[Paper Review] Anisotropic Gigahertz Antiferromagnetic Resonances of the Easy-Axis van der Waals Antiferromagnet CrSBr

Thow Min Jerald Cham, Saba Karimeddiny+4 more|arXiv (Cornell University)|Jun 2, 2022

2D Materials and Applications31 references57 citations

TL;DR

This study reports gigahertz-frequency antiferromagnetic resonances in the van der Waals antiferromagnet CrSBr, using microwave absorption spectroscopy to map resonance modes as a function of applied magnetic field magnitude and angle. The experiments reveal anisotropic dynamics governed by interlayer exchange (µ₀Hₑ = 0.395(2) T) and triaxial magnetic anisotropy (µ₀Hc = 1.30(2) T, µ₀Ha = 0.383(7) T), with in-plane fields enabling control of mode hybridization via spin-flop transitions and symmetry selection rules.

ABSTRACT

We report measurements of antiferromagnetic resonances in the van der Waals easy-axis antiferromagnet CrSBr. The interlayer exchange field and magnetocrystalline anisotropy fields are comparable to laboratory magnetic fields, allowing a rich variety of gigahertz-frequency dynamical modes to be accessed. By mapping the resonance frequencies as a function of the magnitude and angle of applied magnetic field we identify the different regimes of antiferromagnetic dynamics. The spectra show good agreement with a Landau-Lifshitz model for two antiferromagnetically-coupled sublattices, accounting for inter-layer exchange and triaxial magnetic anisotropy. Fits allow us to quantify the parameters governing the magnetic dynamics: at 5 K, the interlayer exchange field is $\mu_0 H_E =$ 0.395(2) T, and the hard and intermediate-axis anisotropy parameters are $\mu_0 H_c =$ 1.30(2) T and $\mu_0 H_a =$ 0.383(7) T. The existence of within-plane anisotropy makes it possible to control the degree of hybridization between the antiferromagnetic resonances using an in-plane magnetic field.

Motivation & Objective

• To characterize the gigahertz-frequency antiferromagnetic resonance modes in the easy-axis van der Waals antiferromagnet CrSBr.
• To quantify the interlayer exchange field and triaxial magnetic anisotropy parameters in CrSBr using microwave spectroscopy.
• To investigate how applied magnetic fields, particularly in-plane fields, control the hybridization between acoustic and optical antiferromagnetic modes.
• To understand the role of magnetic anisotropy and symmetry in selecting observable resonance modes via Landau-Lifshitz modeling.
• To establish a quantitative framework for tuning antiferromagnetic dynamics in 2D magnetic materials for spintronic device integration.

Proposed method

• Microwave absorption spectroscopy using a coplanar waveguide to probe antiferromagnetic resonances in single-crystal CrSBr at 5 K.
• Application of external DC magnetic fields at variable angles (H∥ and H⊥ relative to the Néel vector) to map resonance frequency dependence.
• Use of a two-port vector network analyzer with low microwave power (-20 dBm) to ensure linear response and avoid heating effects.
• Modeling of the two-sublattice system using coupled Landau-Lifshitz equations with macrospin approximation, including interlayer exchange (−HE ˆm₂) and triaxial anisotropy (−Hc(ˆm·ĉ)ĉ − Ha(ˆm·â)â).
• Fitting of measured resonance spectra to the Landau-Lifshitz model to extract interlayer exchange and anisotropy fields.
• Symmetry analysis using 2-fold rotational invariance about the a-axis to explain selective excitation of acoustic modes in H⊥ configuration.

Experimental results

Research questions

• RQ1 How do the gigahertz-frequency antiferromagnetic resonance modes in CrSBr depend on the magnitude and orientation of applied magnetic fields?
• RQ2 What are the quantitative values of the interlayer exchange field and triaxial magnetic anisotropy fields in CrSBr at low temperature?
• RQ3 How does the presence of in-plane anisotropy in CrSBr enable control over mode hybridization using in-plane magnetic fields?
• RQ4 Why are only certain resonance modes (e.g., acoustic) observed in specific field configurations, and how does symmetry govern this selection?
• RQ5 To what extent do the experimental resonance spectra agree with predictions from a two-sublattice Landau-Lifshitz model including triaxial anisotropy?

Key findings

• At 5 K, the interlayer exchange field in CrSBr is quantified as µ₀Hₑ = 0.395(2) T, confirming weak interlayer coupling enabling gigahertz dynamics.
• The hard-axis anisotropy field is µ₀Hc = 1.30(2) T, and the intermediate-axis anisotropy field is µ₀Ha = 0.383(7) T, indicating strong triaxial anisotropy.
• Resonance spectra show a discontinuous transition at H∥ ≈ ±0.4 T, consistent with a spin-flop transition where the Néel vector reorients by 90° before saturating.
• In the H⊥ configuration (field along a-axis), only the acoustic mode is observed due to 2-fold rotational symmetry, which suppresses the optical mode.
• The optical mode is selectively excited only when the applied field breaks the symmetry, such as in H∥ configuration where both modes appear.
• Temperature-dependent fits show that the anisotropy and exchange parameters decrease with increasing temperature, approaching the Néel temperature (Tₙ ≈ 132 K).