Co-appearance of superconductivity and ferromagnetism in a Ca$_2$RuO$_4$ nanofilm crystal

TL;DR

This study demonstrates high-temperature superconductivity co-occurring with ferromagnetism in Ca$_2$RuO$_4$ nanofilm crystals, revealing novel quantum states and superconductor-insulator transitions induced by film thickness and bias current.

Contribution

It reports the first observation of high-temperature superconductivity coexisting with ferromagnetism in Ca$_2$RuO$_4$ nanofilms, highlighting the effects of reduced dimensionality.

Findings

Superconductivity with $T_c$ up to 64 K in Ca$_2$RuO$_4$ nanofilms.

Coexistence of ferromagnetism at 180 K and superconductivity.

Superconductor-insulator transition controlled by bias current and film thickness.

Abstract

By tuning the physical and chemical pressures of layered perovskite materials we can realize the quantum states of both superconductors and insulators. By reducing the thickness of a layered crystal to a nanometer level, a nanofilm crystal can provide novel quantum states that have not previously been found in bulk crystals. Here we report the realization of high-temperature superconductivity in Ca$_2$RuO$_4$ nanofilm single crystals. Ca$_2$RuO$_4$ thin film with the highest transition temperature $T_c$ (midpoint) of 64~K exhibits zero resistance in electric transport measurements. The superconducting critical current exhibited a logarithmic dependence on temperature and was enhanced by an external magnetic field. Magnetic measurements revealed a ferromagnetic transition at 180~K and diamagnetic magnetization due to superconductivity. Our results suggest the co-appearance of superconductivity and ferromagnetism in Ca$_2$RuO$_4$ nanofilm crystals. We also found that the induced bias current and the tuned film thickness caused a superconductor-insulator transition. The fabrication of micro-nanocrystals made of layered material enables us to discuss rich superconducting phenomena in ruthenates.

Full text

.1 Introduction

The search for high-temperature (high-$T_{c}$) superconductors is a fascinating topic in condensed matter physics. It is widely believed that high-$T_{c}$ superconductivity in cuprates emerges from doped Mott insulators Bednorz . Recently, $4d$ and $5d$ transition metal oxides with a layer perovskite structure have attracted much attention because the possibility of the emergence of high-$T_{c}$ superconductivity has been recognized in several studies Chaloupka ; Feng ; Kim . Indeed, monolayer films in iron pnictides indicate the enhancement of $T_{c}$ to above 100 K Jia . By tuning the film thickness in the monolayer to the nanometer range, transition metal dichalcogenides realize an exotic ground state different from that of bulk crystals due to a negative pressure effect Tsen ; Goli . Thus, the layered nanoscale film crystals play a key role when we explore the emergence of high-$T_{c}$ superconductivity in layered perovskite $4d$ and $5d$ transition metal oxides, which may allow us to detect superconductivity on mesoscopic scales.

For unconventional superconductors in cuprates Lake ; Chang_PRB , ruthenates Maeno , iron pnictides Kamihara , organic Oka and heavy-fermion materials Saxena ; Aoki , it is important to reveal the interplay between superconductivity and magnetism. Magnetic interactions are closely related to the mechanism of superconductivity, which attracts electrons towards each other. The antiferromagnetic correlations in high-$T_{c}$ cuprate superconductors lead to spin-singlet $d$-wave pairing states. In contrast, ferromagnetic correlations favour spin-triplet pairing states. The superfluidity of 3He Volovik is a leading physical system in which spin-triplet pairing is realized at very low temperatures. The coexistence of superconductivity and ferromagnetism in uranium compounds Saxena ; Aoki has attracted much attention. Layered perovskite Sr2RuO4 ($T_{c}=1.5$ K) is a leading candidate for a spin-triplet and chiral $p$-wave superconductor in quasi-two-dimensional electron systems Maeno_RMP ; Nobukane_PRB . In rutheno-cuprate superconductors Felner ; Tallon , superconductivity and ferromagnetism appear to coexist in different layers of layered perovskite structures where the superconductivity is confined to the antiferromagnetic CuO2 planes and is not caused by the spin-triplet pairing associated with the ferromagnetism of the RuO2 planes. However, high-$T_{c}$ ferromagnetic superconductors have yet to be found, while the spin-triplet superconductivity and superfluidity that have been reported were realized at very low temperatures. Here we report the observation of high-$T_{c}$ superconductivity related to ferromagnetism in Ca2RuO4 crystals with a nanoscale thickness. A Ca2RuO4 thin film exhibits zero resistance and diamagnetic magnetization at high temperature as evidence of superconductivity. Intriguingly, the enhancement of the critical current and the diamagnetic component for the applied magnetic field reveal the co-appearance of superconductivity and ferromagnetism. Moreover, we also found that the induced bias current and the tuned film thickness cause a superconductor-insulator (SI) transition. The superconductivity in Ca2RuO4 thin film crystals is expected to be robust against external magnetic fields, and play an important role when applied to a topological quantum computation Nayak_RMP .

The electronic states in layered perovskite $A_{2}$RuO4 have various phases that depend on metallic elements $A$ nakatsuji_jpsj . The ruthenate Sr2RuO4 is a superconductor below a transition temperature $T_{c}$ of 1.5 K Maeno . The substitution of Sr with Ca chemically pressurises the perovskite and causes the lattice distortion of RuO6 octahedra, which strongly modifies the electronic structures. As a consequence, a ruthenate where $A=$Ca2-xSrx becomes a paramagnetic metal or an antiferromagnetic metal depending on the doping rate $x$ nakatsuji_prl ; Friedt ; Gorelov . At $x=0$, the large degree of lattice distortion turns Ca2RuO4 into a band-Mott insulator with an antiferromagnetic correlation sutter ; das . In contrast, an electron doping system where $A=$Ca2-xLax Cao and thin films Miao shows a transition to ferromagnetic ordering. Experimental control of the distortions in Ca2RuO4 drives the transition from an insulator to a metal by applying hydrostatic and uniaxial pressure nakamura_prb ; Braden ; nakamura_jpsj ; taniguchi and by applying electric fields nakamura_srep and bias current sow . Such physical pressures are considered to release the distortion of octahedra. Interestingly, an ac susceptibility measurement performed in bulk Ca2RuO4 in the 9 $\sim$ 14 GPa range Alireza showed a transition to the superconducting phase below 0.4 K. Pressurization plays a key role in modifying the electric states in the ruthenate family. A third way of controlling the lattice distortion might be to tune the dimensionality of Ca2RuO4 crystal. Recent studies have reported the effects of negative pressure on lattice distortion when the thickness of the exfoliated films decreases to the nanometer range Tsen ; Goli . We have already reported the novel transport properties of Sr2RuO4 nanofilm single crystals nobukane_srep . In this article, we describe superconducting phenomena at high temperature induced by ferromagnetism in thin films of Ca2RuO4.

.2 Results and Discussion

Figure 1a shows the powder X-ray diffraction (XRD) patterns for Ca2RuO4. All the peaks can be well indexed with an orthorhombically distorted K2NiF4 structure characterized by a long $c$-axis (space group: L-Pbca). Minor peaks corresponding to the CaRuO3 ($\ast$) and Ca2RuO4 ($\sharp$) (S-Pbca) phases were also observed. The estimated CaRuO3 phase was $\sim 5\%$ whereas the amount of Ca2RuO4 (S-Pbca) was $\sim 6\%$. The lattice parameters $a=5.350(2)$ Å , $b=5.343(3)$ Å , and $c=12.278(5)$ Å  were obtained, which are close to those of the L phase reported for Ca2RuO4 under pressure Braden and Ca2-xSrxRuO4 Friedt . We found that the Ca2RuO4 nanofilm crystals were L phase at room temperature and ambient pressure. The impurity phase CaRuO3 is a paramagnetic metal down to low temperature in bulk Cao_113 . Although the behaviour of a ferromagnetic metal in CaRuO3 films has been reported Rana , they are different from the electric and magnetic properties of our samples. CaRuO3 films exhibit no diamagnetism Rana . In addition, we were able to distinguish layered Ca2RuO4 and CaRuO3 (cubic) by observing the crystal shape using a scanning electron microscope. We measured selected Ca2RuO4 nanofilm crystals as shown in the inset of Fig. 1c.

Figure 1b shows the temperature dependence of the longitudinal resistivity $\rho$ of Ca2RuO4 nanofilm crystals and the dependence of magnetic susceptibility $M/H$ on temperature at 10 Oe for powders weighing 5.2 mg (sample A). The resistivity $\rho=10^{-4}-10^{-2}~{}\Omega~{}\mathrm{cm}$ at 290 K of the samples is much lower than that in the $ab$-plane $\rho_{ab}\sim 6~{}\Omega\cdot$cm in bulk Ca2RuO4 (S phase) and is more like the resistivity of the L phase under hydrostatic pressure above 0.5 GPa nakamura_prb . This behaviour is consistent with the XRD result obtained with thin film crystals. We found a drop in the resistivity to zero and a diamagnetic component for samples with a broad transition behaviour of $\rho$ and $M/H$. Magnetization data are discussed in detail in Fig. 2. In Fig. 1c, the dependence of resistivity on temperature was not suppressed when a magnetic field was applied parallel to the $c$ axis. Moreover, Fig. 1d shows the current-voltage ($I-V$) characteristics of sample 3 for several magnetic fields at 0.53 K, which are vertically shifted for clarity. In $B=0$, the result clearly shows supercurrents of $|I_{c}|<13$ nA for the low bias current region, which strongly suggests the presence of superconductivity in a Ca2RuO4 thin film. The supercurrent was observed at 5 K even in 17 T (see Supplementary Fig. S2e). The superconductivity in the measured samples is robust for the applied magnetic field. Interestingly, the supercurrent increases as the magnetic field increases. Our results show that superconductivity is enhanced by an applied magnetic field, although the external magnetic field generally suppresses superconductivity in conventional superconductors. We also observed hysteresis with the supercurrent in the $I-V$ curves for sample 3 as shown in the inset of Fig. 1e. The hysteresis behaviour reveals a superconducting phase property because the hysteresis is a characteristic feature of small Josephson junctions, Josephson junction arrays and superconducting nanowires zant_phaseslip . The result suggests that a number of superconducting domains emerge locally at low temperature and that such domains interact with one another through the Josephson coupling. Similar behaviour also occurs in a phase-slip in superconducting nanowires Tinkham_book . In Fig. 1e, the critical current $I_{c}$ is enhanced at low temperatures. Although the Josephson critical current in conventional superconductors is described by the Ambegaokar-Baratoff relation Ambegaokar , the $I_{c}$ anomaly cannot be explained by this relation (the dotted line in Fig. 1e). Considering that the applied magnetic field enhances rather than suppresses the superconductivity, we use that Josephson critical current relation between chiral $p$-wave superconductors Barash ; Asano , $I_{c}(T)=aI_{c0}~{}\mathrm{ln}\left(\frac{b\Delta}{T}\right)\mathrm{sin}\Phi$, where $a$ and $b$ are constants of the order of unity, and the phase difference $\Phi$. The fitting result is shown in Fig. 1e, where we fixed $\mathrm{sin}\Phi=1$. The blue solid line with the logarithmic dependence fits nicely with our experimental data. This result suggests that the superconductivity of Ca2RuO4 nanofilm crystals realizes the chiral $p$-wave state. The deviation of the data from the fitting curve below 10 K seems to be saturation of $I_{c}$, which changes with the transparency of the junction Barash . Moreover, in Ref. Asano , a suppression of $I_{c}$ has been reported when the angular momentum of Cooper pairs in two chiral domains align in anti-parallel. We emphasize that the critical current is larger than that in $s$-wave junctions. We note that the broad transition behaviour of $\rho$ and $M/H$ is accentuated in two-dimensional (2D) superconductivity. A similar broad transition with $\Delta T=30-40$ K has been reported in YBa2Cu3O7-δ films matsuda ; Leng and FeSe film Shiogai . The Berezinskii, Kosterlitz and Thouless Berezinskii ; Kosterlitz_Thouless (BKT) transition for a 2D superconductor was observed in our samples (See Supplementary Text and Fig. S2). Our samples show two onset temperatures $T_{c~{}\mathrm{High}}^{\mathrm{on}}$ of $80-100$ K (light green) and $T_{c~{}\mathrm{Low}}^{\mathrm{on}}$ of $\sim 50$ K (green). The highest onset temperature 96 K was observed. The $T_{c~{}\mathrm{High}}^{\mathrm{on}}$ value is close to the temperature at which diamagnetism begins to appear in Fig. 1b, and the $T_{c~{}\mathrm{Low}}^{\mathrm{on}}$ value corresponds to the temperature at which the diamagnetic component is at its maximum.

To clarify the diamagnetism of the superconductivity, we performed magnetic measurements for powders weighing 5.2 mg (sample A) and 2.6 mg (sample B). Figures 2a and  2b show the dependence of magnetic susceptibility on temperature for the standard field-cooling (FC) process. The susceptibility of $\sim 5.0\times 10^{-5}$ emu/cm3 above $T_{\mathrm{Curie}}=$180 K is consistent with that reported for bulk Ca2RuO4 nakatsuji_jpsj ; taniguchi ; sow . Below $T_{\mathrm{Curie}}$, spontaneous magnetization increases sharply as shown in the inset of Fig. 2a. We also observed a magnetic hysteresis loop below $T_{\mathrm{Curie}}$ (see Supplementary Fig. S3), which indicates a ferromagnetic state. The non-saturating behaviour of the magnetization in high fields reflects the weak itinerant ferromagnetism of Ca2RuO4 thin films. In reports containing similar results to ours, the itinerant ferromagnetism in Ca2RuO4 appears in the “L” phase of bulk Ca2RuO4 nakatsuji_jpsj , La-doped Ca2RuO4 Cao and epitaxial thin films Miao . Surprisingly, a diamagnetic component in our nanofilm crystals appears as shown in Figs. 2a and 2b. We observed the diamagnetic behaviour even in 7 T as shown in Fig. 1c. This means that superconductivity is not eliminated by a magnetic field of 7 T, which is consistent with transport results. Recently, current-induced diamagnetism has been reported in bulk Ca2RuO4 sow . However, the result we obtained in a low field is sufficiently larger than the value of the diamagnetism in Ref. sow . Here we performed two types of subtractions to estimate the diamagnetic component. We first isolated the diamagnetic component $(\Delta M/H)_{\mathrm{min}}$ by subtracting the peak value of the magnetic susceptibility at $\sim$130 K from data points for each field as shown in Figs. 2c and  2d. The diamagnetism value was $\left(4\pi\Delta M/H\right)_{\mathrm{min}}\sim-0.09~{}\mathrm{emu/cm^{3}}$ at 10 Oe. We also performed an analysis using a fitted curve with temperature dependent magnetization in the itinerant ferromagnetism (see Supplementary Fig. S4). In ferromagnetic superconductors, the itinerant ferromagnetic fit has been subtracted off to reveal the superconducting part Aoki ; Paulsen . The diamagnetism for our samples lies within the range of $(4\pi\Delta M/H)_{\mathrm{min}}=-0.09~{}\mathrm{emu/cm^{3}}<4\pi\Delta M/H<(4\pi\Delta M/H)_{\mathrm{max}}=-0.32~{}\mathrm{emu/cm^{3}}$ at 10 Oe. Here we note that the diamagnetic behaviour is qualitatively the same regardless of the subtraction approach. The diamagnetism is reproduced in measured samples. Interestingly, the diamagnetization at 10 Oe is about 500-1000 times stronger than that in other non-superconducting materials such as highly oriented pyrolytic graphite and bismuth. There are no phenomena that show such giant diamagnetism other than superconductivity. Therefore, this result is evidence that Ca2RuO4 nanofilm crystals exhibit high-$T_{c}$ superconductivity. We note that a giant diamagnetic response above $T_{c}$ has been reported in cuprates Li and FeSe Kasahara . Their experiments reveal giant diamagnetism as a precursor to superconductivity and pseudogap formation. The diamagnetism response above $T_{c}$ for our samples may be considered the signature of preformed Cooper pairing (see Supplementary Information).

Next, to realize a ferromagnetic order, we cooled a powder of sample B at 5000 Oe from 190 K to 145 K ($<T_{\mathrm{Curie}}=180$ K), and then measured the temperature dependence of the magnetization in fields of 5, 8, 10, 12, 15 and 100 Oe from 145 to 2 K (see Supplementary Fig. S5). We raised the temperature to 190 K ($>T_{\mathrm{Curie}}=180$ K) before performing each measurement. The magnetic susceptibility result for sample B is shown in Fig. 2e. In Fig. 2f, the diamagnetic component $\left(4\pi\Delta M/H\right)_{\mathrm{min}}$ is plotted by subtracting the peak value of the susceptibility, which is similar to the behaviour of sample B in Fig. 2d. Moreover, to compare the diamagnetism values, Fig. 2g shows the result of an FC measurement from 190 to 2 K at 5 Oe and the result for an FC measurement from 145 to 2 K at 5 Oe after cooling from 190 to 145 K while applying a magnetic field of 5000 Oe. Interestingly, we found that the diamagnetic components were enhanced by ferromagnetic ordering in sample B. This means that superconductivity and ferromagnetism coexisted. The results of the electric transport and magnetic measurements suggest that the superconductivity emerges locally below $T_{\mathrm{Curie}}$ and that a drop in the resistance to zero is detected through the transport when the superconducting domain increases in size in the presence of a ferromagnetic correlation in Ca2RuO4 thin films. We note that our results for high-$T_{c}$ superconductivity in nanofilm crystals are inconsistent with the transition to the superconducting phase at $T_{c}=$ 0.4 K in bulk Ca2RuO4 under high pressures exceeding 9 GPa Alireza . We believe this to be due to the difference in the temperature at which the ferromagnetic phase appears. In nanofilm crystals, ferromagnetic ordering appears below 180 K, whereas bulk Ca2RuO4 exhibits ferromagnetism below 30 K Alireza .

The effects of quantum fluctuations in two dimensions would be more dominant in a Ca2RuO4 film. In Fig. 3a, we plot the sheet resistance $R_{\Box/layer}=\rho/d$ of sample 2 as a function of temperature for different bias currents $I$, where the interlayer distance of Ca2RuO4 $d=6.13$ Å . Correspondingly, $R_{\Box/layer}$ is the resistance per square per RuO2 layer. In the low temperature range from 4.2 to 20 K, for $I<I_{\mathrm{QCP1}}=100$ nA, $R_{\Box/layer}$ decreases with decreases in temperature, while $R_{\Box/layer}$ increases with decreases in temperature for $I>I_{\mathrm{QCP1}}$. Recently, by tuning the DC current, a current-induced metal-insulator transition has been realized in bulk Ca2RuO4 sow . The electronic states in Ca2RuO4 are sensitive to DC current. Our results suggest that the application of a DC current induces a transition from 2D superconductivity to an insulator. The critical current density value for high-$T_{c}$ thin film superconductors is $j_{c}>10^{4}$ A/cm2  Talantsev . At $I_{\mathrm{QCP1}}=100$ nA in Fig. 3a, the current density estimated as $j\approx 8.3\times 10^{2}$ A/cm2 is much smaller than $j_{c}$ (see Supplementary Table S1 and Text). We note that a current-driven SI transition has been reported in cuprate thin film superconductors Santos . Figure 3b shows the bias current dependence of $R_{\Box/layer}$ for different temperatures from 4.2 to 20 K. The crossing point is $I_{\mathrm{QCP1}}=100~{}\mathrm{nA}$, $R_{\mathrm{QCP1}}=16.5~{}\mathrm{k}\Omega\sim\frac{8}{\pi}\frac{h}{4e^{2}}$. Near the SI transition point, the sheet resistance should obey $R_{\Box}(I,T)=\frac{h}{4e^{2}}f\left[\frac{c_{0}(I-I_{c})}{T^{1/z\nu}}\right]$, where $c_{0}$ is a constant making the argument dimensionless, and $I_{c}$ is a current at a quantum critical point. The dynamical and correlation-length exponents are denoted by $z$ and $\nu$, respectively fisher . To determine the critical exponent $z\nu$ from the experimental results, we use $(dR_{\Box/layer}/dI)_{I=I_{c}}$ at a fixed $T$, i.e., $(dR_{\Box/layer}/dI)_{I=I_{c}}=\frac{c_{0}h}{4e^{2}}T^{-1/z\nu}\tilde{R^{\prime}}(0)$, where $\tilde{R^{\prime}}(0)$ is finite. The critical exponent $z\nu$ at low temperature was found to be 1.5 by plotting $(dR_{\Box/layer}/dI)_{I=I_{\mathrm{QCP1}}})$ as a function of $T^{-1}$ as shown in  Fig. 3d. The inset in Fig. 3b shows the scaling behaviour of the sheet resistance, where we use $I_{\mathrm{QCP1}}=100$ nA and $z\nu=1.5$. The results show that all of the resistance data below 20 K fall on a universal curve. Similarly, we performed a scaling analysis in a high temperature range of 30 to 45 K. Figure 3c and its inset show the bias current dependence of $R_{\Box/layer}$ for different temperatures and the universal curve at $z\nu=0.64$, where $I_{\mathrm{QCP2}}=1960$ nA and $R_{\mathrm{QCP2}}=38.1~{}\mathrm{k}\Omega\sim 6\frac{h}{4e^{2}}$ were used. We observed two critical exponents as shown in Fig. 3d. Our result is very similar to two-stage quantum critical behaviour and the critical exponents reported in a magnetic-field-induced SI transition Lesueur ; Popovic . Indeed, the critical exponent for the scaling analysis estimated from $I-V$ characteristics with $I^{*}_{\mathrm{QCP}}=\pm 140$ nA for sample 4 (inset in Fig. 3e) was $z\nu=0.68$ at low temperature as shown in Fig. 3e, which is consistent with that in the high-temperature region for sample 2. Sample 2 contains more disorder or inhomogeneity than sample 4 from resistivity results. Therefore, quantum phase fluctuations seems to play an important role at low temperature.

Now we discuss the two critical exponents in a 2D superconductor. In general, the behaviour in a quantum (or classical) critical phase transition is classified in universality classes that depend on the properties of the system such as its symmetries and dimensionality. The critical exponents for disordered systems must satisfy the Harris criterion, which is represented by $\nu\geq 2/d$, where $d$ is the spatial dimensionality fisher . The dynamical exponent is assumed to be $z=1$ due to the long-range Coulomb interaction between charges. The critical exponent of $\nu\sim 2/3$ corresponds to the (2+1)D XY model for a 2D superconductor Lesueur . In contrast, the critical exponent $\nu=3/2$ suggests that the SI transition is explained by a Bose glass in two dimensions. Previous papers have reported quantitatively similar values for the critical exponent in InOx Paalanen , Nd2-xCexCuO4 Tanda , $\alpha-$MoGe Yazdani and La2-xSrxCuO4 Bollinger films. The critical value of $R_{\mathrm{QCP1}}$ is very close to the universal resistance $\frac{8}{\pi}\frac{h}{4e^{2}}$ predicted by the superconductor to Mott-insulator transition Fisher_Girvin . At low temperature, the contribution of disorders caused by quantum fluctuations is enhanced and may appear as intrinsic inhomogeneities on a micro-nanoscale with the coexistence of superconducting and non-superconducting domains in strongly correlated 2D superconductors. We note that, at present, we cannot determine the universality class for our samples because classical percolation ($\nu=4/3$) and quantum percolation ($\nu=7/3$) models have been reported as the expected critical exponents of $\nu\geq 1$ Steiner . We observed hysteresis with the supercurrent in the $I-V$ curves for sample 2 as shown in the inset in Fig. 3d. This agrees well with the existence of the arrays of superconducting domains (Fig. 3d) explained by $z\nu=3/2$ for disordered (strongly correlated) superconductors. One reason why a DC current-induced SI transition occurs is that the coupling between the superconducting domains is broken as the DC current is increased. Thus, a current-driven SI transition occurs. Another reason is that an SI transition is caused by driving the ferromagnetic superconducting domains (walls) by applying a DC current.

Figure 3f shows the dependence of the resistivity $\rho$ on temperature for different thicknesses of Ca2RuO4 single crystal. In general, the resistivity in conventional metals becomes an intrinsic property irrespective of their size and shape. As the sample thickness decreases, the resistivity in thin films tends to increase due to the contribution of dislocations and impurities. Our result in Fig. 3f is the complete opposite of the above case. The resistivity of Ca2RuO4 thin flakes is thickness dependent and decreases as the thickness decreases to the nanometer range. Surprisingly, the resistivity for $10-30$ nm thick samples decreases below $T_{c}^{\mathrm{on}}$, while sample 7 with a thickness of 300 nm exhibits insulating behaviour. The critical thickness is 50 nm. We discuss the reasons for the different transport properties of samples with approximately the same thickness of $\sim 10$ nm (see Supplementary Table S2 and Text). By reducing the thickness to the nanometer range, we succeeded in controlling the electronic states from an insulator to a superconductor.

Below, we explain the reasons for the superconducting behaviour in a Ca2RuO4 thin film. As shown in Fig. 4, the electronic properties in a Ca2RuO4 thin film are qualitatively different from those in a Mott insulator Ca2RuO4. Previous studies have partially explained the reasons for the difference. Octahedra consisting of RuO6 in bulk Ca2RuO4 have three types of distortion (flattening, tilting, and rotating) Friedt ; nakamura_prb ; Braden ; nakamura_jpsj ; taniguchi . The application of physical or chemical pressure releases the distortion, which leads to a transition from the Mott insulating phase to the ferromagnetic metallic phase Friedt ; nakamura_prb ; Braden ; nakamura_jpsj ; taniguchi . We discuss why the thin films are metallic rather than insulating. When the thickness of a layered thin film decreases to the nanometer range Tsen ; Goli ; nobukane_srep , the effects of negative pressure can release the distortion of the octahedra. The results of our first-principle calculation in Fig. 4 partially support this argument. The figure summarizes the relationship between the number of RuO2 layers along the $c$ axis and the tilting angle of the octahedra from the $c$ axis (see Supplementary Table S3 and Text). The tilting angle decreases and the distance along the $c$ axis increases as the number of layers decreases. The calculation also suggests that there is a uniform ferromagnetic metal phase in a Ca2RuO4 monolayer in the absence of flattening distortion. Actually, a change of a few percent in the lattice constant and the distortion of the octahedra affect the electric and magnetic properties in transition metal oxides with a layered perovskite structure such as RuO6 Miao ; Dietl ; Steppke , CuO6 Thio and IrO6 Crawford ; Korneta . Therefore, the suppression of the lattice distortion under a negative pressure is responsible for the superconducting properties in a thin film single crystal.

Finally, we discuss the pairing symmetry of superconductivity in Ca2RuO4 flakes. We revealed that the temperature dependence of $I_{c}$ can be understood by the fitting in chiral $p$-wave superconductors. The critical current and diamagnetism was enhanced by the applied magnetic field. These results suggest the possibility of spin-triplet Cooper pairing in Ca2RuO4. We must undertake further experimental studies to clarify the mechanism of the pairing symmetry and unconventional vortices tafari ; Bert ; Stolyarov using STM and a scanning SQUID microscope.

.3 Conclusion

In conclusion, we have studied electric transport and magnetic properties in a Ca2RuO4 thin film. Our transport experiments show the logarithmic dependence of the $I_{c}$ on temperature, and the enhancement of $I_{c}$ under an external magnetic field applied perpendicular to the conducting plane. Magnetic measurements revealed the ferromagnetic transition and the diamagnetism caused by superconductivity. We observed current-induced and film-tuned SI transitions in a Ca2RuO4 thin film, which are phenomena unique to 2D superconductors.

.4 Methods

To obtain micro-nanoscale Ca2RuO4 single crystals, we synthesized Ca2RuO4 crystals with a solid phase reaction. We prepared CaCO3 (99.99$\%$, Kojundo Chem.) and RuO2 (99.9$\%$, Kojundo Chem.) powders. The mixed powder was heated at 1070 ∘C for 60 hours. The mixture was then cooled gradually to room temperature. We repeated the heating and cooling process several times. The Ca2RuO4 crystal structure was analysed by using XRD (Rigaku Miniflex600) with Cu $K\alpha$ radiation. The samples were dispersed in dichloroethane by sonication and deposited on a SiO2(300 nm)/Si substrate. We then fabricated gold electrodes using standard electron beam lithography methods. The sample thickness was determined from scanning electron micrographs obtained with a sample holder tilt of 70 degrees.

We performed electric transport measurements with the four-terminal method. To cover a wide $T$ and $B$ range and avoid an experimental artifact in the measurement system, we used several different cryostats: a homemade 3He refrigerator at $T$ down to 0.5 K with magnetic fields up to 7 T, a 3He system (Heliox, Oxford) at $T$ down to 0.23 K with magnetic fields up to 17 T and a Physical Property Measurement System (PPMS, Quantum Design) with fields up to 9 T. All leads were equipped with $RC$ filters ($R=1$ k$\Omega$ and $C=22$ nF). In the DC measurements, a bias current was supplied by a DC current source (6220, Keithley) and the voltage was measured with a nanovoltmeter (2182, Keithley). We measured the temperature dependence of resistivity for bias current $I$ by the current reversal method. We confirmed that the contact resistance was $2-10$ k$\Omega$.

We performed magnetization measurements as a function of magnetic field and temperature using a Magnetic Property Measurement System (MPMS, Quantum Design) with applied magnetic fields up to 7 T and a temperature range of $2-300$ K. The Ca2RuO4 nanofilm crystal powders was encapsulated.

Acknowledgements

We thank Y. Tabata, K. Nakatsugawa, T. Kurosawa, K. Yamaya, S. Takayanagi, T. Matsuura, K. Inagaki, T. Honma, K. Ichimura, N. Matsunaga, N. Sakaguchi, and Y. Asano for experimental help and useful discussions. This work was supported by JSPS KAKENHI (No.17K14326), Inamori Foundation, Iketani Science and Technology Foundation and Samco Science and Technology Foundation.

Author contributions

H.N. and S.T. designed the experiments. H.N., K.Y., Y.O., K.I., K.T. and T.N. synthesized the high-quality samples and analysed the crystal structure. H.N., K.Y., Y.O. and K.I. performed the transport and magnetic measurements and analysed the data. Y.K. performed the first-principle calculation. K.N., T.A. and S.T. helped interpret the results. H.N. drafted the manuscript. All the authors read and approved the final manuscript.

Competing Interests

The authors declare that they have no competing interests.