Observation of ferrotoroidic domains

Abstract

Domains are of unparalleled technological importance as they are used for information storage and for electronic, magnetic and optical switches. They are an essential property of any ferroic material. Three forms of ferroic order are widely known: ferromagnetism, a spontaneous magnetization; ferroelectricity, a spontaneous polarization; and ferroelasticity, a spontaneous strain. It is currently debated whether to include an ordered arrangement of magnetic vortices as a fourth form of ferroic order, termed ferrotoroidicity. Although there are reasons to expect this form of order from the point of view of thermodynamics, a crucial hallmark of the ferroic state--that is, ferrotoroidic domains--has not hitherto been observed. Here ferrotoroidic domains are spatially resolved by optical second harmonic generation in LiCoPO4, where they coexist with independent antiferromagnetic domains. Their space- and time-asymmetric nature relates ferrotoroidics to multiferroics with magnetoelectric phase control and to other systems in which space and time asymmetry leads to possibilities for future applications.

Vortex ferroelectric domains

“…The extension to ferroelectrics was made around 1984 by Ginzburg et al [8] and was recently further developed using ab initio calculations by Naumov et al [9]. We note that toroidal domains can arise for two unrelated physical reasons: (1) finite size effects and boundary conditions (present work) and (2) magnetoelectric coupling in multiferroic materials [7,8,[10][11][12]. The present work does not involve magnetism.…”

Morphology and Agglomeration Control of LiMnPO4 Micro- and Nanocrystals

“…20 This is highlighted by the recent discovery of unusual ferrotoroidic domains in LiMPO4 with M = Co or Ni which is discussed in terms of future data storage devices. 21 In this work, we investigate the tailored synthesis of dispersed and agglomerated LiMnPO 4 with dimensions between ∼100 nm and several µm aiming at fundamental information which enables tailoring nano-and microscaled material. We demonstrate that control of the size and shape of LiMnPO 4 crystals as well as of the particles' tendency to (oriented) agglomeration is possible by applying a fast and low-energy synthesis route, starting from environmentally harmless and non-hazardous precursors.…”

Magnetoelectric control of frozen state in a toroidal glass

“…All the data shown in Fig. 1a were taken after ME field cooling with E [1][2][3][4][5][6][7][8][9][10] ¼ 1 MV m À 1 and selected H [110] . Below 9 K, magnetoelectrically induced P [1][2][3][4][5][6][7][8][9][10] develops in all the data.…”

“…When t is non-zero, an off-diagonal and antisymmetric linear ME effect is allowed, that is, Pp À t  H and Mpt  E, which are obtained from the free energy expansion analysis 6,7 . Thus, magnetic insulators showing a ferrotoroidic order (for example, Ga 2-x Fe x O 3 and LiCoPO 4 ) can exhibit the antisymmetric linear ME effect [8][9][10] .…”