Magnetism and Magnetic Materials

Magnetismand Magnetic Materials

Magnetismand Magnetic Materials

TheAnisotropy in materials and how it affects the magnetic properties ingeneral

Anisotropyrefers to the quality of exhibiting some properties with values thatare different when in different directions along the axes[CITATION Kha14 l 1033 ].This property is mostly observed within the single crystals of solidcompounds or elements where ions, molecules or atoms are arranged inregular lattice. In contrast, due to randomdistribution of particles in liquids, particularly gases, they arerarely isotropic. Magnetic anisotropy implies that theantiferromagnetic or ferromagnetic axis of the sample is along afixed direction. Hard magnetism is an indication of strong easy-axisanisotropy. The near zero anisotropy results to the soft magnets.Tendency for magnetization on easy axis is dependent on energydensity.

Anisotropyis used is describing situations where the properties of materialsvary systematically depending on direction. In the study ofmechanical properties of materials, the term isotropic is used torefer to the characteristics of materials having identical propertyvalues in all directions. Some of the common anisotropic materialsinclude wood since the material properties are perpendicular anddifferent parallel to the grain[ CITATION Coe10 l 1033 ].

Theisotropic materials are majorly used because of the ease in shapingand their behavior can be easily predicted. The materials can becustom-made based on forces that the object is anticipated toexperience. The analysis of material properties can be understood byanalyzing the symmetry of the crystal structure. Such results are inmost cases assumed to hold for the alloys too though this is unclearwhen alloy constituents are not distributed in a random manner. Forinstance, a dilute magnetic semiconductor exhibiting in-planemagnetocrystalline (Ga,Mn)As is not affected by GaAs lattice symmetry[ CITATION Rod13 l 1033 ].

Themagnetic anisotropy acts as a prerequisite for the hysteresis inferromagnetism. This implies that without magnetic anisotropy, theferromagnetic can only exhibit the properties of a superparamagnet. Magnetically anisotropic materials can demonstratehysteresis as long as there is presence of exchange interactionenergy. Anisotropyis dependent on temperature and tends to zero in zero applied fields.Anisotropy is caused by crystal structure, micro-scale texture andshape of the sample. The shape anisotropy gets its energy fromdemagnetizing fields that is dependent on direction of the sample’smagnetization. The magnetocrystalline anisotropy is a function ofcrystal symmetry and results from the interaction between thespin-orbiting coupling and the field of the crystal[ CITATION Cul11 l 1033 ].

Theanisotropic energy density [f an (m)] can be expressed as a functionof spherical angles θ and φ. This is expressed as

Themagnetocrystalline anisotropy influences greatly the uses offerromagnetic materials in industry. Materials that have highmagnetic anisotropy have high coercivity which makes them very hardto demagnetize, hence the name ‘hard’ magnetic materials. Thesematerials are mainly used to make permanent magnets. For instance,the high anisotropic rare-earth metals make them ideal for makingrare-earth magnets. When making the magnets, the magnetic field isused in aligning the micro-crystalline metal grains to ensure thatall the ‘easy’ axes of magnetization point towards the samedirection so as to freeze a strong magnetic field in the material.

Converselylow coercitivity results in materials having low magnetic anisotropysince their magnetization can be changed easily, hence the name‘soft’ magnetic materials. These materials are mainly used inmaking magnetic cores for inductors and transformers. They requiresmall energy to change the magnetization direction and this plays amajor role in minimizing the core losses and energy dissipationwithin the core of the transformers as the direction changes due toalternating current[ CITATION Rod13 l 1033 ].

Thecubic anisotropy

Thecubic anisotropy is the anisotropy that results when the anisotropyenergy density has a cubic symmetry[ CITATION Rud08 l 1033 ].This mostly occurs where there is spin-lattice coupling within thecubic crystals. This is characterized by existence of threeprivileged directions. The typical expansion of anisotropy densityhappens within the Cartesian coordinates and is expressed as below.


Neglectingvalues greater than fourth term,when,then there will be six equivalent minimum (positive and negative)that correspond to the directions (x, y, z). Contrariwise, when a situation that is more complex arises eight equivalent minima inthe directions that point the vertices of the cube. Below is arepresentation of cubic anisotropy at

CubicAnisotropy Source [ CITATION Rud08 l 1033 ]

Generallyspeaking, when compared to uniaxial anisotropy, cubic anisotropy isrelatively smaller due to the higher crystal symmetry. As a result,many magnetic materials that are soft have low coercive force andhigh permeability as a result of cubic crystal structures whose cubicanisotropy is low[ CITATION Aha12 l 1033 ].

TheTetragonal Anisotropy

Atetragonal anisotropy refers to the type of the anisotropy where thetetragonal cell comprises of three axes positioned at right anglestwo are equal to each other and one is either shorter or longer thanthe rest two. The changes occur as a result of domain wall motion anwhen the saturated crystal is longer towards the magnetizationdirection than demagnetized crystal, the single domain comprising thesaturated crystals should be built from unit cells that are slightlyextended towards the magnetization vector[ CITATION Bur04 l 1033 ].

Reasonswhy the tetragonal anisotropy is needed for better magneticproperties unlike the cubic anisotropy.

Forcubic anisotropy, the resultant material has weak magnetic propertiesdue to the weak shape of the structure[ CITATION Kur16 l 1033 ].The stacks in this anisotropy cannot be scaled to 10nm node. Also,cubic anisotropyis hard to integrate due to lattice mismatch and low spinpolarization. Tetragonal anisotropy is more preferred when bettermagnetic properties are need because while the cubic anisotropy ispurely isotropic, the tetragonal anisotropic materials possesses highlevel of uniaxial magnetic anisotropy alongside high spinpolarization and tunable saturation magnetization. The tetragonalanisotropic materials have high uniaxial and perpendicular anisotropythat can grow more easily than in cubic anisotropic materials[ CITATION Rod13 l 1033 ].Theenergy expressions for the two types of anisotropy are as shownbelow.

Tetragonal:Ea=K1sin2θ+K2sin4θ+K`2 sin4θcos4φ+K3sin6θ+K`3sin6θsin4φCubic:Ea=K1c(α12α22+ a22α32+ α32α12)+ K2c(α22α22α32)

Whereαirepresentsthe cosine direction of the magnetization, K1ctermsrepresent K1c(sin4θcos2φsin2φ+cos2θsin2θ).Whenθ≈0, φ=0, the equation reduces to K1csin2θ.

Examples:beloware crystal phases of a FePt. (a) is cubic phase, a = c. while (b) istetragonal phase, a≠c

Cubicand Tetragonal phases of FePt crystals Source[ CITATION Cul11 l 1033 ]


Aharoni, A. &amp. (2012). Cylindrical domains in small ferromagnetic spheres with cubic anisotropy. Magnetics, IEEE Transactions on, 24(2), 1892-1894.

Burkert, T., Nordström, L., Eriksson, O., &amp Heinonen, O. (2004). Giant magnetic anisotropy in tetragonal FeCo alloys. Physical review letters, 93(2), 1-10.

Coey, J. M. (2010). Magnetism and magnetic materials. Cambridge: Cambridge University Press.

Cullity, B. D., &amp Graham, C. D. (2011). Introduction to magnetic materials. Hoboken, New Jersey: John Wiley &amp Sons.

Kharel, P., Huh, Y., Al-Aqtash, N., Shah, V. R., Sabirianov, R. F., Skomski, R., et al. (2014). Structural and magnetic transitions in cubic Mn3Ga. Journal of Physics: Condensed Matter, 26(12), 1-9.

Kurt, H., &amp Coey, J. M. (2016). Magnetic and Electronic Properties of Thin Films of Mn-Ga and Mn-Ge Compounds with Cubic, Tetragonal and Hexagonal Crystal Structures. In Heusler Alloys (pp. 157-191). Switzerland: Springer International Publishing.

Rode, K., Baadji, N., Betto, D., Lau, Y. C., Kurt, H., Venkatesan, M., et al. (2013). Site-specific order and magnetism in tetragonal Mn 3 Ga thin films. Physical Review B, 87(18), 1-14.

Rudnick, J. (2008). First-order transition induced by cubic anisotropy. Physical Review B, 18(3), 1406.