Fabrication and properties of lateral Josephson junctions with a RuO₂ weak link

In recent years, there has been a revival of interest in the properties of the metallic rutile oxides CrO₂, RuO₂ and IrO₂, mainly in connection with magnetism, non-trivial Fermi surfaces, and possible spintronics applications [1, 2]. CrO₂ is a half-metallic ferromagnet that in bulk form was long used in magnetic tapes [3] and in thin film form was found of particular interest to study superconducting long rang range proximity effects [4–6]. IrO₂ was researched from a spintronics perspective as a material with large spin–orbit coupling [7, 8]. RuO₂ was long thought to be a normal metal, and in film form often used in low-temperature thermometry, because of ease of use and insensitivity of the resistance to even high magnetic fields. However, in 2017 itinerant antiferromagnetism was discovered [9], with magnetic moments of the order of 0.05 µ_B (with µ_B the Bohr magneton) and a (Néel) ordering temperature above 300 K. This was confirmed in another study [10], and also prompted renewed studies of the anomalous Hall effect [11, 12]. On the other hand, also superconductivity was recently reported in slightly strained films of RuO₂ [13].

Long range proximity effect has been recently observed in Mn₃Ge, resulting from the chiral non-collinear antiferromagnetic spin structure that creates a non-zero Berry phase [14]. The same study also reported that IrMn, a collinear antiferromagnet with moments on the Mn site of the order of 3 µ_B (Bohr magneton) [15], only shows short range supercurrents owing to its trivial topological spin arrangement. RuO₂, although also a collinear antiferromagnet, has been shown to have crystal inversion asymmetry arising from spin-splitting and time-reversal symmetry breaking in the band structure [16–18]. RuO₂ has also been identified as a promising candidate to allow for spin polarized currents which has been substantiated by recent transport measurements conducted on RuO₂ [19–21]. In this work, we investigate the proximity effect in RuO₂ nanostrips by fabricating lateral Josephson junctions, using superconducting amorphous MoGe as electrodes. Since the resistivity of RuO₂ is quite low, we can expect a quite long induced coherence length if the material behaves as a normal metal. Instead, and confirming the presence of (small) magnetic moments, we find a short decay length (ξ) of around 12 nm which indicates the presence of only short range singlet Cooper pairs and absence of long range spin triplets. The paper is organized in the following manner. We begin by examining the nanofabrication process that leads to Selective Area (SA)-grown nanostrips. Subsequently, we proceed to characterize these RuO₂ nanostrips through electrical and magneto-transport measurements. Then we focus on making Josephson junctions (JJ) in which superconducting MoGe are contacted on top of RuO₂ nanostrips with varying lateral gaps and present the results on these junctions.

We grow RuO₂ nanostrips on (100) oriented TiO₂ substrates using the same selective area growth technique as CrO₂ nanostrips [22] since the lattice parameters of TiO₂, RuO₂ and CrO₂ are comparable and they all crystallize with a rutile structure and a tetragonal unit cell. RuO₂ has the attice parameters a = b = 0.4499 nm and c = 0.3107 nm while TiO₂ has the values of a = b = 0.4594 nm and c = 0.2958 nm. Compared to the TiO₂ lattice, the [010] and [001] directions of bulk RuO₂ have a lattice mismatch of approximately −2.1% and +5.0% respectively. Thus, RuO₂ thin films experience tensile strain along [010] while compressive strain along [001].

The fabrication of the RuO₂ nanostrip starts with an HF etch of TiO₂ substrate. This is then followed by depositing a SiO_x layer, which in our case has a thickness of approximately $25~$nm, and electron beam patterning to create a positive resist mask with the desired device structure. Subsequently, the trench is selectively etched using reactive ion etching (RIE). We have observed that both underetching and overetching the trench is detrimental for a successful growth, similar to the case of CrO₂. RuO₂ nanostrips are subsequently grown in the trenches using chemical vapor deposition (CVD) in a two-zone furnace. During this process, the substrate temperature is maintained at 390 °C while the precursor (C₅H₅)₂ Ru is heated to 80 °C in the presence of an O₂ carrier gas flow. Figure 1(a) shows the SEM image of an epitaxially grown RuO₂ nanostrip along the [001] direction. RuO₂ also grows on the surface of SiO_x [23] albeit much more slowly than on TiO₂ which helps to prevent merging of small crystals of RuO₂ of a few tens of nanometers in diameter that also form during nanostrip growth.

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Figure 1(b) shows the temperature dependence of the resistivity, ρ_xx (T) of a typical RuO₂ nanostrip, that was patterned as a Hall Bar of width around 650 nm, thickness around 100 nm and with a distance between the contacts around $2.6\,\,\mu$m. The 300 K resistivity ρ₃₀₀ is $71\,\,\mu\Omega$.cm while the low-temperature (10 K) specific resistance ρ₁₀ is $13.5\,\,\mu\Omega$.cm. This gives a residual-resistivity ratio (RRR, the ratio between ρ₃₀₀ and ρ₁₀) of around 5.3. The nanostrip has a positive temperature coefficient of resistance at all temperatures including at low temperatures, as seen in inset of figure 1(b), which suggests very little or no grain boundary scattering of electron and a high crystal quality of the RuO₂ nanostrips.

We further characterized RuO₂ nanostrip through Hall measurements at different temperatures. Figure 1(d) shows measurements of the Hall resistivity as a function of an out-of-plane magnetic field for different temperatures in a range from 300 K to 10 K. The data are represented as ρ_xy as function of magnetic field, with $\rho_{xy} = \frac{V_{xy}t}{I}$. Here, V$_{xy}$ is the transverse voltage, I is the measurement current, and t is the thickness of the nanostrip. $\rho_{xy}(\mu_0 H)$ is linear for all the measured temperatures and the field with a slope that corresponds to electron-like charge carriers. Carrier density (n) and mobility (µ_e ) follow in a one-band model from $\rho_{xy} = - \frac{\mu_0H}{e\cdot n}$ and $\mu_e = \frac{\sigma_{xx}}{e\cdot n}$ where, σ_xx is $1/\rho_{xx}$. Their values and temperature dependence are plotted in figure 1(c). It is interesting to note that charge carrier density decreases with temperature and is nearly 4 times lower at 10 K than at 300 K.

Junction fabrication: To fabricate the lateral JJs (figure 2(a)), the initial step involved using SA technique to grow RuO₂ nanostrips with dimensions of approximately $30~\mu$m in length and $250~$nm in width, along the [001] direction. Superconducting contacts were fabricated by a combination of e-beam lithography and focused ion beam (FIB) milling (FIB). First, a liftoff resist structure was prepared, with a trench of about 2 micron wide, perpendicular to the nanostrip. Then, $100~$nm of MoGe was sputter deposited at a pressure of $5 \times 10^{-3}~$mbar, leading to the contact strip after lift-off. Finally, the weak link was created using FIB etching using a 10 keV Ga ion beam with a beam current of 15 pA. This way of preparing junctions is similar to earlier work we performed on various disk structures [24, 25]. In this way, three different junction devices were fabricated, with an edge-to-edge gap between the MoGe contacts of 32 nm (J1), 61 nm (J2) and 105 nm (J3). Here, a caveat is needed. In particular the 32 nm trench is both hard to make uniform, and proved not easy to measure in the SEM. The estimate should rather be 27 nm–38 nm. Moreover, the cut for this sample also made the nanostrip locally smaller. For the wider bridges, fewer issues were experienced. Also, generally, the cuts were quite deep, meaning that the RuO₂ bridge was thinner than its nominal value. Still, some clear conclusions can be drawn, as we will discuss below. Figures 2(a) and (b) shows the SEM images (false color) of the devices J1 and J2 respectively, consisting of RuO₂ nanostrip (blue) and MoGe electrodes (peach) on top of RuO₂. Figures 2(c) and (d) give their corresponding resistive transitions. The critical temperature of the MoGe is about 7 K, and visible as a tiny step (in J1), or a deviation from constant resistance (J2). A clear drop in resistance due to the contacts going superconducting is not expected, since this is a 4-point measurement. The normal state resistance in both cases (about 3 Ω for J1, 0.8 Ω for J2) is quite different, mainly due to the difference in trench depth. The transition temperature T_c , defined by the midpoint of the resistive transition, was also different, about 5.5 K for J1, and about 4 K for J2. These devices, with the smallest gaps, showed clear Josephson junction behavior. Device J3 with a 105 nm gap proximized only partially, meaning that zero resistance was not reached till 1.5 K. Table 1 summarizes the basic device parameters.

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Table 1. Critical current at measured temperature, normal resistance, junction length and the corresponding critical voltage of three Josephson junction devices based on nominally 100 nm thick and 250 nm wide RuO₂ nanostrips, contacted with 100 nm thick superconducting MoGe.

Device	T (K)	$I_c\,({\mu}A$)	$R_n\,(\Omega)$	$d_s\,(nm)$	$V_c\,({\mu}V)$
J1 (E5−2.1)	1.8	121	2.85	32 ±6	345
J2 (H4−1.1)	1.8	33	0.86	61	28.3
J3 (E5−1.2)	1.5	0	3.11	105	0

We measured the zero-field current(I)–voltage(V) behavior of the two JJs J1 and J2 as function of temperature. Typical IV characteristics are shown in figures 3(a) and (b) while figures 3(c) and (d) shows the color plot of I versus the derivative-dV/dI. We extracted the $I_c(T)$ from the onset of a change in the derivative, shown by the dashed line (white) in the figures 3(c) and (d). With this criterion, the temperature of the onset of supercurrent roughly coincides with the temperature of the midpoint of the resistive transition. At the lowest temperatures, I_c has become nearly constant. These low-temperature values show a strong decrease of I_c with increasing gap, dropping from 121 µA in J1 to 33 µA in J2.

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We also employed a different way of extracting I_c , by fitting the I-V characteristics to an analytical expression, derived from the work of Ambegaokar and Halperin [26]. More details on the fit can be found in the appendix. The fits work quite well. I_c is generally found to be only slightly higher than obtained with the derivative criterion, and the temperature dependence is the same. This is shown in figures 3(e) and (f).

We further fabricated and measured device J3 with a gap d_s = 105 nm, which did not reach zero resistance. Figure 4(a) shows the R(T) measurement from 300 K down to 1.5 K. We observe that the resistance becomes constant below 10 K, with a value of $3.7~\Omega$ around 8 K. When the MoGe electrodes become superconducting at 6.8 K the resistance starts to decrease again (after a small dip-peak excursion) but does not reach $0~\Omega$. The dip-peak feature hints at a slightly inhomogeneous superconducting transition [27] This behavior suggests that the RuO₂ nanostrip did not proximize completely over the whole length of the junction. In contrast, a reduction of around 41% in resistance from the normal state resistance is seen when the temperature is lowered to 1.5 K. This reduction translates to a proximity length of about 20 nm extending from each contact.

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Using the three JJ devices parameters, the coherence length ξ of the supercurrents can be estimated. For this, we use the decay of the coupling strength, given by the product $I_cR_N = V_c$. This ensures that the actual dimensions of the bridge, as given by R_N , are taken into account correctly. We fit $V_c(d_s)$ using an exponential decay function $V_c(d_s) \propto exp(-\frac{d_s}{\xi})$. There are only three data points,but the fit does show compatibility with exponential behavior. For our devices we estimate ξ ≈ 12 nm as shown in the figure 4(d). This matches quite well with the proximity length that we estimated to be induced in the longer junction J3. We also note that the order of magnitude reflects the size of the Ru-moment: in the collinear AF magnet IrMn, with a Mn moment of 3 µ_B , the coherence length was estimated 3–5 nm [14] (even quite large for such moments, possibly because it is an AF); in weak ferromagnets such as Pd$_{1-x}$Ni_x or Cu$_{1-x}$Ni_x , it is found that the superconducting decay length (the dirty-limit coherence length ξ_F ) is of the order of 5 nm for magnetic moments in the range 0.1–0.2 µ_B [28–30]. Finding 12 nm for an AF with moments of 0.05 µ_B appears quite reasonable.

We further measured our devices in the magnetic field and observed a Fraunhofer-like damped oscillatory response of I_c , as expected for a Josephson Junction. Figures 5(a) and (b) shows the color plot of the magnetic field interference pattern $I_c(\mu_0$H). In the case of J1, we measured at a temperature of 2.5 K while the field was varied between −130 mT to 130 mT. For J2, we measured at 1.5 K while the field was varied from 0 to 185 mT. For J2 in particular, the first and second minimum, and thereby the width of the lobes, can be estimated fairly well to be about 41 mT. To interpret these data, we have to consider the following. In conventional Josephson junctions that are formed by a barrier sandwiched between two superconducting electrodes, sometimes called overlap-type junctions, the (Fraunhofer) interference patterns can be described by

$$\begin{equation} I_c\left(\mu_0H\right) = I_c^{max} \left| \frac{\text{sin}{\left(\frac{\pi\Phi}{\Phi_0}\right)}}{\frac{\pi\Phi}{\Phi_0}}\right| \end{equation} \tag{ 1 }$$

where $I_c^{max}$ is the maximum critical current of the junction at zero field and $\Phi_0 = \frac{h}{2e}$ is the magnetic flux quantum (fluxoid). To give some feeling for this behavior, we display simulated Fraunhofer patterns for lobe widths of 45 mT (J1) and 41 mT (J2) in figures 5(a) and (b) (blue curves).

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The magnetic flux Φ is given by

$$\begin{equation} \Phi = \mu_{0}HA_{flux}^{eff} \;. \end{equation} \tag{ 2 }$$

Here, µ₀ H is the external applied magnetic field in the interface plane of the junction, and $A_{flux}^{eff}$ is the effective area of the junction. Using this description for our planar junctions, but with the applied field now perpendicular to the junction plane, we note that zero values for I_c are reached when $\Phi = n \Phi_0$ (with n an integer), so the width of the lobes $\Delta(\mu_0 H) = \Delta B$ is given by $\Delta B = \Phi_0 / A_{flux}^{eff}$. Using the lobe width of 41 mT, this would lead to $A_{flux}^{eff} \approx$ 0.05 µm². In overlap junctions, the area would be given by $(2\lambda_L + d_s)w$, with λ_L the London penetration depth and w the width of the junction device. In lateral junctions one has to be careful with using that description. For the perpendicular fields of this geometry, λ_L should be replaced by the Pearl length $\Lambda = 2 \lambda_L^2 / d$, but also the junction physics becomes different when the thickness d of the superconducting electrode isless than their London penetration depth, as is often the case for planar junctions. In particular, the description changes when the junction width w becomes smaller than the Josephson penetration length $\ell_J$ given by $\Phi_0 / (4 \pi \mu_0 \lambda_L^2 j_c(0)$, with j_c being the (presumed homogeneous) critical current density of the junction. In this scenario, as has been discussed in numerous studies, the electrodynamics becomes non-local, and $I_c(B)$ becomes independent of λ_L and is solely determined by the geometry of the device [25, 31–34]. In our junctions, the thickness d of the MoGe layer (100 nm) is smaller than the bulk London penetration depth (580 nm). Consequently, the relevant penetration depth for the electrodes is given by the Pearl length Λ, calculated to be ${\approx}$6.7 µm. This is significantly larger than the size of electrodes. Using the measured $I_c(0)$ in J2 of about 0.1 mA through a cross-section of w = 250 nm and thickness t = 100 nm, we estimate $\ell_J$ to be ${\approx}$97 nm. The junction width is actually somewhat larger than this, but it was discussed in [34] that non-local electrodynamics still apply. The simple answer for the lobe width in the interference pattern is that $\Delta B = 1.84 \Phi_0 / w^2$[25, 33, 35]. The lobe width $\Delta B = 41$ mT then corresponds to a junction width of 265 nm, quite close to the actual number. We conclude that, under a perpendicular magnetic field, our junctions show the behavior expected for planar junctions.

In summary, we have grown high quality RuO₂ nanostrips using the Selective Area (SA) growth on a TiO₂ substrate and used these to fabricate planar Josephson junctions with the RuO₂ strip as a weak link. We find these links not to behave as a normal metal; rather, the pair breaking effects are similar to what is found in weak ferromagnets such as CuNi and PdNi. The estimated coherence length of the weak link is about 12 nm. Moreover, the junctions behave as expected for planar junctions of such dimensions under the application of a magnetic field.

Technical support from M B S Hesselberth is gratefully acknowledged. This work is part of the research program of the Netherlands Organisation for Scientific Research (NWO). The work was supported by the Intel Corporation through Grant CG#38084911. The work was further supported by the EU COST action CA16218 'Nanocohybri' and by a grant from the Leiden-Delft Consortium 'NanoFront'.

The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.

Appendix. A.1. A shorted junction

We also measured a device where voltage probes are shorted. Figure A1(a) shows that at the device becomes superconducting below the T_c of MoGe. The response of the device in magnetic field as expected shows the current hardly varies. This is in sharp contrast to the Fraunhofer-like pattern of junctions in figure 5.

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Appendix. A.2 Closeup of a RuO₂ nanostrip

Figure A2 shows a high resolution scanning eletron micrograph of two epitaxially grown RuO₂ nanostrips of similar width of around 250 nm. In both cases, well defined crystal facets can be seen clearly. In (a) the width of the nanostrip is completely inside the trench. There are very small and thin crystals on SiO_x but away from the trench. However, for (b) thin crystal shards are attached to the side along the length of the strip. A probable explanation is that RuO₂ is known to grow on SiO_x surface. The growth on SiO_x is at a much slower rate. At the edge of the trench on both sides, these small crystals merged with the strip to give the above irregular growth.

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Appendix. A.3 Fitting IV characteristics

Figure A3 shows the I–V measurements at 2 K (in black) for both junctions J1 (a) and J2 (b). They were fitted by the following expression, derived from the work of Ambegaokar and Halperin (A-H)[26, 36]:

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$$\begin{align} V \; = \; \frac{2 I_c R_N}{\gamma_0} \frac{e^{\pi \gamma_0 i} - 1}{e^{\pi \gamma_0 i}} \left[ \; \int_{0}^{2 \pi} e^{-\gamma_0 i \Phi/2} I_0\left(\gamma_0 \text{sin}\frac{\Phi}{2}\right) \,d\Phi \ \right] ^{-1} \end{align} \tag{ 3 }$$

where $\gamma_0 = \Phi_0 I_c/(\pi k_B T)$, $i = I/I_c$, R_N is the normal resistance and I₀ is a modified Bessel function. The A-H fits, given in figure A3 (in red) for both junctions at 2 K, look quite good. The insets show that there is a slight deviation in a small interval near 0 voltage, where the fit shows a sharper corner while the measurement is more rounded. We ascribe that to instrumental noise. The values for I_c obtained in this way were plotted in figures 3(e) and (f).