Remnance (or remanence or residual magnetism also residual magnetization ) Sometimes the term retentivity is used for remanence.

Remanence and Coercivity
Remanence or remanent magnetization is the magnetization left behind in a ferromagnetic material (such as iron) after an external magnetic field is removed.
Remnance (or remanence) occurs within ferromagnetic materials and is the flux density which remains in a magnetic material when any externally applied field is removed (H = 0). For materials used in permanent magnets you usually need a high value of remnance. For transformers you need low remnance. See the paragraph on hysteresis for more details.
Remnance is also what makes possible all magnetic recording technologies; including the hard disk drive on which this text was stored until you loaded it into your browser.
The equivalent term residual magnetization is generally used in engineering applications. In transformers, electric motors and generators a large residual magnetization is desirable (see also electrical steel). In many other applications it is an unwanted contamination, for example a magnetization remaining in an electromagnet after the current in the coil is turned off. Where it is unwanted, it can be removed by degaussing.
Sometimes the term retentivity is used for remanence measured in units of magnetic flux density.

Remanence: When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization (B) when the imposed magnetizing field (H) is removed. Remanence is a measure of how strong a magnetization remains in a material after an externally applied magnetizing force is removed remains in a material after an externally applied magnetizing force is removed.
High values of remanence and coercivity are sought for permanent magnets, so that the magnets will retain a strong field and not be demagnetized in response to external magnetic interactions. Materials with high remanence and coercivity are known as magnetically “hard”, and are contrasted against materials with low coercivity and remanence which are known as magnetically “soft”. Magnetically soft materials are preferred for transformer cores and inductors because they require less energy to magnetize and demagnetize. This is desirable in transformers, inductors, and other AC magnetic devices because less energy is irretrievably lost as heat in the process of re-orienting the magnetic domains, which is done once every cycle of the applied AC power. Consequently, such transformers are more efficient.

Coercive force or Coercivity: is a measure of how permanent a magnet is, ie. what amount of magnetic force it takes to reverse its magnetization. Materials with high coercive force require high magnetizing H fields to become magnetized or demagnetized. Coercive force is defined as that amount of magnetizing H-field needed to return the magnetization B of a magnet to zero, after it has been magnetized. Coercive force also varies with material composition and grain structure, and may be modified by annealing or cold working.
In materials science, the coercivity, also called the coercive field or coercive force, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation. Thus coercivity measures the resistance of a ferromagnetic material to becoming demagnetized. Coercivity is usually measured in oersted or ampere/meter units and is denoted Hc. It can be measured using a B-H Analyzer or magnetometer.
Ferromagnetic materials with high coercivity are called magnetically hard materials, and are used to make permanent magnets. Permanent magnets find application in electric motors, magnetic recording media (e.g. hard drives, floppy disks, or magnetic tape) and magnetic separation.
Materials with low coercivity are said to be magnetically soft. They are used in transformer and inductor cores, recording heads. microwave devices, and magnetic shielding.

Permalloy: Hc: 4 A/m Ms: 10.8 MA/m
Iron: Hc: 80 A/m Ms: 21.5 MA/m
Supermalloy: Hc: 0.2 A/m Ms: 8 MA/m