FR-02 Energy Landscape of Noncollinear Exchange Coupled Magnetic Multilayers
Creators: George Lertzman-Lepofsky
Afan Terko
Sabri Koraltan
Dieter Suess
Erol Girt and Claas Abert
Publisher: name: IEEE
Year: 2025

Spin-transfer and spin-orbit torque magnetic random-access memory (STT/SOT-MRAM) designs promise to combine the density and low-cost of dynamic RAM, the performance of static RAM, and the non-volatility of traditional magnetic hard drives [1], and yet the switching currents and write-error-rates of state-of-the-art devices remain unacceptably large [2,3]. In this work [4], we conduct an exploration of the energy landscape of two coupled ferromagnetic layers with perpendicular-to-plane uniaxial anisotropy, Ku, using finite-element micromagnetic simulations [5]. These multilayers can be used to produce noncollinearity in the reference layers of STT/SOT-MRAM cells [6], which has been shown to increase the performance of these classes of MRAM by ensuring a non-zero spin-torque at the beginning of switching processes [7]. We show that there exists a range of values of the interlayer exchange coupling constants, J1 and J2, for which the magnetic state of these multilayers can relax into either one or two energy minima, depending on the initial conditions of the multilayer, parallel (PP) or antiparallel (AP), Fig. 1. A noncollinear antiparallel state with one minimum is optimal for use in STT/SOT devices and Fig. 1(c) shows that there is a wide range of experimentally achievable coupling constants that can produce such alignment. This range increases with the difference in the ferromagnetic layer anisotropies. We further investigate the thermal stability of the structures in the two minima regions, using string method simulations to determine the energy barriers. We show that the stabilities of the minima increase with increasing difference in the anisotropy of the ferromagnetic layers. Finally, we provide an analytical solution to the location of the minima in the energy landscape of coupled macrospins, which has good agreement with our micromagnetic results for a simplified case involving ferromagnetic layers with the same thickness and anisotropy.References: [1] A. V. Khvalkovskiy, D. Apalkov, S. Watts, et al., J. Phys. D: Appl. Phys., Vol. 46, p.074001 (2013). [2] A. D. Kent and D. C. Worledge, Nat. Nanotechnol., Vol. 10, p.187 (2015). [3] D. C. Worledge, 2023 IEEE International Reliability Physics Symposium (IRPS), p.1 (2023) [4] G. Lertzman-Lepofsky, A. Terko, S. Koraltan, Physical Review B, Vol. 109, p.224421 (2024). [5] C. Abert, L. Exl, F. Bruckner, J. Magn. Magn. Mater., Vol. 345, p.29 (2013). [6] Z. R. Nunn, C. Abert, D. Suess, and E. Girt, Sci. Adv., Vol. 6, p.eabd8861 (2020). [7] R. Sbiaa, J. Phys. D:Appl. Phys., Vol. 46, p.395001 (2013).
Spin-transfer and spin-orbit torque magnetic random-access memory (STT/SOT-MRAM) designs promise to combine the density and low-cost of dynamic RAM, the performance of static RAM, and the non-volatility of traditional magnetic hard drives [1], and yet the switching currents and write-error-rates of state-of-the-art devices remain unacceptably large [2,3]. In this work [4], we conduct an exploration of the energy landscape of two coupled ferromagnetic layers with perpendicular-to-plane uniaxial anisotropy, Ku, using finite-element micromagnetic simulations [5]. These multilayers can be used to produce noncollinearity in the reference layers of STT/SOT-MRAM cells [6], which has been shown to increase the performance of these classes of MRAM by ensuring a non-zero spin-torque at the beginning of switching processes [7]. We show that there exists a range of values of the interlayer exchange coupling constants, J1 and J2, for which the magnetic state of these multilayers can relax into either one or two energy minima, depending on the initial conditions of the multilayer, parallel (PP) or antiparallel (AP), Fig. 1. A noncollinear antiparallel state with one minimum is optimal for use in STT/SOT devices and Fig. 1(c) shows that there is a wide range of experimentally achievable coupling constants that can produce such alignment. This range increases with the difference in the ferromagnetic layer anisotropies. We further investigate the thermal stability of the structures in the two minima regions, using string method simulations to determine the energy barriers. We show that the stabilities of the minima increase with increasing difference in the anisotropy of the ferromagnetic layers. Finally, we provide an analytical solution to the location of the minima in the energy landscape of coupled macrospins, which has good agreement with our micromagnetic results for a simplified case involving ferromagnetic layers with the same thickness and anisotropy.References: [1] A. V. Khvalkovskiy, D. Apalkov, S. Watts, et al., J. Phys. D: Appl. Phys., Vol. 46, p.074001 (2013). [2] A. D. Kent and D. C. Worledge, Nat. Nanotechnol., Vol. 10, p.187 (2015). [3] D. C. Worledge, 2023 IEEE International Reliability Physics Symposium (IRPS), p.1 (2023) [4] G. Lertzman-Lepofsky, A. Terko, S. Koraltan, Physical Review B, Vol. 109, p.224421 (2024). [5] C. Abert, L. Exl, F. Bruckner, J. Magn. Magn. Mater., Vol. 345, p.29 (2013). [6] Z. R. Nunn, C. Abert, D. Suess, and E. Girt, Sci. Adv., Vol. 6, p.eabd8861 (2020). [7] R. Sbiaa, J. Phys. D:Appl. Phys., Vol. 46, p.395001 (2013).