Oblique spin injection to graphene via geometry controlled magnetic nanowires

Introduction

Efficient generation of spin accumulation in an appropriate transport medium, and control over the consequent diffusive spin signals, are two of the most crucial elements of spintronic devices^1,2. Graphene is an ideal material for spin transport, owing to its high electron mobility, low spin orbit coupling strength, and gate tuneable carrier density^3,4,5,6,7. Furthermore, encapsulating graphene between two layers of hexagonal-boron nitride (hBN), an insulating isotrope of graphite, is known to greatly increase its quality as both a charge and spin transport medium, with significant improvements to electron mobility and spin diffusion lengths reported^{8,9,10,11,12,13}. Making a Van der Waals heterostructure comprising insulating outer layers, inherently presents challenges in contacting graphene, with conventional top contacts no longer a viable option. A promising alternative is the use of one-dimensional (1D) edge contacts, where electrodes make contact with the graphene channel only along its atomic edge¹⁴. Such contacts have been shown to be far less invasive than top contacts^15,16,17, and have recently been implemented, in the case of magnetic nanowire electrodes, for efficient spin injection and long range spin transport¹⁸.

Here, we investigate how the geometry of these magnetic nanowires can be exploited to define the polarisation of a spin population injected into a high quality graphene device¹⁹. The magnetic nanowires are engineered with considerable shape anisotropy (Fig. 1a), such that the easy axis points along their length. Moreover, as the nanowires cross the 2D material heterostructure the easy axis tilts out-of-plane at the interface with the graphene (Fig. 1d). As such, the local magnetisation vector is oblique at the point of spin injection; in other words, it is described by both in-plane and out-of-plane components (Fig. 1d). To explore the effect of the magnetisation angle on diffusive spin transport through the graphene channel, we conduct standard spin valve (magnetic field in-plane) and Hanle spin precession (magnetic field out-of-plane) measurements^5,20,21. We find the spin valve response displays a Hanle-like line shape, implying that the oblique magnetisation transmits an out-of-plane component to the polarisation of the injected spin population, which precesses around the in-plane magnetic field. By analysing the precession curve observed in our spin valve measurements, and comparing the results to those extracted from standard Hanle spin precession data, we quantify the relative magnitudes of in-plane and out-of-plane spin polarisation and use this information to reconstruct the angle of the total polarisation vector. The extracted angle is consistent with the inclination of the magnetic nanowire at the graphene interface, evidencing that the effect is geometric in nature. Previous demonstrations of generation of out-of-plane injected spin polarisation in lateral devices, have utilised complex physics such as the anomalous spin Hall effect²², magnetocrystalline anisotropy within Van der Waals magnets²³, or generation within graphene itself via proximity-induced spin-orbit coupling²⁴. Hence, exploiting device geometry provides an alternative, and relatively simple, technique for defining spin polarisation in spintronic devices.

Oblique spin injection to graphene via geometry controlled magnetic nanowires — **Fig. 1: Characterisation of device A.**

Results

Geometry characterisation

We fabricate a total of four devices (A–D) in line with the methods used in our previous work (see Methods)¹⁸. Such devices have previously shown high electronic quality, with charge carrier mobilities > 10 m² V⁻¹ s⁻¹, and demonstrated efficient spin transport with spin relaxation lengths > 10 μm¹⁸. One aspect of this architecture that remains unexplored, is the geometry of the magnetic nanowires that form the 1D contacts. The nanowire design results in an easy axis dictated by shape anisotropy, which points along the length of the wire. Therefore, switching of the in-plane magnetisation, M_∣∣, can be achieved with relatively low magnetic fields, as expected for Co nanowires with dominant shape anisotropy²⁵. However, owing to the geometry of the nanowires as they traverse the sides of heterostructure, the easy axis is inclined and the magnetisation gains a small out-of-plane component, M_⊥, at the injection point (Fig. 1d).

Figure 1a, b show optical and AFM images of device A, respectively. Profiles taken from the AFM scan show the total height of this heterostructure to be ~ 50 nm (Fig. 1c), which is comparable to the thickness of the Co within the nanowire ~ 60 nm. The thicknesses of our four heterostructures are varied by selection of hBN flakes (thickness decreases from A to D), while the thickness of the Co layer in the nanowires is kept constant across all devices (60 nm). The role of heterostructure thickness, t, which is determined entirely by the encapsulating hBN layers, is an important consideration in the geometric treatment of the magnetisation. Aside from protecting the graphene from environmental contamination and giving rise to high charge mobilities, using thicker flakes of hBN (>20 nm) is expected to lead to a greater magnitude of M_⊥ in the nanowires, relative to a given thickness of Co. It should be noted that the etching process used has to be optimised for thicker flakes. Using AFM profile data for device A, the angle of inclination of the nanowires is found to be θ = 42 ± 8°.

Oblique spin injection

We investigate the effect of the nanowire geometry on diffusive spin transport, by performing non-local (Fig. 1a) spin precession (Hanle) and spin valve (SV) measurements, on device A^5,26. For Hanle measurements, a magnetic field, B_⊥, is applied along the z-axis, perpendicular to the plane of the channel, causing precession of the in-plane component of the spin polarisation, P_∣∣, as the carriers diffuse through the channel (Fig. 2a). The observed Hanle response is characteristic of spin precession through the graphene channel (Fig. 2c). When B_⊥ = 0 there is a peak in the non-local signal, R_NL, as the spin polarisation is fully co-linear with the magnetisation of the electrode. As B_⊥ increases, R_NL decreases to a minimum, at B_⊥ ~ ± 100 mT, implying a full π-rotation of the spin polarisation at the detector electrode. For B_⊥ > ± 100 mT, R_NL flattens out, suggesting the spin signal is fully dephased before reaching the detector. This effect is inverted for the two relative orientations of the injector-detector magnetisations: parallel (↑↑) and anti-parallel (↑↓) (Fig. 2a, c).

**Fig. 2: Defining Hanle and spin valve (SV) measurement configurations.**

For spin valve measurements, the magnetic field, B_∣∣, is applied along the y-axis, co-linear with the easy axis of the magnetic nanowires (Fig. 2b, d). The SV response seen here is unique to the geometry of our devices. The expected switches between the ↑↑ and ↑↓ states are observed at B_∣∣ ~ ± 40 mT (open squares, Fig. 2d). However, the non-local signal associated with the ↑↑ state, outside of the switching region, features a line shape reminiscent of that of a Hanle measurement (filled squares, Fig. 2d). We define this line shape as the Hanle-like background of the spin valve measurement. This phenomenon arises from the precession of an out-of-plane component in the spin polarisation, P_⊥, imprinted on the injected spin population by the magnetisation of the magnetic nanowire at the injection point. This component is also injected during Hanle measurements but will not precess in this case, as it is co-linear with the applied magnetic field. To determine whether the Hanle-like background is truly spin-dependent (i.e., magnetic in origin), we perform a minor hysteresis loop, by reversing the direction of the magnetic field as soon as a switch occurs between the ↑↑ and ↑↓ states. The result of this process is shown in Fig. 2d by the open green and blue circles. The curve between the switches is inverted depending on whether the nanowire magnetisations are arranged parallel or antiparallel, as is the case for precession measurements, implying that the observed line shape is indeed spin-dependent. Therefore, providing additional evidence that the detected Hanle-like background arises from the precession of the out-of-plane component of injected spins.

Electronic angle reconstruction

Figure 3a shows representative spin precession data for two types of experiments: (i) full Hanle signal, defined as R_s−∣∣ = (R_NL↑↑ − R_NL↑↓)/2, representing precession of a large in-plane spin component and (ii) the Hanle-like background from the SV experiment, with the switches removed, representing precession of a small out-of-plane spin component (R_s−⊥ = R_NL). We use a DC voltage, V_BG, applied between the silicon substrate, which acts as a global back gate (Fig. 1a), and the graphene channel, to control the carrier density in graphene, n^3,4. The data is taken at a fixed charge carrier density where the non-local signal is maximum (n = 1.5 × 10¹² cm⁻²; V_BG = 20 V). A linear background is removed from both data sets, which arises due to Hall effect in the presence of a magnetic field. Both spin precession signals are fitted to the steady state solution to the Bloch equation, as has been discussed elsewhere^{5,26,27,28,29}. This process is repeated for data taken over a range of carrier densities (n = 0.5 − 2.5 × 10¹² cm⁻²), which enables estimations of the spin relaxation time, τ_s, spin diffusion coefficient, D_s, and contact polarisation, P. These values allow us to quantify the spin diffusion length, ({lambda }_{s}=sqrt{{D}_{s}{tau }_{s}}), the value of which is consistent across the two separate measurement techniques, with an average of λ_s = 6.8 ± 0.4 μm (Fig. 3b).

**Fig. 3: Magnetisation angle reconstruction from spin transport.**

The polarisation vector, P, is useful for studying the geometry of the device, as it is formed from orthogonal components of different magnitudes, P_⊥ and P_∣∣. It relates to the non-local signal measured in the channel, R_NL, as⁵,

$${R}_{NL}=frac{rho {P}^{2}{lambda }_{s}}{2W}{e}^{-L/{lambda }_{s}},$$

(1)

where we assume P_i = P_d = P (P_i and P_d are injector and detector polarisation, respectively), ρ is the resistivity of graphene, while W and L are the channel width and length, respectively. Hence, the observed difference in magnitude between the precession data extracted from SV and Hanle measurements, reflects the difference in the magnitude of the respective components of the polarisation, P_⊥ and P_∣∣. Figure 3c shows the evolution of these two components of polarisation against carrier density, with P_⊥ being consistently smaller than P_∣∣ throughout. At high density (n ≥ 2 × 10¹² cm⁻²), the signal to noise ratio of R_NL decreases, as it is proportional to P² and ρ Eq. (1), both of which decrease at high ∣n∣ (Fig. 3c)¹⁸. Hence, reliable fits are harder to perform as n increases, especially for Hanle-like backgrounds, which are considerably smaller in magnitude than the full Hanle signal. So, only data up to n = 2 × 10¹² cm⁻² are used in the angle calculation. From the ratio P_⊥/P_∣∣, we reconstruct the angle of the overall spin polarisation vector, (theta =arctan ({P}_{perp }/{P}_{| | })). Note that this method yields an inclination angle which is insensitive to variations in the magnitude of the polarisation from contact to contact, being only sensitive to variations on its inclination. The extracted θ has an average value of 36.0 ± 3. 0°, over the carrier density range explored (Fig. 3d).

Discussion

The extracted average value of θ agrees within experimental error with the angle of the nanowire extracted from AFM profilometry. Furthermore, the calculated value of θ remains constant with changing n, confirming that it reflects the geometry of the magnetic nanowire. Hence, we demonstrate geometric control over the spin polarisation injected into a graphene spin transistor.

We investigate the consistency of oblique spin injection across several devices of varying heterostructure thickness, all with a 60 nm thick Co layer in the nanowires. The right column of Fig. 4 shows spin valve signals measured from devices B, C, and D, with heterostructure thicknesses t ≈ 52.0 nm, t ≈ 27.5 nm, and t ≈ 14.8 nm, respectively. In all cases, the magnitude of charge carrier density is comparable to that of the measurement on device A. Starting with the thickest of these stacks, device B (Fig. 4c), a Hanle-like background is observable in the spin valve signal, with a magnitude R_s−⊥ ∝ P_⊥ (Eq. (1)). Likewise, the magnitude of the switches is 2R_s−∣∣ ∝ P_∣∣ (Fig. 4c). Hence, the ratio between these magnitudes can be used to approximate the inclination angle of the nanowire, which, for device B is found to be θ ≈ 28 ± 5°. Moving to the middle case, device C, the spin valve background shows a subtle line-shape, implying this thickness is a boundary for achieving detectable out-of-plane spin polarisation. The angle extracted here is θ ≈ 20 ± 3°. Finally, for the thinnest case, device D, the spin valve background is mostly flat. Here, the only measurable feature is a faint hysteresis loop around B ~ − 30 mT, consistent with prior observation of Hall signal close to 1D magnetic contacts¹⁶. As such, the angle of the nanowire cannot be evaluated for this device, implying that any out-of-plane component in the magnetisation of the nanowire is below the resolution of the measurement. It is expected that using this approximate method should be less accurate for evaluating the nanowire geometry than the full Hanle analysis laid out above. Nevertheless, the angles follow the expected trend with decreasing thickness. Hence, the role of heterostructure thickness, relative to the Co layer thickness, is crucial in achieving a geometrically defined out-of-plane component in the nanowire magnetisation and, in turn, the spin polarisation.

**Fig. 4: Connection between heterostructure thickness, t, and observed Hanle-like background.**

Conclusions

In conclusion, we exploit spin transport in an encapsulated graphene spin valve device to characterise the magnetisation vector of a magnetic nanowire acting as a 1D edge contact. This relatively simple approach provides an alternative method of spin vector magnetometry that relies only on pure spin signal, enabling a quantitative analysis of a nanoscale magnetic region. Importantly, we demonstrate that the geometry of Van der Waals heterostructures can be engineered to define the angle of spin injection into 2D materials. The use of geometry to control the generation of out-of-plane spin is comparatively simpler than alternative methods based on unconventional spin-orbit effects^22,24 and is generally applicable to any magnetic material without the need of magnetocrystalline anisotropy²³. Such structures can potentially be applied for the study of spin anisotropy in low-dimensional materials³⁰ via the use of a geometrically defined oblique spin accumulation.

Methods

Individual flakes of 2D material (both hBN and graphene) are isolated via mechanical exfoliation, then subsequently stacked into hBN/graphene/hBN heterostructures via the dry peel transfer technique^8,31. Heterostructures are separated from a highly doped Si substrate, used as an electrostatic gate, by a 290 nm SiO₂ layer. Reactive ion etching is used, along with a polymer hard mask, to engineer a long, narrow transport channel out of the heterostructure (Fig. 1a). After etching, the sides of the stack are angled and a small ledge of graphene is left exposed at the edges (Fig. 1b, c). This permits one-dimensional electrical contact to the heterostructure by deposition of ferromagnetic metal nanowires^16,32. The nanowire pattern is defined in a polymer layer via electron beam lithography, before metal is deposited via electron beam evaporation; materials used for all devices are 60 nm Cobalt (Co) with a 20 nm Gold (Au) capping layer.