Non-equilibrium dynamics of spin-lattice coupling

Abstract

Quantifying the dynamics of normal modes and how they interact with other excitations is of central importance in condensed matter. Spin-lattice coupling is relevant to several sub-fields of condensed matter physics; examples include spintronics, high-T_c superconductivity, and topological materials. However, experimental approaches that can directly measure it are rare and incomplete. Here we use time-resolved X-ray diffraction to directly access the ultrafast motion of atoms and spins following the coherent excitation of an electromagnon in a multiferroic hexaferrite. One striking outcome is the different phase shifts relative to the driving field of the two different components. This phase shift provides insight into the excitation process of such a coupled mode. This direct observation of combined lattice and magnetization dynamics paves the way to access the mode-selective spin-lattice coupling strength, which remains a missing fundamental parameter for ultrafast control of magnetism and is relevant to a wide variety of materials.

Fig. 1. Basic structures/characterization of Y-type hexaferrite.

a Crystal structure and b magnetic structure of the Y-type hexaferrite Ba_1.3Sr_0.7CoZnFe₁₁AlO₂₂. The magnetic structure is depicted by the representative magnetic moments of an S block and L block [μ_S (blue arrow) and μ_L (red arrow), respectively], which alternatively stack along [001]. c Proposed spin dynamics of the electromagnon in a Y-type hexaferrite: snapshots of the dynamics at different times, t₁ (phase 0) and t₂ (phase π). A pair of the same adjacent family of magnetic moments (μ_S1 and μ_S2, and μ_L1 and μ_L2) show anti-phase oscillations towards [001]. Such oscillations give rise to transient electric dipole moments along [001] through magnetostriction. d Temperature dependence of the real part, n, and e, the imaginary part, k, of the refractive index n+ik in the THz range, measured by THz-TDS. The white region is a frequency range where no transmission through the sample is detected because of strong absorption. The crystal structure was drawn by VESTA.

Fig. 2. tr-XRD signals.

a The incident THz pump pulse measured with electro-optic sampling at the sample position (see Methods for detail). b, THz pulse spectra, where blue and orange curves indicate data without and with the low-pass filter, respectively. c The (0 0 24) XRD intensity at 20 K as a function of pump-probe delay. The blue data show the XRD response for +E_THz, while the orange data show the response when inverting the phase of the THz electric field (−E_THz). d The FFT spectrum of the diffraction response. e Temperature dependence of the time-dependent diffraction intensity after insertion of a low-pass filter that cuts off components above 3 THz. f The FFT spectra of (e). Dashed lines in (a) and (e) highlight the phase shift of π/2 between the incident THz pulse and the (0 0 24) XRD intensity.

Fig. 3. tr-RSXD magnetic scattering signals.

a The incident THz pulse measured with electro-optic sampling at the sample position. b THz pulse spectrum. c The antiferromagnetic (0 0 4.5) diffraction intensity at various temperatures as a function of pump-probe delay. d The FFT spectra of (c). Dashed lines in (a) and (c) are guides for the eyes to visualize the phase shift of π between the incident THz pulse and the magnetic (0 0 4.5) diffraction intensity.