Nonreciprocal magnons in layered antiferromagnets VPX3(X =S,Se,Te)

Technical Summary: Nonreciprocal Magnons in Layered Antiferromagnets VPX$_3$ (X = S, Se, Te)

Problem Statement
Nonreciprocal magnons, characterized by energy differences in propagation along opposite wavevectors ($k$ and $-k$), are critical for modern spintronic applications. While nonreciprocal behavior is well-established in noncentrosymmetric electronic systems and certain bulk magnets, realizing robust nonreciprocal magnons in two-dimensional (2D) van der Waals (vdW) layered antiferromagnetic (AFM) insulators remains a significant challenge. Existing candidates face limitations: transition metal phosphorus trichalcogenides (MPX$_3$) often possess inversion-symmetric zigzag ground states that forbid nonreciprocity, while honeycomb AFM insulators with Néel order (e.g., MnPS$_3$) typically exhibit extremely weak Dzyaloshinskii-Moriya interactions (DMI) and XY-type spin orders that hinder experimental verification.

Methodology
The authors employ a combined approach of density-functional theory (DFT) calculations and effective spin model analysis to investigate the layered honeycomb antiferromagnets VPX$_3$ (where X = S, Se, Te).

1. DFT Calculations: Used to determine the ground state magnetic configurations, exchange parameters ($J_1, J_2, J_3$), single-ion anisotropy ($K$), and DMI components ($D_x, D_y, D_z$) for monolayer, bilayer, and trilayer structures.
2. Effective Spin Modeling: Constructed a Heisenberg spin Hamiltonian including up to third-nearest-neighbor (3NN) exchange interactions and 2NN DMI.
3. Linear Spin Wave (LSW) Theory: Solved using the Holstein-Primakoff transformation and Bogoliubov transformation to derive magnon dispersion relations.
4. Many-Body Effects: Incorporated magnon-magnon interactions (four-magnon terms) to assess the stability of nonreciprocity at elevated temperatures.
5. Symmetry Analysis: Analyzed the role of inversion symmetry ($P$), time-reversal symmetry ($T$), and their combined effective symmetry ($T'$) in governing the existence of nonreciprocal modes.

Key Contributions and Results

• Identification of Robust Nonreciprocal Magnons: The study identifies VPX$_3$ (particularly VPSe$_3$ and VPTe$_3$) as ideal candidates for robust nonreciprocal magnons. The nonreciprocity arises primarily from a "giant" second-nearest-neighbor (2NN) DMI between V$^{2+}$ ions, driven by heavy ligands (Se, Te) despite the weak spin-orbit coupling of the vanadium ions.
• Monolayer Behavior:
  • In monolayers, the Néel order breaks inversion symmetry, and the 2NN DMI ($D_z$) breaks the effective time-reversal symmetry ($T'$), leading to nonreciprocal magnon bands.
  • The energy difference between $K$ and $K'$ points ($\epsilon_r$) is substantial: ~3.2 meV for VPTe$_3$, ~2 meV for VPSe$_3$, and ~0.4 meV for VPS$_3$.
  • The nonreciprocity persists and can even be enhanced at higher temperatures when magnon-magnon interactions are included.
  • Néel Vector Dependence: A novel finding is the asymmetric periodic dependence of $\epsilon_r$ on the orientation of the Néel vector. The nonreciprocity is modulated by the angles of the Néel vector, offering a potential route to probe AFM order parameters in the 2D limit.
• Layer-Dependent Odd-Even Effects:
  • Bilayers: In bilayer VPX$_3$ with antiferromagnetic (AFM) interlayer coupling, the magnetic order preserves inversion symmetry ($P$), resulting in symmetric magnon bands ($\epsilon(k) = \epsilon(-k)$) and the absence of nonreciprocal magnons.
  • Trilayers: In trilayers, the magnetic order naturally breaks $P$ symmetry, restoring nonreciprocal magnons. However, the system exhibits three distinct magnon bands with varying nonreciprocity directions and magnitudes.
  • Tunability: The magnitude of nonreciprocity in trilayers is strongly coupled to the interlayer coupling strength ($J_c$). Since $J_c$ can be tuned via external pressure (e.g., 5 GPa increases $J_c$ to ~2 meV), the nonreciprocal properties are highly tunable.
• Scaling Behavior: For multilayer systems with ferromagnetic interlayer coupling, the nonreciprocity of the minor band decreases as the layer number ($l_n$) increases, following a $\epsilon_r \propto 1/\sqrt{l_n}$ trend for $l_n > 3$. This confirms the fundamentally 2D nature of the phenomenon.

Significance and Claims
The paper claims to provide a solution to the elusive problem of finding robust nonreciprocal magnons in 2D vdW antiferromagnets. The significance lies in three main areas:

1. Material Platform: VPX$_3$ offers a material system with giant 2NN DMI and robust Néel order, overcoming the limitations of previous candidates like MnPS$_3$.
2. Control Mechanisms: The study demonstrates that nonreciprocal magnons in these systems can be controlled not only by the intrinsic DMI but also by external parameters such as layer number, interlayer coupling (via pressure/strain), and the orientation of the Néel vector.
3. Detection of Order Parameters: The asymmetric periodic dependence of nonreciprocity on the Néel vector suggests a novel experimental method for probing AFM order parameters in the 2D limit, potentially via magnon Hall transport phenomena.

The authors conclude that these findings offer a promising foundation for future wave-based, ultra-compact spintronic applications, emphasizing the high degree of tunability and the unique layer-dependent physics of these layered antiferromagnets.