Abstract
A theory of micromorphic continua, applied to electromagnetic solids, is exploited to study magnetoelectric effects at equilibrium. Microcurrents are modeled by the microgyration tensor of stationary micromotions, compatibly with the balance equations for null microdeformation. The equilibrium of the continuum subject to electric and magnetic fields is reformulated accounting for electric multipoles which are related to microdeformation by evolution equations. Polarization and magnetization are derived for uniform fields under the micropolar reduction in terms of microstrain and octupole structural parameters. Nonlinear dependance on the electromagnetic fields is evidenced, compatibly with known theoretical and experimental results on magnetoelectric coupling.
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References
Fiebing, M.: Revival of the magnetoelectric effect. J. Phys. D Appl. Phys. 38, R123 (2005)
Khomskii, D.: Classifying multiferroics: mechanisms and effects. Physics 2, 20 (2009)
Maugin, G.A.: Continuum Mechanics of Electromagnetic Solids. Elsevier, Amsterdam (1988)
Eringen, A.C., Maugin, G.A.: Electrodynamics of continua I. Springer, New York (1990)
Romeo, M.: Micromorphic continuum model for electromagnetoelastic solids. ZAMP 62, 513–527 (2011)
Eringen, A.C.: Continuum theory of micromorphic electromagnetic thermoelastic solids. Int. J. Eng. Sci. 41, 653–665 (2003)
Lee, J.D., Chen, Y., Eskandarian, A.: A micromorphic electromagnetic theory. Int. J. Solids Struct. 41, 2099–2110 (2004)
Romeo, M.: A microstructure continuum approach to electromagneto-elastic conductors. Contin. Mech. Thermodyn. 28, 1807–1820 (2016)
Eringen, A.C.: Microcontinuum Field Theories I—Foundations and Solids. Springer, New York (1999)
Romeo, M.: Polarization in dielectrics modeled as micromorphic continua. ZAMP 66, 1233–1247 (2015)
Hirose, S., Haruki, K., Ando, A., Kimura, T.: Mutual control of magnetization and electrical polarization by electric and magnetic fields at room temperature in Y-type \(\text{BaSrCo}_{2-x}\text{Zn}_x\text {Fe}_{11}\text{AlO}_{22}\) ceramics. Appl. Phys. Lett. 104, 022907 (2014)
Resta, R.: Electrical polarization and orbital magnetization: the modern theories. J. Phys. Condens. Matter 22, 123201 (2010)
Solovyev, I.V., Pchelkina, Z.V.: Magnetic-field control of the electric polarization in \(\text{BiMnO}_3\). Phys. Rev. B 82, 094425 (2010)
Baker-Jarvis, J., Kabos, P.: Dynamic constitutive relations for polarization and magnetization. Phys. Rev. E 64, 056127 (2001)
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Romeo, M. On magnetoelectric coupling at equilibrium in continua with microstructure. Z. Angew. Math. Phys. 68, 112 (2017). https://doi.org/10.1007/s00033-017-0860-2
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DOI: https://doi.org/10.1007/s00033-017-0860-2