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Low temperature electrical transport properties of RuO2 and IrO2 single crystals
View the table of contents for this issue, or go to the journal homepage for more 2004 J. Phys.: Condens. Matter 16 8035
(http://iopscience.iop.org/0953-8984/16/45/025)
J. Phys.: Condens. Matter 16 (2004) 8035–8041 PII: S0953-8984(04)82592-X
Low temperature electrical transport properties of
RuO
2
and IrO
2
single crystals
J J Lin1,2, S M Huang1, Y H Lin1, T C Lee1, H Liu3, X X Zhang3,
R S Chen4and Y S Huang4
1Institute of Physics, National Chiao Tung University, Hsinchu 300, Taiwan
2Department of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan 3Department of Physics and Institute of Nano Science and Technology, The Hong Kong
University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China
4Department of Electronic Engineering, National Taiwan University of Science and Technology,
Taipei 106, Taiwan
E-mail: [email protected]
Received 24 June 2004, in final form 11 August 2004 Published 29 October 2004
Online atstacks.iop.org/JPhysCM/16/8035 doi:10.1088/0953-8984/16/45/025
Abstract
We have systematically measured the electrical transport properties of several RuO2and IrO2single crystals over a wide temperature range from 300 K down
to 0.3 K to study the conduction mechanisms in these oxides. Our measured resistivities are in close agreement with the recent band-theory calculations for these materials. The characteristic temperatures for the acoustic-mode and optical-mode phonons are determined. Our measured magnetoresistances are positive and follow the Kohler rule, indicating that the transport properties of these oxides exhibit normal behaviour as described by the Boltzmann equation. In contrast, we do not find any signature of superconductivity down to 0.3 K, though the band-theory calculations predict a superconducting transition temperature of∼5 K. Magnetization measurements suggest a very low level of paramagnetic impurities in our crystals.
1. Introduction
The electronic structures and electrical transport properties of the dioxides RuO2 and IrO2
have recently been extensively studied. For example, the band structures of these dioxides have been calculated by several authors [1–6], while the electrical transport properties have been explicitly calculated by Glassford and Chelikowsky [5]. Experimentally, the electronic and transport properties of these metals have also been investigated over the years [7–10]. It is often accepted that the current understanding of these materials is quite complete. In particular, the electrical resistivities of these materials between 20 and 1000 K have been
8036 J J Lin et al
measured in [9] and recently been reanalysed in [5]. On the other hand, the resistivities and magnetoresistivities of these materials have never been measured down to liquid-helium and sub-kelvin temperatures.
According to the band-structure calculations of Glassford and Chelikowsky [5], the electrical resistivity of RuO2at not-too-high temperatures is comprised of two terms:
(1) the usual Bloch–Gr¨uneisen contribution due to the coupling of electrons with acoustic-mode phonons (characterized by a coupling constantλBG); and
(2) an additional contribution due to the coupling of electrons with optical-mode phonons (characterized by a coupling constantλE).
In this work, we report our measurements of the resistivities and magnetoresistivities of several RuO2and IrO2single crystals over a wide temperature range from 300 K down to 0.3 K. These
two materials are studied together, because they crystallize in the same rutile structure and reveal similar transport properties. By comparing our experimental results with the predictions of [5], we are able to extract the values of the relevant parametersλBG,λE and the Debye
temperature (θD) of these materials.
2. Experimental method
Single crystals of RuO2and IrO2were grown by the method of chemical transport reaction in
a flowing oxygen system as described previously [11, 12]. The gaseous oxide, RuO3or IrO3,
was formed by the reaction
M(solid) +32O2→ MO3(gas)
where M = Ru or Ir, when oxygen was passed over Ru (Ir) metal powder at a temperature of about 1200◦C (1250◦C) and at a flow rate of approximately 100 cm3min−1. The volatile
MO3gas then decomposed and crystallized into highly ordered single crystals of MO2at about
1000◦C. X-ray powder diffraction analysis was performed to establish the tetragonal rutile structure, and Laue backscattering was used to identify the growth habits.
Our samples were irregular in shape. For convenience in resistance and magnetoresistance measurements, we used thin slice-shaped and needle-shaped samples. Typical slices were ∼1–2 mm wide and ∼0.015–0.22 mm thick. Typical needles were ∼0.1–0.2 mm in diameter. Four-probe electrical contacts were made with silver paste, and the typical distance between the voltage probes was∼0.5–1.7 mm. Standard four-proberesistances and magnetoresistances were measured using a Linear Research LR-700 resistance bridge and/or a Keithley 220 current source with a Keithley 182 nanovoltmeter. The resistivities of our samples were computed and estimated to be subject to an uncertainty of about 40–50%, due to the appreciable uncertainties in the dimensions of the samples. Roughly speaking, our room temperature resistivities are ∼100 µ cm in RuO2 and∼50–120 µ cm in IrO2. On the other hand, the resistance
ratio, R(300 K)/R(4 K), for each sample can be measured very accurately. Our values are
R(300 K)/R(4 K) = 81–128 in RuO2and 224–826 in IrO2. For this reason, table 1 lists only
the values of R(300 K)/R(4 K), but not the individual values of ρ, for each sample. It should be noted that our measured resistivities and resistance ratios are in reasonably good agreement with those previously reported by Ryden et al [8].
The resistance measurements of our samples were performed on a standard4He dipper
and an Oxford Heliox 3He cryostat. In the 4He dipper, the temperature was monitored
using a calibrated AlGaAs thermometer. In the Heliox3He refrigerator, a calibrated carbon
glass thermometer was used for monitoring temperatures above 7 K, while a calibrated RuO2thermometer was used for monitoring temperatures below 7 K. The magnetoresistance
0 50 100 150 200 250 300 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 R (T )/ R (300 K) T(K)
Figure 1. Normalized resistance R(T )/R(300 K) as a function of temperature for the (from the bottom up) RuO2-C, RuO2-A, IrO2-A, and IrO2-C single crystals. The symbols are the
experimental data, and the solid curves are the theoretical fits to the sum of equations (1)–(3) as described in the text. For clarity, the data for RuO2-A, IrO2-A, and IrO2-C have been shifted by
+0.2, +0.4, and +0.6, respectively.
Table 1. Values of relevant parameters for RuO2and IrO2single crystals. The uncertainty in the
fitted values ofλBGandλEis±10%, while the uncertainty in the fitted values of θD(θE) is±5%
(±3%). Sample R(300 K)/R(4 K) λBG λE θD(K) θE(K) RuO2-A 119 0.14 0.25 401 813 RuO2-B 128 0.13 0.28 404 811 RuO2-C 81 0.12 0.24 401 813 IrO2-A 826 0.11 0.25 280 889 IrO2-B 224 0.13 0.28 289 885 IrO2-C 243 0.11 0.24 296 870 IrO2-D 328 0.14 0.27 292 850
measurements were performed on an Oxford SM-40004He cryostat equipped with a 6 T
split-coil superconducting magnet. The temperature was monitored with a calibrated carbon glass thermometer.
3. Results and discussion
Figure 1 shows the normalized resistances, R(T )/R(300 K), as a function of temperature for two RuO2 and two IrO2 single crystals. The symbols are the experimental data and the
8038 J J Lin et al
solid curves are the band-theory calculations of [5]. This figure clearly demonstrates that the measured resistances are well described by the theoretical predictions. It should be noted that Ryden et al [8] have previously found that the resistivity in RuO2is essentially independent
of the crystal orientation, i.e., their measured resistivities in the [100], [001], [011], and [111] directions are basically indistinguishable. Based on this observation, the orientation of our crystal with respect to the measuring current need not be specified. In practice, for all crystals, our measuring currents are essentially in the [001] direction.
In the theory of [5], the resistivity of RuO2 is comprised of three terms. The first
contribution is the usual Bloch–Gr¨uneisen term due to the coupling of electrons with acoustic-mode phonons, and is given by
ρBG(T ) = 32π2 ¯h2 p kBTλBG T θD 4 θD/T 0 x5dx 4 sinh2(x/2), (1) wherep is the plasma frequency. The second term is an additional contribution due to the
coupling of electrons with optical-mode phonons (this term is important for transition-metal oxides which contain multi-atom bases), and is given by
ρE(T ) = 8π2 ¯h2 p kBTλE θ E/2T sinh(θE/2T ) 2 . (2)
That is, in this theory, the optical-mode coupling term is treated using the Einstein approximation with a single phonon frequency corresponding to the energy kBθE, where kBis
the Boltzmann constant. The third contribution is due to the usual electron–electron scattering which depends on the square of the temperature, and can be written as
ρee(T ) = AeeT2, (3)
where Aee is a temperature independent parameter. The measured normalized resistivity, ρ(T )/ρ(300 K) = R(T )/R(300 K), can then be fitted to the sum of equations (1)–(3) with λBG,θD,λE,θE, and Aee as adjusting parameters. For real single-crystalline samples having
finite residual resistances, the third term, equation (3), is negligible if the measuring temperature is not extremely high (e.g., several hundred kelvins and higher)5.
Table 1 lists the values of the fitting parameters for our samples. For comparison, Glassford and Chelikowsky obtained the values ofλBG≈ 0.14, λE≈ 0.33, θD≈ 409 K, and θE ≈ 787 K
for RuO2. Experimentally, the ratio of our fitted values ofλBG/λE, which determines the
relative contribution of the acoustic-mode phonon and optical-mode phonon terms, is≈0.5 for both RuO2and IrO2. It should be noted that the values ofθDfor RuO2 reported in previous
measurements were 650± 40 and 900 ± 50 K in [7] and [8], respectively. These previous values were clearly overestimated.
As for IrO2, the values ofθDpreviously reported in [7] (≈470 K) and [8] (=700 ± 100 K)
are significantly higher than our result of≈290 K (see table 1). Unfortunately, no band-structure calculations for the electronic and transport properties of IrO2 are available in the
literature.
In the presence of a magnetic field B and at liquid-helium temperatures, the magnetoresistances for all our RuO2 and IrO2 crystals reveal similar behaviour and are all
positive. (In this work, we focus on the case where the magnetic field is applied perpendicular to the measuring current.) In low magnetic fields, the magnetoresistances vary quadratically with the field, as expected. In higher magnetic fields of the order of tens of kG, depending on temperature and the sample, the magnetoresistances increase somewhat linearly with
5 In practice, the resistivity due to the electron–electron scattering in transition metals is of the order ofρ ee ∼
0 500 1000 1500 2000 2500 3000 0 2 4 6 8 10 0 1 2 3 4 5 6 0 2 4 6 8 ∆ R (B )/ R (0 ) B (T) RuO2 IrO 2 ∆ R (B,T )/ R (0, T ) B[R(300 K)/R(T )] (T)
Figure 2. Normalized magnetoresistanceR(B, T )/R(0, T ) = [R(B, T ) − R(0, T )]/R(0, T ) as a function of the normalized magnetic field B[R(300 K)/R(T )] for the RuO2-B single crystal
at 10.0, 20.0, and 30.0 K, and the IrO2-A single crystal at 6.0, 10.0, and 20.0 K. For each crystal,
the normalized magnetoresistance obeys the Kohler rule and the magnetoresistances measured at different temperatures overlap closely and (the symbols) are indistinguishable. The inset shows the normalized magnetoresistance as a function of magnetic field for the IrO2-A single crystal at
four temperatures (from the top down): 4.2, 10.0, 20.0, and 30.0 K.
increasing field up to our highest measuring field of 5.5 T. The inset of figure 2 shows the magnetoresistances as a function of magnetic field for an IrO2crystal at four temperatures as
indicated in the caption to figure 2. Quantitatively, a plot of the normalized magnetoresistance, [R(B, T )− R(0, T )]/R(0, T ), versus the normalized field, B[R(300 K)/R(T )], indicates that the measured magnetoresistances closely obey the Kohler rule [14] below about 30 K. That is, for every sample, the normalized magnetoresistances measured at different temperatures scale with the normalized magnetic field. Above about 30 K, the contribution from the optical-mode term becomes non-negligible, and a small deviation from the Kohler rule is observed. The normalized magnetoresistances illustrating the Kohler rule for one representative IrO2and one
RuO2single crystal measured at several temperatures are plotted in the main panel of figure 2.
This observation of an ‘orthodox’ magnetoresistance phenomenon supports the Glassford– Chelikowsky prediction [5] that the transport properties of RuO2exhibit normal behaviour as
described by the Boltzmann equation.
With the values of the electron–phonon coupling constantsλBGandλEbeing determined,
and assuming the renormalized Coulomb pseudopotentialµ∗ = 0.1, one might be tempted to predict a superconducting transition temperature of∼5 K in RuO2 [5, 16]. To test this
conjecture, we have performed careful resistance measurements down to 0.3 K. Figure 3 shows the normalized resistance, R(T )/R(5 K), as a function of temperature for one IrO2
8040 J J Lin et al 0.1 1 10 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 R (T)/ R (5 K) T (K)
Figure 3. Normalized resistance R(T )/R(5 K) as a function of temperature for the RuO2-B
(circles), RuO2-A (triangles), and IrO2-B (squares) single crystals below 6 K. For clarity, the data
for the RuO2-B have been shifted by +0.05. The data for the RuO2-A reflect the largest possible
uncertainties in our measurements due to the smallness of the sample resistance.
remain constant down to 0.3 K, with no sign of an abrupt drop to a zero resistance for any sample. The finite residual resistance reflects the existence of a low concentration of defects or impurities in the samples. Thus, to clarify whether our crystals might contain a minute amount of magnetic impurities, we have performed magnetization measurements between 2 and 300 K, using a Quantum Design SQUID magnetometer. Our measured magnetizations above several tens of kelvins are consistent with previous results [15]. Below around 35 K, however, we found a slight increase in magnetization with decreasing temperature, indicating the presence of a low level of paramagnetic impurities in the crystals. Quantitatively, our measured low temperature magnetizations are well described by the Curie law from which an estimate of a magnetic impurity level of 20 ppm in both RuO2and IrO2 could be inferred, if we assume
that the paramagnetic impurities are mainly due to Fe3+ions. This estimate is in satisfactory
consistency with the spectrographic analysis of our starting Ru and Ir metals. Generally, a level of 20 ppm of magnetic impurities would barely suppress the superconducting transition [17], if such a transition does exist initially, as speculated in [5, 16]. Whether spin fluctuations or other detrimental mechanisms (e.g., strong electron–electron interactions) might play a role in suppressing superconductivity in RuO2deserves further study.
4. Conclusion
We have systematically measured the resistivities of several RuO2 and IrO2 single crystals
of temperature agree well with the recent band-structure calculations. Our magnetoresistance measurements also demonstrate that the transport properties of these dioxides exhibit normal behaviour as described by the Boltzmann equation.
Acknowledgment
This work was supported by the Taiwan National Science Council through Grant No NSC 92-2120-M-009-007.
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![Figure 2. Normalized magnetoresistance R(B, T )/R(0, T ) = [R(B, T ) − R(0, T )]/R(0, T ) as a function of the normalized magnetic field B[R (300 K)/R(T )] for the RuO 2 -B single crystal](https://thumb-ap.123doks.com/thumbv2/9libinfo/7666805.140934/6.892.230.666.130.532/figure-normalized-magnetoresistance-function-normalized-magnetic-single-crystal.webp)
