The magnetic and electrical properties of Co 3 TeO 6 single crystals with corundum-related structure reveal a magnetic-field-induced polarization below 21 K. A sharp peak in the specific heat at ≈18 K indicates a reconstructive-type first-order phase transition. From second-harmonic generation measurements, breaking of inversion symmetry is evident and the point-group symmetry was determined as m. The temperature and magnetic-field dependences of the magnetic and electrical polarizations are discussed in the light of the SHG results.

The inversion of inhomogeneous physical states has great technological importance; for example, active noise reduction relies on the emission of an inverted sound wave that interferes destructively with the noise of the emitter, and inverting the evolution of a spin system by using a magnetic-field pulse enables magnetic resonance tomography. In contrast to these examples, inversion of a distribution of ferromagnetic or ferroelectric domains within a material is surprisingly difficult: field poling creates a single-domain state, and piece-by-piece inversion using a scanning tip is impractical. Here we report inversion of entire ferromagnetic and ferroelectric domain patterns in the magnetoelectric material CoTeO and the multiferroic material MnGeO, respectively. In these materials, an applied magnetic field reverses the magnetization or polarization, respectively, of each domain, but leaves the domain pattern intact. Landau theory indicates that this type of magnetoelectric inversion is universal across materials that exhibit complex ordering, with one order parameter holding the memory of the domain structure and another setting its overall sign. Domain-pattern inversion is only one example of a previously unnoticed effect in systems such as multiferroics, in which several order parameters are available for combination. Exploring these effects could therefore advance multiferroics towards new levels of functionality.

A theoretical description of the sequence of magnetic phases in Co3TeO6 is presented. The strongly first-order character of the transition to the commensurate multiferroic ground state, induced by coupled order parameters corresponding to different wavevectors, is related to a large magnetoelastic effect with an exchange energy critically sensitive to the interatomic spacing. The monoclinic magnetic symmetry C2 of the multiferroic phase permits spontaneous polarization and magnetization as well as the linear magnetoelectric effect. The existence of weakly ferromagnetic domains is verified experimentally by second harmonic generation measurements.At variance with structural transitions which alter the lengths and orientations of the chemical bonds, the spin ordering occurring in magnetic phases has in most cases a negligible effect on the structural lattice. An important exception is represented by the class of magnetostructural transitions occurring in multiferroic compounds in which the magnetic ordering in the multiferroic phase induces simultaneously a change in the atomic structure, which permits the emergence of a spontaneous polarization. 1,2 However, the measured changes of lattice parameters found in the multiferroic phases are generally small, i.e. of the order of 10 −3Å , and do not affect the second-order character of the transitions to these phases. 3,4 Here, we describe theoretically the sequence of phases recently reported in Co 3 TeO 6 5,6 in which a strongly first order transition, characterized by substantial discontinuities of the lattice parameters and a remarkable delta-shape peak of the specific heat, yields a multiferroic ground state displaying magnetoelectric properties. The observed structural changes are related to the coupling between the magnetic order-parameters involved at the transition, which correspond to different propagation wave-vectors, in contrast with the standard situation found in multiferroic transitions where the coupled order-parameters generally pertain to the same kvector. 3,7 Neutron powder diffraction studies 6,8 show that below the paramagnetic phase described by the space group G P = C2/c1 the Co 3 TeO 6 undergoes a sequence of three antiferromagnetic phases, summarized in Fig. 1. 9 They are associated with three different k-vectors of the centred monoclinic Brillouin-zone: k 1 = (0, 0.480, 0.055), k 2 = (0, 0, 0) and k 3 = (0, 1/2, 1/4).

Mn 3 TeO 6 has a trigonal corundum related structure (space group R3), and orders in an incommensurate antiferromagnetic (AFM) structure at T N ≈ 24 K. A weak ferroelectric order below T * ~ 21 K has recently been reported. In order to investigate possible structural changes below T N leading to the observed dipole order, we have performed a detailed study of the crystal and magnetic structures of Mn 3 TeO 6 using neutron powder diffraction (NPD) in the temperature range of 5-40 K. Complementary low-temperature second harmonic generation (SHG) measurements were performed in order to confirm the reported dipole order at T * . No change in the rhombohedral symmetry associated with a possible displacive phase transition at T * was observed in the long-range structural correlations, and it appears that Mn 3 TeO 6 keeps the same incommensurately modulated magnetic spin structure with the propagation vector k = (0; 0; 0.43) in the whole temperature range from 5 to 24 K.

In this Letter, there were four incorrect figure citations. In the sentence "However, at −2.4 T we obtain a domain pattern that is nearly identical to that at +2.4 T (Fig. 2b), but with the brightness of each domain inverted ( Fig. 2d). ", Fig. 1a and d were wrongly cited. In the sentence "The reversal occurs via intermittent formation and shifts of domain walls (Fig. 2c). ", Fig. 1c was wrongly cited. In the sentence "According to the magnetic-field dependence of the SHG interference shown in Fig. 2e, integrated over the range −3 T to +3 T over two spots of about 500 μm, the most substantial domain variations occur between −0.2 T and +0.2 T. ", Fig. 1e was wrongly cited. These errors have been corrected online. CORRECTIONS & AMENDMENTS2 2 N O V E M B E R 2 0 1 8 |