Entropy-Reduced Retention Times in Magnetic Memory Elements : A Case of the Meyer-Neldel Compensation Rule

Author / Creator

MMM 2020 (2020)

Conferences

MMM 2020 R3: MRAM, Magnetic Logic, and Related Devices (2020)

Available as

Online

Summary

The Meyer-Neldel (MN) rule, also known as entropy-enthalpy compensation, is a peculiar phenomenon that has been reported across diverse fields of the natural sciences, in semiconductors, chemical r...

The Meyer-Neldel (MN) rule, also known as entropy-enthalpy compensation, is a peculiar phenomenon that has been reported across diverse fields of the natural sciences, in semiconductors, chemical reactions, biology, etc [1]. In magnetism, it was very recently observed in the decay of the skyrmion lattice [2]. Consider a family of thermally activated processes whose rates k obey an Arrhenius-type law, i.e., k = f0 exp(-βΔE), in which ΔE is the internal energy barrier, β = (kBT)-1 is Boltzmann's factor, and f0 is the Arrhenius prefactor - the so-called "attempt frequency". If the Meyer-Neldel rule applies, the prefactor scales like an exponential of the energy barrier. In this work, we compute the mean waiting time between thermally activated magnetization reversals in a nanodisk, with parameters that resemble that of a free CoFeB layer, as used in magnetic random access memories [3]. We use two independent approaches, namely Langer's theory [4] and forward flux sampling [5]. By varying the perpendicular anisotropy, and the interfacial Dzyaloshinkii-Moriya interaction (DMI), we find that the Arrhenius prefactor can take extreme, seemingly non-physical values up to 1021 Hz, which is orders of magnitude beyond the typically assumed value of 109 Hz, and vary drastically as a function of material parameters. We show that it behaves like an exponential of the energy barrier, ΔE, which stems from a linear variation of the activation entropy, ΔS, with the energy barrier, thereby demonstrating a new case of the Meyer-Neldel rule (Fig. 1). Our results show that the Arrhenius prefactor is not an attempt frequency, because it also contains an important entropic contribution which cannot be neglected in complex systems. This suggests that modelling information retention times with a barrier-independent prefactor in magnetic storage elements is not justified [6].References: [1] A. Yelon, B. Movaghar, and R. Crandall, Reports on Progress in Physics, Vol. 69, p.1145 (2006) [2] J. Wild, T. N. Meier, S. Pollath et al., Science Advances, Vol. 3, p. e1701704 (2017) [3] J. Sampaio, A. Khvalkovskiy, M. Kuteifan et al., Applied Physics Letters, Vol. 108, p.112403 (2016) [4] J. S. Langer, Annals of Physics, Vol. 54, p. 258 (1969) [5] R. J. Allen, P. B. Warren, and P. R. ten Wolde, Physical Review Letters, Vol. 94, p. 018104 (2005) [6] L. Desplat and J.-V. Kim, submitted (2020)

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