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We report field-induced switchable polarization (P ~ 0.2 -0.8 µC/cm 2 ) below the Néel temperature of chromium (T N Cr ) in weakly ferromagnetic rare-earth orthochromites, RCrO 3 (R=rare-earth) but only when the rare-earth ion is magnetic.Intriguingly, the polarization in ErCrO 3 (T C = 133 K) disappears at a spinreorientation (Morin) transition (T SR ~ 22 K) below which the weak ferromagnetism associated with the Cr-sublattice also disappears, demonstrating the crucial role of weak ferromagnetism in inducing the polar order. Further, the polarization (P) is strongly influenced by applied magnetic field, indicating a strong magnetoelectric effect. We suggest that the polar order occurs in RCrO 3 , due to the combined effect of poling field that breaks the symmetry and the exchange field on R-ion from Crsublattice stabilizes the polar state. We propose that a similar mechanism could work in the isostructural rare-earth orthoferrites, RFeO 3 as well.

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It is argued that in the mixed state of a type II superconductor, because of the difference of the chemical potential in a superconducting versus normal state, the vortex cores may become charged.The extra electron density is estimated. The extra charge contributes to the dynamics of the vortices; in particular, it can explain in certain cases the change of the sign of the Hall coefficient below T, . frequently observed in the high temperature superconductors.The transition of a system to a superconducting state leads to a change of the chemical potential of the electrons [1 -3]. In a material which has two electronic subsystems, one of which becomes superconducting, the other remaining normal, this change of the chemical potential causes a charge redistribution between these subsystems below T,[2]. This is qualitatively easy to understand: Below T, there is an energy gain for the condensed charge carriers, and it is therefore energetically favorable to transfer some charge carriers from the normal to the condensate region.The effect is of general character and should occur in any superconductor.However, the charge transfer is determined by the magnitude of (6/eF), where 5 is the energy gap and eF the Fermi energy. Therefore the charge redistribution is, in particular, important in the high temperature superconductors (HTSCs), because of their relatively large value of 6/eF. It was shown in Ref.[2] that it can explain several anomalies observed in the HTSCs at and below T, .We want to point out in this Letter that the change of the chemical potential below T, may also lead to charging of a vortex core in the mixed state of a type II superconductor. Assuming that the vortex core is a region of normal metal surrounded by superconducting material the corresponding difference in the chemical potential leads to a redistribution of the electrons. The extra charge of the cores gives rise to an additional force on vortices; in particular, for an appropriate sign of the charge this force can lead to a sign change of the Hall coefficient, which is frequently observed experimentally in the HTSCs [4 -7].The theoretical treatment carried out in [1,2] gives the following expression for the change of the chemical potential p, of the electrons below T, for a model with a constant densit of states:~' (T) p(T) = po-(1) 4p, o for a less than half-filled band. For p, o ) D/2, where D is the bandwidth, the term -5 /4p, o in (1) is substituted by + 5 /4(Dp, o). For the general case of an arbitrary density of states N(e) the corresponding formula has the form [2] 1 BN p(T) = po c~'(T), N(eF) ae (2) There is yet another contribution to the chemical potentialthe kinetic energy of the superfluid motion around the vortex core [10,11] ns f11v r 6p, = -' n 2 (4) Here n, and n are the superAuid and total electron densities. Note that the terms (1) and (4) perfectly match at r = s: The condition that the kinetic energy of the superAuid motion equals the condensation energy, or that the corresponding velocity is equal to the depairing velocity,...