Japanese Journal of Applied Physics 49 (2010) 020209

RAPID COMMUNICATION

Transport Properties in a Single Domain of Microscale Sr2 RuO4 Single Crystals
Hiroyoshi Nobukane, Katsuhiko Inagaki, Satoshi Tsuchiya, Yasuhiro Asano, Koichi Ichimura, Kazuhiko Yamaya,Shigeru Takayanagi, Ikuto Kawasaki1 , Kenichi Tenya2 , Hiroshi Amitsuka1 , and Satoshi Tanda
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan1
Department of Physics, Hokkaido University, Sapporo 060-0810, Japan2
Department of Education, Shinshu University, Nagano 380-8544, JapanReceived July 28, 2009; accepted October 30, 2009; published online February 5, 2010
We report our approach to measuring the transport properties in a single chiral order parameter domain of microscale Sr2 RuO4 single crystals.
Sr2 RuO4 single crystals were grown by the solid-phase reaction. Microscale single crystals were deposited from a dispersed liquid, and selectedfrom the result of the chemical composition and crystallinity of the dispersed crystals. The selected crystals attached to gold electrodes showsuperconducting properties. We also found the anomalous current–voltage characteristics that show that induced voltage is an even function ofbias current. # 2010 The Japan Society of Applied Physics
DOI: 10.1143/JJAP.49.020209

nisotropic superconductors1–3) stimulate much interest in a nontrivial order parameter ﬁeld, but havedomain conﬁgurations due to the internal degrees
of freedom of the order parameter. The size of a single
domain is considered to be on the micro–nanoscale. In
Sr2 RuO4 ,4) which is a promising candidate of spin-triplet
chiral p-wave superconductor (i.e., spin S ¼ 1 and orbitalangular momentum L ¼ 1), polar Kerr eﬀect measurements5) and Josephson tunneling measurements6) suggested
the single chiral domain sizes to be 1– 50 mm. The coherence
length of Sr2 RuO4 is ab ð0Þ ¼ 66 nm in the ab-plane. The
experimental data of Sr2 RuO4 on the millimeter scale should
be considered as a result of ensemble-averaging overpossible chiral domain conﬁgurations. Hence, transportmeasurements of a microscale Sr2 RuO4 crystals are very
important in both fundamental studies and potential applications for realizing topological quantum computation.7)
Recently, a microfabrication technique using a focused ion
beam has been reported for Sr2 RuO4 –Ru eutectic systems.8)
Since such eutectic systems show 3 K phase superconductivity to be inhomogeneous and ﬁlamentary,4,9) we need amicroscale Sr2 RuO4 crystal with no ruthenium inclusion inorder to study phenomena peculiar to a single chiral domain.
However, experiments on microscale pure crystals ofSr2 RuO4 are still limited.10)
In this paper, we report our approach to measuring thetransport properties in a single chiral order parameterdomain of microscale Sr2 RuO4 single crystals. For microscale Sr2 RuO4 crystals with no ruthenium inclusion norimpurities as determined from the results of analyses,
electrical contact was formed by welding using electron
beam irradiation. The transition temperature of the Sr2 RuO4
single crystals was consistent with the result for bulk
Sr2 RuO4 . Moreover, we found that the induced voltage V isan even function of the bias current I, while V is usually anodd function of I in four terminal measurements.
In micro-nanofabrication methods, it is necessary to solve
two essential issues: crystallinity and electrical contact. Theﬁrst concerns the degradation of the crystallinity of microscale superconducting samples. Nanofabrication techniques
for the epitaxial growth of nanoscale cuprates have beenreported.11) These epitaxial methods cause problems of grain

A

Present address: Department of Physics, Asahikawa Medical College,
Asahikawa, Hokkaido 078-8510, Japan.

Sr2RuO4 synthesis
Crystal analysis

Electrode fabrication• X-ray diffraction analysis• Secondary ion-microprobe

mass spectrometry

Welding

Sample selection

Transport measurement• Dispersion and deposition• Energy dispersion spectroscopy• Electron backscatter diffraction

Fig. 1.
ments.

pattern

Procedure from the synthesis of Sr2 RuO4 to transport measure-formation. The second concerns the diﬃculty in theformation of an electrical contact.9) The surface of a cleaved
crystal may have an insulator layer, and a poly(methylmethacrylate) (PMMA) resist may also remain between thesample and the gold electrodes. Therefore, electron beamlithography, which is used to study carbon nanotubes andgraphene, cannot be applied directly to layered crystals.
Considering these issues, we selected microscale single
crystals from among dispersed crystals and welded themto gold electrodes by electron beam irradiation in order tomeasure transport properties. Figure 1 shows the procedurefrom sample growth to transport property measurements.
Sr2 RuO4 single crystals were synthesized by the solid-phasereaction. Microscale single crystals were deposited from adispersed liquid, and selected from the chemical composition and crystallinity of the dispersed microscale crystals.
For the selected samples, they were ﬁrmly attached to goldelectrodes and then heated by electron beam irradiation toimprove contact resistance. In the following paragraphs, wewill describe this procedure in detail.
For the growth of microscale Sr2 RuO4 single crystals, weused the solid-phase reaction. We prepared SrCO3 and RuO2
(both 99.9% pure, Kojundo Chem.) powders. Firstly, thepowder mixture, which had a total weight of 10 g, wasplaced in a furnace at 400  C for 4 h to exclude CO2 gas. Themixed powder was then sintered in Al2 O3 boats in air at990  C for 60 h. The mixture was cooled gradually from 990
to 450  C over 6 h. The samples were kept at 450  C for 12 h
to introduce oxygen into the crystals and then cooled slowly
to room temperature. After grinding and pressing, the020209-1# 2010 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 49 (2010) 020209

H. Nobukane et al.

samples were sintered again at 1070  C for 60 h. We
removed the sample surface in contact with the Al2 O3 boats.
We determined the crystal structure of Sr2 RuO4 and theconcentration of impurities. X-ray diﬀraction analysis wasused to determine the structure of the Sr2 RuO4 crystals. Theobserved peaks were ﬁtted to a body-centered tetragonal unit
cell of the K2 NiF4 type with the lattice constants a ¼ b ¼
3:867 (0:004) Å and c ¼ 12:73 (0:01) Å.12) Since thesuperconductivity of Sr2 RuO4 is destroyed by nonmagnetic
and magnetic impurities,13) we performed a detailed analysisof impurities using secondary ion-microprobe mass spectrometry (SIMS) for the samples in the same batch with themeasured microscale Sr2 RuO4 . The result of the SIMS
shows that the concentration of the Al in the sample is lessthan 100 ppm.
We selected microscale Sr2 RuO4 single crystals on thebasis of the results of the chemical composition andcrystallinity. The samples were dispersed in dichloroethaneby sonication for 30 min and deposited on an oxidized Si
substrate where thick gold markers and contact pads had
been inscribed. As another technique in which microscale
crystals are put on substrates,14) the mechanical exfoliationof Sr2 RuO4 crystals on substrates was performed successfully. We observed typical samples about 50 nm to 500 mmin length. Energy dispersion spectroscopy (EDS; JEOL EX641750JMU) was used to determine the components of themicroscale samples on the substrate. The atomic ratio of Srto Ru elements was 2 : 1, which was consistent with thatof the bulk crystal. We also conﬁrmed that the dispersedcrystals had no boundaries nor ruthenium inclusions on thesample surface by observing the crystal orientation using anelectron backscatter diﬀraction pattern (EBSP; OIM TSL15)).
Figure 2 shows the result of the EBSP. By this technique,the crystal orientation is represented as a color variation (seethe inset of Fig. 2). The red region indicates that the crystal
orientation is in the same direction. In other words, themicroscale Sr2 RuO4 shows single crystals in the ab-plane.
Thus, the EBSP method is eﬃcient in proving that the grown
crystals are single crystals on the microscale.
On the analyzed samples, we fabricated gold electrodes byoverlay e-beam lithography and then performed local
welding by electron beam irradiation. Figure 3(a) shows amicrograph of the microscale Sr2 RuO4 (sample B). Here,the size of sample A is 13:0  6:67  0:34 mm3 . The size ofsample B is 2:50  1:88  0:10 mm3 . The spacings between
the voltage electrodes are 4.0 mm (sample A) and 0.63 mm(sample B). In lithography, the PMMA resist was 1.4 mm
thick in bilayers. Lift-oﬀ was performed with acetone atroom temperature for 3 h, and then in boiling acetone for
30 min. Since the fabricated sample surface may have aninsulator surface of layered crystals and a residual PMMA
resist between the sample and the gold electrodes, it isdiﬃcult to form electrical contact. In order to solve theseproblems, welding is performed. Figure 3(b) shows schematic of welding. We locally heated each electrode on thesamples for 15 s by irradiation with a beam current of2  107 A, which was monitored by detecting the probe
current between the sample stage and the beam ﬁlament.16)
Welding was performed at several sites on each electrode.
As the result, contact resistance decreased dramaticallyfrom 10 –100 k to a value below the sample resistance(001)

Microscale Sr2RuO4

1μ m

Fig. 2. (Color online) Result for microscale Sr2 RuO4 single crystal(sample B) measured using the electron backscatter diffraction pattern.
The color variations of the inset represent the crystal orientations. The redregion shows a single crystal in the ab-plane.

Goldelectrodes

(a)

(b)

Electron beamirradiation

V-I-

I+
V+
Sr2RuO4
1μ m

Sr2RuO4

Substrate

Fig. 3. (Color online) (a) Micrograph of sample B connected to goldelectrodes. (b) Schematic of welding by electron beam irradiation.

at room temperature. We conﬁrmed that contact resistance
did not increase with decreasing temperature. The fabricated samples were cooled to low temperatures several
times, and kept there to form electrical contact with gold
electrodes.
The measurements were performed in a dilution refrigerator (Oxford Kelvinox) with a base temperature of 60 mK.
All measurement leads were shielded. The lead lines wereequipped with low-pass resistance–capacitance ﬁlters (R ¼1 k, C ¼ 22 nF). Silver wires 50 mm in diameter wereattached to the gold contact pads using a silver paste. In theDC measurements, a bias current was supplied using aprecise current source (Keithley 6220) and the voltage wasmeasured with a nanovoltmeter (Keithley 182) via fourterminal measurements.
We observed the superconducting properties of microscale Sr2 RuO4 . Figure 4(a) shows the superconducting
transition temperature Tc ¼ 1:59 K and transition temperature width T  30 mK in zero magnetic ﬁeld. We
measured the temperature dependence of resistivity for bias
current I ¼ 1 mA by the current reversal method. The
properties of sample A are consistent with the properties ofbulk Sr2 RuO4 single crystals.13) Figure 4(b) shows Tc ¼
1:69 K and T  200 mK. The resistivity of sample B
retained its ﬂat tail below Tc . We consider that a ﬁnite
resistivity shows a ﬂow of vortices owing to quantum
ﬂuctuations of the phase .17,18) These results indicate that
we were successful in observing the superconducting
properties of the synthesized and selected microscale
Sr2 RuO4 single crystals. The procedure will promote
fundamental studies of spin-triplet chiral p-wave Sr2 RuO4and its potential applications to topological quantum

020209-2# 2010 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 49 (2010) 020209

V (μV)

0.4
0.2
96mK0T

0−50I (μA)

5T > Tc

0.1

0.1
V (μV)

ρab (μΩ cm)

to the single domain scale. The phenomenon is related tophase slip, which is caused by quantum ﬂuctuations inmicroscale superconductors.19) To understand the anomalouseﬀect, we suggested an unconventional vortex model in thesingle domain of Sr2 RuO4 .10) We need to further study thetransport properties of microscale Sr2 RuO4 single crystals.
In summary, we studied the transport properties in a single
chiral domain of microscale Sr2 RuO4 single crystals.
Microscale Sr2 RuO4 single crystals were selected by detailed analyses. To measure the transport properties, gold
electrodes were ﬁrmly attached to the crystals by welding
with electron beam irradiation. The microscale Sr2 RuO4
showed the superconducting properties. Anomalous I–V
characteristics were observed.

T<Tc(a)0.2

H. Nobukane et al.

04.2K
0T

−0.1−5

Tc= 1.59 K

00120I (μA)

354T (K)42.0 T

1 63 mK, 0T0T
Tc = 1.69K

2V (μV)ρab (μΩ cm)

60−1

4.2K, 0T

−500

Acknowledgments The authors thank A. Ishii, T. Toshima, T.
Matsuura, J. Ishioka, and T. Kuroishi for experimental help and useful
discussions. This work was supported by a Grant-in-Aid for the 21stCentury COE program on ‘‘Topological Science and Technology’’ from theMinistry of Education, Culture, Sports, Science and Technology of Japan.
H.N. acknowledges support from the Japan Society for the Promotion ofScience.

H⊥c(b)

120I (μA)
354T (K)Fig. 4. Temperature dependence of resistivity of microscale Sr2 RuO4 .
(a) Sample A shows zero resistivity in zero magnetic field. (b) A finite
resistivity is seen in sample B below Tc . Insets show the results of DC
measurements. Above Tc , the I–V curve shows ohmic conduction. Incontrast, below Tc , an anomalous I–V curve is observed. We eliminatedoffset voltage. The anomalous behavior is reproduced in both samples.

computation. The procedure can also be adjusted in studiesof microscale single crystals in anisotropic superconductors
such as copper-based and recently reported iron-basedmaterials.
Furthermore, in both samples A and B, we observed
anomalous current–voltage (I–V) characteristics. In general,
the induced voltage V is an odd function of the bias current
I. The I–V curves show ohmic conduction above Tc [seeinset of Figs. 4(a) and 4(b)]. However, below Tc , the results
show that V is an even function of I. With decreasing
temperature, anomalous voltage increases in zero magnetic
ﬁeld. With increasing magnetic ﬁeld, anomalous voltage
decreases at low temperature. We measured the diﬀerential
resistance dV=dI as a function of I in the AC measurements.
The eﬀect has been conﬁrmed in both DC and AC
measurements.10) More importantly, the anomalous behavior
is reproduced in both samples A and B. We consider that theanomalous induced voltage clearly exhibits a property of thesingle chiral domain because our sample size is comparable

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020209-3# 2010 The Japan Society of Applied Physics