Optimization of spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers

Abstract

We present experimental data and their theoretical description on spin Hall magnetoresistance (SMR) in bilayers consisting of a heavy metal (H) coupled to in-plane magnetized ferromagnetic metal (F), and determine contributions to the magnetoresistance due to SMR and anisotropic magnetoresistance (AMR) in five different bilayer systems: W/Co 20 Fe 60 B 20 , Co 20 Fe 60 B 20 /Pt , Au/Co 20 Fe 60 B 20 , W/Co, and Co/Pt. The devices used for experiments have different interfacial properties due to either amorphous or crystalline structures of constitutent layers. To determine magnetoresistance contributions and to allow for optimization, the AMR is explicitly included in the diffusion transport equations in the ferromagnets. The results allow determination of different contributions to the magnetoresistance, which can play an important role in optimizing prospective magnetic stray field sensors. They also may be useful in the determination of spin transport properties of metallic magnetic heterostructures in other experiments based on magnetoresistance measurements. Spin Hall magnetoresistance (SMR) is a phenomenon that consists in resistance dependence on the relative orientation of magnetization and spin accumulation at the interface of ferromagnet and strong spin-orbit material (such as 5d metals 1-8 , topological insulators 9 , or some 2D systems 10). In transition metals such as W and Pt, the spin accumulation results from spin current driven by the spin Hall effect (SHE) 11-14. The spin current diffuses then into the ferromagnet or exerts a torque on the magnetization while being backscattered. Due to the inverse spin Hall effect (ISHE), the backscattered spin current is converted into a charge current that flows parallel to the bare charge current driven by external electric field, which effectively reduces the resistance 3,4. One of the most important advantages of driving spin currents by SHE is that the spin currents can be induced by a charge current flowing in the plane of the sample 15. This may remedy some obstacles on the road to further miniaturization of prospective electronic components, which have been encountered in spin-valves and magnetic tunnel junctions when the electric field is applied perpendicularly to interfaces. One of the drawbacks, however, is that the strength and effectiveness of such subtle effects depend strongly on the quality and spin properties of interfaces 16-23. Although early SMR experiments were performed on heavy-metal/ferromagnetic-insulator bilayers 1 , recent efforts are focused on the bilayers with ferromagnetic metallic layers, such as Co or Co 20 Fe 60 B 20 ones 5,7 , which are currently more relevant for applications. When the magnetization is parallel to the spin accumulation, the spin current from the heavy-metal can easily diffuse into the ferromagnetic metal (influencing its spin transport properties and spin accumulation on the ferromagnetic metal side) [5,24-30. This is especially important when an additional spin sink (another heavy-metal layer or an antifer...

Study of Spin–Orbit Interactions and Interlayer Ferromagnetic Coupling in Co/Pt/Co Trilayers in a Wide Range of Heavy-Metal Thickness

“…For Pt, i.e., for χ = HM , the charge current density reads where ρ HM is the resistivity of the Pt layer, θ SH is the spin Hall angle defined as the charge-to-spin current conversion efficiency at a very thick HM layer limit, and μ s , y HM ( z , m 1(2) ) is the spin accumulation, while for the ferromagnetic layers, i.e., χ = F 1 (χ = F 2) where ρ F 1( F 2) is the resistivity of the corresponding ferromagnetic layer, θ AMR is the AMR in the thick ferromagnetic limit (assumed for simplicity the same in both ferromagnetic layers). For more details, see, e.g., ref ( 37 ).…”

“…Moreover, the effective fields, H DL and H FL (cf. Section 3.1 ), due to SHE and spin accumulation at the interfaces can be expressed as follows and To fit the appropriate magnetoresistance relations obtained from eq 7 , we use the following parameters: 37 , 54 − 56 ρ HM = 59 μΩ cm, ρ F 1( F 2) = 72.5 μΩ cm, λ HM = 1.8 nm, λ F 1 = λ F 2 = 7 nm, θ SH = 8%, θ AMR = 0.15%, β 1 = β 2 = 0.3, G s (1) = G s (2) = G r (1) = G i (1) = 10 15 Ω –1 m –2 , and G r (2) = G i (2) = 0.4 G r (1) . The parameters were also used to calculate SOT effective fields that turn out to be pivotal in the interpretation of the experimental data presented in Section 4.3 .…”

“… 32 , 33 Therefore, interface engineering and quantifying the REE become significant for the optimization of SOT-based devices. 34 − 36 The spin currents injected into the F layer and SOTs may be examined by electric measurements through its magnetoresistance 37 − 39 and the anomalous Hall effect (AHE). 40 The change of the resistance of the hybrid structure caused by the above effects is referred to as spin Hall magnetoresistance (SMR).…”

Anisotropy and Current Control of Magnetization in SrRuO3/SrTiO3 Heterostructures for Spin-Memristors

“…The longitudinal resistance is predominately attributed to AMR arising from conducting through the metallic SRO. It is typically observed that in heavy metal/ferromagnetic metal systems contributions from AMR are significantly larger than those arising from spin Hall magnetoresistance (Karwacki et al, 2020). AMR is typically composed of two components (crystalline and non-crystalline) that have different microscopic origins.…”

Unidirectional spin Hall magnetoresistance and spin-orbit torques in HM$_1$/Co/HM$_2$ trilayer systems

“…Recently, a new MR effect has been found in heavy metal (HM)/ferromagnetic insulator (FMI) hybrid structures called the spin Hall magnetoresistance (SMR). It has been intensively studied [6][7][8][9] with additional discussions and reports on HM/ferromagnetic metal (FMM) hybrids [10][11][12]. The SMR is based on the spin Hall effect (SHE) [13][14][15][16], which occurs in the HM and converts a charge current into a perpendicular spin current.…”