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Enhanced spin-orbit coupling in a heavy metal via molecular coupling

Heavy metals are key to spintronics because of their high spin-orbit coupling (SOC) leading to efficient spin conversion and strong magnetic interactions. When C60 is deposited on Pt, the molecular interface is metallised and the spin Hall angle in YIG/Pt increased, leading to an enhancement of up to 600% in the spin Hall magnetoresistance and 700% for the anisotropic magnetoresistance. This correlates with Density Functional Theory simulations showing changes of 0.46 eV/C60 in the SOC of Pt. This effect opens the possibility of gating the molecular hybridisation and SOC of metals.


I. INTRODUCTION
The spin-orbit interaction is perhaps the most crucial mechanism in the design of magnetic structures and metal device physics. It determines the magnetocrystalline anisotropy, is key to the propagation and electrical conversion of spin currents, determines the magnitude of interfacial mechanisms such as the Dzyaloshinskii-Moriya interaction and guides new paths of research, such as the generation of Majorana fermions and energy band engineering of topological insulators. The SOC controls as well the efficiency of experiments such as the spin Hall, spin torque or spin Seebeck effects. All these are key to reducing the power consumption of computing and electronic devices, an issue that is quickly coming to the forefront of technology. However, currently we can only tune the SOC by static means, such as doping, preventing the design of architectures where spin, charge and magnetic interactions can be reversibly modified to enhance device performance or to achieve new functionalities.
The Spin Hall magnetoresistance (SHMR) offers a means to quantify the SOC. It is observed when a current flows in thin (~nm) heavy metal layers, frequently Pt, deposited on a magnetic insulator such as the yttrium iron garnet Y3Fe5O12 (YIG). 1,2-4 SHMR has been observed in several heavy metal/ferromagnetic insulator systems and even in metallic bilayers. [5][6][7][8] Intrinsic and extrinsic spindependent scattering mechanisms generate a spin current perpendicular to the charge current. [9][10][11][12] This spin current generates charge accumulation and an additional Hall voltage. The SHMR can then be measured by rotating the magnetic field in order to change the magnetisation vector and measuring the voltage for a constant applied current. These experiments are valuable in unravelling the spin-dependent scattering mechanisms and quantify the strength of the SOC in a metal. The ratio of the spin to charge current is known as the spin Hall angle: = | |/| |. 9,13,14 has technological relevance, as it is correlated with the torque exerted on ferromagnets in spin transfer torque memories. 15 Increasing the SHMR and can therefore result e.g. in lower power or smaller switching currents for such devices. By tuning the SOC in a traditional YIG/Pt structure with a molecular layer, we can also differentiate spin transport effects based on their physical origins. 16,17 At metallo-molecular interfaces, the electronic and magnetic properties of both materials change due to charge transfer and hybridisation. [18][19][20][21][22] This can lead to the emergence of spin ordering and spin polarised transport, [23][24][25][26] change the anisotropy of a ferromagnet, 22 33 The C60 overlayer leads to a resistivity that is typically 20% (5 nm Pt) to 60% (1 nm Pt) lower than for pure Pt. According to DFT simulations, only the first C60 layer in contact with Pt is conducting, which would result in a hybrid interface resistivity of ~2-10 ·cm.
Below ~25 K, dimensional effects such as localization and the Hanle effect play an important role, resulting in an upturn of the resistivity. For Pt/C60, the interface results in a larger effective conducting layer thickness, reducing dimensional effects such that the upturn in resistivity is smaller or non-existent (Fig. 1b).
The interface also affects the magnetotransport properties of the metal. For fields perpendicular to the film, there is a magnetoresistance (MR) due to spin accummulation of the order of 10 -4 that saturates at the out-of-plane anisotropy field of the YIG film, some 0.15 T for a 170 nm film at room temperature and no higher than 0.5 T for any film or temperature measured. Above this field range, other contributions, such as Koehler magnetoresistance and the aforementioned quantumdimensional effects become significant. This results in linear and parabolic contributions to the MR. 34 For a YIG(170nm)/Pt(3nm) sample, the C60 layer enhances the spin accumulation MR by about a factor 3 due to an enhanced Pt spin orbit coupling, but reduces other contributions because of the increased effective (conducting) thickness of the Pt/C60 bilayer. The molecular overlayer therefore offers a means to distinguish between the spin accummulation, strengthened by C60, and other effects, e.g. weak localisation, that are weakened by the conducting interface -see Fig. 1c. where the YIG film is saturated out of plane. 6 The SHMR is measured by rotating the angle  in Fig. 1a, with the H field changing from transverse to perpendicular -always orthogonal to the electrical current but varying from parallel to perpendicular to the spin current. The change in resistivity is fitted to a cos ( ) function, and the amplitude is taken to be the SHMR (see Supplementary Information). As seen above, if the field exceeds the anisotropy field of the YIG film, other orientation-dependent contributions take place and confuse the results. At 0.5 T, the SHMR values obtained for Pt/C60 are higher for all temperatures and film thicknesses, demonstrating that C60 enhances the SOC in Pt (Fig. 2a). This enhancement is correlated with an increase of the spin Hall angle (Fig. 2b). 35,36 However, the change is highly dependent on the Pt thickness and the relative contribution of the Pt interface atoms to the spin scattering. We observe larger molecular modifications when the Pt layer deviates from its optimum value of ~2.5 nm. For the thinnest measured films of 1.5 nm, when the spin diffusion length is probably longer than the film thickness at all temperatures, the largest molecular effect is observed at 5 K. For a 5 nm Pt film, thicker than the spin diffusion length at all temperatures, the largest measured change takes place at room temperature ( Fig. 2c and Supplementary Information). The

III. TRANSMISSION ELECTRON MICROSCOPY
The fabrication of YIG films can lead to elemental diffusion and defects that change the magnetic properties of the ferrimagnet and the interpretation of transport measurements. Thus, these effects must be carefully characterized at the atomic scale. Figs with Pt, can affect the magnetization and anisotropy direction of the YIG layer. 37 This could be at the origin of the minor loops we observe in the perpendicular field direction in some YIG films.

IV. LOW-FIELD ANISOTROPIC MAGNETORESISTANCE AND MAGNETISATION
For Pt grown on YIG, an additional change in resistance is observed when the direction of an applied magnetic field is changed w.r.t. the electrical current. The origin of this AMR is controversial.
It has been attributed to a proximity-induced magnetization of Pt, which is close to the Stoner criterion, but it is also claimed that there is no evidence for this induced magnetization in YIG/Pt. 16,17 The AMR is characterized by the presence of peaks, positive or negative depending on the field direction, at fields below 20 mT for YIG grown on GGG. This low field AMR (LF-AMR) resembles that observed in magnetic thin films with domain wall scattering. 38,39 Due to SOC, in most magnetic materials domain walls reduce the resistance for in-plane fields, and increase it for out of plane fields. This domain wall AMR peaks at the coercive field Hc of the magnet, for the greatest magnetic disorder and domain wall density. When the field is perpendicular, the LF-AMR peaks occur at higher fields, are broader and the AMR values are higher than for in-plane fields. Furthermore, the position of out-of-plane and in-plane LF-AMR peaks coincides with the coercivity of the perpendicular minor YIG loops (Fig. 3c and Supplementary Information), which could point to a YIG surface layer with an out-of-plane easy axis. We find that the LF-AMR has the same shape and peak position with or without a molecular overlayer. However, the magnitude of the LF-AMR is larger when C60 is present.
This molecular effect is stronger for the perpendicular than the longitudinal direction -increased by factors of 3 and 1.7 for 2 nm Pt at room temperature. The difference can be attributed to an enhanced SOC for Pt and the larger perpendicular magnetic anisotropy that may be induced by C60 (Fig. 3d). 22 For samples grown on YAG substrates, the in-plane coercivity is increased by 1-2 orders of magnitude, and the LF-AMR peaks appear at higher fields. The perpendicular LF-AMR peaks for  The LF-AMR peak position (coercivity of the YIG surface) and peak width (saturation field of the YIG surface), increase as the temperature is lowered (Figs. 4a-b). Typically, the AMR measured at high fields is reported to vanish above 100-150 K. If measuring at 3 T, where quantum localisation and other effects are strong, we observe this same decay with temperature. However, The LF-AMR values are not so strongly dependent on temperature, in particular for the thinner films. C60 not only increases the LF-AMR value, but it also makes it less temperature dependent, so that the LF-AMR ratio can be up to a factor 7 higher for thin Pt/C60 films at room temperature. (Fig. 4c) The LF-AMR depends on the Pt thickness, , as ( − ) (Fig. 4d). We identify the value of , approximately 1 nm, as the interfacial YIG/Pt region contributing to the magnetoresistance. This relationship is not affected by the C60 layer, although the magnitude is uniformly higher with molecules. Consistent with DFT simulations, the increased AMR peak value is due to an enhanced SOC for the bottom Pt layers. Since the C60 is not in contact with YIG, it cannot alter its magnetic structure and the position of the peaks.

V. CONCLUSION
Our results show that molecular overlayers can tune the spin orbit coupling of heavy metals, as observed in SHMR and AMR measurements. Additionally, the molecular layers aid in distinguishing the origin of spin scattering mechanisms, such as the coupling with YIG surface magnetisation, with a LF-AMR measurable at high temperatures. The enhancement of SOC and spin Hall angle with molecular layers has a wide range of applications, e.g. to reduce the power requirements of spin transfer torque memories. Given the dependence on surface hybridisation and charge transfer, the effect could be controlled via an applied electrical potential. This is an important development, as nearly all other methods to alter the spin-orbit coupling of a material are static. The inverse spin Hall effect can be modified by gating with macroscopic layers of ionic liquids, but changes to the SOC are undetermined and the electrical conversion may only be quenched. 40 Materials can be doped during fabrication to increase the spin-orbit effect, but that becomes fixed in a circuit, i.e. static. Using molecules that can be gated offers a dynamic response -the transport properties of an active circuit, e.g. to control the direction and magnitude of pure spin currents.