Multiferroics: from magnetoelectric memories to photonic devices

In conventional media light propagation is reciprocal, that is counter-propagating beams experience the same refractive index. However, reciprocity can be violated in magnetoelectric materials, where the refractive index depends not only on the polarization of light but also on the ±k direction of the propagation [1]. Such unidirectional transmission is the consequence of the dynamic magnetoelectric effect emerging in materials with simultaneously broken time reversal and spatial inversion symmetries. This phenomenon, which has been exclusively observed in non-centrosymmetric (polar or chiral) materials with finite magnetization [2-5], may allow the development of optical diodes transmitting unpolarized light in one, but not in the opposite, direction [5].
Here, we demonstrate that LiCoPO₄ with a fully compensated antiferromagnetic ground state, i.e. with zero net magnetization, can also exhibit unidirectional transmission [6]. Following an appropriate magnetoelectric poling in crossed electric and magnetic fields, we succeeded to realize the unidirectional transmission as a remnant effect in this compound. The unidirectional transmission likely originates from a ferrotoroidic order which can be viewed as the cross-product of antiferroelectricity and antiferromagnetism coexisting in LiCoPO₄. The sign of the magnetoelectric effect can be set by the poling electric and magnetic fields via the establishment of mono-domain ferrotoroidic states, and can be read via the optical-diode effect.  
[1] D. Szaller, S. Bordacs and I. Kezsmarki, Phys. Rev. B 87, 014421 (2014).
[2] I. Kezsmarki et al., Phys. Rev. Lett. 106, 057403 (2011).
[3] S. Bordacs et al., Nat. Phys. 8, 734 (2012).
[4] I. Kezsmarki et al., Nat. Commun. 5, 3203 (2014).
[5] I. Kezsmarki et al., Phys. Rev. Lett. 115, 127203 (2015).
[6] V. Kocsis et al., to be published.