The property that the ease of magnetization depends on the crystal direction. In iron, <100> is the easy axis. A large value raises coercivity, and a small one raises permeability.
Japanese name: 結晶磁気異方性
Magnetocrystalline anisotropy appears in 4 practice questions across 1 topic, including Magnetic materials.
Field: Magnetic materials
Magnetocrystalline anisotropy is the property that a material's energy depends on which crystal direction the magnetization points along. In cubic crystals, with α₁, α₂ and α₃ as the direction cosines of the magnetization, it is written E = K₁(α₁²α₂² + α₂²α₃² + α₃²α₁²) + …. Iron has a positive K₁ ≈ 4.8×10⁴ J/m³ (room temperature) with <100> as the easy axis, and nickel has a negative K₁ with <111> as the easy axis. For uniaxial materials such as hexagonal cobalt it is written E = K_u sin²θ, with θ the angle from the c axis, and K_u for cobalt is about 4×10⁵ J/m³. The unit is energy per unit volume, J/m³.
Magnetization is carried mainly by spin, but spin is coupled to the orbital motion of electrons by spin–orbit interaction, and the orbitals have preferred orientations in the crystal field created by the surrounding ions. Through this coupling, the direction of magnetization comes to distinguish crystal directions. The 4f electrons of rare earths have a large orbital contribution, giving extremely large anisotropy, as in Nd₂Fe₁₄B (K₁ ≈ 4.9×10⁶ J/m³) and SmCo₅. A guide to the field needed to pull the magnetization away from the easy axis is the anisotropy field HA = 2K/(µ₀Ms); µ₀HA is about 0.06 T for iron but reaches about 7.5 T for Nd₂Fe₁₄B.
Magnetocrystalline anisotropy is not the only reason energy depends on the direction of magnetization. In elongated particles and thin films, the demagnetizing field makes the magnetization prefer the long direction or the film plane; this is shape anisotropy. The coercivity of alnico magnets comes mainly from the shape anisotropy of an elongated ferromagnetic phase. There is also stress-induced anisotropy from the combination of stress and magnetostriction, and induced anisotropy created by heat treatment in a magnetic field. The difference is that magnetocrystalline anisotropy is a property of the substance itself, set by composition and temperature, whereas shape anisotropy and induced anisotropy can be changed through microstructure and processing.
In permanent magnets, larger anisotropy makes the magnetization harder to reverse and raises the upper limit of coercivity, so materials with large K are chosen and sintered with the easy axes of the grains aligned. In soft magnetic materials anisotropy is instead made small; in permalloy, K₁ is brought close to 0 by composition. In nanocrystalline soft magnetic alloys, the grain size is made smaller than the magnetic correlation length so that the anisotropies of individual grains average out and cancel. Grain-oriented electrical steel, which aligns iron's easy axis <100> with the rolling direction, is an example of putting anisotropy to use. Because anisotropy constants fall faster than saturation magnetization as temperature rises, values at the service temperature matter for magnets used hot.
Answer: B. Its magnetocrystalline anisotropy and magnetostriction are both nearly zero, so domain walls move and magnetization rotates easily
A high permeability requires the magnetization to change greatly in a weak field. Magnetization rotation is hindered by magnetocrystalline anisotropy, and if there is magnetostriction, the magnetoelastic energy coupled to internal stresses hinders domain-wall motion. In the Fe–Ni system, at compositions around 80% Ni both the magnetocrystalline anisotropy constant and the magnetostriction constant approach zero, and heat treatment that adjusts the degree of ordering can make the anisotropy even smaller, so a very high permeability is obtained. The saturation flux density of permalloy is considerably lower than that of pure iron (about 2.2 T), so the option citing a saturation magnetization larger than that of pure iron is wrong. Making grains nanometer-sized so that the anisotropy averages out is the idea behind nanocrystalline soft magnetic alloys, not the reason for permalloy.
Answer: A. The grains are aligned in the Goss orientation {110}<001>, so the easy axis <100> points along the rolling direction
Iron is cubic, and because of magnetocrystalline anisotropy the <100> directions are the easiest to magnetize (easy axes) and the <111> directions the hardest. Grain-oriented electrical steel is given coarse grains in the Goss orientation, with {110} planes parallel to the sheet surface and <001> along the rolling direction, by secondary recrystallization using inhibitors (fine MnS or AlN precipitates). Magnetized along the rolling direction, it therefore approaches saturation in a weak field and its loss is small. The option treating <111> as the easy axis confuses the easy and hard axes. Non-oriented electrical steel, with random orientations, is used for motor cores, where the direction of the flux rotates. Si is added to raise the electrical resistivity and reduce eddy-current loss.
The easy axis is the crystal direction of lowest magnetocrystalline anisotropy energy, along which saturation is reached at low field; the hard axis is the direction of highest energy, which needs a strong field to saturate. In iron, <100> is the easy axis and <111> the hard axis, which can be measured as differences in the magnetization curves of a single crystal along each direction.
A common method uses a torque magnetometer, which rotates a single-crystal specimen in a magnetic field and measures the torque pulling the magnetization back toward the easy axis. Other methods measure magnetization curves along the easy and hard axes and obtain the anisotropy energy from the area between them, or derive it from the ferromagnetic resonance frequency.
It depends on the application. In permanent magnets, larger anisotropy allows higher coercivity and is an advantage. In soft magnetic materials such as transformer cores, the magnetization must change at low field, so the smaller the anisotropy the better. In magnetic recording there is a balance: large enough to keep the recorded data, but moderate enough to write.
Magnetization rotation is hindered by magnetocrystalline anisotropy, and if there is magnetostriction, the magnetoelastic energy coupled to internal stresses hinders domain-wall motion.
What is the main reason permalloy, Fe with about 78% Ni, sh…Iron is cubic, and because of magnetocrystalline anisotropy the <100> directions are the easiest to magnetize (easy axes) and the <111> directions the hardest.
Grain-oriented electrical steel (Fe with about 3% Si) used …Nd₂Fe₁₄B is tetragonal and, owing to the contribution of the Nd 4f electrons, has a strong uniaxial magnetocrystalline anisotropy along the c axis, with µ₀HA reaching about 7.5 T.
What is the main material reason that neodymium magnets, wi…Nd₂Fe₁₄B has a rather low Curie temperature of about 310°C, and as the temperature rises its magnetocrystalline anisotropy falls and its coercivity drops sharply.
What is the main purpose of adding Dy or Tb to neodymium ma…Saturation magnetization Coercivity Recrystallization Eddy-current loss Magnetic domain Curie temperature Maximum energy product Domain wall Ferrimagnetism Superparamagnetism