Electrical properties analysis of materials with ferroic order

Abstract

M. Smari et al. have synthesized and investigated dielectric–electric properties of La_0.5Ca_0.5−xAgMnO₃ manganites. In this letter we emphasize that the data analysis in the paper is partially not reasonable.

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First of all it should be admitted, that the Curie–Weiss law is valid only for the static dielectric permittivity (i.e. ε′(ω → 0) when ε′′/ε′ → 0) and close to the phase transition temperature,² while the frequency dependent dielectric permittivity ε′(ω) should be applied for the more general approach, for example:³where ε*(ω) is related to distributions of relaxation times f(τ). The electrical conductivity of La_0.5Ca_0.5−xAgMnO₃ is very high over the entire temperature range and at different frequencies, so that ε′′/ε′ is also very high and no static dielectric permittivity data is presented in ref. 1. Moreover, far and very close to the phase transition temperature discrepancies from the Curie–Weiss law always appear even for pure ferroelectrics and these discrepancies are substantially temperature dependent.² Therefore, the conclusion in ref. 1 that “in La_0.5Ca_0.1AgMnO₃ is observed the dielectric transition at 200 K, while such transition is not observed in La_0.5Ca_0.5AgMnO₃” is not reasonable.

Another interesting effect observed in La_0.5Ca_0.5−xAgMnO₃ is related to the maximum of the imaginary part of the complex dielectric permittivity ε′′, for x = 0 its position is frequency dependent while for x = 0.4 its position is frequency independent. In ref. 1 it was incorrrectly explained by “relaxor dielectric behaviour” for x = 0 and “normal dielectric behaviour” for x = 0.4. It should be admitted that La_0.5Ca_0.5AgMnO₃ does not demonstrate ferroelectric relaxor properties, because the loss tangent is very high and the maximum position of the real part of the complex dielectric permittivity is almost frequency independent. Why is the dielectric behaviour of La_0.5Ca_0.5AgMnO₃ and La_0.5Ca_0.1AgMnO₃ different? The complex dielectric permittivity ε* = ε′ − iε′′ is related to the complex electrical impedance Z* = Z′ − iZ′′:

Often for conductors when ω → 0, Z′ reaches its static value Z′_stat is related to the dc conductivity and Z′′ ≈ 0. In this case ε′′ = 1/(ε₀ωZ′) = σ_dc/ε₀ω (where σ_dc is the dc conductivity) and the temperature behaviour of dielelectric loss ε′′ resembles the temperature behaviour of the dc conductivity. This situation is clearly observed for La_0.5Ca_0.1AgMnO₃. However, for La_0.5Ca_0.5AgMnO₃ Z′′ is not zero even at low frequencies (below 100 Hz in ref. 1). In this case the temperature behaviour of the dielelectric loss ε′′ is substantially frequency dependent. For example, for resistivity (R) and capacitance (C) connected in serial the complex electrical impedance is:

By combination of eqn (2)–(5) it is possible to conclude, that in this case the maximum position of dielectric loss ε′′ should be frequency dependent. Therefore, the difference in the electric behaviour between La_0.5Ca_0.1AgMnO₃ and La_0.5Ca_0.5AgMnO₃ is mainly related with different values of the dc conductivity and the critical frequency (the frequency at which the value of the conductivity σ(x) deviates from the dc plateau). Moreover, below room temperature the antiferomagnetic phase transition was observed in La_0.5Ca_0.5−xAgMnO₃.⁴ The anomalies of the conductivity and the dielectric permittivity (the last is related with the conductivity via the Kramers–Kroning relation) observed in La_0.5Ca_0.5−xAgMnO₃ are related with this antiferomagnetic phase transition. Can it be observed the multiferroic behaviour in La_0.5Ca_0.5−xAgMnO₃? In order to answer this question measurements at higher frequencies (where ε′′/ε′ → 0) should be performed.

Acknowledgements

This research is funded by the European Social Fund under the Global Grant measure.

References

1. M. Smari, H. Rahmouni, N. Elghoul, I. Walha, E. Dhahri and K. Khirouni, RSC Adv., 2015, 5, 2177.
2. J. Grigas, Microwave Dielectric Spectroscopy of Ferroelectrics and Related Materials, Gordon and Breach/OPA, Amsterdam, 1996, p. 335.
3. J. Macutkevic, S. Kamba, J. Banys, A. Brilingas, A. Pashkin, J. Petzelt, K. Bormanis and A. Sternberg, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 104106.
4. M. Smari, I. Walha, E. Dhahri and E. K. Hill, J. Alloys Compd., 2013, 579, 564.

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