Chin. Phys. B
Vol. 28, No. 5 (2019) 057702The c-axis complex permittivity and electrical impedance in BaFe 2 As 2 : Experimental examination on transformation validity ∗
Yongqiang Li(李永强)1,†, Xinzhe Du(杜新哲)2,†, Dongliang Gong(龚冬良)3, Qirui Yang(杨綦睿)2, Wenliang Zhang(张汶良)3, Tao Xie(谢涛)3, Bo Feng(冯波)2, Kai Chen(陈恺)2,‡,
Huiqian Luo(罗会仟)3, Junming Liu(刘俊明)1,§, and Jinsong Zhu(朱劲松)1
1National Laboratory of Solid State Microstructures, Nanjing University, Nanjing210093, China 2School of Science, Nanjing University of Science and Technology, Nanjing210094, China
3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing100190, China
(Received 22 January 2019; revised manuscript received 6 March 2019; published online 4 April 2019)
Complex permittivity and electrical impedance have been measured along thec-axis in single crystals BaFe2As2, which are the conductors known as the parent compound of 122-type iron superconductor. The resultant relative errors defined in the study indicate the existence of the transformation between complex permittivity and electrical impedance in the conductors, and these two physics quantities possibly reveal different aspects of the consistent superconductivity- relevant physics picture.
Keywords:complex permittivity, electrical impedance, BaFe2As2, transformation validity PACS:77.22.Ch, 87.63.Pn, 43.60.Ek DOI:10.1088/1674-1056/28/5/057702
1. Introduction
Transformation among physics quantities is an impor- tant basis to describe inherent relevance and consistency among different physics processes. For example, the present transformation between complex permittivity and electrical impedance (Eq. (1)) dictates the effect of equivalence between charge migration and electrical dipole reorientation in insula- tors. In other words, charges migrate in a short range to reori- ent local electrical dipoles, and then possibly, in a long range even through the bulk, to pin at material-electrode interfaces, as measured as capacitance that is encountered when form- ing an AC electric field. We, in fact, agree that all migrating charges are as displacement current for bulk polarization, and this is the reason why the bulk conductivity is included in the imaginary part of the complex permittivity (Eq. (1)). More specifically, in the very simple case of a linear, homogeneous, isotropic insulator, the transformation is simplified in the form of scalar rather than second rank tensor, as follows:[1]
ε∗ = ε0−iσ
ω = [iωC0Z∗]−1= [iωC0(R−iX)]−1
=
ωC0 R2+X2−1
(X−iR), (1)
with
ε0= [ωC0 R2+X2
]−1X, (2) ε00= [ωC0 R2+X2
]−1R, (3)
whereε∗is the complex permittivity,ε0is the real part of the complex permittivity,ε00is the imaginary part of the complex permittivity, i =√
−1, σ is the bulk conductivity, ω is the angular frequency, andω=2πf,f is the frequency of the ap- plied AC voltage,C0is the vacuum capacitance,Z∗is the elec- trical impedance,Ris the resistance, andXis the reactance, in most cases, ε0, ε00,R, and X are functions of f. The trans- formation shows that, besides of their modulation on the bulk polarization, the short- or long-range migrating charges may produce the inductance effect, while the long-range ones defi- nitely contribute to the bulk conductivity or the resistance. The transformation is valid in insulators, such as CaCu3Ti4O12.[2,3]
However, in the case that there are no local dipoles in conduc- tors, the question arises of what role the migrating charges play, and the transformation validity may be questioned. The investigation into the transformation validity, to some extent, makes us reinspect these physics quantities as the parameter, and highlight the physics difference in the two processes, to describe the phenomena as accurately as possible. Preceded from experiments, it may further outline the limitation of mea- suring accuracy, and show us the need for improvement of measurement specification, method, and instrument.
As one parent compound of iron-based superconductors, single crystals of BaFe2As2could be used as an investigated example. Only on the a- or b-axis do the tetragonal-to-
∗Project supported by the National Natural Science Foundation of China (Grant No. 11004106), the National Basic Research Program of China (Grant No. 2015CB946502), the Chinese Academy of Sciences (Grant No. SPRP-B: XDB25000000), and the Youth Innovation Promotion Association of Chinese Academy of Sciences.
†These authors contributed equally to this work.
‡Corresponding author. E-mail:[email protected]
§Corresponding author. E-mail:[email protected]
© 2019 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 057702-1
Chin. Phys. B
Vol. 28, No. 5 (2019) 057702 orthorhombic structural transition at temperature Ts and theantiferromagnetic phase transition below nearly the same tem- peratureTs≈TN≈138 K take an effect, and, therefore, thec- axis electrical property is independent of thea- orb-axis ones, and the complex permittivity and electrical impedance could be simplified as a scalar, and the electrical measurement on c-axis is only required perpendicular to thea–bplane. In this study, we examine the transformation validity between com- plex permittivity and electrical impedance inc-axis of single crystal BaFe2As2.
2. Experiments
High-quality single crystals of BaFe2As2 were grown by the self-flux method that has been reported elsewhere.[4]
By using a diamond wire cutting machine, all of the sin- gle crystals were cut into plates with the dimensions of 2.8 mm×2.8 mm×0.28 mm. Silver conductive paints (186- 3600, RS components, UK) were painted on both surfaces of the specimens and two gold wires were welded and then dried by infrared light in the air, making two electrodes and two external wires, respectively. The room-temperature measure- ment on both complex permittivity and electrical impedance was obtained by using a Hewlett-Packard impedance/grain- phase analyzer, model 4294A (HPIGPA, Agilent Co., USA) and the room-temperature standard sample stage. The min- imum measured value of impedance is 3 mΩ, with the ba- sic impedance accuracy ±0.08%, the work frequency range is from 40 Hz to 110 MHz with 1 mHz resolution. A si- nusoidal voltage with peak voltage of 200 mV from 100 Hz to 1 MHz was applied, and the peak voltage was selected to guarantee that both the complex permittivity and electri- cal impedance were measured within the range of precision.
To confirm the data reliability, we utilized the sample stage of a physical property measurement system (PPMS, Quantum Design Co. USA). After the specimen measurements were fin- ished, the silver electrodes, gold wires, and other components were directly connected to the instrument, their complex per- mittivity and electrical impedance values were measured and subtracted as background data.
3. Results and discussion
Using the parallel plate capacitor method with the dielec- tric mode (parallel capacitor)Cp–Dand the impedance mode R–X, we directly obtain the capacitance of the single crystals C=ε0ε0S/d, the dielectric loss D=tgδ =ε00/ε0,R, andX, respectively, whereε0is the vacuum dielectric constant,S is the electrode area, anddis the thickness of the measured sin- gle crystals. Based on the previous work, we can distinguish the values ofε0,ε00,R, andXin thecaxis from those in thea
andbaxes. We can easily derive the following relation from Eq. (2):
ε00/ε0=R/X. (4) The examination of the transformation validity is simplified to compare the values ofε00/ε0with those ofR/X. Bothε00 and Rare the numerator of the fraction, and their positional sym- metry indicates that the loss caused by the long-range charge migration is the origin of resistance. The positional symmetry ofε0andX as the denominator attenuates that the short-range charge migration modulates the local dipoles, and simultane- ously, triggers the oscillation of the local dipoles for building up an inherent magnetic field to resist the change of the charge migration.
Figure1shows the measured values ofε00/ε0andR/Xby using the standard sample stage of HPIGPA at room tempera- ture. Below 105Hz, both the original values ofε00/ε0andR/X are randomly dispersive, which is due to the interference of environmental electrical signals or noises. However, the val- ues show a certain degree of repeatability above 105Hz. The average data of ε00/ε0 and R/X, as shown in Figs.1(b) and 1(d), show the same variation tendency as the original values do (Figs.1(a)and1(c)).
10-2 100 102 104 106
10-2 100 102 104 106
10-2 100 102 104 106
102 104 106 dozens of original measurements
(a)
Frequency/Hz
R/X
average data
(b)
dozens of original measurements
(c)
average data
(d)
ε″/ε′ε″/ε′
102 104 106 Frequency/Hz
10-2 100 102 104 106
R/X
Fig. 1.Dozens of original measurements of (a)ε00/ε0, (c)R/X, and (b), (d) their average data. The inset in panel (b) shows the standard sample stage of the HPIGPA.
057702-2
Chin. Phys. B
Vol. 28, No. 5 (2019) 057702102 104 106 Frequency/Hz
102 104 106 Frequency/Hz
102 104 106 Frequency/Hz
102 104 106 Frequency/Hz 10-2
100 102 104 106
ε″/ε′
10-2 100 102 104 106
ε″/ε′
dozens of original measurements
(a)
background
(b)
average after backgound removal
(c)
dozens of original measurements
(d)
background
(e)
average after backgound removal
(f)
background (g) dozens of original measurements
(h) average after backgound removal
10-2 100 102 104 106
R/X
10-2 100 102 104 106
R/X
Fig. 2.Dozens of original measurements, background, and the average data after background removal ofε00/ε0from 102Hz to 106Hz ((a)–(c)) and from 103Hz to 106Hz ((d)–(f)), respectively. (g) and (h) The same forR/X, respectively. The inset in panel (c) shows the sample stage of the PPMS.
To evaluate the effect of the standard sample stage, we used another sample test stand in PPMS (the inset in Fig.2(c)) and the measured data are shown in Fig. 2. As shown in Fig.2(a), dozens of measurements show that the original val- ues ofε00/ε0are not dispersive above 104Hz and the repeata- bility is good, and the case is similar for the background val- ues. Using the data of dozens of measurements and the back- ground data (Figs.2(a)and2(b)), we subtract theε00/ε0values of the single crystal as shown in Fig.2 (c). In the measured frequency range, the values are far larger than 1, and these sin- gle crystals are good conductors which are consistent with the previous results. For confirming the value repeatability above 104Hz, we changed the minimum measured frequency from 102Hz to 103Hz, as shown in Fig.1(d). Without doubt, the values ofε00/ε0above 104Hz are reliable. Therefore, we cau- tiously use the values ofε00/ε0from 104Hz to 106Hz to com- pare the values ofR/X in the same frequency range, while we attribute the value dispersion below 104Hz to the interference from other unshielded signals. Similar dispersion is also found in the values ofR/Xbelow 104Hz, as shown in Figs.2(g)and 2(h). The average data, after background removal, show the same magnitude range from 10−2to 106as those ofε00/ε0do, and their frequency dependence is similar, which indicates the existence of the transformation validity.
104 105 106 Frequency/Hz
104 105 106 Frequency/Hz E1
E2
standard sample stage (a)
Relative error/%
sample stage of PPMS (b)
of HPIGPA 100
10-1 101 102 103 104
Relative error/%
0.01 0.1 1
10 E1
E2
Fig. 3.Relative errorsE1andE2of the data measured in (a) the stan- dard sample stage of the HPIGPA and (b) the sample stage of the PPMS, respectively.
To quantitatively examine the transformation validity, we define the relative errors
E1=|(ε00/ε−R/X)/(R/X)| ×100%, or
E2=|(R/X−ε00/ε)/(ε00/ε)| ×100%,
which seem physically equivalent. We use the average date of the experiments in the standard sample stage of the HPIGPA 057702-3
Chin. Phys. B
Vol. 28, No. 5 (2019) 057702 above 105Hz (Figs.1(b)and1(d)), and the average data afterbackground removal in the sample stage of the PPMS above 104 Hz, to calculate the relative errors and the results are shown in Fig.3. The relative errors of the data measured in the standard sample stage of HPIGPA show the poor repeti- tion, and are even in the range from 10−1to 103. However, those in the sample stage of PPMS show better results as small as ∼0.1%, and indicate the existence of the transformation validity. Hence, we can tell the difference in measurement ac- curacy between the standard sample stage of HPIGPA and the sample stage of PPMS, and there is the possibility to improve it.
4. Conclusion
In summary, complex permittivity and electrical impedance are measured along c-axis of single crystals
BaFe2As2, which are conductors, by using the same equip- ment with two different sample stages. The transformation between the complex permittivity and electrical impedance in the conductor is tried to be validated. Although there is an indication of the transformation validity, the improvement on the measuring accuracy should be done for the experimental evidence.
References
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[3] Guo Y Y, Guo Y J, Wei T and Liu J M2015Chin. Phys. B24127701 [4] Chen Y, Lu X, Wang M, Luo H Q and Li S L2011Supercond. Sci.
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