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

Ruthenium dioxide (RuO2) is a metallic rutile oxide with a number of interesting properties. For a long time, it was considered to be a highly conductive normal metal and a Pauli paramagnet. Recently, it was found that the material is antiferromagnetic, with small magnetic moments of the order of 0.05 Bohr magneton and an ordering temperature above 300 K. The presence of magnetic moments should have clear consequences when trying to induce superconductivity in RuO2. We used a selective area chemical vapor deposition method to grow nanostrips of RuO2 on TiO2 substrates. On these nanostrips, superconducting contacts were made of MoGe, and a weak link was fabricated with a Focused Ion Beam. We find that the device behaves as a Josephson junction, including a Fraunhofer-like response to a magnetic field, for distances between the contacts below 70 nm. We estimate the induced singlet coherence length ξ to be about 12 nm, which seems a reasonable number when small magnetic moments are present.


Introduction
In recent years, there has been a revival of interest in the properties of the metallic rutile oxides CrO 2 , RuO 2 and IrO 2 , mainly in connection with magnetism, non-trivial Fermi surfaces, and possible spintronics applications [1,2].CrO 2 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][5][6].IrO 2 was researched from a spintronics perspective as a material with large spin-orbit coupling [7,8].RuO 2 was long thought to be a normal metal, and in film form Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.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 RuO 2 [13].
Long range proximity effect has been recently observed in Mn 3 Ge, 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.RuO 2 , although also a collinear antiferromagnet, has been shown to have crystal inversion asymmetry arising from spin-splitting and timereversal symmetry breaking in the band structure [16][17][18].RuO 2 has also been identified as a promising candidate to allow for spin polarized currents which has been substantiated by recent transport measurements conducted on RuO 2 [19][20][21].In this work, we investigate the proximity effect in RuO 2 nanostrips by fabricating lateral Josephson junctions, using superconducting amorphous MoGe as electrodes.Since the resistivity of RuO 2 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 RuO 2 nanostrips through electrical and magnetotransport measurements.Then we focus on making Josephson junctions (JJ) in which superconducting MoGe are contacted on top of RuO 2 nanostrips with varying lateral gaps and present the results on these junctions.

Selective area growth of RuO 2 nanostrips
We grow RuO 2 nanostrips on (100) oriented TiO 2 substrates using the same selective area growth technique as CrO 2 nanostrips [22] since the lattice parameters of TiO 2 , RuO 2 and CrO 2 are comparable and they all crystallize with a rutile structure and a tetragonal unit cell.RuO 2 has the attice parameters a = b = 0.4499 nm and c = 0.3107 nm while TiO 2 has the values of a = b = 0.4594 nm and c = 0.2958 nm.Compared to the TiO 2 lattice, the [010] and [001] directions of bulk RuO 2 have a lattice mismatch of approximately −2.1% and +5.0%respectively.Thus, RuO 2 thin films experience tensile strain along [010] while compressive strain along [001].
The fabrication of the RuO 2 nanostrip starts with an HF etch of TiO 2 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 CrO 2 .RuO 2 nanostrips are subsequently grown in the trenches using chemical vapor deposition (CVD) in a twozone furnace.During this process, the substrate temperature is maintained at 390 • C while the precursor (C 5 H 5 ) 2 Ru is heated to 80 • C in the presence of an O 2 carrier gas flow.Figure 1(a) shows the SEM image of an epitaxially grown RuO 2 nanostrip along the [001] direction.RuO 2 also grows on the surface of SiO x [23] albeit much more slowly than on TiO 2 which helps to prevent merging of small crystals of RuO 2 of a few tens of nanometers in diameter that also form during nanostrip growth.
Figure 1(b) shows the temperature dependence of the resistivity, ρ xx (T) of a typical RuO 2 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 µm.The 300 K resistivity ρ 300 is 71 µΩ.cm while the lowtemperature (10 K) specific resistance ρ 10 is 13.5 µΩ.cm.This gives a residual-resistivity ratio (RRR, the ratio between ρ 300 and ρ 10 ) 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 RuO 2 nanostrips.
We further characterized RuO 2 nanostrip through Hall measurements at different temperatures.Figure 1(d) shows measurements of the Hall resistivity as a function of an outof-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 ρ xy = Vxyt I .Here, V xy is the transverse voltage, I is the measurement current, and t is the thickness of the nanostrip.ρ xy (µ 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 ρ xy = − µ0H e•n and µ e = σxx e•n where, σ xx is 1/ρ 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 RuO 2 nanostrips with dimensions of approximately 30 µm 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 × 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 RuO 2 bridge was thinner than its nominal value.Still, some clear conclusions can be drawn, as we will discuss below.Figures 2(a  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.

Results and discussion
We measured the zero-field current(I)-voltage(V) behavior of the two JJs J1 and J2 as function of temperature.Typical 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 Ω 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 Ω.The dip-peak feature hints at a slightly inhomogeneous superconducting transition [27] This behavior suggests  that the RuO 2 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.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 c R 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 ) ∝ exp(− ds ξ ).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 Rumoment: 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 dirtylimit coherence length ξ F ) is of the order of 5 nm for magnetic moments in the range 0.1-0.2µ B [28][29][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  shows the color plot of the magnetic field interference pattern I c (µ 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 overlaptype junctions, the (Fraunhofer) interference patterns can be described by   where I max c is the maximum critical current of the junction at zero field and Φ 0 = 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).
The magnetic flux Φ is given by Here, µ 0 H is the external applied magnetic field in the interface plane of the junction, and A eff flux 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 Φ = nΦ 0 (with n an integer), so the width of the lobes ∆(µ 0 H) = ∆B is given by ∆B = Φ 0 /A eff flux .Using the lobe width of 41 mT, this would lead to A eff flux ≈ 0.05 µm 2 .In overlap junctions, the area would be given by (2λ 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 Λ = 2λ 2 L /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 ℓ J given by Φ 0 /(4π µ 0 λ 2 L 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][32][33][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 ≈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 ℓ J to be ≈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 ∆B = 1.84Φ 0 /w 2 [25,33,35].The lobe width ∆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.

Summary
In summary, we have grown high quality RuO 2 nanostrips using the Selective Area (SA) growth on a TiO 2 substrate and used these to fabricate planar Josephson junctions with the RuO 2 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.where γ 0 = Φ 0 I c /(π k B T), i = I/I c , R N is the normal resistance and I 0 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).

Figure 1 .
Figure 1.(a) SEM image (false color) of a RuO 2 nanostrip grown using Selective Area Growth.The magnetic field B is applied out of the plane for Hall characterization measurements.(b) Longitudinal resistivity as a function of temperature for a RuO 2 nanostrip with dimensions of approximately 2.6 µm in length between contacts and 650 nm in width; inset shows the positive temperature coefficient of resistance at lower temperature indicating that high crystal quality.(c) mobility (µe) (top) and charge carrier density (ne) (bottom) at different temperature indicating that the behavior is unlike normal metal where ne stays constant with temperature (d) Hall resistivity as a function of applied field measured at various temperature between 10 K to 300 K.
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.

Figure 2 .
Figure 2. SEM image (false color) of the fabricated Josephson junctions (JJ) comprising RuO 2 nanostrip (in blue) and MoGe as the superconducting contacts (in peach) that are laterally edge to edge separated by (a) 32 nm for J1 and (b) and 61 nm for J2.(c), (d) Resistance vs temperature plot between (10-1.5)K showing the transition temperature (Tc) for the junctions (c) J1 and (d) J2.We have taken Tc as the temperature at which the resistance has decreased to 50% of the normal resistance value, which for J1 is 5.5 K and for J2 is 3.8 K.

Figure 3 .
Figure 3. Current (I) versus Voltage (V) measurements taken above (black) and below (red) the superconducting transition of (a) J1 and (b) J2, respectively.Panels (c), (d) show the behavior of dV/dI as function of I, measured over different temperatures in steps of (c) 200 mK, for J1, and (d) 100 mK, for J2.The dashed white lines show the associated critical current Ic(T), extracted from a differential resistance criterion (0.4 Ω for (c), 0.6 Ω for (d)).Panels (e), (f) show that same Ic(T) (dashed blue line) together with Ic(T) derived from an Ambegaokar-Halperin fit to the I-V characteristics for (e) junction J1 and (f) junction J2.

Figure 4 .
Figure 4. (a) SEM image of the device J3 where ds = 105 nm.(b) I-V characteristics measured at 2.5 K (black) and 1.5 K (red) at zero-field shows very small non-linearity.The inset shows a zoom-in of the non-linear behavior starting to occur at 1.5 K (red).(c) R(T) behavior of J3 measured from 280 K down to 1.5 K.The inset shows the R-T for temperature between 9 K to 1.5 K.A sharp drop in resistance is measured around 6.8 K signaling the superconducting transition MoGe.By 1.5 K, the normal state resistance of the strip has dropped by 41% which is a clear signature of partial proximization of the junction.(d) Vc = IcRn as a function of ds for the 3 JJ devices.The red curve is the fitted exponential decay function which gives coherence length (ξ) in RuO 2 of around 12 nm.

Figure 5 .
Figure 5. I-V characteristics of the JJ devices (a) J1 at 2.5 K and (b) J2 1.2 K when applying out of plane magnetic field.The blue curve is the simulated Fraunhofer pattern (for lobe widths of 45 mT (J1) and 41 mT (J2)) for our devices dimensions, representing the relation between critical current Ic and the applied magnetic flux.The outline (black) in (a) is at 1.6 µV while the outline (black and white) in (b) is at ± 0.33 µV.

Figure A1 .
Figure A1.(a) R(T) between 10 K to 2 K of a shorted -junction device.The device becomes superconducting below 6 K. (b) Color plot of I(µ 0 H) of a shorted-junction device measured at 2 K. Field is applied out of plane to the device interface and varied from 0 to 150 mT.As expected current (I) stays almost constant under the whole range of field.

Figure A2 .
Figure A2.High resolution close up SEM images of two RuO 2 nanostrips.

Figure A3 .
Figure A3.I − V Plots (in black) of J1 (a) and J2 (b) measured at 2 K along with their corresponding A-H fit (in red; see text).The inset shows the small interval of voltage where there is a deviation between the measurement and A-H fit.

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 RuO 2 nanostrips, contacted with 100 nm thick superconducting MoGe.