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Dissecting spin-phonon equilibration in ferrimagnetic insulators by ultrafast lattice excitation

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Science Advances  13 Jul 2018:
Vol. 4, no. 7, eaar5164
DOI: 10.1126/sciadv.aar5164
  • Fig. 1 Ultrafast probing of spin-phonon interactions.

    (A) Experimental principle. A terahertz pump pulse resonantly and exclusively excites optical phonons of a ferrimagnet. The impact on the sample magnetization is monitored by the Faraday rotation θ of a subsequent femtosecond probe pulse. By using an electric insulator, the electronic orbital degrees of freedom remain unexcited (see red crosses). (B) Part of the unit cell of ferrimagnetic YIG. Magnetic Fe3+ ions at tetrahedral d sites and octahedral a sites comprise, respectively, the majority and minority spin sublattice of the ferrimagnet. The pump pulse resonantly excites a TO(Γ) optical phonon associated with a Fe-O stretch vibration at the tetrahedral d site.

  • Fig. 2 Ultrafast phonon-induced dynamics of magnetic order.

    (A) Terahertz absorptance of the BiGa:YIG film (black solid line). Pump intensity spectra are either resonant (red) or nonresonant (blue) with the TO(Γ) phonon absorption band. Open circles show the pump-induced Faraday signal 10 ps after sample excitation as a function of the pump pulse center frequency. (B) Pump-induced change Δθ in Faraday rotation for resonant and off-resonant pumping on ultrafast and (C) microsecond time scales normalized to the equilibrium Faraday signal θ0 = θ(−2 ps). The incident fluence is 10 mJ cm−2. Panel (B) also shows the isotropic transient change in the sample transmittance for resonant pumping (thin black solid line). Dashed lines in (B) and (C) are single-exponential fits with time constants of τfast = 1.6 ps and τslow = 90 ns, respectively. The inset of (C) displays the ultrafast Faraday signal Δθ(10 ps) as a function of the incident pump-pulse fluence. Data are taken at a temperature of 296 K.

  • Fig. 3 Two regimes of spin-lattice equilibration.

    (A) Equilibrium Faraday rotation θ0 = θ(−2 ps) versus ambient temperature T0 along with a fit to an analytical function (thin solid line). (B) Pump-induced change Δθ in the Faraday rotation at t = 10 ps (red symbols) and 1 μs (blue) after pump-pulse arrival. The black curve is the change (∂θ0/∂T0T in the Faraday rotation expected from the increase ΔT of the sample temperature due to heating by the pump pulse. θ0(T0) is taken from (A) (thin solid line), and ΔT = 0.39 K is calculated from the absorbed pump energy and the heat capacity of the excited volume.

  • Fig. 4 Atomistic spin-dynamics simulations.

    (A) Schematic of our model of ultrafast spin-phonon coupling. Thermal motion of the O2− ion modulates the superexchange constant Jad of the adjacent a-Fe3+ and d-Fe3+ spins, thereby enabling transfer of spin angular momentum between a- and d-spin sublattices. (B) Evolution of a- and d-spin sublattice magnetizations as obtained by atomistic spin-dynamics simulations. From 0 to 0.5 ps, thermal modulation of the exchange constant Jad is switched on (orange square). The variance of the Jad fluctuation is proportional to the difference ΔT between crystal lattice and spin temperature. To obtain agreement of the slope of ΔMa(t) with that found in the experiment directly after pump excitation (−0.1% ps−1; see Fig. 2B), where ΔT = 0.39 K (see Fig. 3B), an approximately three times smaller ∂Jad/∂u of ~10 Jad Å−1 than used here has to be chosen.

  • Fig. 5 Constrained state and spin-phonon equilibration in YIG.

    (A) Calculated change in sublattice magnetization Ma and Md per increase of temperature T0, without and with the constraint of constant spin angular momentum. The constrained and unconstrained ∂Md/∂T0 curves exhibit good qualitative agreement with the measured Faraday signals Δθ(10 ps) and Δθ(1 μs) versus T0 shown in Fig. 3B. (B) Schematic of spin-phonon equilibration in YIG. [1] Pump-excited TO(Γ) phonons [2] increase the population of other lattice modes. The increased thermal modulation of the a-d exchange by ΔJad(t) leads to [3a] transfer of angular momentum between a- and d-spin sublattices, accompanied by [3b] energy transfer from the phonon to the spin system on the time scale τfast = 1.6 ps. The resulting state is constrained by ΔMa + ΔMd = 0 and decays by [4] transfer of angular momentum and energy between crystal lattice and electron spins on the τslow = 90 ns scale. This process is mediated by SO and/or SSMD coupling.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/7/eaar5164/DC1

    Supplementary Methods

    1. Details of YIG ab initio calculations.

    Fig. S1. Experimental details.

    Fig. S2. Supporting pump-probe data.

    Fig. S3. Nonmagnetic signal contributions.

    Fig. S4. Ab initio phonon calculations.

    Fig. S5. Supporting data of atomistic spin-dynamics simulations.

    Fig. S6. Calculated equilibrium sublattice magnetizations.

    References (4648)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Methods
    • 1. Details of YIG ab initio calculations.
    • Fig. S1. Experimental details.
    • Fig. S2. Supporting pump-probe data.
    • Fig. S3. Nonmagnetic signal contributions.
    • Fig. S4. Ab initio phonon calculations.
    • Fig. S5. Supporting data of atomistic spin-dynamics simulations.
    • Fig. S6. Calculated equilibrium sublattice magnetizations.
    • References (4648)

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