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Characterization of spin relaxation anisotropy in Co using spin pumping

Yi Li, Wei Cao, and W. E. Bailey
Phys. Rev. B 94, 174439 – Published 23 November 2016

Abstract

Ferromagnets are believed to exhibit strongly anisotropic spin relaxation, with relaxation lengths for spin longitudinal to the magnetization significantly longer than those for spin transverse to the magnetization. Here, we characterize the anisotropy of spin relaxation in Co using the spin pumping contribution to Gilbert damping in noncollinearly magnetized Py1xCux/Cu/Co trilayer structures. The static magnetization angle between Py1xCux and Co, adjusted under field bias perpendicular to film planes, controls the projections of longitudinal and transverse spin current pumped from Py1xCux into Co. We find nearly isotropic absorption of pure spin current in Co using this technique; fits to a diffusive transport model yield the longitudinal spin relaxation length <2 nm in Co. The longitudinal spin relaxation lengths found are an order of magnitude smaller than those determined by current-perpendicular-to-planes giant magnetoresistance measurements, but comparable with transverse spin relaxation lengths in Co determined by spin pumping.

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  • Received 12 February 2015
  • Revised 23 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.174439

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yi Li*, Wei Cao, and W. E. Bailey

  • Materials Science and Engineering, Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA

  • *yl2600@columbia.edu
  • web54@columbia.edu

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Issue

Vol. 94, Iss. 17 — 1 November 2016

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Images

  • Figure 1
    Figure 1

    (Left) Noncollinear magnetization alignment of the F1/N/F2 trilayer at the FMR condition for F1. (Right) m1 is driven into precession, pumping spin current into m2, with spin components both longitudinal (σL) and transverse (σT) to the m2 magnetization.

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  • Figure 2
    Figure 2

    (a) Perpendicular (nc-FMR) resonance field μ0Hres for Py1xCux single layers and Py1xCux/Cu/Co trilayers, x=00.4, as a function of frequency ω/2π. (b) Effective magnetization μ0Meff extracted from (a) as a function of x. (c) Resonance linewidths μ0ΔH1/2 of the Py0.8Cu0.2 single layer and trilayer as a function of frequency ω/2π. The spin pumping enhancement is clearly visible in the increased slope (α) of the trilayer data; the low-frequency deviation is discussed in Fig. 3. (d) Effective spin mixing conductances geff of Py1xCux/Cu/Co, Py1xCux/Cu/Pt, and Co/Cu/Pt.

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  • Figure 3
    Figure 3

    pc- and nc-FMR linewidths for single (Py) and trilayer (Py/Cu/Co) structures, introducing MgO interlayers to suppress spin pumping. Dashed lines are linear fits to pc-FMR linewidths. Solid curves assume (magnetostatic) interlayer coupling of 10 mT acting on Py and reproduce the low-frequency upturn in linewidth, seen to be present equally with and without MgO. (Inset) enhancements of nc-FMR linewidth over pc-FMR linwidth for the three samples.

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  • Figure 4
    Figure 4

    Spin pumping contribution to linewidth in pc- and nc-FMR. (a)–(d) Linewidth enhancement of Py1xCux between single layers and trilayers in pc- and nc-FMR, x=0.10.4. Solid lines are linear fits to the pc data (crosses); dashed curves are predicted from Eq. (1) using λsrL=38 nm. The shadows at ω/2π10 GHz denote where the low-frequency linewidth broadenings are significant.

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  • Figure 5
    Figure 5

    Angle-dependent linewidth ratio ΔH1/2tri/ΔH1/2single. The shadowed region shows the average with error bar (1.50±0.02). (Inset) Angular dependence of μ0ΔH1/2 for Py0.8Cu0.2 and Py0.8Cu0.2/Cu/Co at ω/2π=10 GHz. Solid lines are macrospin calculations.

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  • Figure 6
    Figure 6

    (a) Magnetization configuration of the asymmetric F1/N/F2 trilayer. (b) An instant in which the spin polarization of Is1pump is orthogonal to both m1 and m2. μsN is also orthogonal to m1 and m2. (c) An instant in which the spin polarization of Is1pump is in the same plane of m1 and m2. μsN is also in the same plane of m1 and m2.

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  • Figure 7
    Figure 7

    Resonance peak of Co and Py0.8Cu0.2 independently measured in Py0.8Cu0.2/Cu/Co with θH=18 (a) and 9 (b). The resonance frequency of Py0.8Cu0.2 are both 10 GHz. The resonance frequency of Co is adjusted so that the μ0Hres of Co is equal to Py0.8Cu0.2. Dashed curves show the theoretical prediction of Co resonance signals.

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