To determine which compound is metallic and ferromagnetic, we need to understand two key concepts: metallic character and ferromagnetism.

Metallic Character

Metallic character refers to the ability of an element or compound to conduct electricity due to the presence of free electrons. In transition metal oxides, metallic behavior occurs when the metal ions are in mixed valence states or when the compound has a partially filled d-band, allowing electron delocalization.

Ferromagnetism

Ferromagnetism is a property where materials exhibit strong magnetic attraction and can retain magnetization. It arises from the parallel alignment of magnetic moments (due to unpaired electrons) in domains. For ferromagnetism, the material must have unpaired electrons and a positive exchange interaction favoring parallel spin alignment.

Analysis of Options

Let's evaluate each compound:

• VO₂: Vanadium dioxide is known for its metal-insulator transition but is not typically ferromagnetic. It shows metallic conductivity above 68°C but is not ferromagnetic.
• CrO₂: Chromium dioxide is a ferromagnetic compound with a Curie temperature of about 386 K. It is metallic and widely used in magnetic recording tapes due to its strong ferromagnetism.
• MnO₂: Manganese dioxide is an insulator and antiferromagnetic, not ferromagnetic or metallic.
• TiO₂: Titanium dioxide (rutile) is an insulator and diamagnetic, with no metallic conductivity or ferromagnetism.

Conclusion

Among the options, only CrO₂ is both metallic and ferromagnetic. This is due to its crystal structure and electronic configuration, which allow for electron delocalization and parallel spin alignment.

Related Topics

Ferromagnetism in Materials: Ferromagnetic materials like iron, cobalt, nickel, and some compounds like CrO₂ have unpaired electrons that align parallel, creating a net magnetic moment. The exchange interaction energy is positive, favoring this alignment.

Metallic Oxides: Some transition metal oxides exhibit metallic conductivity due to overlapping d-orbitals or mixed valence states, enabling electron flow. Examples include ReO₃, CrO₂, and TiO at high temperatures.

Key Formulae

While no specific formula is directly applied here, understanding magnetic moment can be relevant. For an ion, the magnetic moment $\mu$ is given by:

$\mu =\sqrt{n(n+2)}{\mu }_B$

where $n$ is the number of unpaired electrons and ${\mu }_B$ is the Bohr magneton. Ferromagnetic materials have high $\mu$ values due to many unpaired electrons.