rho_0+AB^2)^{-1}$, yielded a positive $C_0$ and a chirality-changing scattering time $\tau_v\approx 2.8\times 10^{-12}$ s from the temperature dependence of $1/C_0$ versus $T^2$ [2106.04710]. In the field-polarized regime, the breaking of $S=\Theta\cdot \tau_{1/2}$ splits each Dirac point into two Weyl nodes with calculated separations $k_{w1}=0.1096$ Å$^{-1}$ and $k_{w2}=0.227$ Å$^{-1}$; the intrinsic anomalous Hall conductivity was estimated as $\sigma_{xy}^A\approx 2.1\times 10^2\,\Omega^{-1}\mathrm{cm}^{-1}$ [2106.04710].

ARPES and DFT later refined the orbital content and near-$E_F$ dispersion. Polarization-dependent ARPES at $9$ eV found a small $\Gamma$-centered Fermi-surface ring formed by nearly linear Dirac-like bands observed along $\Gamma$–$M$ and $\Gamma$–$K$, with the contour expanding systematically at binding energies $0$, $-100$ meV, $-300$ meV, and $-500$ meV [2605.23836]. The minimal in-plane Hamiltonian was written as
$$
H(\mathbf{k})=\hbar v_F(k_x\sigma_x+k_y\sigma_y)+m(\mathbf{k})\sigma_z,
$$
with $m(\mathbf{k})=M-B(k_x^2+k_y^2)$ and $v_F$ on the order of $3$–$6\times 10^5$ m/s extracted from ARPES slopes [2605.23836]. Orbital-projected DFT showed that these low-energy bands derive predominantly from As $4p$ and Ag $4d$ orbitals, with the Eu $4f$ manifold sitting $\sim -2$ eV below $E_F$ [2605.23836]. In polarization-dependent measurements, $p$ polarization enhanced even-parity orbitals and $s$ polarization enhanced odd-parity orbitals, producing complementary intensity modulation on the Fermi-surface ring [2605.23836].

The same ARPES study reported a higher-order van Hove point at $E-E_D\simeq -0.1$ eV in DFT, arising from opposite curvature along $k_z$ and $k_{x,y}$, with an enhanced bulk DOS at the same binding energy [2605.23836]. Across the AFM transition, Fermi surfaces and dispersions at $9$ K and $30$ K were essentially identical within experimental resolution, and DFT comparisons between nonmagnetic and AFM phases likewise showed negligible splitting or reconstruction near $E_F$ [2605.23836]. This observation directly counters the simple expectation of a large low-energy exchange reconstruction.

A separate ARPES study performed in the helical-order context found that all measured bands lie $\sim 0.5$ eV lower in energy than in DFT; aligning theory with experiment required a rigid upward shift of $+0.5$ eV to the calculated bands [2605.19347]. In that alignment, the higher-order Weyl nodes predicted for the helical phase lie just above the ARPES chemical potential and were not directly observed [2605.19347].

## 5. Surface and boundary phenomena

Surface electronic structure calculations reflect the magnetic-order dependence of the bulk topology [2107.13345]. In the paramagnetic Dirac-semimetal phase, the side surface normal to $y$ exhibits surface-projected Dirac points connected by two Fermi arcs, one for each Dirac-point pair [2107.13345]. This is a characteristic surface manifestation of the bulk accidental Dirac nodes on $\Gamma$–$A$.

For AFM-$z$, surface features are obscured by bulk bands, although the nontrivial $Z_4$ index implies higher-order topology and expected hinge modes [2107.13345]. In the mirror-topological semimetal regimes, the side surface normal to $y$ hosts a Dirac-type surface cone at $\bar\Gamma$ in AFM-$x$, protected by $M_z$ and $M_x$, while AFM-$y$ supports a single Dirac cone shifted away from $\bar\Gamma$, protected by $M_z$ only [2107.13345]. These states represent the surface counterpart of the nonzero mirror Chern numbers.

In FM-$z$, the side surface normal to $y$ displays the expected Weyl connectivity: each projected double Weyl point $W_2$ emits two Fermi arcs, whereas the linear Weyl points emit single arcs [2107.13345]. In this sense, EuAgAs offers within a single material a direct comparison among Dirac-point projections, crystalline-topological surface cones, and Weyl-arc networks.

Surface calculations in the $(001)$ geometry for the AFM phase also showed gapped Dirac crossings and topological surface resonances, and this was used to argue that access to the AM phase could realize symmetry-protected spin-split topological states [2605.16242]. By contrast, in the helical phase the experimentally measured Fermi surface changed only minimally because the folded bands near $\Gamma$ carried negligible spectral weight [2605.19347]. The boundary phenomenology is therefore highly state selective: some phases yield clear arc or cone signatures, while others mainly advertise their topology through hinge or resonance features.

## 6. Tunability, nonequilibrium control, and broader significance

The most distinctive materials-level attribute of EuAgAs is the multiplicity of control parameters that can move it among proximate magnetic and topological sectors. Magnetic-order control was proposed to switch reversibly among a Dirac semimetal, a triply-degenerate semimetal, a mirror TCI-like semimetal, and a Weyl semimetal, with concomitant changes from surface Fermi arcs to surface Dirac cones [2107.13345]. The FM phase can be accessed in calculation or by applied field; one later study explicitly described the forced FM phase as reachable for example by $B\approx 3$ T, where each Dirac point splits into a pair of Weyl points protected by the $6_3$ screw symmetry [2605.16242].

Hydrostatic pressure provides a second route. DFT predicts an AFM-to-AM transition at $P_c\simeq 14$ GPa, driven by the change in sign of $J_2$ and accompanied by momentum-dependent non-relativistic spin splitting characteristic of the AM phase [2605.16242]. This places EuAgAs among the few systems proposed as controllable platforms for topological altermagnetism rather than merely static altermagnetic candidates.

Ultrafast optical excitation provides a third route. Time-resolved differential reflectivity at $800$ nm using $\sim 35$ fs pulses found at low fluence a fast rise followed by a $\sim 1$ ps decay, described by
$$
\Delta R(t)/R = G(t)\otimes [A(1-e^{-t/\tau_{\mathrm{build}}})e^{-t/\tau}+C],
$$
with $\tau_{\mathrm{build}}\approx 50$ fs and an instrument-response width $w\approx 35$ fs [2411.10756]. Above $T_N$, the relaxation followed a two-temperature model with $G_{e\text{–}ph}\approx 1\times 10^{17}$ W m$^{-3}$ K$^{-1}$ [2411.10756]. At $3.5$ K, the fluence dependence showed a sign reversal of $\Delta R/R$ at a critical fluence $F_C\approx 33\,\mu$J/cm$^2$, with $\tau(F)$ increasing by $\sim 30\%$ through $F_C$; this was interpreted as a laser-driven AFM$\rightarrow$FM switch that transiently transforms an AFM Dirac semimetal into an FM Weyl semimetal on a subpicosecond timescale [2411.10756]. Above $T_N$, at $25$ K, the same sign reversal was absent [2411.10756].

These control pathways are the basis of the proposed applications. The literature associates EuAgAs with spin-polarized surface transport, magneto-optical devices, high-sensitivity magnetic sensors, low-dissipation interconnects, 1D dissipationless channels based on higher-order hinge modes, spin-orbit-torque devices, topological magnetic memory elements, chiral-anomaly-based sensors, and THz-speed magnetic memory [2107.13345; 2106.04710; 2411.10756]. A cautious reading is nevertheless warranted. The ground-state magnetic structure is not presented identically across all studies, and some topological features remain prediction-led or lie above the experimentally accessed Fermi level [2605.16242; 2605.19347]. Even so, the accumulated evidence converges on a narrower conclusion: EuAgAs is a strongly tunable magnetic topological semimetal in which subtle changes of magnetic order, field, pressure, or optical excitation reorganize both the quasiparticle content and the accessible boundary responses.

Source: https://www.emergentmind.com/topics/euagas