Hexagonal ferrite
Hexagonal ferrites or hexaferrites are a family of ferrites with hexagonal crystal structure. The most common member is BaFe12O19, also called barium ferrite, BaM, etc. BaM is a strong room-temperature ferrimagnetic material with high anisotropy along the c axis. All the hexaferrite members are constructed by stacking a few building blocks in a certain order. Basic building blocks

S block 
The S block is very common in hexaferrites, which has a chemical formula of MeS6O82+. MeS are smaller metal cations, for example, Fe and other transition metals or noble metals. The S block is essentially a slab cut along the  plane of an AB2O4 spinel. Each S block has one A layer and one B layer. The A layer features MeS-centered tetrahedron and MeS-centered octahedron, while the B layer is made up of edge-sharing MeS-centered octahedron. Both A and B layers have the same chemical formula of MeS3O42+. R block 

The R block has a chemical formula of MeLMeS6O112-. MeL are larger metal cations, for example, alkaline earth metals (Ba, Sr,) rare earth metals, Pb, etc. The point group symmetry of the R block is . The large metal cations are located in the middle layer of the three hexagonally packed layers. This block is also composed of face-sharing MeS-centered octahedra and MeS-centered trigonal bipyramids. T block 
The T block has a chemical formula of MeL2MeS8O142-. The point group symmetry of the T block is . One T block consists of 4 oxygen layers with the two MeL atoms substituting two oxygen atoms in the middle two layers. In one T block, there are both MeS-centered octahedra and MeS-centered tetrahedra. Family nembers

M-type ferrite 
M-type ferrite is made up of alternating S and R blocks in the sequence of SRS*R*. (* denotes rotating that layer around the c axis by 180°.) The chemical formula of M-type ferrite is MeLMeS12O19. Common examples are BaFe12O19, SrFe12O19. It exhibits  space group symmetry. For BaFe12O19, a = 5.89 Å and c = 23.18 Å. M-ferrite is a very robust ferrimagnetic material, thus widely used as fridge magnets, card strips, magnets in speakers, magnetic material in linear tape-open. W-type ferrite 
W-type ferrite, like the M-type, consists of S and R blocks, but the stacking order and the number of blocks are different. The stacking sequence in a W-ferrite is SSRS*S*R* and its chemical formula is MeLMeS18O27. It exhibits  space group symmetry. One example of W-type ferrite is BaFe18O27, with a = 5.88 Å and c = 32.85 Å.

R-type ferrite 
R-type ferrite has a chemical formula of MeLMeS6O11 with a space group of . Unlike other hexaferrites, R-type ferrite doesn't have an S block. Instead, it only has single B layers extracted from the S block. The stacking sequence is BRB*R*. Y-type ferrite 
Y-type ferrite has a chemical formula of MeL2MeS14O22 with a space group of . One example is Ba2Co2Fe12O22 with a = 5.86 Å and c = 43.5 Å. Y-type ferrite is built up with S and T blocks with an order of 3(ST) in one unit cell. There is no horizontal mirror plane in a Y-type ferrite. Z-type ferrite 
Z-type ferrite has a chemical formula of MeL3MeS26O41 with a space group of . It has a complicated stacking of SRSTS*R*S*T* in one unit cell. Some Z-type members may have sophisticated magnetic properties along different directions. One example is Ba3Co2Fe24O41 with a = 5.88 Å and c = 52.3 Å.

X-type ferrite 
X-type ferrite has a chemical formula of MeL2MeS30O46 with a space group of . The stacking order is 3(SRS*S*R*) in one unit cell. One example is Sr2Co2Fe28O46 with c = 83.74 Å.

References 

Ferromagnetic materials
Ceramic materials