Title: Summary Multiferroics

Choose the correct statement.

- A multiferroic is a material that has two or more primary ferroic orders (ferroelectricity, ferromagnetism and ferroelasticity) in the same phase. (correct)
- A multiferroic is a material that has two or more primary ferroic orders (ferroelectricity, ferromagnetism and ferroelasticity), each in different domains throughout the material.

- Piezoelectricity is the result of the coupling of ferroelectricity and ferroelasticity. (correct)
- Piezoelectricity is the result of the coupling of ferroelectricity and ferropiezism.

- Magnetoelectric materials, that is, those presenting both ferroelectricity and ferromagnetism, are quite rare. (correct)
- Magnetoelectric materials, that is, those presenting both ferroelectricity and ferromagnetism, are common.

- Magnetoelectric multiferroics are uncommon because ferroelectricity (FE) and ferromagnetism (FM) are favoured by different crystal chemistries. FE is favoured by empty d-shells transition metals, whereas most ferrromagnets have partially-filled d-shells. (correct)
- Magnetoelectric multiferroics are uncommon because ferroelectricity (FE) and ferromagnetism (FM) are favoured by different crystal chemistries. FM is favoured by lone-pair active cations and FE by partially-filled d or f shells.

- New multiferroics can be designed using a ferroelectric A-site cation with a stereochemically active electron lone pair and a ferromagnetic B-site cation, such as a magnetic transition metal. (correct)
- New multiferroics can be designed using Europium, a rare-earth element that combines both ferroelectricity and ferromagnetism.

- In weak ferromagnetism, a small spontaneous magnetic moment occurs because of the tilting of atomic magnetic moments, caused by an anistropic exchange, the Dzyaloshinskii-Moriya interaction. (correct)
- In weak ferromagnetism, a small spontaneous magnetic moment occurs because of the rotation of octahedra due to a small tolerance factor, which in turn tilts the atomic magnetic moments (Dzyaloshinskii-Moriya interaction).

- The second strategy in designing multiferroics consists of a ferromagnetic A-site cation, with a magnetic atom, and a ferroelectric B-site cation, with an empty d-shell transition metal. (correct)
- The second strategy in designing multiferroics consists of a ferroelectric A-site cation, with an empty d-shell transition metal, and a ferromagnetic B-site cation, with such a tolerance factor that permits a Jahn-Teller distortion.

- The Born Effective Charge (BEC) of an ion is a useful concept to identify ferroelectrically active ions. (correct)
- The Born Effective Charge (BEC) corresponds to the integral of the Wannier function of an ion over all space.

- A magnetic moment is space-inversion symmetric, but it breaks time-reversal symmetry. (correct)
- A magnetic moment is time-reversal symmetric, but it breaks space-inversion symmetry.

- Other approaches to making multiferroics are geometric considerations, spiral magnets and charge ordering. (correct)
- Other approaches to making multiferroics are the use of skyrmions, geometric considerations and Mott transitions.