Imaging switchable magnetoelectric quadrupole domains via nonreciprocal linear dichroism

Abstract

Parity-odd magnetoelectric multipoles such as magnetic quadrupoles and toroidal dipoles contribute to various symmetry-dependent magnetic phenomena and formation of exotic ordered phases. However, the observation of domain structures emerging due to symmetry breaking caused by these multipoles is a severe challenge because of their antiferromagnetic nature without net magnetization. Here, we report the discovery of nonreciprocal linear dichroism for visible light (~4% at 1.8 eV) in a magnetic quadrupole ordered phase of antiferromagnetic Pb(TiO)Cu 4 (PO 4) 4 , which enables the identification of magnetic quadrupole domains of opposite signs. Symmetry considerations indicate that nonreciprocal linear dichroism is induced by the optical magnetoelectric effect, i.e., the linear magnetoelectric effect for electromagnetic waves. Using the nonreciprocal linear dichroism, we successfully visualize spatial distributions of quadrupole domains and their isothermal electric-field switching by means of a transmission-type polarized light microscope. The present work exemplifies that the optical magnetoelectric effect efficiently visualizes magnetoelectric multipole domains responding to external perturbations.

NQR and NMR spectra in the odd-parity multipole material CeCoSi

“…The NQR frequencies are split into seven due to the contribution from the internal magnetic field arising from the first term in Eq. (31). Meanwhile, the NQR frequencies for Co A and Co B sites are the same, which indicates that there is no sublattice-dependent splitting in the presence of the oddparity T (c) y .…”

Chirality and magnetic quadrupole order inPb(TiO)Cu4(PO4)4probed by interference scatter

“…5(b) is not symmetric with respect to E pole (bias field ≈ + 0.5 MV m -1 ) though the fraction of Q+ and Q− domains is ideally equal with each other when a sample is zero-field cooled. We consider that the observed bias effect could be related to a memory effect of the domain structure previously reported in Pb(TiO)Cu 4 (PO 4 ) 4 [8] whose domains are likely pinned by defects formed during crystal growth or other reasons such as local thermal inhomogeneity created in the sample.…”

“…Such a state is not ideal to examine the contribution of the magnetic quadrupole order. In Pb(TiO)Cu 4 (PO 4 ) 4 showing a linear ME effect [5], a monodomain state of Q+ or Q− is achieved by the simultaneous application of a poling electric field (E pole ) and a poling magnetic field (B pole ) during cooling from the paramagnetic phase to the AFM phase (ME cooling) [8]. Therefore, we carried out RXD measurements after poling in both E pole and B pole applied along the [010] direction.…”

“…Among various multipoles, magnetic quadrupoles, which are second-rank magnetic multipoles, are one of the most fundamental parityand time-odd multipoles breaking both space-inversion and time-reversal symmetries. Recently, magnetic quadrupoles are attracting growing interest in the study of cross-coupled physical phenomena such as the linear magnetoelectric (ME) effect, nonreciprocal linear dichroism, the Edelstein effect, and the magnetopiezoelectric effect [5][6][7][8]. (Anti)ferroic magnetic quadrupole order has been reported in several magnetic materials including A(TiO)Cu 4 (PO 4 ) 4 (A = Ba, Sr, and Pb) [5].…”

“…This means that ferroic q x 2 −y 2 -type quadrupole order develops in the AFM phase. Recently, remarkable nonreciprocal linear dichroism induced by an optical ME effect, i.e., a linear ME effect for visible light, was reported in the ferroquadrupole ordered phase of Pb(TiO)Cu 4 (PO 4 ) 4 [8]. Furthermore, by using the optical ME effect, spatial distributions of a pair of magnetic quadrupoles, i.e., quadrupole domains [Q+ and Q− domains depicted in the upper and the lower panels in Fig.…”