Magnetoelectric Cr2O3 and relativity theory

Abstract

Abstract. Relativity theory is useful for understanding the phenomenology of the magnetoelectric effect of the antiferromagnet chromium sesquioxide Cr2O3 in two respects: (i) One gets a clear idea about the physical dimensions of the electromagnetic quantities involved, in particular about the dimensions of the magnetoelectric moduli that we suggest to tabulate in future as dimensionless relative quantities; (ii) one can recognize and extract a temperature dependent, 4-dimensional pseudoscalar from the data of magnetoelectric experiments with Cr2O3. This pseudoscalar piece of Cr2O3 is odd under time reflections and parity transformations and is structurally related ("isomorphic") to the gyrator of electric network theory, the axion of particle physics, and the perfect electromagnetic conductor of electrical engineering.

Functional approach to electrodynamics of media

“…Finally, we remark that a covariant approach to the electromagnetic response functions has already been suggested by Hehl et al [35,68,72] with a fourth-rank constitutive tensor χ. These constitutive relations generalize the equation D = ε 0 ε r E to the case of linear bi-anisotropic materials [94].…”

“…Since often the properties of these materials are determined by nanoscale resonant inclusions ("meta-atoms") [30], macroscopic averaging procedures have also come under intense investigation [31][32][33]. Further systems with magnetoelectric coupling include the prototype material Cr 2 O 3 [34][35][36], single-phase multiferroics [37][38][39][40], composite multiferroics and multiferroic interfaces [41][42][43][44] as well as systems with Rashba spin-orbit coupling [45][46][47]. Topological insulators show the topological magnetoelectric effect [48][49][50], which becomes observable if the surface response is separated from the bulk contribution by breaking the time-reversal symmetry [51,52], for example, through the introduction of ferromagnetism [53][54][55].…”

Covariant response theory and the boost transform of the dielectric tensor

“…In particular, one may consider instead of the standard relations (2.1)-(2.2) a generalized constitutive relation (see Refs. [43,[48][49][50]), which reads in an adapted notation…”

Asymmetric band diagrams in photonic crystals with a spontaneous nonreciprocal response

“…Therefore, we consider a periodic structure wherein the unit cell is formed by an It is interesting to investigate how strong is the spectral asymmetry in a realistic photonic crystal wherein the Tellegen parameter  has magnitude comparable to the magnetoelectric parameter of 23 Cr O [41]. 10a and the frequency range near the band gap is zoomed in Fig.…”