---
title: 'Monolayer Ti2TeSO: High-Chern Janus Ferromagnet'
url: https://www.emergentmind.com/topics/monolayer-ti2teso
type: topic
---

# Monolayer Ti2TeSO: High-Chern Janus Ferromagnet

Searching arXiv for the specified paper and closely related records to ground the article in current literature.
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Monolayer Ti\(_2\)TeSO is a two-dimensional ferromagnetic half-semi-Weyl-metal proposed as a high-Chern-number Chern insulator that realizes the quantum anomalous Hall effect (QAHE) with \(C=2\) [2509.02654]. In the reported first-principles and Monte Carlo study, the material combines a square Janus crystal structure, symmetry-protected Weyl points in the majority-spin channel, a substantial spin-orbit-coupling-induced gap of \(\sim 92.8\) meV, dual dissipationless chiral edge channels, controllable valley polarization, and a Curie temperature of \(161\) K. The resulting picture is a single monolayer in which topological transport, valley degrees of freedom, and ferromagnetism are simultaneously present, with proposed relevance to spintronics, topological quantum physics, and nonvolatile multistate memory architectures [2509.02654].

## 1. Crystal structure and stability

Monolayer Ti\(_2\)TeSO adopts a square (tetragonal) Janus structure in space group \(P4mm\) (No. 99) with point-group \(C_{4v}\) [2509.02654]. The optimized lattice constants are \(a=b=4.15\) \AA. The primitive cell contains five atoms, arranged as a Ti-O layer sandwiched between Te on the top side and S on the bottom side. Typical bond lengths from geometry optimization are Ti-O \(\simeq 2.00\) \AA, Ti-Te \(\simeq 2.60\) \AA, and Ti-S \(\simeq 2.35\) \AA, and the Ti atoms are in a distorted octahedral environment with Ti-O-Te/S bond angles close to \(90^\circ\) and \(120^\circ\).

The reported stability analysis includes both dynamical and thermal criteria. The phonon dispersion shows no imaginary modes over the entire two-dimensional Brillouin zone, which confirms dynamical stability. Thermal stability is examined by ab initio molecular dynamics at \(300\) K for \(5\) ps in a \(3\times 3\) supercell, where no structural reconstruction is observed and the energy fluctuations remain within \(\pm 10\) meV per unit. This combination of phonon stability and finite-temperature robustness indicates that the monolayer is not merely a formal structural model but a dynamically and thermally stable two-dimensional phase under the reported conditions [2509.02654].

## 2. Spin-resolved electronic structure and half-semi-Weyl-metal character

Without spin-orbit coupling, the spin-resolved band structure is strongly asymmetric between the two spin channels [2509.02654]. In the majority-spin channel, two symmetry-protected linear band crossings appear exactly at the Fermi level: one on the \(\Gamma\)-X line and one on \(\Gamma\)-Y. These crossings belong to different irreducible representations, \(A'\) and \(A''\) of \(C_s\), which forbids hybridization. By contrast, the minority-spin channel is semiconducting with a gap \(\simeq 1\) eV. The system is therefore described as a fully spin-polarized half-semi-Weyl-metal state, with \(100\%\) spin polarization at \(E_F\).

The orbital character near the Fermi level is reported to derive from Ti-\(d_{z^2}/d_{xy}\), Te-\(p_x/p_y\), and S-\(p_z\) states. This orbital composition places transition-metal \(d\) states and chalcogen/pnictogen-like \(p\) states directly in the low-energy manifold. A plausible implication is that the low-energy topology is governed not only by magnetic exchange splitting but also by the orbital-selective band connectivity that permits symmetry-protected Weyl crossings in only one spin sector.

A common simplification would be to identify the material merely as a ferromagnetic semiconductor with spin splitting. That description is incomplete in the reported calculation. The defining feature is instead the coexistence of a semiconducting minority-spin channel and majority-spin Weyl points pinned to the Fermi level, which is why the material is classified specifically as a half-semi-Weyl-metal rather than a generic spin-polarized two-dimensional magnet [2509.02654].

## 3. Spin-orbit coupling, Berry curvature, and topological classification

When spin-orbit coupling is included, a direct band gap \(\Delta_{\mathrm{SOC}} \simeq 92.8\) meV opens at each Weyl point [2509.02654]. The same calculation reports band inversion between Ti-\(d\) and Te/S-\(p\) states, which is taken as the signature of a topological phase transition. In this regime, the Berry curvature for each occupied band \(n\) is defined as

\[
\Omega_n(k) = -2\, \mathrm{Im}\langle \partial_{k_x}u_n(k) \mid \partial_{k_y}u_n(k)\rangle,
\]

and the total Berry curvature is \(\Omega(k)=\sum_n \Omega_n(k)\). The calculated \(\Omega(k)\) is concentrated around the former Weyl points, where the Berry-curvature hot spots have the same sign.

The topological invariant is the Chern number,

\[
C = \frac{1}{2\pi} \int_{BZ} d^2k\, \Omega(k),
\]

for which numerical integration yields \(C=2\). The anomalous Hall conductivity is therefore

\[
\sigma_{xy} = C e^2/h = 2 e^2/h,
\]

and the calculation shows a quantized plateau within the SOC gap, specifically within \(\pm 46\) meV around \(E_F\). On a semi-infinite ribbon along \([010]\), two chiral edge modes per boundary traverse the bulk gap, confirming a high-Chern-number \((C=2)\) Chern insulator [2509.02654].

The significance of \(C=2\) in this context is operational as well as topological. The reported edge spectrum implies dual dissipationless chiral edge channels rather than the single edge channel associated with \(C=1\). This directly addresses the limitation, emphasized in the abstract, that systems with only one edge state can hinder practical applications [2509.02654].

## 4. Valley polarization and its control mechanisms

The study reports two independent control routes for valley polarization: uniaxial strain and magnetization-direction manipulation [2509.02654]. Under \(1\%\) uniaxial strain along \(x\), the \(C_4\) symmetry is broken, which lifts the degeneracy between the two valleys on \(\Gamma\)-X and \(\Gamma\)-Y. The resulting valley splitting is \(\Delta E_v \simeq 20\) meV between the conduction-band minima. Despite this symmetry breaking, the anomalous Hall conductivity remains quantized at \(2 e^2/h\), and two edge channels persist. The reported interpretation is the coexistence of QAHE and anomalous valley Hall effect.

The second control parameter is the direction of magnetization. The angle \(\theta\) is defined between the in-plane magnetization and the \(x\)-axis. Without SOC, one Weyl point on \(\Gamma\)-Y remains gapless for \(\theta=0^\circ\), while the \(\Gamma\)-X Weyl point acquires a gap of \(\simeq 82.4\) meV. As \(\theta\) rotates from \(0^\circ\) to \(90^\circ\), the two valley gaps, denoted \(\Delta_1\) along \(\Gamma\)-X and \(\Delta_2\) along \(\Gamma\)-Y, exchange: \(\Delta_1\) decreases and \(\Delta_2\) increases linearly, reaching \(\Delta_1 \leftrightarrow \Delta_2\) inversion at \(\theta=90^\circ\). The reported conclusion is that valley-polarization reversal can be achieved solely by magnetization rotation [2509.02654].

These results place monolayer Ti\(_2\)TeSO at the intersection of topological transport and valleytronics. In the strict sense reported in the paper, the two valleys are not only symmetry-related features of the band structure; they are active control targets whose energy ordering can be selected by strain or by rotating the magnetization. This suggests a route to multistate operation in which topological edge transport and valley-selective electronic structure are present simultaneously.

## 5. Magnetic ground state and finite-temperature ferromagnetism

The calculated magnetic ground state is ferromagnetic [2509.02654]. Relative to the FM state at \(0\) meV, the competing magnetic configurations are higher in energy: Neél AFM at \(161\) meV, stripe AFM at \(79\) meV, zigzag AFM at \(122\) meV, and the nonmagnetic state at \(462\) meV. The local magnetic moment on Ti is \(\simeq 0.8\, \mu_B\).

To parameterize magnetic interactions, the study adopts the Heisenberg model

\[
H = J_1 \sum_{\langle ij\rangle} S_i \cdot S_j + J_2 \sum_{\langle\langle ij\rangle\rangle} S_i \cdot S_j + A \sum_i (S_{iz})^2.
\]

The reported parameters are

\[
J_1 = (E_{FM} - E_{Ne\acute{e}l})/8 = -20.19 \text{ meV}/S^2,
\]

\[
J_2 = [E_{FM}+E_{Ne\acute{e}l} - 2E_{Stripe}]/16 = 0.26 \text{ meV}/S^2,
\]

and a magnetic anisotropy

\[
A = 1.04 \text{ meV}/S^2.
\]

From Monte Carlo simulations, the Curie temperature is obtained from the susceptibility peak as \(T_C \simeq 161\) K [2509.02654].

The coexistence of a sizable SOC gap and \(T_C \simeq 161\) K is central to the physical interpretation advanced in the paper. The authors state that this temperature scale indicates the plausibility of coexistence of valley polarization and topological states at elevated temperatures. A cautious reading is that the material is positioned between low-temperature topological model systems and room-temperature device aspirations: the reported \(T_C\) approaches liquid-\(\mathrm{N}_2\) temperatures, while the AIMD stability analysis extends to \(300\) K.

## 6. Device implications and conceptual significance

The reported application logic follows directly from the topological and valleytronic properties [2509.02654]. A high-Chern-number state with \(C=2\) implies two parallel dissipationless edge channels, which the paper identifies as ideal for multi-channel interconnects with reduced contact resistance. Tunable valley polarization, achieved either by \(1\%\) uniaxial strain or by magnetization rotation, is proposed as a basis for nonvolatile multistate memory elements using the valley degree of freedom. The relatively large SOC gap of approximately \(93\) meV and the moderate Curie temperature of \(161\) K are cited as indicators of feasible operation at elevated temperatures in spintronics and topological quantum devices.

Within the scope of the reported results, monolayer Ti\(_2\)TeSO is significant because several ingredients that are often pursued separately are realized in one two-dimensional ferromagnet: a fully spin-polarized half-semi-Weyl-metal state before SOC, a SOC-driven \(C=2\) Chern-insulating state, two chiral edge modes per boundary, and externally tunable valley splitting [2509.02654]. This suggests a materials platform in which QAHE, high-Chern-number edge transport, and valley control are not competing effects but mutually compatible features of the same electronic structure.

A further conceptual point is that the material addresses two practical bottlenecks identified in the abstract: spin entanglement and the possession of only one edge state \((C=1)\). In the reported monolayer, the minority-spin states lie far away from the Fermi level, while the majority-spin channel hosts the relevant Weyl physics. After SOC opens the gap, the resulting topological state carries \(C=2\), not \(C=1\). In that sense, the Ti\(_2\)TeSO monolayer is presented not simply as another two-dimensional QAHE candidate, but as a specific high-Chern-number ferromagnetic Janus monolayer in which multi-channel dissipationless transport and valley-selective control emerge from the same microscopic framework [2509.02654].

Source: https://www.emergentmind.com/topics/monolayer-ti2teso