Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

Berger, Jorge

doi:10.1103/physrevb.75.184522

Cited by 19 publications

(34 citation statements)

References 63 publications

(119 reference statements)

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“…The parameter NA in the ballistic limit is a function of the domain wall resistance [2] R DW with NA ¼ e 2 nAR DW Á=P@ ¼ e 2 n DW Á 2 =P@ with n the electron density, A the lateral cross section of the wire, DW ¼ R DW A=Á the DW resistivity. For n ¼ 5:6 Â 10 28 m À3 in Co [25], a DW resistivity DW ¼ 3:9 Â 10 À10 m can be derived from the T sample ¼ 250 K value ( DW ¼ 0:9 Â 10 À10 m for T sample ¼ 300 K) that agrees with the DW resistivity measured by Aziz et al [26] in similar Ptð3:5 nmÞ=Coð0:6 nmÞ=Ptð1:6 nmÞ structures at room temperature ( DW ¼ 2:3 Â 10 À10 m). The momentum transfer is thus a possible mechanism to explain our experimental results.…”

Section: -2 Densitymentioning

confidence: 99%

Nonadiabatic Spin Transfer Torque in High Anisotropy Magnetic Nanowires with Narrow Domain Walls

et al. 2008

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Current induced domain wall (DW) depinning of a narrow DW in out of plane magnetized ðPt=CoÞ 3 =Pt multilayer elements is studied by magnetotransport. We find that for conventional measurements Joule heating effects conceal the real spin torque efficiency and so we use a measurement scheme at a constant sample temperature to unambiguously extract the spin torque contribution. From the variation of the depinning magnetic field with the current pulse amplitude we directly deduce the large nonadiabaticity factor in this material and we find that its amplitude is consistent with a momentum transfer mechanism. DOI: 10.1103/PhysRevLett.101.216601 PACS numbers: 72.25.Ba, 75.60.Ch, 75.75.+a The recent discovery that a spin-polarized current can displace a domain wall (DW) through the spin transfer from conduction electrons to the local magnetization [1] has opened up an alternative approach to manipulate magnetization. Current induced domain wall motion (CIDM) has been investigated experimentally so far in detail in permalloy (Py; Ni 80 Fe 20 ) nanowires characterized by wide DWs (>100 nm) where the spin of a conduction electron is expected to follow adiabatically the magnetization direction as the electron passes across the DW [1,2]. A key question that has been raised is whether the spin transfer effect contains nonadiabatic contributions due to spin relaxation or nonadiabatic transport [2][3][4][5][6]. It was predicted [3,7] that from the efficiency of the spin transfer effect, which is measured by probing the dependence of the DW propagation magnetic field on the injected current, the nonadiabaticity can be deduced. However, in Py nanowires, the complicated 2D spin structures of the DWs prevent direct comparison to 1D models and a meaningful comparison to full 2D micromagnetic simulations is only possible if the exact spin structure during pulse injection is known, which is generally not the case. In particular, the wall deformations and transformations that have been observed [8] can render the results impossible to interpret in terms of the nonadiabaticity.To obtain simple DW spin structures, out-of-plane magnetized materials with a strong uniaxial anisotropy can be used where the simple Bloch or Néel DW spin structure is more apt for an analysis using an analytical 1D model including the nonadiabatic torque terms. In addition, a larger nonadiabaticity is expected in these materials due to the larger magnetization gradient for such narrow DWs [2,4,9]. This larger nonadiabaticity may explain the high efficiency of the current induced DW depinning reported recently in such materials [10,11]. However, another major obstacle for the determination of the nonadiabaticity from the dependence of the DW depinning magnetic field on current is that Joule heating strongly affects the thermally activated DW depinning. For experiments carried out at a constant cryostat temperature, it is thus hard to extract directly the contribution from the spin transfer torque.In this Letter we probe CIDM in out-of-plane magnetized ðPt=C...

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Section: -2 Densitymentioning

confidence: 99%

Nonadiabatic Spin Transfer Torque in High Anisotropy Magnetic Nanowires with Narrow Domain Walls

et al. 2008

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“…The case of fluctuations in open wires, or of rings that do not enclose magnetic flux, was studied elsewhere [3].…”

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confidence: 99%

A Nonconventional Scenario for Thermal Equilibrium

Berger

2007

Found Phys

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“…The only modification that is required in order to apply the procedure of Ref. 16 is in the boundary condition forψ, which in the case that flux Φ is enclosed becomesψ(L) = exp(2πiΦ/Φ 0 )ψ(0).…”

Section: A One-dimensional Loopsmentioning

confidence: 99%

The influence of thermal fluctuations on uniform and nonuniform superconducting rings according to the Ginzburg–Landau and the Kramer–Watts-Tobin models

Berger¹

2011

J. Phys.: Condens. Matter

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We evaluate the influence of thermal fluctuations on superconducting rings that enclose a magnetic flux, using the time-dependent Ginzburg-Landau model (TDGL) or the Kramer-Watts-Tobin model (KWT), while thermal fluctuations are accounted for by means of Langevin terms. This method is applicable in situations where previous methods are not, such as for nonuniform loops, rings with large width to radius ratio and loops with large coherence length to perimeter ratio. We evaluate persistent currents, the position and statistical behavior of flux-induced vortices, and the lifetime of metastable fluxoid states. The influence of nonuniformity on the persistent current does not depend strongly on the details of the cross section profile; it depends mainly on its first harmonic, but not only on it. As a consequence of nonuniformity the maximum of the persistent current shifts to smaller fluxes and the passage between fluxoid states remains non-hysteretic down to lower temperatures than in the case of a uniform sample. Our results obtained using TDGL agree remarkably well with recent measurements of the persistent current in superconducting rings and with measurements of the position of a vortex that mediates between fluxoid states in an asymmetric disc with a hole; they could also provide a plausible explanation for the unexpectedly short measured lifetimes of metastable states. Comparison of TDGL and KWT indicates that they lead to the same results for the persistent current, whereas KWT leads to larger lifetimes than TDGL.

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Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

Cited by 19 publications

References 63 publications

Nonadiabatic Spin Transfer Torque in High Anisotropy Magnetic Nanowires with Narrow Domain Walls

Nonadiabatic Spin Transfer Torque in High Anisotropy Magnetic Nanowires with Narrow Domain Walls

A Nonconventional Scenario for Thermal Equilibrium

The influence of thermal fluctuations on uniform and nonuniform superconducting rings according to the Ginzburg–Landau and the Kramer–Watts-Tobin models

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