Time-resolved magnetic relaxation of a nanomagnet on subnanosecond time scales

Liu, H.; Bedau, D.; Sun, J. Z.; Mangin, Stéphane; Fullerton, Eric E.; Katine, J. A.; Kent, Andrew D.

doi:10.1103/physrevb.85.220405

Cited by 20 publications

(4 citation statements)

References 24 publications

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“…We consider a material with saturation magnetization M s = 713 × 10 3 A/m, exchange constant A = 8.3 × 10 −12 J/m, and anisotropy constant K = 403 × 10 3 J/m 3 -parameters similar to those of Co/Ni thin film nanomagnets studied experimentally in Refs. [13][14][15]. A constant field perpendicular to the film µ 0 H z was applied with a maximum magnitude equal to the coercive field, defined by…”

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confidence: 99%

Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

Chaves-O'Flynn

Vanden‐Eijnden

Stein

et al. 2013

Journal of Applied Physics

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Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The leading-order dependence of magnetization reversal rates are governed by the energy barrier the system needs to surmount in order for reversal to proceed. In this paper we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than the magnetization flipping as a rigid unit, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases the energy barriers are smaller than those expected for coherent magnetization reversal.Thin film elements with perpendicular magnetic anisotropy (PMA) can have magnetization directions that are thermally stable at room temperature at the nanometer scale, a feature that makes them useful in information storage and processing, for example in patterned media [1] and spin-transfer MRAM [2]. A key issue in determining stability is how the energy barriers and transition states of these elements depend on their lateral size. For elements larger than the exchange length (typically ∼ 5 nm in transition metal ferromagnets) the assumption of coherent reversal of the magnetization breaks down and the transition state is not uniformly magnetized. Due to the multiscale character of micromagnetism, analytical calculations are complicated and transition states have been calculated only for a handful of physical systems [3][4][5]. Numerical calculations are usually necessary for the majority of systems. In this paper, we use the string method [6] to find the transition states and activation energies in thin film elements with PMA.Transition state theory indicates that reversal occurs through states corresponding to critical points of the magnetization energy functional, where ∇ M E = 0. The probability for thermally induced magnetization reversal is expected to follow the Arrhenius law e −U/kBT where U is the energy difference between the transition state and the metastable configuration [7]. Here, we identify the minimum energy paths (MEPs) on the energy landscape, which allow us to determine the transition states; we then study the dependence of these states, along with their corresponding energy barriers, on sample size and geometry. Our two main conclusions are: (i) typically, models that assume uniform magnetization seriously overestimate the magnitude of the activation energy, especially in larger systems; and (ii) even in situations where the assumption of uniform...

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Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

Chaves-O'Flynn

Vanden‐Eijnden

Stein

et al. 2013

Journal of Applied Physics

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“…A similar process has also been studied experimentally: the relaxation of excited magnetic states in adsorbates. [38][39][40] Indeed, in the case of supported magnetic objects, electrons from the substrate continuously collide with adsorbates and go back into the substrate, and they can induce magnetic transitions in the adsorbate in a similar manner as tunneling electrons; in this way, an excited magnetic state can be de-excited by an electron-hole pair creation 35,41,42 (see a review in Ref. 43).…”

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confidence: 99%

Magnetic reversal of a quantum nanoferromagnet

Gauyacq

Lorente

2013

Phys. Rev. B

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When the external magnetic field applied to a ferromagnetically coupled atomic chain is reversed suddenly, the magnetization of the chain switches, due to the reversal of all the atomic magnetic moments in the chain. The quantum processes underlying the magnetization switching and the time required for the switching are analyzed for model magnetic chains adsorbed on a surface at 0 K. The sudden field reversal brings the chain into an excited state that relaxes towards the system ground state via interactions with the substrate electrons. Different mechanisms are outlined, ranging from the global stepwise rotation of the chain macrospin induced by spin-flip collisions with substrate electrons in the pure Heisenberg chain (Néel-Brown process) to a correlation-mediated direct switching process in the presence of strong magnetic anisotropies in short chains (the global spin of the chain reverses in a single electron interaction). The processes for magnetization switching induced by electrons tunneling from a scanning tunneling microscope tip are also analyzed.

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“…The process studied may therefore be described as a thermally activated single energy barrier crossing with no memory effect, as shown for other DW depinning processes [34,35]. This telegraph noise behavior is a slow dynamic regime (from several seconds to a few minutes) in which thermal activation plays an important role, in contrast to the faster dynamic regime (below few milliseconds) in which other phenomena dominate [36][37][38].…”

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confidence: 89%