Proposal of a measurement scheme to detect the influence of

5.2. Proposal of a measurement scheme to detect the influence of magnetic moments on spin transport

Experiments on weak localization and universal conductance fluctuations in strong in-plane magnetic fields have found a significant contribution to dep-hasing from magnetic moments [103]. Temperature dependent measurements revealed a g factor around 2 suggesting that the magnetic moments can success-fully be pinned by moderate in-plane magnetic fields. Magnetic moments in graphene can form due to carbon vacancies or chemisorbed hydrogen, lea-ding to a sp³ hybridization [104–107]. Localized magnetic moments acting as resonant scatterers were proposed as an efficient source of spin relaxation [108,109], see also subsection1.3.7. The fact that no spin relaxation aniso-tropy in graphene on SiO2 was found, points to the direction that magnetic moments indeed are a dominating source of spin relaxation [206].

The direct influence of magnetic moments unintentionally present in pris-tine graphene on spin transport in graphene has not been shown yet. In the following we propose a measurement scheme to detect the influence of mag-netic moments on spin transport. This concept is based on the fact that a static configuration of the magnetic moments aligned collinear to the injecting magnetic contacts will not lead to any dephasing of the electron spin during a resonant scattering event. In general, the direction of the magnetic moments of the resonant scattering sites are random and fluctuate in time. However, in a large magnetic field a Zeeman splitting occurs for the magnetic moments.

If temperature is low enough, all magnetic moments will occupy the lowest energy level. This will lead to a static configuration of the magnetic moments aligned with the external magnetic field. Therefore, the combined influence of magnetic field (Ez= gµBB) and temperature (kBT) will lead to a clear picture of the contribution of magnetic moments to the spin relaxation. Since large magnetic fields (and obviously low temperatures) are required (B ≥ ^k_gµ^B_B^T), the only possible injector and detector configuration will be a parallel alignment of the two electrodes’ magnetization. It is obvious that the large magnetic field needs to be applied in-plane as otherwise significant orbital contributi-ons would be expected (Hall effect and Quantum Hall effect). Therefore to address the magnetic moment related spin relaxation the measurement of the non-local resistance as a function of in-plane magnetic field and temperature is needed.

First, the room temperature characteristics of a multilayer graphene spin-valve are discussed. In a second step the low temperature spin transport is presented and the influence of a strong in-plane magnetic field is investigated.

5. Spin transport in graphene spin valves

5.2.1. Room temperature characterization of a two-layer CVD hBN/multilayer graphene spin valve

Fig.5.6 shows the device consisting of a few layer graphene spin transport channel with a two-layer CVD hBN tunnel barrier³. Cobalt electrodes with varying width were used as injectors and detectors of spin polarized current.

The sheet resistance Rsq '200 Ω was found to depend only weakly on gate voltage most probably due to the few layer nature of the graphene. The RCA was found to be around 3 kΩ µm² to 4 kΩ µm², determined from three terminal measurements. Clear spin valve signals are observed for different contact pairs as shown in Fig.5.6(a). The overall signal decreases with length exponentially with a spin relaxation length λs = 1.7 µm. The spin relaxation length is slightly shorter than the contact spacing, which is 2 µm (measured from the middle of the contacts). Over a length of 2 µm a clear Hanle signal was found, as shown in Fig.5.6 (c). The data shown here is the difference of the Hanle signal in parallel and in anti-parallel configuration as similarly done above. The extracted spin lifetime τs = 220 ps and diffusion constant D = 0.014 m²s⁻¹ yields a spin relaxation length of λs =1.8 µm, which is in good agreement with the length dependence of RN L. Since the spin channel is a few layer graphene flake, the density of states is unknown and therefore the charge diffusion constant Dc is also unknown. We therefore cannot compare the spin diffusion constant Dsto the charge diffusion constant Dc.

(a) (b)

I V

20 μm L

Figure 5.6. Device image and sketch. (a) shows an optical image of the device and in (b) a schematic drawing is shown, indicating the length of the spin transport channel with L.

3Part of the fabrication was performed by Simon Karsten.

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5.2. Proposal of a measurement scheme to detect the influence of magnetic

Figure 5.7. Non-local spin valve at RT. (a) shows the non-local spin-valve measurement for different contact pairs (different lengths between injection detection contact pairs). The R^PN L was set to zero for all measurements to compare them on a single graph. The spin signal ∆RNL is shown on a loga-rithmic scale in (b) as a function of length together with a linear fit to extract λs. (c) shows a Hanle measurement, which is the difference of the parallel and anti-parallel configuration.

5.2.2. Low temperature spin transport - signatures of magnetic moments?

As introduced in subsection 1.3.5, the non-local resistance in a spin valve is given by the difference in chemical potential of the spin up component below each detector normalized to the injecting current. Obviously the contact polarization determines how efficient the injection and detection is. However, for the following consideration the absolute value of the polarization does not matter and it is expected to be independent of in-plane magnetic field. In a non-local geometry, the chemical potential is given by the exponential decay with the spin relaxation length λs as well as by the effective resistance of the graphene (where λs goes in linearly). If the pinning of the magnetic moments results in a significantly longer spin relaxation time τs, the spin relaxation length λs = √

τsD is also increased. A longer λs will then lead to a larger spin accumulation µs in the graphene channel. Fig. 5.8 shows the spin accumulation µ^↑s for different values of λs for the device geometry shown in Fig.5.6. A moderate increase in λs leads to a substantial increase in µ^↑s below the detector contact C3 and nearly no change below the second detector contact C4. Therefore, an increase in RN L with in-plane magnetic field is expected if magnetic moments are pinned and are a substantial source of spin relaxation. In this very simple argumentation the contacts were assumed to probe exclusively the spin-up chemical potential µ^↑s. However, the efficiency of each contact to detect µ^↑s is given by the contact polarization, which is generally not unity. Therefore, the expected change in RN L will be smaller,

5. Spin transport in graphene spin valves

but the effect will be present.

-1.0 -0.5 0.0 0.5 1.0

µs (a.u.)

14 12 10 8 6 4 2 0

L (µm) λs = 1.7 µm λs = 2.0 µm λs = 2.7 µm

Figure 5.8. Spin up chemical potential for different λs: The spin up chemical potential a parallel contact geometry is shown for different values of λs as a function of distance. The vertical black lines indicate the position of the four contacts involved in a non-local spin valve.

Measurements at low temperatures

In the following, all transport experiments were carried out in DC. Fig.5.9(a) shows spin valve measurements at 4 K and 50 mK, demonstrating spin trans-port at these temperatures. In (b) the non-local resistance is shown for higher By values for 4 K and 50 mK. In principle RN L should not depend on By at fields larger than the coercive fields of the involved injector and detector if the influence of magnetic moments is neglected for the moment. However, the measurements in Fig.5.9(b) show some dependence of RN Lon By, which can be due Hall effects of a small out-of-plane component of Byfor example. Hall effects can appear in non-local geometries if the contact is not homogeneously coupled to the graphene channel over the full width of the graphene channel.

Pin-holes are an extreme form of such an inhomogeneous contact and have been shown to give rise to field dependent background in spin valve and Hanle measurements [207]. In order to eliminate these influences and to get rid of the large background, the RN L(4K) was subtracted from all other RN L measure-ments in order to visualize the influence of the in-plane field and temperature on the spin component alone, see Fig.5.10. The peak in RN Lat zero Bymight be explained by weak localization that arises due to a finite out-of-plane com-ponent. Small misalignments of the sample plane with respect to By were found in other studies (see section7.5) in the same measurement system.

The normalized RN Lcurves are shown in Fig.5.10. Overall, the normalized RN L varies on the order of 1 Ω with maxima slightly above 2 T. For positive

106

5.2. Proposal of a measurement scheme to detect the influence of magnetic

Figure 5.9. Spin valve measurements at low temperature: (a) shows spin valve measurements at low temperature and (b) shows the non-local resis-tance up to very large in plane fields By. The sweep direction of the magnetic field is indicated by black arrows.

By, the maximum in RN L shifts to smaller magnetic fields for lower tempe-ratures. In addition the maximum increases in absolute value. This trend is highlighted by the black arrow. For negative Bya maximum is also observed for all temperatures but no clear trend is visible.

1.0

Figure 5.10. Normalized non-local resistance:The normalized non-local resistance is shown for different temperture as a function of in plane magnetic field By.

An increase in RN L with increasing |By|is indeed expected for the pinning of magnetic moments as this would lead to a longer τs and hence to longer λs leading to a larger difference in µs between contact 3 and 4, as shown schematically in Fig. 5.8. Furthermore, the increase in RN L should happen at lower |By|for lower temperatures as the magnetic moments are easier to freeze out at lower temperature.

5. Spin transport in graphene spin valves

Since contact 3 and 4 are ferromagnetic (non-local voltage detection), they will be aligned parallel at large |By|and therefore both will sense the spin-up chemical potential. For very long λs, they will sense both the same chemical potential and hence the RN L will reduce for even larger |By|. To sum up, all the observations for By>0 seem to support the hypothesis of the pinning of magnetic moments.

The fact that the RN L for By<0 shows a slightly different behaviour than for By>0 cannot confirm the influence of magnetic moments on spin trans-port. The observed behaviour of RN L with By and temperature is therefore most probably due to some other influences. Phase coherent processes could play a role at such low temperatures [208]. Signatures of that are observed as possible WL contribution at very small Bythat can arise from a small out-of-plane component which is a result of a misalginment of the Bywith respect to the sample plane. To sum up, no conclusive picture can be given that would explain the observed line shape in Fig.5.10.