Spontaneous non-reciprocal reflection of light from antiferromagnetic Cr₂O₃

Abstract

The nflection of light from a medium with ordered spin smclure characterized by the breakdown of time-reversal and parity s y " e v y is exgected to be non-reciprocal even if the net magnetic moment of the medium equals Zem. We repoa on the fust experimental observation of sponmwnk non-recipmcal mtarion and circular dichroism in spin magnetoelectric Cr203. Nokrecipmcal effects were obmved M o w the antifemmagnetic tansition temperahlre Tw = M7 U and their temperahre behaviour roughly obrresponds to that of the order parameter. Observed values of (1 -4) x for the magnetoelecuic susceptibility in the optical range are several orden of magnitude higher than predicted earlier. This increase of the susceptibility is presumably atuibutable lo eleclmnic dipole transitions in the optical range. tutroductionAmong different optical phenomena in crystals a particular type of effect may be assigned to the so-cklled non-reciprocal (NR) effects. They are characterized by different phase velocities and/or attenuations for light waves travelling via the same optical path but in opposite directions. The most typical exaniples of these effects are the Faraday rotation observed in transmission and the Ken effect observed in reflection (see e.g. [l]). As far as we know, up until now non-reciprocal optical effects were observed exclusively in media possessing a magnetic moment. This moment can be induced by a magnetic field in dia-and paramagnets or can arise spontaneously, ai in feqoor ferrimagnets. A magnetic moment induced by an electric current may also give rise to non-recipmcal phenomena [2]. In all these cases the timereverd symmetry (1') is broken; that is, the crystal may be in two different states converted into one another by the operation 1' .There exists a special class of magnetically ordered materials in which below the magnetic transition temperature TN there is no net magnetic moment, but in addition to the timereversal symmetry breaking the parity symmetry (7) is also broken. At the same time the combined symmetry operation i' is retained. Magnetoelectrics (ME) are the most well known and widely studied materials [ 3 4 belonging to this class. Soon after the discovery of ME, theoretical analysis of light propagation in magnetoelectric antiferromagnets showed 17-10] that new optical phenomena should be found, when the spatial dispersion is taken into account. These phenomena, though beiig in some manifestations similar to those observed in media with a net magnetic moment, may exhibit some important differences. Some of these effects have been observed iecently in "ission in 1111. Since these new phenomena are related to the spatid~dispepion they have smaller values as compared with

Theory of Ferromagnetism inCa1−xLaxB6Murakami1, Shindou2, Nagaosa3 et al. 2002Phys. Rev. Lett.161230View full textAdd to dashboardCite

“…As for the Γ 25 , similar effect can be found. (IV) The optical non-reciprocal (NR) effect in reflection is predicted to occur, as is similar to Cr 2 O 3 [23]. This effect will occur only below the Néel temperature.…”

“…This effect will occur only below the Néel temperature. Generally, RI-invariant materials with broken Rand I-symmetry will exhibit the NR effect [23].…”

Calculation for polar Kerr effect in high-temperature cuprate superconductors

“…Thus the ground state of the bilayer breaks TRS in each plane, but since the inversion symmetry (P ) about the mid point between the planes is also broken, the product P T is conserved, allowing the system to have a nonzero polar Kerr effect despite conserving the global TRS and being an OAF 36,37 . The magnetoelectric effect and PKE in another antiferromagnet Cr 2 O 3 were predicted theoretically in 38,39 , and subsequently observed in experiments [40][41][42][43][44] . The Hall conductance of a single layer described by a d + id mean field Hamiltonian can be calculated using the formalism of linear response theory and Kubo formula 30 .…”

Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries

“…This will be the case for instance in situations where time-reversal symmetry is broken in the form of ferromagnetism, p-wave superconductivity (likely present in Sr 2 RuO 4 72 ), magnetoelectrics 34,[73][74][75] , chiral spin liquids 76,77 or in some proposed recent [33][34][35] or older [19][20][21][22][23][24][25][26][27]78 models for the pseudogap state of the hightemperature superconductors.…”

“…There are two degenerate ground states that are related to each other by either inversion or timereversal. As pointed out originally by Dzyaloshinskii 56 the magnetic symmetry of Cr 2 O 3 allows linear magnetoelectric effects [73][74][75][79][80][81][82] e.g. an electric field can cause a magnetization (with proportionality α ij ) and a magnetic field can cause a polarization.…”