Edgar Ascher

Some Properties of Ferromagnetoelectric Nickel‐Iodine Boracite, Ni3B7O13I

Ferroelectricity and weak ferromagnetism have been found to set on simultaneously in Ni3B7O13I at about 64°K. This is evidenced by dielectric hysteresis, spontaneous Faraday effect, quadratic magnetoelectric hysteresis, etc. The strong coupling between the mutually perpendicular spontaneous polarization—[001]—and spontaneous magnetization—[110]—is such that, when the former is reversed, the latter turns by 90°. The magnetic point group is most probably m′m2′. Dielectric constant, magnetic, and magnetoelectric susceptibilities and magnetic coercive field are shown as a function of temperature.

Dielectric properties of boracites and evidence for ferroelectricity

Abstract The dielectric constants of Ni-Cl, Ni-Br, Co-Br and Co-I boracites have each a maximum at a temperature which coincides with that of a phase transformation we have observed optically. Motion of ferroelectric domain walls under an applied electric field has been sought for in Ni-Cl boracite and found to occur at temperatures as far as 80° below that of the phase transition.

Magnetic susceptibilities of some 3d transition metal boracites

Abstract Effective magneton numbers and Curie-Weiss temperatures of eleven 3d-metal boracites have been determined from susceptibility versus temperature measurements. All investigated boracites display negative Curie-Weiss temperatures. CrI and NiIboracites become anti-ferromagnetic at about 90° and 120°K, respectively. NiIboracite shows an anomalous peak of susceptibility at about 60°K which coincides with the temperature of the simultaneous onset of ferro-electricity and weak ferromagnetism.

Permutation representations, epikernels and phase transitions

The subgroups that arise in phase transitions from a high-symmetry phase are characterized as those subgroups that are maximal with respect to the property of acting trivially on a given non-zero subspace Ui of the representation space Mi of a given irreducible representation Ti of H. In the case of subgroups of finite index the problem is reduced to that of studying faithful irreducible representations of finite groups. The use of permutation representations considerably simplifies the theory. Tables of the equitranslation epikernels of the space groups are given.

Algebraic aspects of crystallography. II. Non-primitive translations in space groups

AbstractTaking into account the fact that space groups are groups of transformations of Euclideann-dimensional space, non-equivalent systems of non-primitive translations are defined. They can be brought into one-to-one correspondence with the elements of the groupH1 (K, Rn/Zn) or with those of the groupH1 (K, Zn/kZn)/H1 (K, Zn). (K is a point group of orderk.) The consistency of these findings with the results of Part I is given by the isomorphisms

Are antiferroelectricity and other physical properties 'hidden' in spinel compounds?

H^2 (K,Z^n ) \cong H^1 (K,R^n /Z^n ) \cong H^1 (K,Z^n /kZ^n )/H^1 (K,Z^n ).

Higher-order magneto-electric effects

Theorems are proved giving the conditions for cohomology groupsHq (K, A) to be zero. These conditions are fulfilled in particular ifA=Rn andK is a subgroup ofGL (n, R) that either is compact (thenq>0) or has a finite normal subgroup leaving no element ofRn invariant (thenq≧0). This implies that the affine, the Euclidean and the inhomogeneous Lorentz groups are the only extensions ofRn by the corresponding homogeneous groups. By way of illustration, the theory of this paper is applied to two 2-dimensional space groups.

Optical study on the ferroelectric orthorhombic phase of Fe-I-boracite

For a phase transition between two phases of symmetries H and L<H, the authors reconsider the problem of finding the irreducible representation Ti of H that (according to Landaus theory) determines the transition. They show how this representation can be found directly (without going into the intricacies of the theory of induced representations and Landaus theory) from the permutation representation of H determined by the pair L<H. In all the examples considered, the group L is maximal with respect to the property that it acts trivially on some non-zero subspace of the representation space Mi of Ti.