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Recent progress in the thermodynamics of ferrotoroidic materials

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Recent theoretical and experimental progress on the study of ferrotoroidic materials is reviewed. The basic field equations are first described and then the expressions for magnetic toroidal moment and toroidization are derived. Relevant materials and experimental observation of magnetic toroidal moment and toroidal domains are summarized next. The thermodynamics of such magnetic materials is discussed in detail with examples of ferrorotoidic phase transition studied using Landau modelling. Specifically, an example of application of Landau modelling to the study of toroidocaloric effect is also provided. Recent results of polar nanostructures with electrical toroidal moment are finally reviewed.
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  • Departament d’Estructura i Constituents
    de la Matèria, Facultat de Física, Universitat de Barcelona,
    Diagonal 647, 08028 Barcelona, Catalonia
  • Departament d’Estructura i Constituents
    de la Matèria, Facultat de Física, Universitat de Barcelona,
    Diagonal 647, 08028 Barcelona, Catalonia
  • Theoretical Division, Los Alamos National Laboratory,
    Los Alamos, New Mexico 87545, USA
  • [1] V. K. Wadhawan, Introduction to Ferroic Materials, Gordon andBreach, 2000.
  • [2] H. Schmid, On ferrotoroidics and electrotoroidics, magnetotoroidicsand piezotoroidics effects, Ferroelectrics 252, 41-50(2001).
  • [3] N. A. Spaldin, M. Fiebig, and M. Mostovoy, The toroidal momentin condensed-matter physics and its relation to the magnetoelectriceffect, J. Phys. Condens. Matter 20, 434203 (2008).[Crossref]
  • [4] D. Khomskii, Classifying multiferroics: Mechanisms and effects,Physics 2, 20 (2009).[Crossref]
  • [5] A. Saxena and T. Lookman, Magnetic symmetry of lowdimensionalmultiferroics and ferroelastics, Phase Trans.84, 421 (2011).
  • [6] V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, Axial toroidalmoments in electrodynamics and solid-state physics, Zh. Eksp.Teor. Fiz. 90, 590 (1986) [Sov. Phys. JETP 63, 344 (1986)].
  • [7] V. M. Dubovik and V. V. Tugushev, Toroid moments in electrodynamicsand solid-state physics, Phys. Rep. 187, 145 (1990).[Crossref]
  • [8] V. M. Dubovik, M. A. Martsenyuk, and B. Saha, Materials equationsfor electromagnetism with toroidal polarization, Phys. Rev.E 61, 7087 (2000).[Crossref]
  • [9] Yu. V. Kopaev, Toroidal ordering in crystals, Phys. Uspekhi 52,1111-1125 (2009).[Crossref]
  • [10] B. B. Van Aken, J. P. Rivera, H. Schmid, and M. Fiebig, Observationof ferrotoroidic domains, Nature 449, 702 (2007).
  • [11] I. I. Naumov, L. Bellaiche, and H. Fu, Unusual phase transitionsin ferroelectric nanodisks and nanorods Nature 432, 737-740(2004).
  • [12] S. Prosandeev, I. Ponomareva, I. Naumov, I. Komev, and L. Bellaiche,Original properties of dipole vortices in zero-dimensionalferroelectrics, J. Phys.: Condens. Mat. 20, 193201 (2008).[Crossref]
  • [13] S. Prosandeev, A. Malashevich, Z. Gui, L. Louis, R. Walter, I.Souza, and L. Bellaiche, Natural optical activity and its controlby electric field in electrotoroidic systems, Phys. Rev. B 87, 195111(2013).[Crossref]
  • [14] M. E. Lines and M. A. Bösch, Magnetogyration, Phys. Rev. B 23,263 (1981).[Crossref]
  • [15] I. S. Zheludev, O. G. Vlokh, and V. A. Sergatyuk, Magnetogyrationand other phenomena described by second-rank axial tensors,Ferroelectrics 63, 97 (1985).
  • [16] D. B. Litvin, Property tensors and ferrotoroidic domains, Ferroelectrics376, 354 (2008).
  • [17] D. B. Litvin, Ferroic classifications extended to ferrotoroidic crystals,Acta Cryst. A 64, 316 (2008).[Crossref]
  • [18] D. B. Litvin, On the symmetry analysis of surface induced effects,Ferroelectrics 460, 173 (2014).
  • [19] P. Toledano, D. D. Khalyavin, and L. C. Chapon. Spontaneoustoroidal moment and field-induced magnetotoroidic effects inBa2CoGe2O7, Phys. Rev. B 84, 094421 (2011).[Crossref]
  • [20] H. Toyosaki, M. Kawasaki, and Y. Tokura, Atomically smooth andsingle crystalline MnTiO3 thin films with a ferrotoroidic structure,Appl. Phys. Lett. 93, 072507 (2008).[Crossref]
  • [21] D. G. Sannikov, Phenomenological theory of the magnetoelectriceffect in some boracites, JETP 84, 293-299 (1998).
  • [22] B. Mettout, P. Toledano, and M. Fiebig, Symmetry replicationand toroidic effects in the multiferroic pyroxeneNaFeSi2O7, Phys.Rev. B 81, 214417 (2010).[Crossref]
  • [23] J. D. Jackson, Classical electrodynamics, Wiley, New York 1974.
  • [24] R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism,Oxford Univ. Press, 2004.
  • [25] I. A. Beardsley, Reconstruction of the magnetization in a thin filmby a combination of Lorentz microscopy and external field measurements,IEEE Trans. Mag. 25, 671-677 (1989).[Crossref]
  • [26] S. Prosandeev and L. Bellaiche, Hypertoroidal moment in complexdipolar structures, J. Mater. Sci., 44, 5235-5248 (2009).[Crossref]
  • [27] Vortices of electric moments may occur due to confinement effectsat the nanoscale. See, for instance, S. Prosandeev, I. Ponomareva,I. Naumov, I. Kornev, and L. Bellaiche, Original propertiesof dipole vortices in zero-dimensional ferroelectrics, J. Phys.:Condens. Matter 20, 193201 (2008).
  • [28] M. Baum, K. Schmalzl, P. Steffens, A. Hiess, L. P. Regnault, M.Meven, P. Becker, L. Bohatý, and M. Braden, Controlling toroidalmoments by crossed electric and magnetic field, Phys. Rev. B 88,024414 (2013).[Crossref]
  • [29] K. Sawada and N. Nagaosa, Optical magnetoelectric effect inmultiferroic materials: Evidence for Lorentz force acting on a rayof light, Phys. Rev. Lett 95, 237402 (2005).[Crossref]
  • [30] V. Scagnoli, U. Staub, Y. Bodenthin, R. A. de Souza, M. Garcia-Fernandez, M. Garganourakis, A. T. Boothroyd, D. Prabhakaran,and S. W. Lovesey, Observation of Orbital Currents in CuO, Science332, 696 (2011).
  • [31] A. Gongora T. and E. Ley-Koo, Complete electromagnetic multipoleexpansion including toroidal moments, Rev. Mex. Fis. 52,188 (2006).
  • [32] D. G. Sannikov, Ferrotoroics, Ferroelectric 354, 39-43 (2007).
  • [33] Yu. F. Popov, A. M. Kadomtseva, G. P. Vorob’ev, V. A. Tomofeeva,D. M. Ustinin, A. K. Zvezdin, and M. M. Tegeranchi,Magnetoelectriceffect and toroidal ordering in Ga2−xFexO3, JEPT 87, 146-151(1998).
  • [34] Yu. F. Popov, A. M. Kadomtseva, D. V. Belov, G. P. Vorob’ev,and A. K. Zvezdin,Magnetic-field induced toroidal moment in themagnetoelectric Cr2O3, JEPT Lett. 69, 300-335 (1999).
  • [35] M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, SecondHarmonic Generation and Magnetic-Dipole-Electric-DipoleInterference in Antiferromagnetic Cr2O3, Phys Rev. Lett. 73, 2127(1994).[Crossref]
  • [36] M. Fiebig, D. Fröhlich, G. Sluyterman V. L. and R. V. Pisarev, Domaintopography of antiferromagnetic Cr2O3 by second harmonicgeneration, Appl. Phys. Lett. 66, 2906 (1995).[Crossref]
  • [37] J. Molenda, Lithium ion batteries - state of art. novel phosphoolivinecathode materials, Mater. Sci.-Poland 24, 61 (2006).
  • [38] A. Szewczyk, M. U. Gutowska, J. Wieckowski, A. Wisniewski, R.Diduszko, Yu. Kharchenko, M. F. Kharchenko, and H. Schmid,Phase transitions in single-crystalline magnetoelectric LiCoPO4,Phys. Rev. B 84, 104419 (2011).[Crossref]
  • [39] H. Schmid, Some symmetry aspects of ferroics and single phasemultiferroics, J. Phys. Cond. Matter 20, 434201 (2008).[Crossref]
  • [40] A. A. Gorbatsevich and Y. V. Kopaev, Toroidal order in crystals,Ferroelectrics 161, 321 (1994).
  • [41] Yu. F. Popov, A. M. Kadomtseva, S. S. Krotov, D. V. Belov, G.P.Vorob’ev, P. N. Makhov, and A. K. Zvezdin, Features of themagnetoelectric properties of BiFeO3 in high magnetic fields, LowTemp. Phys. 27, 478 (2001).[Crossref]
  • [42] Y. Tokura, Multiferroics–toward strong coupling between magnetizationand polarization in a solid, J. Magn. Magn. Mater.310, 1145 (2007).[Crossref]
  • [43] E. Ressouche, M. Loire, V. Simonet, R. Ballou, A. Stunault, and A.Wildes, Magnetoelectric MnPS3 as a candidate for ferrotoroidicity,Phys. Rev. B 82, 100408 (2010).[Crossref]
  • [44] H.-J. Feng and F.-M. Liu, Ab initio prediction on ferrotoroidicand electronic properties of olivine Li4MnFeCoNiP4O16, ChinesePhys. B 18, 2481 (2009).
  • [45] S.-Y. Lin, W. Wernsdorfer, L. Ungur, A. K. Powell, Y.-N. Guo, J.Tang, L. Zhao, L. F. Chibotaru, and H.-J. Zhang, Coupling Dy3triangles to maximize the toroidal moment, Angewndte Chemie124, 12939 (2012).
  • [46] A. B. Harris, A system exhibiting toroidal order, Phys. Rev. B 82,184401 (2010).[Crossref]
  • [47] T. Castán, A. Planes, and A. Saxena, Thermodynamics of multiferroicmaterials, in Mesoscopic Phenomena in MultifunctionalMaterials, ed. by A. Saxena and A. Planes, Springer Series inMaterials Science, Vol. 198, pp. 73-108, Springer-Verlag, Berlin,2014.
  • [48] Y. Yamaguchi and T. Kimura, Magnetoelectric control of frozenstate in a toroidal glass, Nature Commun. 4, 2063 (2013).
  • [49] X. Ren, Y. Wang, K. Otsuka, P. Lloveras, T. Castan, M. Porta,A. Planes, and A. Saxena, Ferroelastic nanostructures andnanoscale transitions: Ferroics with point defects, MRS Bull. 34,838 (2009).[Crossref]
  • [50] O. Gutfleisch, M. A. Williard, E. Brück, C. H. Chen, S. G. Sankar,and J. P. Lin, Magnetic materials and devices for the 21st century:stronger, lighter and more energy eficient, Adv. Mater. 27, 821-842 (2011).[Crossref]
  • [51] A. Planes, T. Castán, and A. Saxena, Thermodynamics of multicaloriceffects in multiferroics, Philos. Mag. 94, 1893-1908(2014).[Crossref]
  • [52] T. Castán, A. Planes, and A. Saxena, Thermodynamics of ferrotoroidicmaterials: Toroidocaloric effect, Phys. Rev. B 85, 144429(2012).[Crossref]
  • [53] C. Ederer and N. Spaldin, Towards a microscopic theory oftoroidal moments in bulk periodic crystals, Phys. Rev. B 76, 214404 (2007).[Crossref]
  • [54] M. Dawber, I. Szafraniak, M. Alexe, and J. F. Scott, Self-patterningof arrays of ferroelectric capacitors: description by theory of substratemediated strain interactions, J. Phys. Condens. Matter 15,L667-L671 (2003).
  • [55] S. D. Bader, Opportunities in nanomagnetism, Rev. Mod. Phys.78, 1-15 (2006).[Crossref]
  • [56] A. Gruverman, D. Fu, H.-J. Fan, I. Vrejoiu, M. Alexe, R. J. Harrison,and J. F. Scott, Vortex ferroelectric domains, 20, 342201 (2008).
  • [57] R. G. P. McQuaid, L. J. McGilly, P. Sharma, A. Gruverman, and A.Gregg,Mesoscale flux-closure domain formation in single-crystalBaTiO3, Nature Commun. 2, 404 (2011).[Crossref]
  • [58] R. K. Vasudevan, Y. C. Chen, H. H. Tai, N. Balke, P. Wu, S. Bhattacharya,L. Q. Chen, Y. H. Chu, I. N. Lin, S. V. Kalinin, and V.Nagarajan, Exploring topological defects in epitaxial BiFeO3 thinfilms, ACS Nano 5, 879 (2011).[Crossref]
  • [59] C. T. Nelson, B. Winchester, Y. Zhang, S. J. Kim, A. Melville, C.Adamo, C. M. Folkman, S. H. Baek, C. B. Eom, D. G. Schlom, L.Q. Chen, and X. Pan, Spontaneous vortex nanodomain arrays atferroelectric heterointerfaces, Nano Lett. 11, 828 (2011).[Crossref]
  • [60] N. Balke, B. Winchester, W. Ren, Y. H. Chu, A. N. Morozovska,E. A. Eliseev, M. Huijben, R. K. Vasudevan, P. Maksymovych, J.Britson, S. Jesse, I. Kornev, R. Ramesh, L. Bellaiche, L. Q. Chen,and S. V. Kalinin, Enhanced electrical conductivity at ferroelectricvortex cores in BiFeO3, Nature Phys. 8, 81 (2012).
  • [61] S. Prosandeev, A. R. Akbarzadeh, and L. Bellaiche, Discoveryof incipient ferrotoroidics from atomistic simulations, Phys. Rev.Lett. 102, 257601 (2009).[Crossref]
  • [62] J. Wang and T.-Y. Zhang, Effect of long-range elastic interactionson the toroidal moment of polarization in a ferroelectric nanoparticle,Appl. Phys. Lett. 88, 182904 (2006).[Crossref]
  • [63] S. Prosandeev, I. Ponomareva, I. Kornev, I. Naumov, and L. Bellaiche,Controlling toroidal moment by means of an inhomogeneousstatic field: An Ab Initio study, Phys. Rev. Lett. 96, 237601(2006).[Crossref]
  • [64] W. J. Chen, Y. Zheng, and B. Wang, Vortex domain structures inferroelectric nanoplatelets and control of its transformation bymechanical load, Sci. Reports 2, 1-8 (2012).
  • [65] S. Prosandeev, I. Ponomareva, I. Kornev, and l. Bellaiche, Controlof vortices by homogeneous fields in asymmetric ferroelectricand ferromagnetic rings, Phys. Rev. Lett. 100, 047201 (2008).[Crossref]
  • [66] G. Thorner, J. M. Kiat, C. Bogicevic, and I. Kornev, Axial hypertoroidalmoment in a ferroelectric nanotorus: A way to switch localpolarization, Phys. Rev. B, 89, 220103R (2014).[Crossref]
  • [67] L. Y. Guo, M. H. Li, Q. W. Ye, B. X. Xiao, and H. L. Yang, Electricaltoroidal dipole response in split-ring resonator metamaterials,Eur. Phys. J. B 85, 208 (2012).[Crossref]
  • [68] C. Ederer, Toroidal moments as indicator for magneto-electriccoupling: the case of BiFeO3 versus FeTiO3, Eur. Phys. J. B 71,349 (2009).[Crossref]
  • [69] S. Miyahara and N. Furukawa, Theory of magneto-optical effectsin helical multiferroic materials via toroidal magnon excitation,Phys. Rev. B 89, 195145 (2014).[Crossref]
  • [70] V. L. Ginzburg and V. N. Tsytovich, Fields and radiation of toroidaldipole moments moving uniformly in a medium, Zh. Eksp. Teor.Fiz. 88, 84 (1985) [Sov. Phys. JETP 61, 48 (1985)].
  • [71] J. A. Heras, Electric and magnetic fields of a toroidal dipole in arbitrarymotion, Phys. Lett. A 249, 1 (1998).
  • [72] K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev,Toroidal metamaterials, New J. Phys. 9, 324 (2007).
  • [73] T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I.Zheludev, Toroidal dipolar response in a metamaterial, Science330, 1510 (2010).
  • [74] Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, Low-loss andhigh-Q planar metamaterial with toroidal moment, Phys. Rev. B87, 115417 (2013).[Crossref]
  • [75] Z.-G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, Toroidal dipoleresponse in a multifold double-ring metamaterial, Opt. Exp. 20,13065 (2012).[Crossref]
  • [76] J. Li, J. Shao, J.-Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai,Optical responses of magnetic-vortex resonance in double-diskmetamaterial variations, Phys. Lett. A 378, 1871 (2014).
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