p.41
p.57
p.95
p.129
p.145
p.169
p.179
p.189
p.209
Recent Applications of Landau-Ginzburg Theory to Ferroelectric Superlattices: A Review
Abstract:
This article briefly reviews recent developments of Landau-Ginzburg theory to ferroelectric phase transitions in superlattices. An overview of the contributions of Landau-type theory to study ferroelectric superlattices is given. Recent findings from first-principles calculations and experiments on intermixing, local polarization coupling and polar discontinuity at interfaces that are not address in these contributions are highlighted. This is followed by a review of recent developments of Landau-Ginzburg theory that addresses these emergent phenomena at interfaces, which is the focus of this review article. The Landau-Ginzburg approach to ferroelectric superlattices with spatial distribution of polarization is outlined. It describes the formation of intermixed layer with properties different from those of both layers. These intermixed layers are mutually coupled through the local polarization at interfaces. Polarization continuity or continuity at interfaces is determined by the nature of the intermixed layer formed at the interface region. Recent results obtained in investigating superlattices comprised primarily of ferroelectric and paraelectric materials are discussed. The results include modulated polarizations, phase transitions, dielectric susceptibilities and switching behaviors.
Info:
Periodical:
Pages:
145-167
Citation:
Online since:
June 2012
Authors:
Keywords:
Price:
Сopyright:
© 2012 Trans Tech Publications Ltd. All Rights Reserved
Citation:
[1] J. M. Gregg: J. Phys.: Condens. Matter Vol. 15 (2003), p. V11.
[2] K. M. Rabe: Current Opinion in Solid State and Mater. Science Vol. 9 (2005), p.122.
[3] M. Dawber, K. M. Rabe and J. F. Scott: Rev. Mod. Phys. Vol. 77 (2005), p.1083.
[4] H. M. Christen, D. H. Kim and C. M. Rouleau: Appl. Phys. A Vol. 93 (2008), p.807.
[5] P. Zubko, S. Gariglio, M. Gabay, P. Ghosez and J. -M. Triscone: Annu. Rev. Condens. Matter Phys. Vol. 2 (2011), p.141.
[6] J. F. Scott: Ferroelectric memories (Springer-Verlag, Berlin 2000).
[7] J. Muralt: J Micromech. Microeng. Vol. 10 (2000), p.136.
[8] M. Dawber, C. Lichtensteiger, M. Cantoni, M. Veithen, P. Ghosez, K. Johnston, K. M. Rabe and J. -M. Triscone: Phys. Rev. Lett. Vol. 95 (2005), p.177601.
[9] E. Bousquet, M. Dawber, N. Stucki, C. Lichtensteiger, P. Hermet, S. Gariglio, J. -M. Triscone and P. Ghosez: Nature Vol. 452 (2008), p.732.
DOI: 10.1038/nature06817
[10] G. Rijnders and D. H. A. Blank: Nature Vol. 433 (2005), p.369.
[11] M. Dawber, N. Stucki, C. Lichtensteiger, S. Gariglio, P. Ghosez and J. -M. Triscone: Adv. Mater. Vol. 19 (2007), p.4153.
[12] T. Tsurumi, T. Ichikawa, T. Harigai, H. Kakemoto and S. Wada: J. Appl. Phys. Vol. 91 (2002), p.2284.
[13] N. Wang, H.B. Lu, W.Z. Chen, T. Zhao, F. Chen, H.Y. Peng, S.T. Lee and G.Z. Yang: Appl. Phys. Lett. Vol. 75 (1999), p.3464.
[14] J. C. Jiang, X. Q. Pan, W. Tian, C. D. Theis and D. G. Schlom: Appl. Phys. Lett. Vol. 74 (1999), p.2851.
[15] H. Tabata, H. Tanaka and T. Kawai: Appl. Phys. Lett. Vol. 65 (1994), p. (1970).
[16] J. Kim, Y. Kim, Y.S. Kim, J. Lee, L. Kim and D. Jung: Appl. Phys. Lett. Vol. 80 (2002), p.3581.
[17] B. D. Qu, M. Evstigneev, D.J. Johnson and R.H. Princes: Appl. Phys. Lett. Vol. 72 (1998), p.1394.
[18] H. -N. Tsai, Y. -C. Liang and H. -Y. Lee: J. Cryst. Growth Vol. 284 (2005), p.65.
[19] S. -J. Chiu, Y. -T. Liu, H. -Y. Lee, G. -P. Yu and J. -H. Huang: J. Cryst. Growth Vol. 334 (2011), p.90.
[20] T. Zhao, Z. -H. Chen, F. Chen, W. -S. Shi, H. -B. Lu and G. -Z. Yang: Phys. Rev. B Vol. 60 (1999), p.1697.
[21] T. Shimuta, O. Nakagawara, T. Makino, S. Arai, H. Tabata and T. Kawai: J. Appl. Phys. Vol. 91 (2002), p.2290.
[22] A. Q. Jiang, J. F. Scott, H. Lu and Z. Chen: J. Appl. Phys. Vol. 93 (2003), p.1180.
[23] S. Ríos, A. Ruediger, A. Q. Jiang, J. F. Scott, H. Lu and Z. Chen: J. Phys.: Condens. Matter Vol. 15 (2003), p. L305.
[24] W. Tian, J. C. Jiang, X. Q. Pan, J. H. Haeni, Y. L. Li, L. Q. Chen, D. G. Schlom, J. B. Neaton, K. M. Rabe and Q. X. Jia: Appl. Phys. Lett. Vol. 89 (2006), p.092905.
DOI: 10.1063/1.2335367
[25] D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe and X. X. Xi: Science Vol. 313 (2006).
[26] A. Sarkar and S. B. Krupanidhi: J. Appl. Phys. Vol. 101 (2007), p.104113.
[27] J. Hiltunen, J. Lappalainen, J. Puustinen, V. Lantto and H. L. Tuller: Opt. Express Vol. 16 (2008), p.8219.
DOI: 10.1364/oe.16.008219
[28] Z. W. Xiong, W. G. Sun, X. M. Wang, F. Jiang and W. D. Wu: J. Alloys Compd. Vol. 513 (2012), p.300.
[29] P. Zubko, N. Stucki, C. Lichtensteiger and J. -M. Triscone: Phys. Rev. Lett. Vol. 104 (2011), p.187601.
[30] J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber and P. G. Evans: Phys. Rev. Lett. Vol. 107 (2011), p.055501.
[31] H. M. Christen, E. D. Specht, D. P. Norton, M. F. Chisholm and L. A. Boatner: Appl. Phys. Lett. Vol. 72 (1998), p.2535.
[32] E. D. Specht, H. M. Christen, D. P. Norton and L. A. Boatner: Phys. Rev. Lett. Vol. 80 (1998), p.4317.
[33] J. Sigman, D. P. Norton, H. M. Christen, P. H. Fleming and L. A. Boatner: Phys. Rev. Lett. Vol. 8 (2002), p.097601.
[34] H. N. Lee, H. M. Christen, M. F. Chisholm, C. M. Rouleau, and D. H. Lowndes: Nature Vol. 433 (2005), p.395.
[35] S. S. A. Seo, J. H. Lee, H. N. Lee, M. F. Chisholm, W. S. Choi, D. J. Kim, J. Y. Jo, H. Kim J. Yu and T. W. Noh: Adv. Mat. Vol. 19 (2007), p.2460.
[36] M. H. Corbett, R. M. Bowman, and J. M. Gregg and D. T. Foord: Appl. Phys. Lett. Vol. 79, (2001), p.815.
[37] Y. L. Yu: Appl. Phys. Lett. Vol. 85 (2004), p.979.
[38] Y. Lu and R. J. Knize: J. Phys. D: Appl. Phys. Vol. 37 (2004), p.2432.
[39] H. Tabata, in: Ferroelectric Thin Films: Relaxor superlattices: Artificial control of the ordered-disordered state of B-site ions in perovskites, edited by M. Okuyama and Y. Ishibashi, volume 98 of Topics in Applied Physics, Part III, Springer-Verlag, Berlin (2005).
[40] R. Ranjith, R. Nikhil and S. B. Krupanidhi: Phys. Rev. B Vol. 74 (2006), p.184104.
[41] N. Lemée, E. Dooryhée, H. Bouyanfif, F. Le Marrec, M. Nemoz, J. L. Hodeau and M. G. Karkut: Phys. Rev. B Vol. 78 (2008), p. 140102R.
[42] R. Kretschmer and K. Binder: Phys. Rev. B Vol. 20 (1979), p.1065.
[43] D.R. Tilley and B. Zeks: Solid State Commun. Vol. 49 (1984), p.823.
[44] L. -H. Ong, J. Osman and D.R. Tilley: Phys. Rev. B Vol. 63 (2001), p.1141109.
[45] Y. Ishibashi, H. Orihara and D.R. Tilley: J. Phys. Soc. Jpn. Vol. 67 (1998), p.3292.
[46] K. -H. Chew, Y. Ishibashi, F. G. Shin and H. L. W. Chan: J. Phy. Soc. Jpn. Vol. 72 (2003), p.2972.
[47] Y. Ishibashi, in: Ferroelectric Thin Films: Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films, edited by M. Okuyama and Y. Ishibashi, volume 98 of Topics in Applied Physics, Part I, Springer-Verlag, Berlin (2005).
[48] Y. Ishibashi and M. Iwata: J. Phys. Soc. Jpn. Vol. 77 (2008), p.104707.
[49] M. Iwata and Y. Ishibashi: J. Phys. Soc. Jpn. Vol. 79 (2010), p.074709.
[50] Y. Ishibashi, M. Iwata and A. M. A. Musleh: J. Phys. Soc. Jpn. Vol. 76 (2007), p.104702.
[51] M. Iwata and Y. Ishibashi: J. Phys. Soc. Jpn. Vol. 78 (2009), p.104707.
[52] J.F. Scott, H.M. Duiker, P.D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler and S. Eaton: Physica B Vol. 150 (1988), p.160.
[53] E. -K. Tan, J. Osman and D.R. Tilley: Solid State Commun. Vol. 117 (2001), p.59.
[54] J. Osman, D. R. Tilley, R. Teh, Y. Ishibashi, M. N. A. Halif and K. -H. Chew: Eur. Phys. J. B Vol. 52 (2006), p.143.
[55] A. M. Alrub and L. -H. Ong: J. Appl. Phys. Vol. 109 (2011), p.084109.
[56] D. Schwenk, F. Fishman and F. Schwabl: Ferroelectrics Vol. 104 (1990), p.349.
[57] S. Li, J. A. Eastman, J. M. Vetrone, R. E. Newhnam and L. E. Cross: Philos. Mag. B Vol. 76 (1997), p.47.
[58] B. D. Qu, W. L. Zhong and R. H. Prince: Phys. Rev. B Vol. 55 (1997), p.11218.
[59] J. Shen and Y. -Q. Ma: Phys. Rev. B Vol. 61 (1999), p.14279.
[60] Y. -Q. Ma, J. Shen and X. -H. Hu: Solid State Commn. Vol. 114 (2000), p.461.
[61] J. Shen and Y. -Q. Ma: J. Appl. Phys. Vol. 90 (2001), p.5031.
[62] P. G. Gennes: Solid State Commun. Vol. 1 (1963), p.132.
[63] I. B. Misirlioglu, G. Akcay, S. Zhong and S. P. Alpay: Appl. Phys. Lett. Vol. 101 (2007), p.036107.
[64] V. A. Stephanovich, I. A. Luk'yanchuk and M. G. Karkut: Phys. Rev. Lett. Vol. 94 (2005), p.047601.
[65] A. P. Levanyuk and I. B. Misirlioglu: J. Appl. Phys. Vol. 110 (2011), p.114109.
[66] Y. Zheng and C.H. Woo: Appl. Phys. A Vol. 97 (2009), p.617.
[67] D. C. Ma, Y. Zheng and C.H. Woo: Acta. Mater. Vol. 57 (2009), p.4736.
[68] L. -H. Ong, T. -Y. Lee and K. -H. Chew: Ceram. Int. Vol. 38S (2012), p. S3.
[69] K. -H. Chew, L. -H. Ong and M. Iwata: Current Appl. Phys. Vol. 11 (2011), p.755.
[70] L. Cui, T. Q. Lu, X. Xu, J. Zhou: J. Appl. Phys. Vol. 105 (2009), p.104104.
[71] P. N. Sun, L. Cui and T. Q. Lu: Chin. Phys. B Vol. 18 (2009), p.1658.
[72] Q. Zhang, L. Cui and T. Q. Lu: Physica B Vol. 406 (2011), p.2284.
[73] T. Q. Lu and W. Cao: Phys. Rev. B Vol. 66 (2002), p.02410.
[74] K. -H. Chew, L. -H. Ong, J. Osman and D. R. Tilley: Appl. Phys. Lett. Vol. 77 (2000), p.275.
[75] L. -H. Ong and T. -Y. Lee: Ferroelectrics Vol. 401 (2010), p.251.
[76] L. -H. Ong, J. Osman and D. R. Tilley: Phys. Rev. B Vol. 65 (2002), p.134108.
[77] L. -H. Ong, J. Osman and D. R. Tilley: Ferroelectrics Vol. 355 (2007), p.130.
[78] A. L. Roytburd, S. Zhong and S. P. Alpay: Appl. Phys. Lett. Vol. 87 (2005), p.092902.
[79] A. Artemev, B. Geddes, J. Slutsker and A. Roytburd: J. Appl. Phys. Vol. 103 (2008), p.074104.
[80] F. A. Urtiev, V. G. Kukhar and N. A. Pertsev: Appl. Phys. Lett. Vol. 90 (2007), p.252910.
DOI: 10.1063/1.2751134
[81] S. Prokhorenko and N. A. Pertsev: J. Appl. Phys. Vol. 110 (2011), p.074116.
[82] I. B. Misirlioglu: Appl. Phys. Lett. Vol. 94 (2009), p.172907.
[83] S. Zhong, S. P. Alpay, A. L. Roytburd and J. V. Mantese: IEEE Trans. Ultrason. Ferroelectr. Freq. Control Vol. 53 (2006), p.2349.
[84] I. B. Misirlioglu, M. Alexe, L. Pintilie and D. Hesse: Appl. Phys. Lett. Vol. 91 (2007), p.022911.
DOI: 10.1063/1.2757127
[85] H. P. Wu, A. P. Liu, L. Z. Wu, and S. Y. Du: Appl. Phys. Lett. Vol. 93 (2008), p.242909.
[86] M. B. Okatan, I. B. Misirlioglu and S. P. Alpay: Phys. Rev. B Vol. 82 (2010), p.094115.
[87] N. A. Pertsev, P. E. Janolin, J. -M. Kiat and Y. Uesu: Phys. Rev. B Vol. 81 (2010), p.144118.
[88] J. H. Qiu: Solid State Comm. Vol. 150 (2010), p.1052.
[89] L. Yang and X. -P. Peng: Phys. Lett. A Vol. 375 (2011), p.4091.
[90] J. H. Qiu and Q. Jiang: Solid State Comm. Vol. 149 (2009), p.1549.
[91] B. Li, J. B. Wang, X. L. Zhong, F. Wang, B. L. Liu, X. J. Lou and Y. C. Zhou: Europhys. Lett. Vol. 95 (2011), p.67004.
[92] N. A. Pertsev and M. Tyunina: J. Appl. Phys. Vol. 109 (2011), p.126101.
[93] B. Yang, D. -M. Zhang, C. -D. Zheng, J. Wang and J. Yu: J. Phys. D: Appl. Phys. Vol. 40 (2007), p.5696.
[94] C. -D. Zheng, D. -M. Zhang, X. -M. Liu, B. Yang, X. -J. Liu and J. Yu: Chin. Phys. Lett. Vol. 27 (2010), p.017702.
[95] K. Abe, O. Furukawa and H. Inagawa: Ferroelectrics Vol. 87 (1988), p.55.
[96] M. Iwata and Y. Ishibashi, in: Ferroelectric Thin Films: Analysis of ferroelectricity and enhanced piezoelectricity near morphotropic phase boundary, edited by M. Okuyama and Y. Ishibashi, volume 98 of Topics in Applied Physics, Part III, Springer-Verlag, Berlin (2005).
[97] T. Hosokura, N. Iwaji, T. Nakagawa, A. Ando, H. Takagi, Y. Sakabe and K. Hirao: Cryst. Growth Des. Vol. 11 (2011), p.4253.
DOI: 10.1021/cg200713c
[98] T. Mizoguchi, H. Ohta, H. -S. Lee, N. Takahashi and Y. Ikuhara: Adv. Funct. Mater. Vol. 21 (2011), p.2258.
[99] T. Ohnishi, H. Koinuma and M. Lippmaa: Appl. Surf. Sci. Vol. 252 (2006), p.2466.
[100] D. D. Fong, C. Cionca, Y. Yacoby, G. B. Stephenson, J. A. Eastman, P. H. Fuoss, S. K. Streiffer, C. Thompson, R. Clarke, R. Pindak and E. A. Stern: Phys. Rev. B Vol. 71 (2005), p.144112.
[101] J. Shin, A. Y. Borisevich, V. Meunier, J. Zhou, E. W. Plummer, S. V. Kalinin and A. P. Baddorf: ACS Nano Vol. 4 (2010), p.4190.
[102] C. -L. Hung, Y. -L. Chueh, T. -B. Wu and L. -J. Chou: J. Appl. Phys. Vol. 97 (2005), p.034105.
[103] Y. Ishibashi, N. Ohashi and T. Tsurumi: Jpn. J. Appl. Phys. Part 1 Vol. 39 (2000), p.186.
[104] V. R. Cooper, K. Johnston and K. Rabe: Phy. Rev. B Vol. 71 (2005), p.144112.
[105] H.M. Christen, E.D. Specht, D.P. Norton, M.F. Chisholm and L.A. Boatner: Appl. Phys. Lett. Vol. 72 (1998), p.2535.
[106] E.D. Specht, H.M. Christen, D.P. Norton and L.A. Boatner: Phys. Rev. Lett. Vol. 80 (1998), p.4317.
[107] J. Sigman, D. P. Norton, H. M. Christen, P. H. Fleming and L. A. Boatner: Phys. Rev. Lett. Vol. 8 (2002), p.097601.
[108] P. Aguado-Puente, P. Garcia-Fernandez and J. Junquera: Phys. Rev. Lett. Vol. 107 (2011), p.217601.
[109] H. Y. Hwang, Y. Iwasa, M. Kawasaki, N. Nagaosa and Y. Tokura: Nature Mater. Vol. 11 (2012), p.103.
[110] H. Das, N. A. Spaldin, U. V. Waghmare and T. Saha-Dasgupta: Phys. Rev. B Vol. 81 (2010), p.235112.
[111] A. Ohtoma and H. Y. Hwang: Nature Vol. 427 (2004), p.423.
[112] N. Reyren, S. Thiel, A. D. Caviglia, L. F. Kourkoutis, G. Hammerl, C. Richter, C. W. Schneider, T. Kopp, A. -S. Ruetschi, D. Jaccard, M. Gabay, D. W. Muller, J. -M. Triscone and J. Mannhart: Science Vol. 317 (2007), p.1196.
[113] A. Brinkman, M. Huijben, M. van Zalk, J. Huijben, U. Zeuitler, J. C. Maan, W. G. van der Wiel, G. Rijnders, D. H. A. Blank and H. Hilgenkamp: Nature Mater. Vol. 6 (2007), p.493.
DOI: 10.1038/nmat1931
[114] Y. Watanabe, M. Okano, and A. Masuda: Phys. Rev. Lett. Vol. 86 (2001), p.332.
[115] Y. Watanabe: Ferroelectrics Vol. 259 (2001), p.21.
[116] Y. Watanabe, in: Ferroelectric Thin Films: Physics of Ferroelectric Interfaces: An Attempt at Nanoferroelectric Physics, edited by M. Okuyama and Y. Ishibashi, volume 98 of Topics in Applied Physics, Springer-Verlag, Berlin (2005).
[117] L. Qiao, T.C. Droubay, T.C. Kaspar, P.V. Sushko and S.A. Chambers: Surf. Sci. Vol. 605 (2011), p.1381.
[118] M. K. Niranjan, Y. Wang, S. S. Jaswal and E. Y. Tymbal: Phys. Rev. Lett. Vol. 103 (2009), p.016804.
[119] Z. Zhang, P. Wu, L. Chen and J. Wang: Appl. Phys. Lett. Vol. 99 (2011), p.062902.
[120] M. E., Lines and A. M., Glass: Principles and Applications of Ferroelectrics and Related Materials (Clarendon Press, Oxford 1977).
[121] D. D. Fong, G. B. Stephenson, S. K. Streiffer, J. A. Eastman, O. Auciello, P. H. Fuoss and C. Thompson: Science Vol. 304 (2004), p.1650.
[122] K. -H. Chew, L. -H. Ong and M. Iwata, in: Ferroelectrics - Characterization and Modeling: Intrinsic Interface Coupling in Ferroelectric Heterostructures and Superlattices, edited by Mickaël Lallart, chapter 19, InTech, Croatia (2012).
DOI: 10.5772/16518
[123] K. -H. Chew, Y. Ishibashi, F.G. Shin and H.L.W. Chan: J. Phys. Soc. Jpn. Vol. 72 (2003), p.2364.
[124] C. H. Tsang, K. -H. Chew, Y. Ishibashi, and F.G. Shin: J. Phys. Soc. Jpn. Vol. 73 (2004), p.3158.
[125] K. -H. Chew, Y. Ishibashi, and F.G. Shin: J. Phys. Soc. Jpn. Vol. 74 (2005), p.2338.
[126] K. -H. Chew, Y. Ishibashi, and F.G. Shin: Phys. Stat. Sol. (a). Vol. 203 (2006), p.2205.
[127] K. -H. Chew, Y. Ishibashi, and F.G. Shin: J. Phys. Soc. Jpn. Vol. 75 (2006), p.064712.
[128] K. -H. Chew, Y. Ishibashi, and F.G. Shin: Ferroelectrics Vol. 357 (2007), p.133.
[129] K. -H. Chew, M. Iwata, F. G. Shin and Y. Ishibashi: Integr. Ferroelectr. Vol. 100 (2008), p.79.
[130] K. -H. Chew, M. Iwata and F. G. Shin: Ferroelectrics Lett. Sect. Vol. 36 (2009), p.12.
[131] Y. Ishibashi and M. Iwata: Ferroelectrics Vol. 354 (2007), p.8.
[132] K. -H. Chew, L. -H. Ong and M. Iwata: J. Appl. Phys. Vol. 110 (2011), p.054108.
[133] Y. Ishibashi: Integr. Ferroelectr. Vol. 2 (1992), p.41.
[134] Y. Ishibashi: J. Phys. Soc. Jpn. Vol. 59 (1990), p.4148.
[135] M. Omura, H. Adachi and Y. Ishibashi: Jpn. J. Appl. Phys. Part 1 Vol. 30 (1991), p.2384.
[136] M. Omura, H. Adachi and Y. Ishibashi: Jpn. J. Appl. Phys. Part 1 Vol. 31 (1992), p.3238.
[137] M. Omura, T. Ishibahi and Y. Ishibashi: Jpn. J. Appl. Phys. Part 1 Vol. 32 (1993), p.4388.
[138] D. Ricinschi, Y. Ishibashi, M. Iwata and M. Okuyama: Jpn. J. Appl. Phys. Part 1 Vol. 40 (2001), p.4990.
[139] L. Baudry and J. Tournier: J. Appl. Phys. Vol. 90 (2001), p.1442.
[140] D. Ricinschi, A. I. Lerescu and M. Okuyama: Jpn. J. Appl. Phys. Part 2-Lett. Vol. 39 (2000), p. L990.
[141] M. Stengel and N. A. Spaldin: Nature Lett. Vol. 443 (2006), p.679.
[142] M. Stengel, D. Vanderbilt and N. A. Spaldin: Nature Mat. Vol. 8 (2009), p.392.
[143] L. -W. Chang, M. Alexe, J. F. Scott and J. M. Gregg: Adv. Mat. Vol. 21 (2009), p.4911.
[144] C. -G. Duan, R. F. Sabrianov, W. -N. Mei, S. S. Jaswal and E. Y. Tsymbal: Nano Lett. Vol. 6 (2006), p.483.
[145] Y. Wang, M. K. Niranjan, K. Janicka, J. P. Velev, M. Ye Zhuravlev, S. S. Jaswal and E. Y. Tsymbal: Phys. Rev. B Vol. 82 (2010), p.094114.