PDF In-plane electrical impedance as a probe for the electron ... - NJU

AIP Advances ^ARTICLE scitation.org/journal/adv

In-plane electrical impedance as a probe for the electron nematicity of BaFe ₂ As ₂

Cite as: AIP Advances9, 035140 (2019);doi: 10.1063/1.5082656 Submitted: 22 November 2018•Accepted: 8 March 2019• Published Online: 19 March 2019

Fan Wu,¹ Yongqiang Li,² Dongliang Gong,³ Wenliang Zhang,³ Tao Xie,³ Jun Yuan,¹ Qirui Yang,¹ Kai Chen,^1,a) Huiqian Luo,³ Junming Liu,² and Jinsong Zhu²

AFFILIATIONS

1School of Science, Nanjing University of Science and Technology, Nanjing 210094, P.R. China

2National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, P.R. China

3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China

a)Corresponding Author:Kai Chen (kai@njust.edu.cn)

ABSTRACT

In-plane electrical impedance has been examined in as-grown single crystals of BaFe2As2, one of the parent compounds of iron-based super- conductors. From the results, it is found that the real part of the impeditivity, namely the AC resistivity, reveals the in-plane anisotropy of the material without any applied uniaxial strain. The imaginary part, i.e., the reactivity, also indicates strong in-plane anisotropy and is linearly dependent on the electrical frequency. Our study demonstrates that electrical impedance is a new and effective method of probing the electron nematicity of iron-based superconductors.

© 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/1.5082656

I. INTRODUCTION

Superconductivity is observed in LaFeAsO1-xFx atTc=26 K,¹ and occurs above 40 K in related compounds or under an exter- nal pressure.^2–4Thus, iron-based superconductors are classified as a new high-Tcsuperconducting family,⁵breaking the McMillan lim- itation based on the strong coupling theory of Bardeen, Cooper, and Schrieffer (commonly known as BCS theory).⁶ Among vari- ous experimental probes for examining high-Tcsuperconductivity in iron pnictides, the transport probe has hitherto been a key com- ponent in elucidating the role of magnetism,⁷the nature of chem- ical and structural tuning,⁸ and the pairing symmetry.^9,10 How- ever, there are many possibilities for the further development of these probes. The transport probe, as a bulk measurement tool unlike scanning tunneling microscopy and other microscopic meth- ods,^11,12provides limited details of the interactions involved in the pairing, such as Coulomb repulsion, spin fluctuation, and electron–

phonon coupling.¹³It is widely believed that high-Tcsuperconduc- tivity in pnictides emerges by tuning the interactions that are already

present in the parent compounds. Further, the DC electric trans- port probe cannot measure the nematic correlations or fluctuations unless a uniaxial pressure is applied to detwin the sample.¹²

Different from the constant voltage applied in the current transport probe for DC resistivity, a sinusoidal perturbation voltage is, in electrical impedance spectroscopy, applied between two ter- minals of the measured bulk, thus inducing an alternating current, as prescriptively applied to insulators. Current electrical impedance spectroscopy uses a two-terminal measurement method, different from the current–voltage four-electrode method commonly used in the transport probe. Here, Ohm’s law still applies. The corre- sponding physical quantity, the electrical impeditivity z^∗, repre- sents the voltage resulting from a reference current flowing through the system.^14–16In Cartesian form, z^∗ is defined as z^∗ =ρ +ix, where the real component ρ is the AC resistivity and the imag- inary x component is the reactivity, which represents the resis- tance of a built-up electric field to a change of voltage, and par- ticularly, the resistance ofa built-up magnetic fieldto a change in current. The intrinsic reactivityxincludes inductive and capacitive

AIP Advances9, 035140 (2019); doi: 10.1063/1.5082656 9, 035140-1

© Author(s) 2019

AIP Advances ^ARTICLE scitation.org/journal/adv

components, x_l andxc, respectively. Thus, we havez^∗ =ρ +i(x_l + xc). In particular, xl indirectly describes a magnetic field sur- rounding the conductor that opposes a change in current by storing and releasing energy (as magnetic flux). Smaller values ofxlindi- cate less stored energy (as magnetic flux) and stronger expulsion of magnetic flux. In our experiments, one parent compound of a 122- type high-temperature pnictide superconductor,¹⁷namely, a single BaFe2As2 crystal, is used as an example to examine the feasibility of impeditivity characterization. As the temperature of BaFe2As2

increases, an antiferromagnetic to paramagnetic phase transition occurs at temperature TN, accompanied by an orthorhombic to tetragonal structural phase transition at temperatureTs (TN=Ts

= TN,s) at 138 K. The cutoff temperature for in-plane resistivity anisotropy corresponds to the C2-to-C4symmetry transition tem- perature of low-energy spin excitation (T^∗>TN,s),¹⁸signifying the dominant role of the electronic nematic-phase in the transport pro- cess. Here, in-plane AC resistivity anisotropy is observed without applying any uniaxial strain to the as-grown BaFe2As2single crys- tals. Moreover, the reactivity along the a- and b-axes in the as-grown

single crystals is linearly dependent on the frequency at all measured temperatures.

II. EXPERIMENTS

High-quality single crystals of BaFe2As2 were grown by the self-flux method.¹⁹ Using a diamond wire cutting machine, all of the specimens were cut into long bars along thex- ory-axes to have typical sizes of 5.9 mm× 2.8 mm× 0.3 mm. Before mak- ing any electrical measurements, silver conductive paint (186-3600, RS components, UK) was painted on both ends of the specimens and then dried by infrared light in the air, and two gold wires were welded to form two electrodes and two external wires. Elec- trical impedance spectroscopy was conducted using a Hewlett- Packard Impedance/Grain-Phase Analyzer (model 4294A, Agilent Co., USA). This allows a minimum measured impedance value of 3 mΩwith a basic impedance accuracy of±0.08%; the frequency ranges from 40 Hz to 110 MHz with 1 mHz resolution. A sinusoidal voltage with a peak of 200 mV from 100 Hz to 1 MHz was applied

FIG. 1. Temperature-dependent AC resistivity of as-grown single crystals at 100 Hz (a), 10 kHz (b), and 1 MHz (c), and lattice and magnetic structures belowT_N,c(d). The top part of (d) shows an example of the measured sample in the sample test stand.

AIP Advances9, 035140 (2019); doi: 10.1063/1.5082656 9, 035140-2

© Author(s) 2019

AIP Advances ^ARTICLE scitation.org/journal/adv

to introduce sinusoidal currents. The peak voltage was selected to guarantee that the electrical impedance was within the range of pre- cision. A Janis closed-cycle refrigerator system (Janis Research Com- pany, Inc., USA) was used for cooling and heating at a constant 2 K/min over 10 K. After measuring the specimens, the electrical impedance of the silver electrodes, gold wires, and other compo- nents was subtracted as background data. Using the analyzer with the cooling component of a Physical Property Measurement Sys- tem (PPMS, Quantum Design Co., USA), impedance measurements with accurate temperature control were conducted to confirm that the impedance results were reproducible.

III. RESULTS AND DISCUSSION

Regarding the temperature-dependent AC resistivity of the as- grown single crystals, the in-plane AC resistivity anisotropy without applied strain can be observed in Fig. 1(a), and the in-plane DC resistivity anisotropy is observed under uniaxial strain.^20–23 ρx is determined as the resistivity of the crystallinea-axis, i.e.,ρx(a), and ρyis the resistivity of the crystallineb-axis, i.e.,ρy(b); here,aandb are defined by the orthorhombic lattice unit cell for easy compari- son with results in detwinned samples (a≈b≈5.6 Å, c = 12.8 Å).

The in-plane AC resistivity anisotropy spans TN,s. When the abrupt changes in bothρx(a)andρy(b)atTN,sare the same as those in the transport probe,^24,25 their temperature dependence below TN,s exhibits more obvious differences. Above TN,s, ρy(b) has an AC resistivity plateau over a wide temperature range, from 196–

226 K. Figures 1(a)–1(c)show that both ρx(a) and ρy(b) are inde- pendent of the frequency in this temperature range. The frequency independence makes it clear that the collinear magnetic exchange

interaction below TN,s is not sufficiently strong to induce large local lattice distortions in response to the frequency perturbations of the alternating electric field; otherwise, a relaxation peak might appear.

In contrast to the AC resistivity being almost independent of frequency, thea-axis reactivity of the as-grown samples, xx(a), varies linearly with the frequency from 100 Hz to 1 MHz at sev- eral temperatures, as shown inFig. 2(a). The linear dependence of the reactivity on frequency suggests that the inductive component is stronger than the capacitive one,²⁶ as the inductive reactivity is linearly proportional to the frequency.²⁷ We can find that the inductance value of Lx(a) is around (2.50±0.01)/2π nH⋅cm at sev- eral temperatures, as shown inFig. 2(b). The inductive reactivity Lx(a)is slightly dependent on the temperature below or aboveTN,s. Figure 2(c)shows theb-axis reactivity,xy(b), of the as-grown crys- tals, respectively. In the as-grown case, thexy(b)curve is different from thexx(a)curve, both in terms of values and temperature depen- dence, and the fittedLy(b)is around (2.70±0.02)/2π nH⋅cm, i.e., the in-plane reactivity anisotropy. In-plane reactivity anisotropy exists below or aboveTN,s, possibly because of nematic fluctuations driven by magnetic interactions,^18,23,28and the fittedLy(b)is almost tem- perature independent. We select the data at 120 K as an example to show the changes in the complex plots of thea- orb-axis ofρ andx(seeFigs. 2(d)). The vertical line segment shows that the crys- tals are excellent conductors, and there is some inductive reactivity effect. Again, the clear frequency dependence suggests that in-plane anisotropy exists in both the resistivity and reactivity. Therefore, the in-plane anisotropy of electrical impeditivity must come from the electron system rather than the lattice, which is expected in the framework of electron nematics.

FIG. 2. Frequency-dependent a- or b- axis reactivity at several temperatures (a and c), temperature dependence of fit- ted inductive reactivity (b), and the com- plex plot of impeditivity at 120 K (d) of as-grown single crystals. The inset in (b) shows the sample test stand of the PPMS.

AIP Advances9, 035140 (2019); doi: 10.1063/1.5082656 9, 035140-3

© Author(s) 2019

AIP Advances ^ARTICLE scitation.org/journal/adv

IV. CONCLUSION

Our investigation on the electrical impedance in as-grown BaFe2As2 single crystals shows that the impeditivity is a compre- hensive physical quantity for characterizing the transport process related to electronic behavior. The in-plane anisotropy for AC resistivity and reactivity can be used as a new probe for electron nematicity in iron-based superconductors without uniaxial pres- sure, where the reactivity can be tuned by the current frequency for more sensitive measurements. Our results indicate the need for fur- ther theoretical studies to understand the electrical impedance in some iron-based superconductors,²⁹ and possible in copper oxide superconductors.³⁰

ACKNOWLEDGMENTS

Fan Wu and Yongqiang Li contributed equally to the work.

This study was financially supported by the National Natural Sci- ence Foundation of China (Grant No. 11004106) and the National 973 Project (Grant No. 2015CB946502).

REFERENCES

1Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,J. Am. Chem. Soc.130, 3296 (2008).

2X. H. Chen, T. Wu, G. Wu, R. H. Liu, H. Chen, and D. F. Fang,Nature453, 761 (2008).

3Z.-A. Ren, W. Lu, J. Yang, W. Yi, X.-L. Shen, Z.-C. Li, G.-C. Che, X.-L. Dong, L.-L. Sun, F. Zhou, and Z.-X. Zhao, Chinese Phys. Lett.25, 2215 (2008).

4H. Takahashi, K. Igawa, K. Arii, Y. Kamihara, M. Hirano, and H. Hosono,Nature 453, 376 (2008).

5P. Johnpierre and R. L. Greene,Nat. Phys.6, 645 (2010).

6W. L. McMillan,Phys. Rev.167, 331 (1968).

7J. H. Chu, J. G. Analytis, C. Kucharczyk, and I. R. Fisher,Phys. Rev. B79, 014506 (2009).

8X. H. Chen, P. C. Dai, D. L. Feng, T. Xiang, and F. C. Zhang,Nat. Sci. Rev.1, 371 (2014).

9I. I. Mazin and J. Schmalian,Physica C469, 614 (2009).

10Q. Si, R. Yu, and E. Abrahams,Nat. Rev. Mat.1, 16017 (2016).

11Z. Y. Du, X. Yang, D. Altenfeld, Q. Q. Gu, H. Yang, I. Eremin, P. J. Hirschfeld, I. I. Mazin, H. Lin, X. Y. Zhu, and H. H. Wen,Nat. Phys.14, 134 (2017).

12P. C. Dai,Rev. Mod. Phys.87, 855 (2015).

13J. Bardeen, L. N. Cooper, and J. R. Schrieffer,Phys. Rev.108, 1175 (1957).

14O. Heaviside,The Electrician, p. 212, 23 July 1886, reprinted as Electrical Papers, p 64, AMS Bookstore.

15A. Kennelly, Impedance, the seventy-sixth meeting of the American Institute of Electrical Engineers, New York (1893).

16A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983).

17G. R. Stewart,Rev. Mod. Phys.83, 1589 (2011).

18X. Y. Lu, J. T. Park, R. Zhang, H. Q. Luo, A. H. Nevidomskyy, Q. M. Si, and P. C. Dai,Science345, 6197 (2014).

19Y. Chen, X. Lu, M. Wang, H. Q. Luo, and S. L. Li,Supercond. Sci. Technol.24, 065004 (2011).

20J.-H. Chu, J. G. Analytis, K. D. Greve, P. L. McMahon, Z. Islam, Y. Yamamoto, and I. R. Fisher,Science329, 824 (2010).

21J.-H. Chu, H.-H. Kuo, J. G. Analytis, and I. R. Fisher,Science337, 710 (2012).

22H.-H. Kuo, J.-H. Chu, S. A. Kivelson, and I. R. Fisher, Science352, 958 (2016).

23Z. Y. Liu, Y. H. Gu, W. Zhang, D. L. Gong, W. L. Zhang, T. Xie, X. Y. Lu, X. Y. Ma, X. T. Zhang, R. Zhang, J. Zhu, C. Ren, L. Shan, X. G. Qiu, P. C. Dai, Y. F. Yang, H. Q. Luo, and S. L. Li,Phys. Rev. Lett.117, 157002 (2016).

24A. E. Böhmer, P. Burger, F. Hardy, T. Wolf, P. Schweiss, R. Fromknecht, M. Reinecker, W. Schranz, and C. Meingast,Phys. Rev. Lett.112, 047001 (2014).

25H. R. Man, X. Y. Lu, J. S. Chen, R. Zhang, W. L. Zhang, H. Q. Luo, J. Kulda, A. Ivanov, T. Keller, E. Morosan, Q. M. Si, and P. C. Dai,Phys. Rev. B92, 134521 (2015).

26D. Gates Earl,Introduction to Electronics(Cengage Learning, p. 153, 2001).

27C. Shamieh and G. McComb,Electronics for Dummies(John Wiley & Sons, 2011).

28W. L. Zhang, J. T. Park, X. Y. Lu, Y. Wei, X. Y. Ma, L. J. Hao, P. C. Dai, Z. Y. Meng, Y.-F. Yang, H. Q. Luo, and S. L. Li,Phys. Rev. Lett.117, 227003 (2016).

29C.-W. Luo, P. C. Cheng, S.-H. Wang, J.-C. Chiang, J.-Y. Lin, K.-H. Wu, J. Y.

Juang, D. Chareev, O. Volkova, and A. Vasiliev,npj Quantum Materials2, 32 (2017).

30J. Wu, A. T. Bollinger, X. He, and I. Bozovic,Nature547, 432 (2017).

AIP Advances9, 035140 (2019); doi: 10.1063/1.5082656 9, 035140-4

© Author(s) 2019