Spin-dependent Mean Free Paths Research Articles

A Monte Carlo study of the spin polarization of secondary electrons

A spin‐involved Monte Carlo simulation model is developed to study the mechanism of the spin polarization of secondary electrons. The spin‐dependent mean free path asymmetry and the Stoner excitation are considered in modeling electron inelastic scattering, and the spin‐dependent excitation mechanism of cascade electrons is introduced according to the spin density of the state of a magnetism sample. The simulation has been performed for Ni and Fe. The simulated results, including secondary electron yields, secondary electron energy spectrum, and spin polarization of secondary electrons, are in good agreement with experimental results. According to the present simulation results, it is concluded that the high spin polarization of secondary electrons less than approximately 5 eV is inherently related to the cascade production process of secondary electrons; a more obvious effect of Stoner excitation is found for Ni but not for Fe because of the lack of unoccupied 3d states for spin‐majority electrons above the Fermi level for Ni. We have further studied the case that an unpolarized thin layer exists on Fe surface; the results show that the spin polarization of secondary electrons can be greatly affected at low primary energies. Copyright © 2012 John Wiley & Sons, Ltd.

Loss of polarization in a hot-electron current through electron-electron scattering

By utilizing the spin-dependent mean free paths in Co, a polarizer-analyzer system for hot electrons has been established, enabling ballistic electron emission microscopy to measure the effects of scattering on the spin-dependent transport of hot electrons. Through the gradual oxidation of Al, it is possible to controllably increase the scattering effects of a Cu–Al–Cu spacer layer. As scattering increases, the measured polarization exiting the spacer decreases. The effect is explained by a straightforward Auger-like hot-electron scattering process which conserves spin flux but reduces the polarization of a hot-electron current through generation of energetic electron-hole pairs.

Determining the spin dependent mean free path in Co90Fe10 using giant magnetoresistance

The spin dependent mean free path in Co90Fe10 is determined as a function of temperature down to 5K using two different spin valve structures. At 5K the spin dependent mean free path for one structure was measured to be 9.4±1.4nm, decreasing by a factor of 3 by 350K. For the other structure, it is 7.5±0.5nm at 5K and decreased by a factor of 1.5 by 350K. In both cases, the spin dependent mean free path approaches the typical thickness of ferromagnetic layers in spin valves at room temperature and, thus, has an impact on the choice of design parameters for the development of new spintronic devices.

Theory of proximity effect in superconductor/ferromagnet heterostructures

We present a microscopic theory of proximity effect in the ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures where S is s-wave low-T_c superconductor and F's are layers of 3d transition ferromagnetic metal. Our approach is based on the solution of Gor'kov equations for the normal and anomalous Green's functions together with a self-consistent evaluation of the superconducting order parameter. We take into account the elastic spin-conserving scattering of the electrons assuming s-wave scattering in the S layer and s-d scattering in the F layers. In accordance with the previous quasiclassical theories, we found that due to exchange field in the ferromagnet the anomalous Green's function F(z) exhibits the damping oscillations in the F-layer as a function of distance z from the S/F interface. In the given model a half of period of oscillations is determined by the length \xi_m^0 = \pi v_F/E_ex, where v_F is the Fermi velocity and E_ex is the exchange field, while damping is governed by the length l_0 = (1/l_{\uparrow} + 1/l_{\downarrow})^{-1} with l_{\uparrow} and l_{\downarrow} being spin-dependent mean free paths in the ferromagnet. The superconducting transition temperature T_c(d_F) of the F/S/F trilayer shows the damping oscillations as a function of the F-layer thickness d_F with period \xi_F = \pi/\sqrt{m E_ex}, where m is the effective electron mass. We show that strong spin-conserving scattering either in the superconductor or in the ferromagnet significantly suppresses these oscillations. The calculated T_c(d_F) dependences are compared with existing experimental data for Fe/Nb/Fe trilayers and Nb/Co multilayers.

Spin dependent mean-free path of low-energy electrons in ferromagnetic materials

Abstract Spin resolved attenuation measurements of electrons transmitted through overlayers of Fe and Co show that the electron inelastic mean free path (IMFP) in these materials is spin-dependent at low energies. The spin-up IMFP is larger than the spin-down IMFP. The values from different studies are in reasonable agreement. The data suggest that the origin of the spin dependence is mainly due to inelastic processes. Effects from spin dependent elastic scattering have not been identified directly in these experiments. The spin filter effect based on preferential attenuation of spin-down electrons can be used as a basis of spin polarization detectors.

Giant tunnel magnetoresistance in multilayered metal/oxide structures comprising multiple quantum wells

From a theoretical point of view, we have investigated the transport properties in metal/oxide multilayer structures of the form M/O/M/O/M/O/M where M represent ferromagnetic layers alternating with three insulating barriers (O = oxide). The two inner magnetic layers form two quantum wells, the depths of which are spin dependent. For particular thicknesses of these magnetic layers, resonances occur in the quantum wells which lead to strong increase in the electron transmission through the insulating barriers. We show that if the magnetization in the successive magnetic layers can be changed from parallel to antiparallel as in spin-valves, then, for particular values of the thicknesses of the two inner magnetic layers, very large magnetoresistance effects can be expected due to the interplay of resonance effects in the two neighbouring quantum wells. The conductivity and magnetoconductivity are calculated within a quantum theory of linear response (Kubo formalism) taking into account the scattering in the magnetic layers. We show that in such a structure, giant tunnel magnetoconductivity can arise not only from a difference between spin up and spin down Fermi wave-vectors in the magnetic layers but also from spin-dependent mean free paths. In the latter case, the effect of the scattering is to induce a spin-dependent broadening of the resonances in the quantum wells.

Anisotropic magnetotransport properties of cobalt thin films

Anisotropic magnetoresistance of order 1% was measured on a series of cobalt films. A − M 2 effect was observed in the out-of-plane magnetoresistance and a large extraordinary Hall effect was also found for applied fields B 0 smaller than the saturation polarisation J s. The origin of the − M 2 effect is discussed in the light of the different spin dependent mean free paths of majority and minority carriers recently measured in cobalt.

Direct measurement of spin dependent mean free paths in metals (abstract)

We describe results obtained using a new spin valve structure that is specifically designed to measure the spin up and spin down mean free paths in ferromagnetic metals. We report how these mean free paths can be measured more directly and with greater accuracy than previous methods, which were based mostly on indirect evidence from magnetoresistance in ternary alloys. The technique is based on the ‘‘backed’’ spin valve layered structure: substrate/seed/80 Å FeMn/50 Å NiFe/23 Å Cu/20 Å NiFe/t Å b/50 Å Ta where the back layer of material b with thickness t is probed by the rest of the structure, which forms a spin polarized conduction electron source. As t is varied the majority carrier mean free path λ+b in the layer b is obtained directly from the form taken by the change in film conductance between parallel and antiparallel magnetization states, ΔG, whose solution of the Boltzmann transport equation shows is well approximated by the form ΔG=ΔG0+ΔGb{1−exp([t−tx]/βλ+b)}, where ΔG0 arises from the 20 Å NiFe layer, tx is the high resistivity region of intermixing at the b layer interfaces, and β≂1 from observations with b=Cu. The minority carrier mean free path in a ferromagnetic layer b, λb, is obtained by comparing ΔG and λ+b with ΔG′, and λb′+, of a nonmagnetic b′ layer of similar resistivity to b; it is a less direct measurement than that of λ+ since it relies on the connection between conductivity and mean free path for the minority subband. We have obtained room temperature results for Ni80Fe20 (λ+=46±3 Å, 0<λ<6 Å), Fe (λ+=15±2 Å, λ=21±5 Å), and Co (λ+=55±4 Å, 0<λ<8 Å). The connection of spin dependent conductivity and mean free paths in ferromagnetic metals is crucial in exploring the mechanism of giant magnetoresistance and, more broadly, is central in all theories of transport in magnetic metals; this new technique should prove a powerful tool in measuring these fundamental quantities.

Giant magnetoresistance of magnetically soft sandwiches: Dependence on temperature and on layer thicknesses.

We present comprehensive results on the magnetoresistive properties of spin-valve sandwiches comprising glass/M(1)/Cu/${\mathrm{Ni}}_{80}$${\mathrm{Fe}}_{20}$/${\mathrm{Fe}}_{50}$${\mathrm{Mn}}_{50}$/Cu, where M(1) is a ferromagnetic transition metal or alloy (Co,Ni,${\mathrm{Ni}}_{80}$${\mathrm{Fe}}_{20}$). We discuss the thermal variation of the magnetoresistance (\ensuremath{\Delta}R/R) and its dependence on the thicknesses of the layers constituting the active part of the spin-value sandwich [i.e., M(1)/Cu/NiFe]. An almost linear decrease of \ensuremath{\Delta}R/R is observed between 77 and 320 K. For a given ferromagnetic material, \ensuremath{\Delta}R/R extrapolates to zero at a temperature ${\mathit{T}}_{0\mathrm{S}\mathrm{V}}$ significantly lower than the Curie temperature, and independent of the ferromagnetic layer thickness. We have identified spin-\ensuremath{\uparrow} and spin-\ensuremath{\downarrow} intermixing by spin-wave scattering as responsible for the thermal decrease of the magnetoresistance. We show that the magnetoresistance arises within the ``active'' parts of the ferromagnetic layers of thickness of about 90 \AA{} located next to the M/Cu interfaces. We give a phenomenological expression relating \ensuremath{\Delta}R/R to the longer of the two spin-dependent mean free paths, and to current shunting in the inactive part of the sandwich. The thickness of the active region is independent of temperature.

Spin-dependent electron attenuation by transmission through thin ferromagnetic films.

Spin-polarized photoemission spectra at low photon energies from ferromagnetic ultrathin Fe layers on Cu(100) show a substantial polarization of the Cu 3d peaks. This is attributed to spin-dependent attenuation in the Fe overlayer. Values of the spin-dependent mean free path at low electron energies are obtained.

The role of inelastic exchange scattering in spin polarization experiments (invited) (abstract)

Inelastic exchange scattering of electrons can result in spin-dependent mean free paths (MFP) for electrons in ferromagnetic transition metals and glasses. The MFP of electrons with spin in the majority-spin direction will be greater than those with spin in the minority direction due to the larger number of empty minority-spin d states into which minority-spin electrons can scatter. This difference in MFP can explain the increase in the spin polarization of secondary electrons in transition metals and glasses that is observed at low energies. In addition, it will be shown that the ratio of the majority to minority spin MFP as a function of energy can be determined directly from measurements of the energy dependence of the secondary electron-spin polarization. A different type of experiment in which exchange is important is the production of Ni Auger electrons by the scattering of metastable He atoms from a Ni surface. The number of Auger electrons produced is found to depend on the relative spin of the He and Ni, parallel or antiparallel. The normalized difference of these two cases is found to increase with increasing energy of the Auger electrons. It is found that this effect is directly related to exchange scattering of the Ni electrons that neutralize the He atoms and that the experimental results can be accounted for by a simple model.