The Multi-Scale Dynamics of All-Optical Exchange Bias Reversal

TL;DR

The paper addresses the challenge of achieving rapid, field-free reprogramming of exchange bias in FM/AFM stacks. It introduces a multi-scale framework that couples ultrafast magnetization dynamics via the layered three-temperature model (M3TM) for the ferromagnetic layers with a thermally activated, grain-resolved Arrhenius model for the antiferromagnet, incorporating a log-normal grain-size distribution to predict $h_{EB}(t)$. Experimentally, it demonstrates all-optical reversal of $H_{EB}$ with a single femtosecond pulse and observes long-term creep of the exchange bias, which the model reproduces as slow AFM-grain relaxation after fs excitation. The results identify key levers—temperature relaxation time $\tau_D$, grain size distribution, and material parameters such as $T_N$ and $K_{AF}$—and show IrMn occupies a favorable regime for stable yet switchable exchange bias, offering design guidelines for optically reprogrammable devices. Overall, the work provides a predictive framework to optimize multi-layer stacks for fast and long-lasting exchange-bias control at ultrafast timescales.

Abstract

Pinning magnetization in a ferromagnetic thin film is commonly realized through exchange biasing with an adjacent antiferromagnet. Field-cooling from above the Néel temperature is a reliable yet slow re-pinning method in exchange-biased systems. For on-demand reprogrammable devices, localized and rapid exchange bias repinning methods are essential. Recent work has shown that femtosecond laser pulses enable field-free reversal of exchange bias in tailored multilayer stacks. Contrary to field-cooling, our experiments with ultrafast excitation reach hitherto unexplored regimes in the exchange bias setting process. Here, we unravel these observations by considering both ultrafast magnetization dynamics on the femto- to picosecond timescale and slow heat-driven dynamics on millisecond timescales and upwards. We develop a microscopic framework of exchange bias setting in a polycrystalline antiferromagnetic thin film like IrMn that provides a complete description of the observations in our present experiments and those found in literature. We expand the use of our model by identifying material platforms and stack designs that lead to optimized performance, aiding further development of optically reprogrammable devices.

Figures (7)

• Figure 1: (a) Experimentally measured map of the exchange bias field magnitude $H_{\mathrm{EB}}$ across a region of the sample that was illuminated by a single femtosecond Gaussian laser spot with a peak fluence of 38mJ□cm. The measurement is performed by Kerr microscopy field sweeps directly after laser excitation, where $H_{\mathrm{EB}}$ is locally extracted from the hysteresis curve field shift. (b) The same measurement as in (a) but performed 100days after illumination. (c) Radial cross-sections of the distribution of $H_{\mathrm{EB}}$ as indicated by the orange and green lines in (a) and (b). (d) A demonstration of the evolution of $H_{\mathrm{EB}}$ from a newly deposited and switched sample over the period of two weeks, for both the annealed (red) and switched (blue) regions from (a). The dashed lines are guides to the eye.
• Figure 2: (a) Overview of the simulated stack, consisting of in total 15 atomic monolayers of Gd, Co, Pt/Co (modeled as a single compound ferromagnet) and IrMn (modeled as a layered antiferromagnet). The symbol $\mathcal{J}_{ij}$ represents the exchange coupling between atoms of species $i$ and $j$. (b) Schematic of the processes modeled by the M3TM framework, exemplified for Gd and Co. The lines represent the energy levels for the various spin quantum numbers $s_{i}$ which are spaced by the exchange splitting $\Delta_{i}$. On top is shown the Elliot-Yafet (EY) spin-flip scattering by creation/annihilation of a phonon and on the bottom is shown the exchange scattering (ex) between two electrons exchanging angular momentum. The green bars on the right represent the occupation fraction $f_{s,\ch{Gd}}$ of each spin level in Gd in equilibrium. (c) The evolution of temperature $T$ over time for illumination by a 58.3e8Jm laser pulse, also taking into account the difference between the electron ($T_{\mathrm{e}}$) and phonon ($T_{\mathrm{p}}$) temperatures within the first picosecond after excitation. The dashed line represents the Néel temperature $T_{\mathrm{N}}$. (d) Evolution of the layer-averaged magnetization $m$ in the Gd (red), Co (blue) and IrMn (green) subsystems, alongside de exchange bias parameter $n_{\mathrm{AF}}$. The dotted line before $0$ and the dashed lines after $\mathtt{\sim}$36ps represent their respective values in thermal equilibrium. Above the plot is indicated which modeling framework – M3TM or Arrhenius – is used in each temporal regime. Four key events are highlighted in roman numerals: (i) laser incidence, (ii) ferromagnetic reversal and remagnetization, (iii) $T$ dropping below $T_{\mathrm{N}}$ and antiferromagnetic remagnetization and (iv) freezing in of the exchange bias. (e) Plot of the log-normally distributed areas of the grains, with parameters $\mu$ and $\sigma$ as used in Eq. \ref{['eq:lognormal']}. The inset illustrates how the Arrhenius law is applied to the antiferromagnet (AFM). When the ferromagnet (FM) is uniformly magnetized up, the grains that contribute positively to the exchange bias have a lower energy than grains that contribute negatively. The energy required for a grain to spontaneously transition from up to down (down to up) is indicated by $E^{+}$ ($E^{-}$).
• Figure 3: (a) The temperature $T$ after laser excitation according to Eq. \ref{['eq:heatkernel']} for $\tau_{\mathrm{D}}=5ns$ (solid line) and $\tau_{\mathrm{D}}=50ns$ (dashed line). Time is measured from the moment that $T$ drops below the Néel temperature $T_{\mathrm{N}}=634K$ of IrMn. (b) Solutions to Eq. \ref{['eq:maf']} of the parameter $n_{\mathrm{AF}}$ for three different grain sizes (see the inset (c) for a distribution of the grain areas and the sampling of the three grain sizes). The smallest grain (red) is taken to be the critical grain area $A_{\mathrm{c}}$ for an antiferromagnet that is $t_{\mathrm{AF}}=5nm$ thick. The solid lines are simulated for a temperature relaxation time of $\tau_{\mathrm{D}}=5ns$ which is typical for the stacks used in the experiment. The dashed lines are simulated for an artificial but achievable value of $\tau_{\mathrm{D}}=50ns$. The solid horizontal lines at the top of (b) are the steady-state solutions of Eq. \ref{['eq:maf']} that represent thermal equilibrium.
• Figure 4: The normalized value of the exchange bias field $h_{\mathrm{EB}}$ reached at various time points $t_{\mathrm{meas}}$ after excitation, plotted as a function of the temperature relaxation timescale $\tau_{\mathrm{D}}$. The values are found by integrating the state of $n_{\mathrm{AF}}$ from the plots in Fig. \ref{['fig:3']} over the entire grain size distribution. The values are normalized to the maximum attainable value $H_{\mathrm{EB,max}}$ corresponding to the limiting case of an infinitely thick antiferromagnet at $T=0K$. The vertical dotted line corresponds to the expected value $\tau_{\mathrm{D}}=5ns$ for our stacks. The horizontal dashed line is the thermal equilibrium value of $h_{\mathrm{EB}}$ at room temperature according to Eq. \ref{['eq:hebeq']}.
• Figure 5: The value of $h_{\mathrm{EB}}$ integrated over all grain areas 1ms after laser excitation for different combinations of Néel temperature $T_{\mathrm{N}}$ and anisotropy constant $K_{\mathrm{AF},0}$. The stars indicate a selection of examples from real-world materials: IrMn Coey2001Vallejo-Fernandez2007Khamtawi2023, PtMn Coey2001Umetsu2006, NiMn Coey2001Vallejo-Fernandez2007Umetsu2006, FeMn Coey2001Vallejo-Fernandez2007 and MnN Meinert2015.