ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 310 (2007) e681–e683 www.elsevier.com/locate/jmmm Grain boundary resistivity of the percolative conduction regime in ruthenium doped manganates P.Q Thanha, H.N Nhata,Ã, H.D Chinhb a Faculty of Physics, Vietnam National University, 334 Nguyen.Trai, Hanoi, Vietnam Department of Inorganic Chemistry, Hanoi University of Technology, Dai Co Viet Str.1, Hanoi, Vietnam b Available online 27 November 2006 Abstract The excellent agreement with experimental data has been achieved in fitting the resistivity of doped manganate–ruthenates for whole temperature range The analysis interpreted the resistivity in terms of percolation of carriers through the system of grain boundaries, having been assumed as the conductive fractal medium The percolative conduction regime has been shown substantial for the K-doped ruthenates [H.N Nhat, H.D Chinh and M.H Phan, Solid State Commun 139 (2006) 456], and we confirm here that this approach also correctly discusses the unusual semiconductor-like behaviours of the doped manganate–ruthenates r 2006 Elsevier B.V All rights reserved PACS: 74.70.Pq; 72.80.Jc; 61.43.Hv Keywords: Ruthenates; Percolation; Resistivity; Grain boundary; Fractal Introduction In perovskite ruthenates, the good metallic conduction may be explained via partial filling of p* states, formed by Ru(t2g)ÀO2pÀRu(t2g) interaction, by the electron transfer from AÀO bonds [2] The important fact is that Ru may exhibit average oxidation state Ru(4Ày)+ instead of mixed state Ruy3+Ru1Ày4+ so induces ferromagnetism [3] even in cases, e.g., SrRuO3 (Tc E160 K), where the ferromagnetism is unexpected, because the super-exchange interaction t2g(d4+)ÀO2pÀt2g(d4+) is strongly anti-ferromagnetic [4] The calculation of electronic structure using LSDA model for the prototype compounds SrRuO3 and CaRuO3 [5] also predicted the ferromagnetism with magnetic moment 2.0 and 1.9 mB The orthorhombic deformation usually reduces the metallic conduction, but, for some cases, the reduction was small, while the angles Ru–O–Ru fell below 1401 [6] In pyrochlores and La0.5K0.5RuO3, the A-site cation chargedisorder appeared important [7,8] The substitution of a non-polar and strongly ionic bonded K1+ in to A-site produced a compound that is structurally less distorted ÃCorresponding author Tel.: +84 558 2216; fax: +84 768 2007 E-mail address: namnhat@hn.vnn.vn (H.N Nhat) 0304-8853/$ - see front matter r 2006 Elsevier B.V All rights reserved doi:10.1016/j.jmmm.2006.11.031 than its prototype but with higher resistivity [8] This was because the cations K1+ prohibit the electron transfer from from AÀO bonds to p* band, so as to reduce metallic conduction The Fermi liquid behaviour of La0.5K0.5RuO3 was well fitted with standard expression r ¼ r0+aT2 and the Fermi level’s density of states was estimated at 5.03 Â 1028 mÀ3/eV However, for To20 K, the resistivity suddenly jumped and the compound become insulator near K The semiconductor-like behaviour was also observed for other ruthenates [1,8] and is not rare for Ru-doped manganates The common feature is that the thermal behaviour of resistivity was difficult to fit, or was fitted within a narrow range of temparature and with low accuracy, by the standard models like band-gap, small polaron and variable range hopping (Fig 1) We have presented a unified platform to intepret these cases in Refs [1,9] Because of the importance of the Ru-doped manganates as the potential candidates for high positive thermoelectric coeficient materials, we here give the reinterpretation of resistivity of Ca0.85Pr0.15Mn1ÀyRuyO3 (y ẳ 0:0020:07) using the formula given in [1] lnb=rị1=D ỵ 1ị ln a ỵ n ln T, (1) ARTICLE IN PRESS P.Q Thanh et al / Journal of Magnetism and Magnetic Materials 310 (2007) e681–e683 ln (ρ/T) ρ [Ωcm] 5.0 12 104 y=0.07 y=0.05 y=0.03 y=0.00 2.5 y=0.07 y=0.05 y=0.03 y=0.00 103 102 10 10 0 100 200 T [K] 300 400 -2.5 -5.0 0.2 0.3 0.4 0.5 y=0.00 y=0.07 y=0.05 y=0.03 0.6 1/T1/4 Fig Check plots for the variable range hopping model for Ca0.85Pr0.15Mn1ÀyRuyO3 show linearity only for Ru-free sample, other cases decline from linearity in higher T Even worst linear fits were obtained by band-gap and small polaron model The inset shows measured data where r is the net resistivity, T is the temperature, D is the fractal dimension of the grain boundary system, b, a and n are the fit constants Accurate result has been achieved using Eq (1) Fig The fits for the percolative conduction regime The mere linearity was observed for the Ru-free sample (y ¼ 0:00) This sample is believed to follow the variable range hopping regime, typically observed in the manganates 0.02 0.04 0.06 T ẳ 1=aị1=n , (2) for which r ¼ N, that is the compound becomes insulator All compounds show T o0:04 K so we have only partly verified (down to K) Evidently, the carrier concentration x decreases to the threshold xc at T0, xTị=xc ẳ xTị=xT ị ẳ aT n (3) At 300 K, this ratio for y(Ru) ¼ 0.07 is four times larger than that for y(Ru) ¼ 0.03 and, at 10 K, this ratio is about 50 times larger The upper limit for density of states at xc is estimated at 1.2 Â 1024 mÀ3/eV (it was 8.6 Â 1022 mÀ3/eV for the K-doped ruthenates [1]) Fig shows the decrease in ln T0 and power factor n according to Ru content Since n is proportionate to ln(x/xc) the larger amount of Ru also has the side effect in decreasing the number of percolative carriers in compound (beside pumping the Fermi carriers) Power factor n 0.08 n logT0 Percolative conduction in Ru-doped manganates The percolation theory assumes that the grain boundary system forms a conductive medium with fractal structure A typical issue of the fractal system is the dependence of measured resistivity on measuring path, which mathematically finalises in the log–log linearity (1) To summarize how Eq (1) has been obtained, observe that the apparent resistivity of a percolation system is proportional to the inverse of effective carrier concentration (x–xc) Using two-layer simple effective medium model, the net resistivity is given by r ffi (L0 /L)ra (L, L0 are grain’s and grain boundary’s linear sizes) The substitution of x(T) ¼ aTnxc into r leads to Eq (1) By fitting it to experiment data, n and a can be found (Fig 2) According to Ref [1] there is a characteristic T0 such that ln (T) n = : resistivity is independent to T -10 -20 lnT0 7.5 ln[(β/ρ)1/D+1] e682 -1 -30 -2 x/xc=1 : turn point to metallic behaviour 0.05 0.10 0.15 0.20 -40 Ru content Fig The development of ln T0 and n according to Ru content The n links to log of carrier concentration and is seen inversed to Ru content The n was linear to Pauling electronegativity of A-site cations in K-doped ruthenates [1] This side effect grows with rising temperature The theoretical extrapolation showed that the ratio x/xc decreases to at room temperature and the percolative conduction regime is totally cancelled for y(Ru) X0.17 Two cases, denoted ‘‘’’ and ‘‘’’’ in Fig 3, have been experimentally confirmed For the first case, y(Ru) ¼ 0.08 and nE0, so x/xc did not depend on T and the resistivity remained almost unchanged in whole temperature range For the second case, y(Ru) ¼ 0.17, so the compound turned to metallic behaviour with standard expression r ¼ r0+aT2 Conclusion Linearity (1) for Ca0.85Pr0.15Mn1ÀyRuyO3 is surprised because we did not expect that a small amount of Ru can ARTICLE IN PRESS P.Q Thanh et al / Journal of Magnetism and Magnetic Materials 310 (2007) e681–e683 change the variable range hopping regime usually observed in manganates However, as the measured resistivity significantly dropped with doping a little Ru, the change in conduction mechanism is possible The obtained linearity (1) strongly supports the conclusion that the percolative conduction plays a substantial role in this class of compounds References [1] H.N Nhat, H.D Chinh, M.H Phan, Solid State Commun 139 (2006) 456 [2] Y Maeno, H Hashimoto, K Yoshida, S Nishizaki, T Fujita, J Bednorz, F Lichtenberg, Nature (London) 372 (1994) 532 e683 [3] M Fernanda, Da Costa, R Greatrex, N.N Greenwood, J Solid State Chem 20 (1977) 381 [4] J.B Goodenough, Magnetism and the Chemical Bond, Interscience, NewYork, 1963 [5] G Santi, T Jarborg, J Phys.: Condens Matter (1997) 9563 [6] T Takeda, M Nagata, H Kobayashi, R Kanno, Y Kawamoto, J Solid State Chem 140 (1998) 182 [7] T He, Q Huang, R.J Cava, Phys Rev B 63 (2000) 024402 [8] H.D Chinh, N Hanh, N Chau, M Itoh, in: A Pucci (Ed.), Physics and Engineering in Evolution, Erlanger, pp, 2005, p 101 [9] P.Q Thanh, H.N Nhat, B.T Cong, in: H Takabe, N.H Luong, Y Onuki (Eds.), Frontiers of Basic Science, Osaka University Press, 2006, p 237 ... n logT0 Percolative conduction in Ru -doped manganates The percolation theory assumes that the grain boundary system forms a conductive medium with fractal structure A typical issue of the fractal... K -doped ruthenates [1] This side effect grows with rising temperature The theoretical extrapolation showed that the ratio x/xc decreases to at room temperature and the percolative conduction regime. .. model The inset shows measured data where r is the net resistivity, T is the temperature, D is the fractal dimension of the grain boundary system, b, a and n are the fit constants Accurate result