Coercivity
In materials science, the coercivity, also called the coercive field, 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.  Coercivity is usually measured in oersted or ampere/meter units and is denoted HC.
When the coercive field of a ferromagnet is large, the material is said to be a hard or permanent magnet.    Permanent magnets find application in electric motors, magnetic recording media (e.g. hard drives, floppy disks, or magnetic tape) and magnetic separation.    A ferromagnet with a low coercive field is said to be soft and may be used in microwave devices, magnetic shielding, transformers or  recording heads.
Coercivity can be measured using a B-H Analyzer.

# Experimental determination
Typically the coercivity of a magnetic material is determined by measurement of the hysteresis loop or magnetization curve as illustrated in the figure.    The apparatus used to acquire the data is typically a vibrating-sample or alternating-gradient magnetometer.    The applied field where the data (called a magnetization curve) crosses zero is the coercivity.    If an antiferromagnetic solid is present in the sample, the coercivities measured in increasing and decreasing fields may be unequal as a result of the exchange bias effect.
The coercivity of a material depends on the time scale over which a magnetization curve is measured.    The magnetization of a material measured at an applied reversed field which is nominally smaller than the coercivity may, over a long time scale, slowly creep to zero.   Creep occurs when reversal of magnetization by domain wall motion is thermally activated and is dominated by magnetic viscosity. The increasing value of coercivity at high frequencies is a serious obstacle to the increase of data rates in high-bandwidth magnetic recording, compounded by the fact that increased storage density typically requires a higher coercivity in the media.

# Theory
At the coercive field, the vector component of the magnetization of a ferromagnet measured along the applied field direction is zero.   There are two primary modes of magnetization reversal: rotation and domain wall motion.    When the magnetization of a material reverses by rotation, the magnetization component along the applied field is zero because the vector points in a direction orthogonal to the applied field.    When the magnetization reverses by domain wall motion, the net magnetization is small in every vector direction because the moments of all the individual domains sum to zero.   Magnetization curves dominated by rotation and magnetocrystalline anisotropy are found in relatively perfect magnetic materials used in fundamental research.  Domain wall motion is a more important reversal mechanism in real engineering materials since defects like grain boundaries and impurities serve as nucleation sites for reversed-magnetization domains.    The role of domain walls in determining coercivity is complex since defects may pin domain walls in addition to nucleating them.   The dynamics of domain walls in ferromagnets is similar to that of grain boundaries and plasticity in metallurgy since both domain walls and grain boundaries are planar defects.

# Significance
As with any hysteretic process, the area inside the magnetization curve during one cycle is work that is performed on the magnet.    Common dissipative processes in magnetic materials include magnetostriction and domain wall motion.    The coercivity is a measure of the degree of magnetic hysteresis and therefore characterizes the lossiness of soft magnetic materials for their common applications.
The squareness (M(H=0)/Ms) and coercivity are figures of merit for hard magnets although energy product (saturation magnetization times coercivity) is most commonly quoted.   The 1980s saw the development of rare earth boride magnets with high energy products but undesirably low Curie temperatures. Since the 1990s new exchange spring hard magnets with high coercivities have been developed.