Article
Reference
Anisotropy of the superconducting transport properties of the LaAlO
3/SrTiO
3interface
REYREN, Nicolas, et al.
Abstract
The superconducting transport properties of the conducting LaAlO3/SrTiO3 interface have been investigated in perpendicular and parallel magnetic fields. A large anisotropy in the transport properties is measured and the two-dimensional nature of the superconducting gas is confirmed. Analyses of the resistance versus temperature and magnetic field, as well as of the correlation length as a function of the magnetic field close to the superconducting critical temperature (about 200 mK), yield an estimate of similar to 10 nm for the superconducting layer thickness.
REYREN, Nicolas, et al . Anisotropy of the superconducting transport properties of the LaAlO
3/SrTiO
3interface. Applied Physics Letters , 2009, vol. 94, no. 11, p. 112506
DOI : 10.1063/1.3100777
Available at:
http://archive-ouverte.unige.ch/unige:114273
Disclaimer: layout of this document may differ from the published version.
1 / 1
Anisotropy of the superconducting transport properties of the LaAlO
3/ SrTiO
3interface
N. Reyren,1,a兲S. Gariglio,1A. D. Caviglia,1D. Jaccard,1T. Schneider,2and J.-M. Triscone1
1DPMC, University of Geneva, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
2Physik-Institut der Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
共Received 16 January 2009; accepted 26 February 2009; published online 18 March 2009兲 The superconducting transport properties of the conducting LaAlO3/SrTiO3 interface have been investigated in perpendicular and parallel magnetic fields. A large anisotropy in the transport properties is measured and the two-dimensional nature of the superconducting gas is confirmed.
Analyses of the resistance versus temperature and magnetic field, as well as of the correlation length as a function of the magnetic field close to the superconducting critical temperature共about 200 mK兲, yield an estimate of⬃10 nm for the superconducting layer thickness. ©2009 American Institute of Physics.关DOI:10.1063/1.3100777兴
At the interface between complex oxides, unexpected electronic properties can be generated, different from those of the constituent materials.1–4This finding suggests that ox- ide “interface engineering” can lead to original physics and possible innovative devices exploiting the large variety of oxide combinations and the richness of their properties.5An impressive amount of work has been triggered by the discovery1 of an electron gas at the interface between two band insulators LaAlO3 共LAO兲 and SrTiO3 共STO兲.6,7 Al- though the debate about the origin of the electron gas at the LAO/STO interface is still ongoing, it has been clearly shown that the growth conditions determine the sheet resis- tance and sheet carrier density of the system,8suggesting that the growth conditions control the amount of oxygen vacan- cies in the STO substrate. In particular, it was shown that growth at very low oxygen pressures leads to a thick con- ducting layer.9–12
Using samples grown at a pressure of 10−4 mbar fol- lowed by oxygen annealing, it has been shown in 2006 in a series of experiments13 that the conductivity at the interface was only observed for LAO thicknesses above or equal to 4 unit cells共uc兲, suggesting that the conductivity measured has some “intrinsic” origin.14 Using similar growth conditions, we have shown in 2007 that this interface is not only con- ducting but also superconducting.2For such samples, a key issue is to determine the thickness of the 共super兲conducting layer. Recently, room temperature studies have been per- formed to estimate the thickness of the electron gas in samples grown at “high” oxygen pressures leading to a value of ⱗ7 nm共Ref. 11兲and⬃1 nm.15
In this letter, we use superconductivity共SC兲to estimate the thickness of the electron gas at low temperatures, mea- suring transport properties of the LAO/STO interface in par- allel and perpendicular magnetic fields. Our analyses yield an estimate of ⬃10 nm for the superconducting layer thickness.
As mentioned above, the properties of the interface de- pend critically on the growth conditions. Here, the LAO thin films have been grown by pulsed-laser deposition on top of 共001兲-oriented TiO2-terminated STO substrates at 800 ° C at an oxygen pressure of 8⫻10−5 Torr. A KrF excimer laser
共wavelength of 248 nm兲 is used to ablate a stoichiometric crystalline LAO target with a fluence of 0.6 J/cm2at a typi- cal frequency of 1 Hz, leading to a deposition rate of about 1 uc for⬃30 pulses. After deposition, the oxygen pressure is raised to 0.2 bar and the temperature keptⲏ500 ° C for 1 h.
The growth is monitored in situ by reflection high-energy electron diffraction, which allows the thickness to be con- trolled at the unit cell level. The epitaxy and the pseudomor- phic growth of the LAO thin films are confirmed by x-ray studies. Samples realized with these conditions undergo a metal-insulator transition at a critical LAO thickness of 4 uc as observed by Thiel et al.13These samples exhibit a resis- tive superconducting transition around 200 mK. Normal state transport measurements and detailed structural characteriza- tion can be found in Ref.16.
The sample presented in this study has a LAO thickness of 4 uc, the experiment has been reproduced on three other samples with LAO thicknesses of 4, 8, and 9 uc. The resis- tance was measured by a dc four-point method in a3He/4He dilution cryostat. On the 4 uc sample, a path that is 100 m wide and 200 m long has been patterned. Data are pre- sented in sheet resistance units. A magnetic field of up to 8 T can be applied, either perpendicular or parallel to the inter- face. In the parallel configuration, the current direction is collinear with the magnetic field and the alignment between the interface and the field is adjusted with a precision of about 0.15° using a piezoelectric goniometer. To precisely determine the alignment between the field and the plane of the interface, 1 T was applied and the angle leading to the highest critical temperature was determined. The precision in the alignment is mainly limited by the noise in the resistance measurement, rather than surface roughness and substrate curvature effects, which were estimated from atomic force microscopy and alpha step analyses. The uncertainty in tem- perature values共ⱗ3 mK兲is mainly due to the heating ramp rate and the thermalization time. The magnetic field is deter- mined with a precision better than 1 mT. Note that below
⬃50 mK, the thermalization of the electrons may be an is- sue, possibly leading to larger uncertainties that are difficult to evaluate. The measurement current has been kept below the critical current determined from voltage versus current 关V共I兲兴 characteristics recorded at different temperatures and magnetic fields.
a兲Electronic mail: [email protected].
APPLIED PHYSICS LETTERS94, 112506共2009兲
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Figure 1 shows sheet resistance versus temperature 关RS共T兲兴 curves for magnetic fields applied perpendicularH⬜ and parallelH储to the interface. In the perpendicular configu- ration 关Fig. 1共a兲兴, a magnetic field of about 150 mT sup- presses SC down to the lowest temperature, in agreement with previous measurements.2For magnetic fields parallel to the interface 关Fig.1共b兲兴, we observed that the width of the transition is relatively unaffected by fields up to 1.3 T, whereas a broadening of the transition is observed in theH⬜ case. This difference in behavior could possibly be related to vortex motion in the perpendicular case.2 In parallel fields ⲏ2.0 T, traces of SC are completely suppressed.
To determine the superconducting thickness, we define Tⴱ共H兲as the temperature at which the sheet resistance is 50%
of RS共T= 400 mK兲.17 Figure 2共a兲 shows the characteristic field0Hⴱ共T兲for the parallel and perpendicular field direc- tions.
We note that the temperature dependence for the parallel field direction follows the standard behavior expected for a two-dimensional film,18 H储ⴱ共T兲⬀关1 −T/Tⴱ共H= 0兲兴1/2. Analy- ses of the perpendicular field data using a mean field ap- proach lead to an in-plane coherence length, 储共T兲
=关⌽0/共20H⬜ⴱ兲兴1/2, of about 70 nm atT= 0;⌽0is the flux quantum. Analyses of the parallel field data assuming a thicknessdmuch smaller than the London penetration depth
and the coherence length lead to a thickness d of 12⫾2 nm. Here the Ginzburg–Landau theory is used18 with d being related to 储共T兲 and H储ⴱ共T兲 by d
=共
冑
3⌽0兲/关储共T兲0H储ⴱ共T兲兴.We also note that the paramagnetic limit 共Clogston–
Chandrasekhar兲seems to be exceeded by a factor of four to five, if the standard Bardeen-Cooper-Schrieffer formula
0Hp=兵关⌬共0兲兴/共B
冑
2兲其= 1.84Tc关T兴is used.19It was shown in earlier work that the current-voltage characteristics of the superconducting interface are consistent with a Berezinskii–Kosterlitz–Thouless 共BKT兲 transition.2 More detailed evidence for a BKT scenario follows from Ref. 20and21. The data of Fig.1 also point to a magnetic
field tuned quantum phase transition. In this case, thermal and quantum fluctuations play an important role and hence the mean field approach and the determination of the mean fieldTcare questionable. We also note that the standard ap- proach does not take into account the presence of vortices.
Finally, the BCS nature of SC is not established in this sys- tem. To circumvent these difficulties, we performed a scaling analysis within the general framework of phase transition studies to determine the superconducting thickness. As de- tailed in Ref. 21, in the presence of fluctuations, the critical field transition line is replaced by a crossover line. Keeping Tⴱas the crossover characteristic temperature, one expects22 关0H储ⴱ共T兲兴2=共⌽0兲/共2d2兲0H⬜ⴱ共T兲. H⬜ⴱ共T兲 and H储ⴱ共T兲 can thus be rescaled by plottingH⬜ⴱ andHⴱ2储 , revealing the thick- ness d. Such a rescaling is shown in Fig. 2共b兲. As can be seen, the best agreement is obtained forH储ⴱ2/H⬜ⴱ ⬇25 leading to a thickness of 11⫾3 nm.
Finally, we performed an analysis of the correlation length ˜ which diverges at the BKT transition temperature TBKT in zero field. However, in the presence of a magnetic field this divergence is removed due to the limiting magnetic length, so that ˜共H⬜,TBKT兲⬀
冑
共⌽0兲/共aH⬜兲 and˜共H储,TBKT兲⬀共⌽0兲/共aH储d兲, wherea⬇3.12 is a universal constant.22The sheet conductance and the correlation length are related by
˜共T兲⬀
冑
f共T兲, where f is the SC fluctuation conductance related to the measured conductance by=0+f,0being the residual conductance.21,22TBKT was determined for the sample investigated here following the procedure described in Ref. 2 and detailed in Ref.21and found to be about 215 mK. Figure3, shows
冑
fas a function of H储−1andH⬜−1/2atTBKT. Analyses of the high field regions reveal the expected behavior and allow a thick-
FIG. 1. 共Color online兲Sheet resistance vs temperature for different mag- netic fields applied共a兲perpendicular and共b兲parallel to the interface.
FIG. 2.共Color online兲 共a兲Characteristic magnetic fields as a function of the temperature forHapplied parallel共dots兲and perpendicular共squares兲to the interface exhibiting a large anisotropy共H储ⴱ/H⬜ⴱ⬇20兲. The inset shows the same data on an enlarged field scale for the perpendicular field configura- tion. The solid line forH储is a fit to the data while the one forH⬜is a guide to the eye.共b兲Scaling analysis of the critical fields as described in the text.
112506-2 Reyrenet al. Appl. Phys. Lett.94, 112506共2009兲
Downloaded 20 Mar 2009 to 129.194.8.73. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
ness of about 7 nm to be determined by taking the ratio of the high field slopes. The deviations observed at low fields are probably due to a size effect that limits the divergence of
˜.21
It is also worth underlining that this interface SC is gen- erated at a highly asymmetric interface where large electric fields in a nonlinear dielectric are expected, leading to a non- homogeneous charge distribution in the out-of-plane direc- tion. The thicknessdestimated here has thus to be seen as a
“characteristic” thickness.
Our estimates of the 共super兲conducting thickness are close to the one obtained by Basletic11and an order of mag- nitude larger than the one recently obtained using X-ray pho- toelectron spectroscopy.15 It is important to note however that the dielectric constant of STO increases dramatically at low temperatures23 leading to a larger screening length.
Finally, Caviglia et al.20 have recently determined the LAO/STO phase diagram using electrostatic doping reveal- ing a dome shaped superconducting region. The thickness of the conducting layer is probably linked to the carrier density at the LAO/STO interface and thus to the doping of the sys- tem. The sample investigated here is slightly “overdoped.”
In conclusion, analyses of the resistivity versus tempera- ture and magnetic field and of the correlation length versus magnetic field at the BKT transition temperature allow the characteristic 共super兲conducting thickness at the LAO/STO interface to be consistently estimated to be about 10 nm.
We would like to thank M. Gabay and J. Aarts for useful discussions and P. Zubko for a careful reading of the manu- script. This work was supported by the Swiss National Sci-
ence Foundation through the National Center of Competence in Research, “Materials with Novel Electronic Properties, MaNEP” and division II, the European Union through the project “Nanoxide” and ESF 共Thiox兲.
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as a function of the inverse of the parallel magnetic field atT=TBKT.共b兲 Square root of the fluctuation sheet conductance as a function of the square root inverse of the perpendicular magnetic field atT=TBKT. Lines are fits to the data in the high field limit.
112506-3 Reyrenet al. Appl. Phys. Lett.94, 112506共2009兲
Downloaded 20 Mar 2009 to 129.194.8.73. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
