We experimentally investigate and quantitatively analyze the spin Hall magnetoresistance effect in ferromagnetic insulator/platinum and ferromagnetic insulator/nonferromagnetic metal/platinum hybrid structures. For the ferromagnetic insulator, we use either yttrium iron garnet, nickel ferrite, or magnetite and for the nonferromagnet, copper or gold. The spin Hall magnetoresistance effect is theoretically ascribed to the combined action of spin Hall and inverse spin Hall effect in the platinum metal top layer. It therefore should characteristically depend upon the orientation of the magnetization in the adjacent ferromagnet and prevail even if an additional, nonferromagnetic metal layer is inserted between Pt and the ferromagnet. Our experimental data corroborate these theoretical conjectures. Using the spin Hall magnetoresistance theory to analyze our data, we extract the spin Hall angle and the spin diffusion length in platinum. For a spin-mixing conductance of 4×1014 ??1m?2, we obtain a spin Hall angle of 0.11±0.08 and a spin diffusion length of (1.5±0.5) nm for Pt in our thin-film samples

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Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids

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Spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids

We discuss recent progress regarding size effects and their incidence upon the coefficients describing charge transport (resistivity, magnetoresistance, and Hall effect) induced by electron scattering from disordered grain boundaries and from rough surfaces on metallic nanostructures; we review recent measurements of the magneto transport coefficients that elucidate the electron scattering mechanisms at work. We review as well theoretical developments regarding quantum transport theories that allow calculating the increase in resistivity induced by electron-rough surface scattering (in the absence of grain boundaries) from first principles—from the parameters that describe the surface roughness that can be measured with a Scanning Tunnelling Microscope (STM). We evaluate the predicting power of the quantum version of the Fuchs-Sondheimer theory and of the model proposed by Calecki, abandoning the method of parameter fitting used for decades, but comparing instead theoretical predictions with resistivity m...

Size effects and charge transport in metals: Quantum theory of the resistivity of nanometric metallic structures arising from electron scattering by grain boundaries and by rough surfaces

We report the electric conductivity of three-dimensional (3D) nanoporous gold at low temperatures and in strong magnetic fields. It was found that topologically disordered 3D nanoporosity leads to extremely low magnetoresistance and anomalous temperature dependence as the characteristic length of nanoporous gold is tuned to be approximately 14 nm. This study underscores the importance of 3D topology of a nanostructure on electronic transport properties and has implications in manipulating electron transport by tailoring 3D nanostructures.

Unusually small electrical resistance of three-dimensional nanoporous gold in external magnetic fields.

The knowledge on the influence of surface roughness and the electron–phonon (el–ph) interaction on electrical transport properties of nanoscale metal films is important from both fundamental and technological points of view. Here we report a study of the temperature dependent electron transport properties of nanoscale copper films by measuring temperature dependent electrical resistivity with thickness ranging from 4 to 500 nm. We show that the residual resistivity, which is temperature independent, can be described quantitatively using both measured vertical surface root-mean-square roughness and lateral correlation length in the nanoscale, with no adjustable parameter, by a recent quasi-classical model developed by Chatterjee and Meyerovich (2010 Phys. Rev. B 81 245409–10). We also demonstrate that the temperature dependent component of the resistivity can be described using the Bloch–Gruneisen equation with a thickness dependent el–ph coupling constant and a thickness dependent Debye temperature. We show that the increase of the el–ph coupling constant with the decrease of film thickness gives rise to an enhancement of the temperature dependent component of the resistivity.

https://iopscience.iop.org/article/10.1088/0957-4484/26/7/075704/pdf

Effects of nanoscale surface roughness on the resistivity of ultrathin epitaxial copper films.

We report measurements of the Hall effect performed on 4 gold films evaporated onto mica substrates where the signal arises primarily from electron-surface scattering. The measurements were performed at low temperatures $T$ ($4\text{ }\text{ }\mathrm{K}\ensuremath{\le}T\ensuremath{\le}50\text{ }\text{ }\mathrm{K}$) under high magnetic field strengths $B$ ($1.5\text{ }\text{ }\mathrm{T}\ensuremath{\le}B\ensuremath{\le}9\text{ }\text{ }\mathrm{T}$), with $\mathbf{B}$ oriented perpendicular to the films.

Size effects under a strong magnetic field: Hall effect induced by electron-surface scattering on thin gold films deposited onto mica substrates under high vacuum.

We report the Hall constant RH, drift mobility μD, and Hall mobility μH measured at 4 K in thin gold films deposited on mica substrates, where the dominant electron scattering mechanism is electron-surface scattering. RH increases with increasing film thickness and decreases with increasing magnetic field. For high magnetic fields B≥6 T, RH turns out to be approximately independent of magnetic field, and its value is close to that of the free electron model. We use the high magnetic field values of RH to determine film thickness. This nondestructive method leads to a determination of film thickness that agrees to within 10% with the thickness measured by other techniques. The theoretical predictions, based upon the theory of Fuchs–Sondheimer and the theory of Calecki, are at variance with experimental observations.

Size effects on the Hall constant in thin gold films

Resistivity of thin gold films on mica induced by electron–surface scattering: Application of quantitative scanning tunneling microscopy

We report measurements of transverse magnetoresistance where the signal can be attributed to electron–surface scattering, together with measurements of the surface roughness of the films on an atomic scale. The measurements were performed with a scanning tunnelling microscope (STM) on four thin gold films evaporated onto mica. The magnetoresistance exhibits a marked thickness dependence: at 4 K and 9 T is about 5% for the thinner (69 nm) film, and about 14% for the thicker (185 nm) film. Sondheimer's theory provides an accurate description of the temperature dependence of the resistivity, but predicts a magnetoresistance one order of magnitude smaller than that observed at 4 K. Calecki's theory in the limit of small roughness correlation length, predicts a resistivity two orders of magnitude larger than observed at 4 K.

Marcelo Robles

Papers

Size effects under a strong magnetic field: Hall effect induced by electron-surface scattering on thin gold films deposited onto mica substrates under high vacuum.

Size effects on the Hall constant in thin gold films

Resistivity of thin gold films on mica induced by electron–surface scattering: Application of quantitative scanning tunneling microscopy

Size effects under a strong magnetic field: transverse magnetoresistance of thin gold films deposited on mica