Controllable unidirectional magnetoresistance in ferromagnetic films with broken symmetry

Shun Wang, Xiaotian Cui, Ronghuan Xie, Changwen Zhang, Yufeng Tian, Lihui Bai, Qikun Huang, Qiang Cao, and Shishen Yan

Phys. Rev. B 107, 094410 – Published 13 March 2023

Abstract

Spin-related unidirectional magnetoresistance (UMR) exhibits nonreciprocal transport to either charge current or magnetization reversal, providing a potential application for direct electrical readout of in-plane magnetization using simple two-terminal geometry. To achieve such a UMR, it is usually believed that an adjacent heavy metal or other materials with strong spin-orbit coupling (SOC) as the spin polarizer is indispensable, leading to most efforts on multilayer structures rather than single-layer ferromagnetic films. Here, we report the observation of UMR in a single CoPt film by introducing a vertical composition gradient to break the structural inversion symmetry. Moreover, unlike conventional heavy-metal/ferromagnetic-metal bilayer films, the UMR in the CoPt film with a positive Co composition gradient is controllable as a function of current amplitude, which shows the decrease, sign reversal, and then enhancement with the increment of current density. These results reveal two competing UMR mechanisms with opposite signs in electrical current dependency, i.e., bulk Rashba effect induced by composition gradients and anomalous Nernst effect driven by a vertical temperature gradient. Our work provides a promising way to manipulate the UMR in a single ferromagnetic film with the combination of charge-spin conversion and magnetothermal effect.

Received 15 December 2022
Revised 21 February 2023
Accepted 28 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.094410

Physics Subject Headings (PhySH)

Magnetoresistance Rashba coupling Spin current Thermomagnetic effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shun Wang¹, Xiaotian Cui ¹, Ronghuan Xie¹, Changwen Zhang¹, Yufeng Tian², Lihui Bai², Qikun Huang^1,2,*, Qiang Cao^1,†, and Shishen Yan ^1,2,‡

¹Spintronics Institute, University of Jinan, Jinan 250022, China
²School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

^*qkhuang@sdu.edu.cn
^†qiangcao@126.com
^‡shishenyan@sdu.edu.cn

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Issue

Vol. 107, Iss. 9 — 1 March 2023

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Images

Figure 1
Angle-dependent longitudinal harmonic resistance of three types of CoPt films with different composition gradients. (a)–(c) Geometric schematic of the measurement and definitions of rotation planes. External magnetic field $H$ is set to 9 kOe. First-harmonic resistance $R_{x x}^{1 ω}$ measured at $J_{x} = 7 \times 10^{6} A / c m^{2}$ for CoPt films with positive (d), negative (g), and without (j) Co composition gradients. A SMR-like behavior is observed in CoPt films with positive and negative Co composition gradients. Second-harmonic resistance $R_{x x}^{2 ω}$ measured at $J_{x} = 7 \times 10^{6} A / c m^{2}$ for CoPt films with positive (e), negative (h), and without (k) Co composition gradients Positive and negative Co composition gradients result in the opposite UMR. Second-harmonic resistance $R_{x x}^{2 ω}$ measured at a high current density of $J_{x} = 1.4 \times 10^{7} A / c m^{2}$ for CoPt films with positive (f), negative (i), and without (l) Co composition gradients. In this case, all samples show the same negative UMR. The green solid lines represent the fit to the raw data.
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Figure 2
UMR hysteresis curves $R_{x x}^{2 ω} - H y$ as a function of current density. As the current density increases from $7 \times 10^{6}$ to $1.4 \times 10^{7} A / c m^{2}$ , the UMR of CoPt films with positive Co composition gradient changes from positive to negative (a), the UMR of CoPt films with negative Co composition gradient remains negative and increases (b), and the UMR of CoPt films without composition gradient is initially absent and gradually becomes negative (c).
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Figure 3
Bulk Rashba unidirectional magnetoresistance. Illustration of bulk Rashba-induced UMR in the case of positive (a) and negative (b) Co component gradients. (c) Schematics of current-induced SOT effective fields. Magnetization is restricted to rotation in the $X$ plane in the presence of an in-plane magnetic field $H_{x}$ , which gives rise to an out-of-plane component of dampinglike effective field $H_{DL}$ . Enlarged anomalous Hall resistance loops measured at $I_{x} = \pm 3 mA$ and a fixed magnetic field $H_{x} = 100$ Oe for CoPt films with positive (d) and negative (f) Co component gradients. Insets show the whole loop. Summarized dampinglike effective field $H_{DL}$ as a function of current densities for CoPt films with positive (e) and negative (g) Co component gradients. Solid lines are a linear fit to the data.
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Figure 4
Contribution of anomalous Nernst effect to unidirectional magnetoresistance. (a) Evaluated temperature of CoPt films with positive Co component gradient as a function of current density. As colored by dark cyan, the temperature is about 308 K at $J_{x} = 7 \times 10^{6} A / c m^{2}$ and 343 K at $J_{x} = 1.4 \times 10^{7} A / c m^{2}$ . (b) Schematic of current-induced anomalous Nernst effect due to the vertical thermal gradient $\nabla T_{z}$ . (c) Measured transverse second-harmonic resistance $R_{x y}^{2 ω}$ for three types of component gradients. (d) $H_{FL}$ contribution $(2 {cos}^{3} φ - cos φ)$ subtracted from the raw data of $R_{x y}^{2 ω}$ in (c).
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