Interlayer magnetophononic coupling in MnBi2Te4

Abstract

The emergence of magnetism in quantum materials creates a platform to realize spin-based applications in spintronics, magnetic memory, and quantum information science. A key to unlocking new functionalities in these materials is the discovery of tunable coupling between spins and other microscopic degrees of freedom. We present evidence for interlayer magnetophononic coupling in the layered magnetic topological insulator MnBi₂Te₄. Employing magneto-Raman spectroscopy, we observe anomalies in phonon scattering intensities across magnetic field-driven phase transitions, despite the absence of discernible static structural changes. This behavior is a consequence of a magnetophononic wave-mixing process that allows for the excitation of zone-boundary phonons that are otherwise 'forbidden' by momentum conservation. Our microscopic model based on density functional theory calculations reveals that this phenomenon can be attributed to phonons modulating the interlayer exchange coupling. Moreover, signatures of magnetophononic coupling are also observed in the time domain through the ultrafast excitation and detection of coherent phonons across magnetic transitions. In light of the intimate connection between magnetism and topology in MnBi₂Te₄, the magnetophononic coupling represents an important step towards coherent on-demand manipulation of magnetic topological phases.

Fig. 1. Phonon anomalies across magnetic phase transitions in MnBi₂Te₄.

a Crystal structure of MnBi₂Te₄. b Eigendisplacements of the A_1g⁽¹⁾ and A_1g⁽²⁾ modes, with arrows denoting displacement of ions. c, d Raman spectra of A_1g⁽¹⁾ (c) and A_1g⁽²⁾ (d) modes in the paramagnetic (PM) and antiferromagnetic (AFM) phases at 0 T, shown in red and blue respectively. e, f Raman spectra of A_1g⁽¹⁾ (e) and A_1g⁽²⁾ (f) modes in the AFM and ferromagnetic (FM) phases at 5 K, shown in blue, and purple respectively. (g, h) The difference between spectra in the AFM and FM phases. i, j Contour plots of the difference upon subtracting the 9 T spectrum, as a function of magnetic field. The dotted lines denote the FM and spin-flop critical fields.

Fig. 2. Phonon intensities track the antiferromagnetic order parameter.

a Temperature-dependent fractional change in integrated intensity, $\mathrm{\Delta }I/I_{35\mathrm{K}}$, of the A_1g⁽²⁾ mode, overlayed on integrated intensity of the (1 0 5/2) neutron diffraction peak from reference. The gray line is a fit to ${A\left(1-T/T_N\right)}^{2\beta }$, with β = 0.35, T_N = 24 K. b The field-dependent fractional change in  integrated intensity, $\mathrm{\Delta }I/I_{9\mathrm{T}}$, of the A_1g⁽¹⁾ and A_1g⁽²⁾ modes. The gray line is the AFM order parameter, given by $M-4.5$ µ_B, where M is the magnetization measured by magnetometry from reference. Error bars are standard deviations in fit values.

Fig. 3. Magnetophononic wave-mixing.

a Schematic of layered magnetic ordering in MnBi₂Te₄, with blue and purple denoting opposite in-plane spin orientations, and gray denoting disordered spins. The antiferromagnetic (AFM) wavevector is shown schematically, labeled “q_AFM”. b The dispersion relations of the A_1g⁽¹⁾ and A_1g⁽²⁾ modes along the c-axis, calculated using density functional theory. The experimental zone-center and zone-boundary phonon frequencies are denoted using colored and empty circles respectively. c Schematic of wave-mixing for zone-center and zone-boundary modes. The wavevectors of the photon (i = incident, r = reflected), phonon, and AFM spin-wave are shown using gray, green, and purple arrows (not drawn to scale). d Modulation of the interlayer exchange coupling $J^{\perp }$ by Raman phonons. Inset shows the eigendisplacements of two representative phonons. e Comparison between the calculated magnetophononic scattering cross-section $∣\frac{d{J}^{\perp }}{du}∣$ and the experimental zone-boundary ratio σ (see text for definition). Error bars are standard deviations in fit values. f Schematic of superexchange (SE) and super-superexchange (SSE), with Δ denoting the interlayer distance, θ denoting the Mn–Te–Mn bond angle, and pink and blue clouds denoting SE and SSE pathways, respectively.

Fig. 4. Ultrafast signatures of magnetophononic coupling.

a Schematic of pump-probe measurement. b Pump-induced changes in the transient reflectivity (ΔR/R) as a function of time delay at various magnetic fields, normalized to the maximum amplitude. The black line is a representative biexponential fit to the 0 T data. c The residual ΔR/R upon subtracting a biexponential fit. d Residual ΔR/R at 0 T, with black dots denoting experimental datapoints and the gray line denoting the fit to the sum of two decaying sinusoidal functions. e Individual decaying sinusoidal components obtained from the fit in (b), corresponding to the A_1g⁽¹⁾ (top) and A_1g⁽²⁾ (bottom) phonons, respectively. f Initial amplitude of the coherent A_1g⁽¹⁾ and A_1g⁽²⁾ phonons, obtained from fit result in (d). The gray line is the antiferromagnetic order parameter from reference. g Measured transient electron diffraction intensity of the (2 2 0) Bragg peak, with black dots denoting experimental datapoints, and the black line denoting the fit to an exponential decay function. Error bars are standard deviations in fit values.