ErSbTe: Heavy Rare-Earth Topological Semimetal

• ErSbTe is a heavy rare-earth compound in the LnSbTe family featuring a layered ZrSiS-type structure and strong 4f magnetism.
• Selective spin–orbit coupling produces a symmetry-protected gapless Dirac crossing alongside a momentum-dependent gapped crossing (~75 meV).
• Low-temperature studies reveal an incommensurate spin-density wave, highlighting the complex interplay between magnetism and topology.

ErSbTe is a heavy rare-earth member of the $1{:}1{:}1$ stoichiometric LnSbTe family $(Ln=$ lanthanide$)$, a materials class that combines the layered ZrSiS/PbFCl-type crystal structure, $4f$-electron magnetism, strong spin–orbit coupling (SOC), and symmetry-enforced topological band features. It has been studied both as a nodal line semimetal candidate and as a magnetically ordered topological semimetal candidate. Current evidence places ErSbTe in a regime where nonsymmorphic symmetry preserves selected Dirac-like crossings, while SOC gaps others, and where low-temperature order is antiferromagnetic but microscopically realized as an incommensurate spin-density wave rather than a simple commensurate collinear state (Elius et al., 10 Aug 2025, Plokhikh et al., 2023).

1. Family placement within LnSbTe

ErSbTe belongs to the LnSbTe series, which crystallizes in the ZrSiS/PbFCl-type structure with space group $P4/nmm$. Within this family, the combination of layered geometry and nonsymmorphic symmetry produces an electronic structure reminiscent of ZrSiS, including Dirac nodal-line states near the Fermi level. The same family also hosts lanthanide magnetism and, in some members, charge-density-wave or structural instabilities. ErSbTe is distinguished in this context as a heavy-$Ln$ compound, where SOC effects are expected to modify the band structure more strongly than in lighter lanthanide analogues (Elius et al., 10 Aug 2025).

This positioning is important because the LnSbTe family is explicitly treated as a platform in which electronic correlations, magnetism, structural instabilities, and topology intertwine. In ErSbTe, that interplay is not merely conceptual: the available measurements connect the symmetry setting of the lattice to the persistence of one protected crossing, connect the heavier lanthanide identity to SOC-driven gap formation at another crossing, and connect the low-temperature magnetic transition to a modulated order parameter rather than a conventional fixed-moment antiferromagnet (Plokhikh et al., 2023).

2. Crystal structure and symmetry setting

ErSbTe crystallizes in the tetragonal $P4/nmm$ space group (No. 129) and is isostructural with other LnSbTe materials. Its crystal structure consists of Sb square-net layers sandwiched between zig-zag Er–Te atomic chains. The calculated lattice parameters are $a=b=4.266~\text{\AA}$ and $c=9.184~\text{\AA}$. The reported atomic positions are Er at Wyckoff $2c$, $(Ln=$0; Sb at $(Ln=$1, $(Ln=$2; and Te at $(Ln=$3, $(Ln=$4 (Elius et al., 10 Aug 2025).

A central feature of this structure is its nonsymmorphic symmetry content. In ErSbTe, the authors state that nonsymmorphic glide-plane symmetry together with time-reversal symmetry $(Ln=$5 protects an out-of-plane nodal line along the $(Ln=$6–$(Ln=$7 direction even when SOC is included. More generally for LnSbTe, symmetry-enforced Dirac crossings are noted at the $(Ln=$8 point, protected by a nonsymmorphic glide plane symmetry $(Ln=$9 combined with $)$0, and along $)$1–$)$2, where another Dirac-like crossing can arise from screw-axis symmetry $)$3 together with inversion symmetry $)$4 (Elius et al., 10 Aug 2025).

These symmetry statements delimit what is and is not expected to survive SOC. They also frame ErSbTe as a compound in which crystallographic symmetry, rather than accidental band overlap, determines the robust part of the low-energy band topology.

3. Electronic band structure observed by ARPES

Angle-resolved photoemission spectroscopy was performed at SSRL beamline endstation 5–2 at $)$5, using incident photon energies including $)$6, $)$7, $)$8, and $)$9. The measured Fermi surface is described as diamond shaped and centered at $4f$0, a motif identified as typical of ZrSiS-type materials. Unlike PrSbTe and NdSbTe, ErSbTe does not show a double-sheet Fermi surface (Elius et al., 10 Aug 2025).

The band features are most prominent near the $4f$1 point. In the Fermi-surface map they are reported as absent exactly at $4f$2, but they become clear in dispersions near $4f$3. Along $4f$4–$4f$5, ARPES resolves bands crossing the Fermi energy, labeled $4f$6 and $4f$7, and these are stated to be projected to intersect over the Fermi energy so as to form a gapless symmetry-enforced Dirac crossing. A second crossing along the same direction is gapped, and this gap evolves in momentum space, becoming maximal along $4f$8–$4f$9. Along $P4/nmm$0–$P4/nmm$1, the $P4/nmm$2 and $P4/nmm$3 bands open a gap of approximately $P4/nmm$4, and second-derivative analysis shows no additional band within that gap. Along $P4/nmm$5–$P4/nmm$6, the dispersion shows no signature of bands over $P4/nmm$7 of binding energy, unlike other LnSbTe materials; the authors note that this direction may host surface bands on the basis of photon-energy dependence (Elius et al., 10 Aug 2025).

Taken together, these measurements establish a selective survival of topological band signatures. The data do not support an everywhere-gapless nodal-line phenomenology in the experimentally accessed near-$P4/nmm$8 states; instead, they support a coexistence of a symmetry-enforced gapless crossing and a momentum-dependent gapped crossing.

4. First-principles description and the role of SOC

The first-principles calculations were carried out using VASP within GGA-PBE, with a plane-wave cutoff of $P4/nmm$9. The $Ln$0 electrons were treated as core states, structural optimization used a $Ln$1 $Ln$2-grid, and the Wannierized tight-binding model was built from Er $Ln$3 and $Ln$4 orbitals together with Sb/Te $Ln$5 orbitals. The resulting model is a 56-orbital, 128-band tight-binding Hamiltonian (Elius et al., 10 Aug 2025).

The calculations explicitly compare band structures with and without SOC. Without SOC, the calculated bands show Dirac crossings characteristic of nodal-line semimetal behavior. With SOC, one crossing remains symmetry protected, while another becomes gapped. The calculations further show Dirac crossings parallel to the $Ln$6–$Ln$7 direction, and these crossings belong to nodal lines extending along $Ln$8–$Ln$9; the nonsymmorphic glide symmetry protects this nodal line even in the SOC-included case (Elius et al., 10 Aug 2025).

The significance of the SOC comparison is twofold. First, it identifies SOC as a critical factor dictating band degeneracy in a manner that depends on the choice of the $P4/nmm$0 atom. Second, it provides a specific explanation for why ErSbTe differs from lighter family members: the heavier rare-earth ion places the system in a regime where SOC is strong enough to gap one crossing without eliminating all symmetry-enforced Dirac physics.

5. Bulk electrical, magnetic, and thermodynamic properties

Bulk characterization combines susceptibility, magnetization, resistivity, and specific-heat measurements. Magnetic susceptibility measured in $P4/nmm$1 along the $P4/nmm$2 axis follows Curie–Weiss behavior over a broad temperature range, with fitted effective moment $P4/nmm$3 and Curie temperature $P4/nmm$4. The negative $P4/nmm$5 is taken to indicate weak antiferromagnetic exchange interactions. A broad maximum appears at about $P4/nmm$6, followed by a clear drop at $P4/nmm$7, with a faster decrease below $P4/nmm$8. No bifurcation is observed between zero-field-cooled and field-cooled susceptibility, consistent with antiferromagnetic order (Elius et al., 10 Aug 2025).

At $P4/nmm$9, field-dependent magnetization is nearly linear up to about $a=b=4.266~\text{\AA}$0, then tends toward saturation around $a=b=4.266~\text{\AA}$1, with no hysteresis. Resistivity measured in $a=b=4.266~\text{\AA}$2 and $a=b=4.266~\text{\AA}$3 is metallic-like in zero field rather than hump-bearing and semimetallic-like. Specifically, the zero-field data do not show the characteristic hump-like feature around $a=b=4.266~\text{\AA}$4 that is common in other LnSbTe materials. With $a=b=4.266~\text{\AA}$5 applied along the $a=b=4.266~\text{\AA}$6-axis, the resistivity shape becomes more similar to that of other LnSbTe systems. The zero-field resistivity saturates near $a=b=4.266~\text{\AA}$7 at low temperature, and because the data extend only to $a=b=4.266~\text{\AA}$8, no distinct magnetic-ordering signature is resolved in $a=b=4.266~\text{\AA}$9 (Elius et al., 10 Aug 2025).

Specific heat adds a thermodynamic perspective. Above $c=9.184~\text{\AA}$0, $c=9.184~\text{\AA}$1 approaches $c=9.184~\text{\AA}$2, close to the Dulong–Petit limit. Below $c=9.184~\text{\AA}$3, a broad Schottky-like anomaly is attributed to crystal-electric-field splitting. At low temperature, distinct anomalies appear at $c=9.184~\text{\AA}$4 and $c=9.184~\text{\AA}$5. The first marks entry into the antiferromagnetically ordered state, whereas the sharper second peak is interpreted as suggestive of a first-order transition, possibly associated with a magnetic-structure reconfiguration (Elius et al., 10 Aug 2025).

These measurements show that ErSbTe is electronically unusual even within LnSbTe. In particular, the absence of the zero-field hump common elsewhere in the family distinguishes its transport phenomenology, while the two low-temperature anomalies indicate that its magnetic phase behavior is more structured than a single second-order ordering event.

6. Microscopic magnetic structure from neutron diffraction

A separate magnetic-structure study places the onset of magnetic ordering in ErSbTe near $c=9.184~\text{\AA}$6. In that work, a Curie–Weiss fit above $c=9.184~\text{\AA}$7 gives $c=9.184~\text{\AA}$8 and $c=9.184~\text{\AA}$9, again consistent with predominantly antiferromagnetic interactions. The decisive microscopic evidence comes from neutron powder diffraction on HRPT at SINQ (PSI), with wavelength $2c$0 over $2c$1. For ErSbTe, comparison of patterns at $2c$2 and $2c$3 shows additional strong reflections at low temperature, establishing bulk magnetic order (Plokhikh et al., 2023).

The magnetic reflections can be indexed by a propagation vector very close to $2c$4, but the refined result is slightly incommensurate: $2c$5 The authors describe this as a tiny deviation from commensurability. Symmetry analysis identifies the relevant Brillouin-zone point as mDT, and the best fit corresponds to the irreducible representation mDT1 with maximal magnetic superspace group $2c$6. An alternative setting is given as $2c$7, and the listed basis transformation from the parent tetragonal cell is $2c$8, $2c$9, $(Ln=$00 (Plokhikh et al., 2023).

The proposed magnetic arrangement is a single-$(Ln=$01, transversal spin-density wave. Only one variable component of the magnetic modulation is required; the ordered moment is along $(Ln=$02, perpendicular to the propagation vector; and the refined moment amplitude is $(Ln=$03. Attempts to lower the symmetry or add more moment components do not improve the refinement and do not yield a constant-moment structure. The physical interpretation is a long-period incommensurate spin-density wave with wavelength on the order of $(Ln=$04, and with nearly antiferromagnetically coupled moments on neighboring Er sites. The same study also notes pronounced diffuse scattering near $(Ln=$05, suggesting that the measured state may still lie close to the ordering transition and may not yet fully represent the ultimate ground state (Plokhikh et al., 2023).

This microscopic result sharpens the magnetic description substantially. ErSbTe is not simply an antiferromagnet in the generic sense used by bulk probes; it is a modulated antiferromagnetic system whose order parameter is incommensurate and sinusoidally varying.

7. Interpretation, relation to topology, and open issues

Two conclusions are secure. First, ErSbTe retains key symmetry-enforced topological features of the LnSbTe family: a gapless Dirac-like crossing associated with nonsymmorphic symmetry remains present in both calculation and ARPES. Second, ErSbTe is not electronically equivalent to a fully SOC-free nodal-line semimetal, because another crossing becomes gapped and the gap reaches about $(Ln=$06 along $(Ln=$07–$(Ln=$08 (Elius et al., 10 Aug 2025).

This distinction matters because the label “nodal line semimetal candidate” can be misunderstood if taken to imply that all relevant low-energy crossings remain gapless. The available evidence instead supports a more selective picture: ErSbTe preserves a nonsymmorphically protected crossing while exhibiting SOC-driven gap opening at another crossing. In the same way, the term “antiferromagnetic order” can obscure the actual magnetic ground state determined by diffraction, which is a nearly commensurate, long-period, single-$(Ln=$09 incommensurate transversal spin-density wave rather than a simple fixed-moment collinear arrangement (Plokhikh et al., 2023).

At the family level, the magnetic-structure study identifies a restricted set of recurring propagation vectors,

$(Ln=$10

and suggests that these may originate from common Fermi-surface nesting tendencies in the topological band structure across LnSbTe. For ErSbTe specifically, the observed nearly commensurate $(Ln=$11 modulation is therefore discussed as potentially linked to the underlying electronic structure, although no direct spectroscopic topological reconstruction driven by magnetic ordering is claimed (Plokhikh et al., 2023).

A plausible implication is that ErSbTe occupies an intermediate regime within LnSbTe: heavy-$(Ln=$12 SOC is strong enough to reshape parts of the nodal-line-derived band manifold, but the lattice symmetry still preserves robust Dirac-like states, and the magnetic sector develops a long-wavelength incommensurate instability rather than a trivial commensurate Néel pattern. That combination makes ErSbTe a particularly clear example of how symmetry protection, SOC, and rare-earth magnetism can coexist without collapsing into a single simplified phase description.