Magnet ABC

(1)
Br, residual induction
The measure of magnetic capability of the magnet.  Br only exists in a closed circuit.  This is like a fully charged battery.
Br is reported in Gauss, kiloGauss, Tesla or miliTesla 
The higher the value of Br, the smaller is the required magnet cross sectional area to perform a specific task

(2)
Hcb, normal coercivity 
The measure of the field required to drive B to zero.  At this point the magnet is not fully demagnetized, but will recoil to some "B" when the field is removed or when the load line increases.  Operating at Hc is like short circuiting a battery for a short time.
Hcb is reported in Oersteds, kiloOersteds, Ampere / meter

(3)
Hci, intrinsic coercivity 
The measure of the magnet's resistance to demagnetization, the demagnetization field required to fully demagnetize.  At this point the magnet is demagnetized inside the magnet.  This is like applying a reverse voltage to a battery or shorting it for a long time.
Hci is reported in Oersteds, kiloOersteds or Ampere/meter
The higher the value of Hci, the smaller is the required magnet thickness (Lm) to withstand a specific demagnetizing influence.

(4) 
 (BH)max, max. energy product
The point on the demag curve where the function of B*H maximizes is theoretically the most efficient operating point.
B*H is referred to as the energy product.
Energy product is reported in Mega Gauss Oersteds or Joule/meter3.
It is generally a figure of merit, used for rapid comparison of different magnet materials.

(5) 
Air gap
 Air gap  is Space between the poles of a magnet in which there exists a useable magnetic field.

(6)
When does Sm-Co require coating?
Sm-Co is typically plated for medical applications to give a "sealing" coat of nickel. This is extra insurance against the rare flake of iron. Nickel can be good insurance against such flaking, by making the surface tougher. It also protects the magnet from sterilizing chemicals and other contaminates. 

(7)
Why are rare earth magnets so expensive?
In the case of the rare earth magnets, the heavy metals used to enhance the magnetic properties are difficult to extract. The magnet-related elements are actually a small fraction of the lanthanides mined, so material cannot be produced in huge quantities. Since the fine powders are pyrophoric, production conditions need to be very tightly controlled, and there is a limit to the size of block that can be formed due to the pressure required. Subsequent machining of the magnets adds more cost. Because the magnets are typically very hard and brittle, grinding and slicing operations are slow. 

(8)
What's the difference between Alnico, Sm-Co & Nd-Fe-B magnet materials?
Alnico is an older magnet material that still has important applications. Its maximum energy product is about 1/5 of Sm-Co materials, but it has excellent elevated temperature properties and has better corrosion resistance. Alnico can be cast into different shapes with various magnetic orientations. The rare earth Sm-Co and Nd-Fe-B magnets have high coercivity, so they do not need to be magnetized in circuit and can be used with low permeance coefficients (i.e. thin discs). These materials also lend themselves to Helmholtz coil testing due to their straight line normal curves. This also makes rare earths ideal for motors and high field dipoles. Sm-Co has a good resistance to thermal demagnetization but is brittle. Nd-Fe-B is less brittle, has poor thermal properties, and is prone to corrosion.