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Contactless conductivity of nanoparticles from electron magnetic resonance lineshape analysis
Solid State Communications 150 (2010) 1518–1520
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Contactless conductivity of nanoparticles from electron magnetic resonance lineshape analysis K.G. Padmalekha, S.V. Bhat ∗ Department of Physics, Indian Institute of Science, Bangalore-560012, India
article
info
Article history: Received 4 May 2010 Received in revised form 9 June 2010 Accepted 10 June 2010 by P. Chaddah Available online 17 June 2010
abstract A contactless method to determine the electrical conductivity of nanoparticles is presented. It is based on the lineshape analysis of electron magnetic resonance signals which are ‘Dysonian’ for conducting samples of sizes larger than the skin depth. The method is validated by measurements on a bulk sample of La0.67 Sr0.33 MnO3 where it gives values close to those obtained from direct measurement of conductivity and is then used to determine the conductivity of nanoparticles of La0.67 Sr0.33 MnO3 dispersed in polyvinyl alcohol as a function of temperature. © 2010 Elsevier Ltd. All rights reserved.
Keywords: A. Nanoparticles D. Dysonian E. Contactless conductivity E. EMR
1. Introduction The electrical conductivity of nanoparticles is an important property from the point of view of applications. However, direct measurement of the conductivity of nanoparticles is a challenging task due to the difficulty involved in the attachment of the electrodes to the particles. Sophisticated techniques involving extensive lithography and patterning or conducting AFM (C-AFM) are occasionally used for this purpose [1–4]. More often, the conductivity is measured on pelletized samples of nanoparticles using the standard four probe method [5]. But in these cases, there usually is a significant contribution of the grain boundary resistance to the overall value and the intrinsic behavior of the nanoparticles is masked. Annealing the pellets to improve the grain-to-grain contact, a procedure followed by some groups, has the disadvantage of increasing the grain size. In this report we introduce a new, contactless method of measuring conductivity of nanoparticles which enables the direct estimation of their conductivity. The method is based on Electron Paramagnetic Resonance (EPR) which is a well established local probe technique used extensively across the fields of physics, chemistry and biology. In this technique, resonance absorption of microwaves across the Zeeman split spin levels of systems with unpaired electrons
∗
Corresponding author. Tel.: +91 080 22932727; fax: +91 080 23602602. E-mail addresses: [email protected] (K.G. Padmalekha), [email protected] (S.V. Bhat). 0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.06.014
is studied as a function of various physico-chemical parameters [6–10]. The contactless technique to measure the conductivity of nanoparticles proposed in this work is based on the analysis of the lineshape of Electron Magnetic Resonance (EMR) signals of the sample recorded with a standard EPR spectrometer. Here we use the term EMR to include ferromagnetic resonance if the sample is ferromagnetic. In the following, we present a proof of the principle by using the technique to determine the conductivity of nanoparticles of La0.67 Sr0.33 MnO3 (LSMO). 2. Experimental details The nanoparticles of LSMO were prepared following the solgel route [11]. Stoichiometric amounts of nitrates of La, Sr and Mn were mixed in a solvent containing equal amounts of ethylene glycol and water. The mixture was heated with stirring until a thick sol was formed. After the solvent had evaporated, the resulting resin was finely ground and annealed at 650 °C to obtain the nanoparticles of LSMO. The magnetization of the sample was measured using a commercial superconducting quantum interference device (SQUID) magnetometer over the temperature range 4–400 K. The nanoparticles were dispersed 1% by weight into the insulating matrix of polyvinyl alcohol by vigorous sonication. The dispersion was dried on a glass plate at 45 °C. The resulting films of a few microns thickness were peeled off from the substrate and used in the subsequent EMR measurements. The EMR signals were recorded using a commercial X-band spectrometer.
K.G. Padmalekha, S.V. Bhat / Solid State Communications 150 (2010) 1518–1520
1519
Fig. 1. XRD and Rietveld analysis of LSMO nanoparticles: experimental (dotted curve) and simulated (solid curve). Inset: SQUID data of LSMO nanoparticles with measuring field of 100 Oe.
Fig. 3. Change in signal shape of the nanoparticles as a function of temperature. Inset: a typical Dysonian signal from the bulk sample at room temperature.
Fig. 2. TEM micrograph of the nanoparticles. Two typical particle sizes are indicated. Inset: size distribution.
3. Results and discussion From the XRD pattern, the particle size (∼15 nm) was obtained by using the Scherrer formula. Rietveld analysis of the XRD (Fig. 1) of the nanoparticles showed that the crystal structure ¯ is rhombohedral (space group R3CH) with the lattice parameters (a = b = 5.49388 Å, c = 13.32294 Å) only slightly different from that of the bulk (a = b = 5.49168 Å, c = 13.33792 Å). The increasing background in the X-ray diffraction (XRD) signal (Fig. 1) at lower angles is an instrumental artifact and was corrected using a baseline fitting software. Magnetization measurements show that the sample is ferromagnetic from room temperature down to 4 K. The transition from ferromagnetism to paramagnetism occurs at ∼350 K (inset to Fig. 1). Transmission electron micrograph (TEM) along with the particle size distribution as inset is shown in Fig. 2. The dark objects seen in the micrograph are particles which are oriented in a different crystallographic plane, which show up as bright objects in a dark field image of the same area. In a standard EPR spectrometer one obtains a symmetric field derivative of the absorbed microwave power as a function of the applied magnetic field. This is a consequence of the magnetic field modulation and phase sensitive detection used while recording the signal. However, if the sample is conducting and the size of the sample is larger than the skin depth δ given by 1
δ= √ (µσ ω)
(1)
where µ, σ and ω are the magnetic permeability and conductivity of the sample and the measuring frequency respectively, then due to mixing of absorptive and dispersive parts of the microwaves the derivative becomes asymmetric. Such lineshapes are called ‘Dysonian’ after F.J. Dyson who first analyzed the phenomenon in detail [12]. The asymmetry, defined in terms of the ratio of the amplitude of the first half of the derivative signal to that of the second half, the so called A/B ratio with A > B, can be quantitatively related to the skin depth δ from which the conductivity can be estimated knowing the permeability µ and the frequency ω. The inset to the Fig. 3 shows the EPR signal from the bulk LSMO sample, which has a typical ‘Dysonian’ lineshape at room temperature. The signals from the nanoparticles from room temperature down to about 220 K shown in the mainframe of the Fig. 3, however, are different in that they show A/B to be less than 1. This ‘anti-Dysonian’ lineshape could be understood as arising from magnetocrystalline anisotropy effects [13] of the ferromagnetic nanoparticles. At lower temperatures, an interesting cross-over occurs at around 220 K to the Dysonian lineshape indicating that the conductivity of the nanoparticles has increased such that the sample size is larger than δ . We focus on the Dysonian signals below this cross-over temperature. A broad EPR signal of the Dysonian shape is described by the following equation [14]: dP dH
=
d dH
A
∆H + α ( H − H 0 ) 4 ( H − H 0 ) 2 + ∆H 2
+
∆H − α (H + H0 ) 4 ( H + H 0 ) 2 + ∆H 2
(2)
where H0 is the resonance field, ∆H is the linewidth and α is the ‘asymmetry parameter’ which gives the fraction of dispersion component mixed with the absorption signal. In a detailed analysis of Dysonian lineshapes, Kodera [15] relates the A/B ratio to the ratio of sample size θ to skin depth δ (Fig. 8 of Ref. [15]). This relationship can be used to estimate θ /δ . Knowing the value of θ by measurements on the sample, one can calculate the value of skin depth δ . Then from Eq. (1), σ can be estimated. While for nonmagnetic samples, µ can be taken to be 1, for ferromagnetic samples such as ours, it is necessary to determine µ independently. We have done it using the magnetization data of the inset to Fig. 1. We have estimated the conductivity of LSMO nanoparticles at various temperatures and the results are presented in Fig. 4. We have also cross-checked the correctness of the method by determining the conductivity of a bulk sample of LSMO prepared using solid-state synthesis. The conductivity values
1520
K.G. Padmalekha, S.V. Bhat / Solid State Communications 150 (2010) 1518–1520
grain boundary contribution though obviously limited to samples which give an EPR/EMR signal of Dysonian shape. The technique requires a much smaller quantity of sample than other contactless methods which work at much lower frequencies [16–20]. Temperature dependence of the conductivity can also be studied giving insight in to the true nature of the conductivity (metallic or otherwise). Acknowledgements The authors would like to thank DST, Government of India, for project funding under NST initiative. KGPL would like to thank D. Banerjee and M.M. Borgohain for help with EMR measurements. Prof. Arun. K. Grover is acknowledged for help with SQUID measurements. Fig. 4. Conductivity values calculated by using Eq. (1). Inset: variation of A/B ratio of nanoparticles with temperature.
obtained by EMR lineshape analysis (8.41 S cm−1 ) and by 4probe electrical conductivity measurement (6.45 S cm−1 ) matched within experimental error. The slightly higher conductivity value obtained using the contactless method could be because the grain boundary resistance is avoided. It is to be noted that a single, average value of the particle size is used for the estimation of the conductivity, while in actuality, there is a distribution of the particle size as shown in the inset to Fig. 2. Moreover, in general, the particles are non-spherical in shape. However, since our samples contain a large number of nanoparticles dispersed in the PVA matrix, a random distribution of the sizes as well as shapes is realized. Therefore the estimated conductivity corresponds to an average value. It would approach the value for an individual nanoparticle as the particles become more and more monodisperse and spherical. 4. Conclusions In summary, we propose and demonstrate a new, contactless method for the measurement of electrical conductivity of nanoparticles which is simple and does not have the problem of
References [1] S. Dhara, H.S. Solanki, V. Singh, A. Narayanan, P. Chaudhari, M. Gokhale, A. Bhattacharya, M.M. Deshmukh, Phys. Rev. B 79 (2009) 121311. [2] H. Suga, Y. Naitoh, M. Tanaka, M. Horikawa, H. Kobori, T. Shimizu, Appl. Phys. Exp. 2 (2009) 055004. [3] I. Amlani, A.M. Rawlett, L.A. Agahara, R.K. Tsui, Appl. Phys. Exp. 80 (2002) 2761. [4] D. Xu, G.D. Watt, J.N. Harb, R.C. Davis, Nano. Lett. 5 (2005) 571–577. [5] Y.H. Huang, Z.G. Xu, C.H. Yan, Z.M. Wang, T. Zhu, C.S. Liao, S. Gao, G.X. Xu, Solid State Commun. 114 (2000) 43. [6] J.A. Weil, J.R. Bolton, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, Wiley-interscience, 1994. [7] J.R. Pilbrow, Transition Ion Electron Paramagnetic Resonance, Oxford University Press, USA, 1991. [8] V.A. Vlaskin, R. Beaulac, D.R. Gamelin, Nano. Lett. 9 (2009) 4376–4382. [9] E.V. Basiuk, E.V. Rybak-Akimova, V.A. Basiuk, D. Acosta-Najarro, J.M. Saniger, Nano Lett. 2 (2002) 1249–1252. [10] T. Rajh, Z. Saponjic, J. Liu, N.M. Dimitrijevic, N.F. Scherer, M. Vega-Arroyo, P. Zapol, L.A. Curtiss, M.C. Thurnauer, Nano Lett. 4 (2004) 1017–1023. [11] S.S. Rao, S. Tripathy, D. Pandey, S.V. Bhat, Phys. Rev. B 74 (2006) 144416. [12] F.J. Dyson, Phys. Rev. 98 (1955) 349. [13] V. Likodimos, M. Pissas, Phys. Rev. B 76 (2007) 024422. [14] J.P. Joshi, S.V. Bhat, J. Magn. Reson. 168 (2004) 284. [15] H. Kodera, J. Phys. Soc. Japan 28 (1970) 89. [16] E.M. Parvin, A. Singfield, W.F. Vinen, G.F. Cox, Supercond. Sci. Technol. 6 (1993) 525. [17] H. Takamura, J. Kobayashi, N. Takahashi, M. Okada, J. Electroceram. 22 (2009) 24. [18] J. Kusmierz, Rev. Sci. Instrum. 78 (2007). [19] A. Pimenov, A. Loidl, Phys. Rev. B 50 (1994) 4204. [20] H. Oike, K. Miyagawa, K. Kanoda, H. Taniguchi, K. Murata, Physica B 404 (2009) 376.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Contactless conductivity of nanoparticles from electron magnetic resonance lineshape analysis K.G. Padmalekha, S.V. Bhat ∗ Department of Physics, Indian Institute of Science, Bangalore-560012, India
article
info
Article history: Received 4 May 2010 Received in revised form 9 June 2010 Accepted 10 June 2010 by P. Chaddah Available online 17 June 2010
abstract A contactless method to determine the electrical conductivity of nanoparticles is presented. It is based on the lineshape analysis of electron magnetic resonance signals which are ‘Dysonian’ for conducting samples of sizes larger than the skin depth. The method is validated by measurements on a bulk sample of La0.67 Sr0.33 MnO3 where it gives values close to those obtained from direct measurement of conductivity and is then used to determine the conductivity of nanoparticles of La0.67 Sr0.33 MnO3 dispersed in polyvinyl alcohol as a function of temperature. © 2010 Elsevier Ltd. All rights reserved.
Keywords: A. Nanoparticles D. Dysonian E. Contactless conductivity E. EMR
1. Introduction The electrical conductivity of nanoparticles is an important property from the point of view of applications. However, direct measurement of the conductivity of nanoparticles is a challenging task due to the difficulty involved in the attachment of the electrodes to the particles. Sophisticated techniques involving extensive lithography and patterning or conducting AFM (C-AFM) are occasionally used for this purpose [1–4]. More often, the conductivity is measured on pelletized samples of nanoparticles using the standard four probe method [5]. But in these cases, there usually is a significant contribution of the grain boundary resistance to the overall value and the intrinsic behavior of the nanoparticles is masked. Annealing the pellets to improve the grain-to-grain contact, a procedure followed by some groups, has the disadvantage of increasing the grain size. In this report we introduce a new, contactless method of measuring conductivity of nanoparticles which enables the direct estimation of their conductivity. The method is based on Electron Paramagnetic Resonance (EPR) which is a well established local probe technique used extensively across the fields of physics, chemistry and biology. In this technique, resonance absorption of microwaves across the Zeeman split spin levels of systems with unpaired electrons
∗
Corresponding author. Tel.: +91 080 22932727; fax: +91 080 23602602. E-mail addresses: [email protected] (K.G. Padmalekha), [email protected] (S.V. Bhat). 0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.06.014
is studied as a function of various physico-chemical parameters [6–10]. The contactless technique to measure the conductivity of nanoparticles proposed in this work is based on the analysis of the lineshape of Electron Magnetic Resonance (EMR) signals of the sample recorded with a standard EPR spectrometer. Here we use the term EMR to include ferromagnetic resonance if the sample is ferromagnetic. In the following, we present a proof of the principle by using the technique to determine the conductivity of nanoparticles of La0.67 Sr0.33 MnO3 (LSMO). 2. Experimental details The nanoparticles of LSMO were prepared following the solgel route [11]. Stoichiometric amounts of nitrates of La, Sr and Mn were mixed in a solvent containing equal amounts of ethylene glycol and water. The mixture was heated with stirring until a thick sol was formed. After the solvent had evaporated, the resulting resin was finely ground and annealed at 650 °C to obtain the nanoparticles of LSMO. The magnetization of the sample was measured using a commercial superconducting quantum interference device (SQUID) magnetometer over the temperature range 4–400 K. The nanoparticles were dispersed 1% by weight into the insulating matrix of polyvinyl alcohol by vigorous sonication. The dispersion was dried on a glass plate at 45 °C. The resulting films of a few microns thickness were peeled off from the substrate and used in the subsequent EMR measurements. The EMR signals were recorded using a commercial X-band spectrometer.
K.G. Padmalekha, S.V. Bhat / Solid State Communications 150 (2010) 1518–1520
1519
Fig. 1. XRD and Rietveld analysis of LSMO nanoparticles: experimental (dotted curve) and simulated (solid curve). Inset: SQUID data of LSMO nanoparticles with measuring field of 100 Oe.
Fig. 3. Change in signal shape of the nanoparticles as a function of temperature. Inset: a typical Dysonian signal from the bulk sample at room temperature.
Fig. 2. TEM micrograph of the nanoparticles. Two typical particle sizes are indicated. Inset: size distribution.
3. Results and discussion From the XRD pattern, the particle size (∼15 nm) was obtained by using the Scherrer formula. Rietveld analysis of the XRD (Fig. 1) of the nanoparticles showed that the crystal structure ¯ is rhombohedral (space group R3CH) with the lattice parameters (a = b = 5.49388 Å, c = 13.32294 Å) only slightly different from that of the bulk (a = b = 5.49168 Å, c = 13.33792 Å). The increasing background in the X-ray diffraction (XRD) signal (Fig. 1) at lower angles is an instrumental artifact and was corrected using a baseline fitting software. Magnetization measurements show that the sample is ferromagnetic from room temperature down to 4 K. The transition from ferromagnetism to paramagnetism occurs at ∼350 K (inset to Fig. 1). Transmission electron micrograph (TEM) along with the particle size distribution as inset is shown in Fig. 2. The dark objects seen in the micrograph are particles which are oriented in a different crystallographic plane, which show up as bright objects in a dark field image of the same area. In a standard EPR spectrometer one obtains a symmetric field derivative of the absorbed microwave power as a function of the applied magnetic field. This is a consequence of the magnetic field modulation and phase sensitive detection used while recording the signal. However, if the sample is conducting and the size of the sample is larger than the skin depth δ given by 1
δ= √ (µσ ω)
(1)
where µ, σ and ω are the magnetic permeability and conductivity of the sample and the measuring frequency respectively, then due to mixing of absorptive and dispersive parts of the microwaves the derivative becomes asymmetric. Such lineshapes are called ‘Dysonian’ after F.J. Dyson who first analyzed the phenomenon in detail [12]. The asymmetry, defined in terms of the ratio of the amplitude of the first half of the derivative signal to that of the second half, the so called A/B ratio with A > B, can be quantitatively related to the skin depth δ from which the conductivity can be estimated knowing the permeability µ and the frequency ω. The inset to the Fig. 3 shows the EPR signal from the bulk LSMO sample, which has a typical ‘Dysonian’ lineshape at room temperature. The signals from the nanoparticles from room temperature down to about 220 K shown in the mainframe of the Fig. 3, however, are different in that they show A/B to be less than 1. This ‘anti-Dysonian’ lineshape could be understood as arising from magnetocrystalline anisotropy effects [13] of the ferromagnetic nanoparticles. At lower temperatures, an interesting cross-over occurs at around 220 K to the Dysonian lineshape indicating that the conductivity of the nanoparticles has increased such that the sample size is larger than δ . We focus on the Dysonian signals below this cross-over temperature. A broad EPR signal of the Dysonian shape is described by the following equation [14]: dP dH
=
d dH
A
∆H + α ( H − H 0 ) 4 ( H − H 0 ) 2 + ∆H 2
+
∆H − α (H + H0 ) 4 ( H + H 0 ) 2 + ∆H 2
(2)
where H0 is the resonance field, ∆H is the linewidth and α is the ‘asymmetry parameter’ which gives the fraction of dispersion component mixed with the absorption signal. In a detailed analysis of Dysonian lineshapes, Kodera [15] relates the A/B ratio to the ratio of sample size θ to skin depth δ (Fig. 8 of Ref. [15]). This relationship can be used to estimate θ /δ . Knowing the value of θ by measurements on the sample, one can calculate the value of skin depth δ . Then from Eq. (1), σ can be estimated. While for nonmagnetic samples, µ can be taken to be 1, for ferromagnetic samples such as ours, it is necessary to determine µ independently. We have done it using the magnetization data of the inset to Fig. 1. We have estimated the conductivity of LSMO nanoparticles at various temperatures and the results are presented in Fig. 4. We have also cross-checked the correctness of the method by determining the conductivity of a bulk sample of LSMO prepared using solid-state synthesis. The conductivity values
1520
K.G. Padmalekha, S.V. Bhat / Solid State Communications 150 (2010) 1518–1520
grain boundary contribution though obviously limited to samples which give an EPR/EMR signal of Dysonian shape. The technique requires a much smaller quantity of sample than other contactless methods which work at much lower frequencies [16–20]. Temperature dependence of the conductivity can also be studied giving insight in to the true nature of the conductivity (metallic or otherwise). Acknowledgements The authors would like to thank DST, Government of India, for project funding under NST initiative. KGPL would like to thank D. Banerjee and M.M. Borgohain for help with EMR measurements. Prof. Arun. K. Grover is acknowledged for help with SQUID measurements. Fig. 4. Conductivity values calculated by using Eq. (1). Inset: variation of A/B ratio of nanoparticles with temperature.
obtained by EMR lineshape analysis (8.41 S cm−1 ) and by 4probe electrical conductivity measurement (6.45 S cm−1 ) matched within experimental error. The slightly higher conductivity value obtained using the contactless method could be because the grain boundary resistance is avoided. It is to be noted that a single, average value of the particle size is used for the estimation of the conductivity, while in actuality, there is a distribution of the particle size as shown in the inset to Fig. 2. Moreover, in general, the particles are non-spherical in shape. However, since our samples contain a large number of nanoparticles dispersed in the PVA matrix, a random distribution of the sizes as well as shapes is realized. Therefore the estimated conductivity corresponds to an average value. It would approach the value for an individual nanoparticle as the particles become more and more monodisperse and spherical. 4. Conclusions In summary, we propose and demonstrate a new, contactless method for the measurement of electrical conductivity of nanoparticles which is simple and does not have the problem of
References [1] S. Dhara, H.S. Solanki, V. Singh, A. Narayanan, P. Chaudhari, M. Gokhale, A. Bhattacharya, M.M. Deshmukh, Phys. Rev. B 79 (2009) 121311. [2] H. Suga, Y. Naitoh, M. Tanaka, M. Horikawa, H. Kobori, T. Shimizu, Appl. Phys. Exp. 2 (2009) 055004. [3] I. Amlani, A.M. Rawlett, L.A. Agahara, R.K. Tsui, Appl. Phys. Exp. 80 (2002) 2761. [4] D. Xu, G.D. Watt, J.N. Harb, R.C. Davis, Nano. Lett. 5 (2005) 571–577. [5] Y.H. Huang, Z.G. Xu, C.H. Yan, Z.M. Wang, T. Zhu, C.S. Liao, S. Gao, G.X. Xu, Solid State Commun. 114 (2000) 43. [6] J.A. Weil, J.R. Bolton, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, Wiley-interscience, 1994. [7] J.R. Pilbrow, Transition Ion Electron Paramagnetic Resonance, Oxford University Press, USA, 1991. [8] V.A. Vlaskin, R. Beaulac, D.R. Gamelin, Nano. Lett. 9 (2009) 4376–4382. [9] E.V. Basiuk, E.V. Rybak-Akimova, V.A. Basiuk, D. Acosta-Najarro, J.M. Saniger, Nano Lett. 2 (2002) 1249–1252. [10] T. Rajh, Z. Saponjic, J. Liu, N.M. Dimitrijevic, N.F. Scherer, M. Vega-Arroyo, P. Zapol, L.A. Curtiss, M.C. Thurnauer, Nano Lett. 4 (2004) 1017–1023. [11] S.S. Rao, S. Tripathy, D. Pandey, S.V. Bhat, Phys. Rev. B 74 (2006) 144416. [12] F.J. Dyson, Phys. Rev. 98 (1955) 349. [13] V. Likodimos, M. Pissas, Phys. Rev. B 76 (2007) 024422. [14] J.P. Joshi, S.V. Bhat, J. Magn. Reson. 168 (2004) 284. [15] H. Kodera, J. Phys. Soc. Japan 28 (1970) 89. [16] E.M. Parvin, A. Singfield, W.F. Vinen, G.F. Cox, Supercond. Sci. Technol. 6 (1993) 525. [17] H. Takamura, J. Kobayashi, N. Takahashi, M. Okada, J. Electroceram. 22 (2009) 24. [18] J. Kusmierz, Rev. Sci. Instrum. 78 (2007). [19] A. Pimenov, A. Loidl, Phys. Rev. B 50 (1994) 4204. [20] H. Oike, K. Miyagawa, K. Kanoda, H. Taniguchi, K. Murata, Physica B 404 (2009) 376.