[Paper Review] Antiferromagnetic resonance and terahertz continuum in $α-$RuCl$_3$

Arielle Little, Liang Wu+9 more|arXiv (Cornell University)|Apr 24, 2017

Magnetism in coordination complexes4 citations

TL;DR

This study uses time-domain terahertz spectroscopy to investigate spin dynamics in the zig-zag antiferromagnet α-RuCl₃, revealing a sharp antiferromagnetic resonance (AFMR) at 2.56 meV below the Néel temperature (7 K), which broadens and shifts under magnetic fields, indicating a transition to a spin-disordered phase. The work establishes a direct, internally calibrated measurement of AFMR spectral weight, placing an upper bound on the contribution of a magnetic excitation continuum to the dc susceptibility.

ABSTRACT

We report measurements of optical absorption in the zig-zag antiferromagnet $α$-RuCl$_3$ as a function of temperature, $T$, magnetic field, $B$, and photon energy, $\hbarω$ in the range $\sim$ 0.3 to 8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that 3-fold rotational symmetry is broken in the honeycomb plane from 2 K to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at $B=0$ that we identify as magnetic-dipole excitation of a zero-wavevector magnon, or antiferromagnetic resonance (AFMR). With application of $B$, the AFMR broadens and shifts to lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the $dc$ susceptibility from a magnetic excitation continuum.

Motivation & Objective

• To probe the dynamic spin response of α-RuCl₃ in the terahertz range to assess its proximity to a quantum spin liquid state.
• To determine the evolution of the antiferromagnetic resonance (AFMR) under varying temperature, magnetic field, and photon energy.
• To measure the spectral weight of the AFMR and constrain the contribution of a magnetic excitation continuum to the dc susceptibility.
• To investigate the origin of a broadband THz conductivity with a linear ω cutoff below 1 meV, potentially linked to spin degrees of freedom.
• To assess the role of Kitaev and parasitic exchange interactions in driving quantum criticality in α-RuCl₃.

Proposed method

• Time-domain terahertz spectroscopy was employed to measure optical absorption in α-RuCl₃ across 0.3–8.3 meV photon energy, with polarization control to probe anisotropy.
• Polarized measurements were used to detect the breaking of 3-fold rotational symmetry in the honeycomb plane from 2 K to 300 K.
• The AFMR frequency, damping rate, and spectral weight were extracted as functions of temperature and magnetic field via Lorentzian fitting of the absorption peak.
• Optical conductivity σ₁(ω) was calculated from the absorption coefficient using σ₁(ω) = 2nY₀α(ω), with Y₀ = 377 Ω⁻¹.
• The spectral weight of the AFMR was directly calibrated internally to bound the contribution of a magnetic excitation continuum to the dc susceptibility.
• Comparisons were made with phonon modes and non-magnetic contributions to rule out lattice or electronic origins of the low-energy THz response.

Experimental results

Research questions

• RQ1 What is the nature of the sharp absorption peak at 2.56 meV observed below T_N = 7 K, and how does it evolve under magnetic fields?
• RQ2 To what extent does the AFMR spectral weight contribute to the dc magnetic susceptibility, and what does this imply about the presence of a spin-liquid-like continuum?
• RQ3 What is the origin of the broadband THz absorption with a linear ω cutoff below 1 meV, and could it be related to spin degrees of freedom?
• RQ4 How does the breaking of 3-fold rotational symmetry in the honeycomb plane vary with temperature and magnetic field?
• RQ5 What is the role of Kitaev and parasitic exchange interactions in driving the observed quantum critical behavior in α-RuCl₃?

Key findings

• A sharp antiferromagnetic resonance (AFMR) peak at 2.56 meV is observed below the Néel temperature (7 K), identified as a zero-wavevector magnon excitation.
• Application of magnetic field causes the AFMR to broaden and shift to lower frequency, consistent with the destruction of long-range magnetic order and a transition to a spin-disordered phase.
• The spectral weight of the AFMR is directly and internally calibrated, allowing an upper bound to be placed on the contribution of a magnetic excitation continuum to the dc susceptibility.
• The optical conductivity σ₁(ω) exhibits a linear ω cutoff below ~1 meV that persists up to room temperature, with σ(0) ≈ 3×10⁻⁴ Ω⁻¹ cm⁻¹, indicating a strongly suppressed dc response.
• The broadband THz absorption cannot be explained by phonon modes or standard electronic transitions, as the dominant phonon resonance is at ~35 meV and Lorentzian fits fall short of the measured low-energy response.
• The observed low-energy THz response resembles theoretical predictions for the Kitaev-Heisenberg model, suggesting a possible spin-origin for the conductivity, with optical conductance per Ru layer ~10⁻⁴(e²/h), comparable to that in Herbertsmithite.