[Paper Review] Thermal conductivity and tunable thermal anisotropy of magnetic CrSBr monolayer

Marta Loletti, Alejandro Molina-Sánchez+3 more|arXiv (Cornell University)|Mar 2, 2026

Thermal properties of materials0 citations

TL;DR

First-principles study of in-plane thermal conductivity in monolayer CrSBr, revealing strong anisotropy (κxx/κyy ≈ 1.8 at 150 K) and showing anisotropy can be tuned by flake size through boundary scattering.

ABSTRACT

We present first-principles calculations of the thermal conductivity, ${\bm κ}$, of monolayer CrSBr, a van der Waals magnetic 2D material. We find a considerable thermal anisotropy, with a ratio $κ_{xx}/κ_{yy}$ of around 1.8. The anisotropy stems from a combined effect of phonon velocities and lifetimes and can be tuned by controlling the flake size by suppressing long mean path phonons.

Motivation & Objective

• Assess the ground-state magnetic order of CrSBr monolayers and its robustness under uniaxial and biaxial strain.
• Compute the full in-plane lattice thermal conductivity tensor κ for CrSBr monolayers at low temperatures (100–150 K).
• Analyze the origin of thermal anisotropy in CrSBr (phonon velocities and lifetimes) and how it is affected by flake size and boundary scattering.
• Evaluate how dimensional confinement can be used as a control knob to tune thermal anisotropy in 2D magnetic materials.

Proposed method

• Perform DFT+U calculations (PBE-D3 with Ueff=4 eV) to optimize CrSBr monolayers with FM and AFM ordering.
• Compute second- and third-order interatomic force constants (IFC2/IFC3) and solve the Boltzmann Transport Equation beyond the relaxation time approximation using almaBTE.
• Compute phonon dispersions with Phonopy/Phono3py ensuring rotational sum rules and 2D ZA mode quadratic dispersion.
• Use an effective thickness equal to bulk CrSBr interlayer spacing to define in-plane κ for the monolayer.
• Analyze convergence of κ with q-point mesh and consider finite-size effects (L) and boundary scattering on κxx and κyy.

Figure 1: (a) Top and (b) side views of ML CrSBr; Cr, S, and Br atoms are represented by blue, yellow, and brown spheres, respectively; $d$ indicates the distance between Br planes.

Experimental results

Research questions

• RQ1 What is the magnetic ground state of CrSBr monolayer and how robust is it under mechanical strain?
• RQ2 What is the in-plane thermal conductivity tensor of CrSBr monolayer at low temperatures, and what drives its anisotropy?
• RQ3 How do phonon velocities and lifetimes contribute to κxx vs κyy, and how are these affected by flake size?
• RQ4 Can geometric confinement modulate the thermal anisotropy in CrSBr monolayers?

Key findings

• κxx and κyy are 86.31 and 43.08 W m−1 K−1, respectively, at 150 K, yielding an anisotropy ratio κxx/κyy ≈ 1.8.
• The full solution of the phonon BTE (almaBTE) differs substantially from the RTA, with notable underestimation of κxx by ~25% in RTA.
• The FM ground state is robust under uniaxial and biaxial strain; ΔEFM−AFM remains negative across ±5% strain, indicating no FM→AFM transition in the studied range.
• Low-frequency phonon group velocities show v_x > v_y (Δv > 0 for ω ≲ 4 THz), contributing to κxx > κyy.
• Phonon lifetimes along x exceed those along y at low frequencies (Δτ > 0), reinforcing the observed anisotropy.
• Flake size modulates anisotropy: as L decreases from infinity to 100 nm, κxx/κyy rises from ~1.5 to ~1.77 (full BTE) but boundary scattering suppresses both components, with a maximum anisotropy around L ~1 μm.
• Boundary scattering suppresses long mean free path phonons, progressively reducing anisotropy in nanoscale flakes; intrinsic anisotropy is recovered in large samples.

Figure 2: (a) Phonon dispersion. (b) Thermal conductivity as a function of temperature. (c) $\Delta v=v_{x}-v_{y}$ and (d) $\Delta\tau=\tau_{x}-\tau_{y}$ as a function of frequency; before subtraction, velocities and lifetimes were averaged over intervals of 1 THz. Phonon lifetimes, $\tau_{i}$ with