Statistical characterization of the spin Hall magnetoresistance in YIG/Pt heterostructures

Abstract

The spin Hall magnetoresistance (SMR) is widely used to study the interplay between charge and spin currents in bilayers of a magnetic insulator and a normal metal. However, not much is known about the spatial variation of the SMR across the surface of one and the same sample. In this work, we investigate the statistical distribution of the SMR in hundreds of nominally identical Hall bar structures patterned into prototypical yttrium iron garnet (YIG)/Pt heterostructures. We find a Gaussian-distributed SMR with a narrow standard deviation of approximately 10$\,$% of the mean value in each YIG/Pt bilayer studied. However, the variation of the mean SMR between different YIG/Pt samples can be as large as ~30$\,$%, despite nominally identical fabrication conditions. This demonstrates that spatial variations of the SMR amplitude must not be neglected, in particular when comparing different heterostructures. On a microscopic level, local variations of the interface quality captured by the spin mixing conductance are the most likely origin for the observed SMR amplitude variations.

Figures (4)

• Figure 1: a) Hall bar device and coordinate system used throughout this study. Via magnetron sputtering, a Pt layer being $t_\mathrm{Pt}$ thick is deposited onto a given YIG film. By using optical lithography hundreds of Hall bars with width $w$ and length $l$ are patterned into the Pt layer. A current $I$ is driven through the device and the voltage $V$ is measured. The magnetization of the YIG layer is rotated in the film plane by an external magnetic field applied at a varying angle $\alpha$. b) Micrograph of sample S1. c) Resistivity modulation and d) normalized magnetoresistance obtained from the three framed Hall bars in b). The SMR ($\Delta \rho/\rho_\mathrm{0}$) is indicated for the measurement shown in blue.
• Figure 2: a) Repeatability of the measurement scheme on a single Hall bar. The contacting and measuring scheme was performed 8 times over an hour. Due to slight laboratory temperature changes, the resistivity of the Pt layer changes. The total temperature change corresponds to 0.15K. The fit to the data yields $\alpha_\mathrm{0} =$ -11.1°, which accounts for the misalignment of the external field. b) The normalized data for all performed measurements yield a mean SMR of 3.41e-4, with the standard deviation $\sigma=$ 0.04e-4, emphasizing the reproducibility of our measuring scheme.
• Figure 3: a), b) and c) Color maps of S1, S2 and S3. Every rectangle corresponds to a Hall bar, where the color of the individual rectangle represents the value of the SMR: In all color maps, the SMR is quite homogeneously distributed, however, a small scattering of the SMR values is visible. Geometrical factors stemming from the fabrication process of the Hall bars can be neglected because of the normalization. The temperature can also be excluded as an explanation, as the variation could only be explained by assuming large temperature changes. Ultimately, intrinsic effects impacting the SMR such as the spin transparency of the YIG/Pt-interface are left in order to explain the standard deviation. d), e) and f) Histograms of the SMR amplitude distribution for samples S1, S2 and S3. For all three samples, a Gaussian distribution of the SMR, can be observed, yielding mean values $\mu$ of 3.54e-4, 4.61e-4 and 4.87e-4 and standard deviations $\sigma$ of 0.27e-4, 0.23e-4 and 0.14e-4, respectively. Therefore, the variation of the SMR on one sample is as small as 10%. However, the SMR variation across multiple samples can be up to 30%.
• Figure 4: a), b) and c) Correlation of the SMR and the resistivity $\rho_\mathrm{0}$ for every Hall bar measured on S1, S2 and S3. The dashed lines indicate the standard deviation of the SMR amplitude and $\rho_\mathrm{0}$, respectively. In a), if the SMR values increase, the resistivity decreases and vice versa, whereas the opposite behavior is expected from Eq. \ref{['eq:SMR1']}. In b) and c), this behavior is not reproduced suggesting that the observed trending is unique to sample S1. d) The mean of all SMR values and resistivity values per sample. The error bars indicate the standard deviation of both the SMR and $\rho_\mathrm{0}$. Additionally, the gray line is a calculation of the SMR according to Eq. \ref{['eq:SMR1']}, revealing a trending depending on $\rho_\mathrm{0}$, which reproduces the measured data well. We used $G=$3e14Ω^-1m^-2 for the dashed line, $G=$5e14Ω^-1m^-2 for the solid line, and $G=$3e15Ω^-1m^-2 for the dash-dotted line.