Consider the idea that Mercury has a solid iron-bearing mantle that is permanently magnetized like a giant bar magnet. Using the fact that iron demagnetizes at temperatures above \(770^{\circ} \mathrm{C}\), present an argument against this explanation of Mercury's magnetic field.

Iron is one of the most common materials known for having magnetic properties. It’s an element that can be magnetized, creating a magnetic field around it. In everyday objects, iron's magnetic properties are harnessed in the form of small magnets, such as those found on refrigerator doors, or at a much more industrial scale, like in the motors of electric machines. What's intriguing about iron is how its magnetic properties are affected by temperature. When iron is in its ferromagnetic state, the atoms align in a common direction, which gives iron its magnetic capabilities. However, when heated to high temperatures, the alignment is disturbed, leading to a loss of magnetization. This property is pivotal when exploring magnetic fields in planetary bodies, like Mercury's magnetosphere.

The Curie temperature, named after the French physicist Pierre Curie, is a critical point for magnetic materials such as iron. It is the temperature at which certain materials lose their permanent magnetic properties to become only paramagnetic. This is a state where the material magnetizes only in the presence of an external magnetic field and does not retain magnetization after the external field is removed. In the case of iron, its Curie temperature is approximately --- --- --- at --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- [...] the Curie temperature is closely related to the microscopic order of atoms and their magnetic moments within the material. Beyond this temperature, the thermal agitation overcomes the magnetic forces aligning the moments, causing a random distribution and thus demagnetization. Understanding the Curie temperature is crucial when analyzing the likelihood of naturally occurring magnetic fields in the environment or in the technological application of magnetic materials.

The temperature of a planet's core is a fundamental aspect of its geological and magnetic properties. For terrestrial planets like Earth and Mercury, the core is primarily made up of metals such as iron and nickel. These metals, in their molten state, can create a dynamo effect, generating a planet's magnetic field. However, the temperature of the core also plays a significant role in whether the metals therein can sustain a magnetic field. If a planet's core temperature is above the Curie temperature of the materials it’s made of – in this instance, iron – it means that the ferromagnetic or permanent magnetism is not sustainable in the core. Instead, what may contribute to the planetary magnetic field has to be dynamic in nature, such as the movement of molten metal, rather than the permanent magnetization of the solid iron-bearing layer. Hence, knowing the core temperature helps scientists infer not only the state of the planetary interior but also gives insights into the mechanics behind magnetic field generation in planets.