# Soft Magnetic Materials & High Frequency Materials

Soft Magnetic Materials/Soft Magnetic Composites/High Frequency Magnetic Materials

Soft magnetic materials are characterized with high magnetic induction (B), high magnetic permeability (μ’-jμ”=dB/dH), low coercivity (Hc), and low loss tangent (tanδ= μ”/ μ’). Loss tangent determines the energy (power) loss in soft magnetic materials or soft magnetic composites.  The power losses is expressed as:

 $P={ P }_{ hys }+{ P }_{ eddy }+{ P }_{ an }+{ P }_{ FMR }={ W }_{ H }f+\frac { k{ B }^{ 2 }{ t }^{ 2 } }{ \rho } { f }^{ 2 }+{ P }_{ an }+{ P }_{ FMR }$ (1)

where $P={ P }_{ hys }={ W }_{ H }f$ is the hysteresis loss and is proportional to the operating frequency () and the area enclosed by BH loop at dc,  the second term is the eddy current loss and is proportional to 2, material thickness (t) perpendicular to the B direction, and is inversely proportional to electrical resistivity ρ, Pan is the anomalous loss, and PFMR­ is the loss due to ferromagnetic resonance that is usually around GHz range.   Soft magnetic materials or soft magnetic composites are widely used in motors and generators, transformers, inductors, magnetic sensors, electromagnetic interference (EMI) shielding materials, and various microwave magnetic devices.   The operating frequency ranges from dc to microwaves. Depending on the operating frequency, one must chose different types of soft magnetic materials or soft magnetic composites that are typically classified as silicon steel/electrical steel/lamination steel, amorphous magnetic materials/nanocrystalline magnetic materials, ferrites, soft magnetic composites, and nanostructured magnetic materials.

Silicon Steel/Electrical Steel/Lamination Steel

Silicon steel, also known as electrical steel or lamination steel, is FeSi alloys with silicon content up to 6.5%.  The addition Si significantly increase the electrical resistivity to about 50 μΩ-cm.  The saturation magnetic induction is above 1.5T and the relative permeability (in reference to that of vacuum) is about 4000.  Two main forms of silicon steels are available: (a) cold-rolled non-grain-oriented steel (CRNGO) has isotropic magnetic properties in any direction and is cheap, and (b) cold-rolled-grain-oriented steel (CRGO) has a higher saturation magnetic induction in along the rolling direction but is more expensive.  Silicon steel is usually coated between laminations to reduce the eddy current loss, to improve corrosion resistance, and to act as lubricant during die cutting.  The magnetic properties of electrical steel are tested according to internationally standard test methods.  Silicon steels are often used in motors, generators, and transformers.  The operation frequency typically is below 20 kHz.  Mechanical strain can significantly deteriorate magnetic properties, which, sometimes, requires the test of materials under stress.

Amorphous Magnetic Materials/Nanocrystalline Magnetic Materials

Because of glass structure of amorphous magnetic materials, they have higher resistivity above 100 μΩ-cm and low magnetic anisotropy, resulting in both lower eddy current loss and hysteresis loss.  In addition, by adjusting the composition, amorphous magnetic materials also have very low magnetostriction, which reduces the energy loss and noise of transformers.  By heat treatment, amorphous magnetic materials can be partially crystallized to form nanocrystalline magnetic materials which further reduces the magnetic anisotropy and increases the saturation magnetic induction.  Typical amorphous magnetic materials contains Fe-Co-Si-B-P-Cu-Nb where Si, B, and P are glass forming elements, Cu promotes nucleation, Nb impedes crystalline grain growth, Co improves the magnetic induction and magnetic phase transformation temperature (Curie temperature).  Amorphous magnetic materials are commonly made by melt-spinning technique that produces ribbon/sheet forms of materials.   Amorphous magnetic materials are fragile and cannot be easily machined.  There are needs to make bulk amorphous magnetic materials that can be achieved via casting methods which are widely used in aluminum die casting and stainless steel casting industries.   Recent researches have also suggested a steel die in which the molten metal flows at low rate and high temperature can be used to produce complete glassy materials.  This provides a unique approach to produce shaped amorphous magnetic parts.   Due to the metallic nature of amorphous materials, the operating frequency of these magnetic materials is still limited below about 100 kHz.

Ferrites

Ferrites are magnetic oxides with insulating properties.  Therefore, ferrites are commonly used in high frequency up to microwave frequency of GHz range.  There are two main classes of ferrites.  One has cubic spinel structure and the other has hexagonal structures.

Cubic Spinel Ferrites

The cubic spinel structure has the composition of MeFe2O4 where Me2+ represents metal cations including Fe2+.  Since the site occupation is very important to understand their magnetic properties,  the cubic spinel ferrites have also been expressed according to their site occupation referred to as normal spinel ferrites with {Me2+}A[Fe23+]BO42- and inverse spinel ferriteswith {Fe3+}A[Me2+Fe3+]BO42-,  where A and B represent the tetrahedral and octahedral sites, respectively.  Many cubic spinel ferrites are inverse or mixed (normal+inverse) spinel ferrites.   The magnetic moments within each sites are typically ferromagnetically coupled (parallel aligned) but between two sites are antiferromagnetically coupled (antiparallel).  Therefore, one can easily compute the total magnetization based on the compositions.   The magnetic properties of ferrites can be modified with substitution of different elements, which have preference of occupying tetrahedral A or octahedral B-sites.   For example, Co2+, Ni2+, Li1+ cations tend to occupy octahedral B-sites whereas Zn2+, Cd2+ prefer tetrahedral A-sites.

The power loss as a function of the magnetic induction for several ferrites

Cubic spinel ferrites have very high permeability but low operating frequency, typically less than 100 MHz.  The most commonly used cubic spinel ferrites are MnZn ferrites of MnxZn1-xFe2O4, and NiZn ferrites of NixZn1-x­Fe2O4.  MnZn ferrites has the highest permeability over 2,000, but the operating frequency is limited below 1MHz.  NiZn ferrites has slightly lower permeability but higher operating frequency up to about 20 MHz.

Z- and Y-type Hexagonal Ferrites

Hexagonal structure promotes magnetic anisotropy and increases ferromagnetic resonant frequency and thus operating frequency.  The hexagonal structure is much more complicated than the cubic spinel structure.  Hexagonal ferrite structure is made of stacked S-, R-, and T-blocks.  S-block with Me2Fe4O8 (Me: metal cations) consists of two hexagonal close-packed oxygen layers.  R-block [BaFe6O11]2- consists of three layers with one oxygen ion in the middle layer replaced by Ba2+ ion substitutionally.   T-block (Ba2Fe8O14) consists of four layers with one Ba2+ ion substituting an oxygen ion in each of the two middle layers.  Two commonly used soft hexagonal ferrites are Co2Z or Z-type and Co2Y or Y-type ferrites, referring to Ba3Co2Fe24O41 and Ba2Co2Fe12O22, respectively.   Co2Z is made of RSTSR*S*T*S* (* refers to the rotation around z-axis by 180°) and Co2Y is made of TSTSTS.   The operating frequency of Co2Z is typical up to 1 GHz whereas Co2Y can be used for above 1 GHz.

Our researches in this area focus on the development of high frequency, low loss ferrites derived from NiZn, Co2Z, and Co2Y.

Soft magnetic composites

The magnetic permeability and ferromagnetic resonance follows the Snoek’s Law:

 $\left( { \mu }_{ r }-1 \right) { f }_{ FMR }=\frac { 2\gamma }{ 3 } \times \left( 4\pi { M }_{ S } \right) \\$ (2)

where μr is the relative magnetic permeability, fFMR is the ferromagnetic resonant frequency, γ is the gyromagnetic ratio of 28 GHz/T, and 4πMs is the saturation magnetization.  Therefore, the product of μr fFMR is proportional to the saturation magnetization of the material.  Consequently, it is desirable to use materials with high saturation magnetization to increase the permeability and ferromagnetic resonant frequency. Metallic ferromagnetic materials have much higher saturation magnetization compared with that of ferrites.  The highest saturation magnetization is found in CoFe alloys of about 2.4T.  Fe has the saturation magnetization of 2.2T.    In order to use metallic ferromagnets at high frequency, one must make them insulating so as to prevent eddy current losses.  Soft magnetic composites or SMC were developed for this purpose.  Soft magnetic composites or SMC typically consists metallic magnetic inclusions, particles or other shaped objects, each of them is coated with insulating materials.  The most common coatings are polymeric materials.   Other oxides such as SiO2, MgO are also used.  The coated particles are compacted to form various core materials.

Our researches in this area focus on the development of soft magentic composites or SMC based on magnetic flakes.

Nanostructured magnetic materials

One important factor to consider in developing high frequency composite materials is the demagnetization effect.  As a magnetic material is placed inside an applied magnetic field (Ha), magnetic poles are induced at the two ends of the material.  The induced poles generates an internal magnetic field, which is opposite to the direction of the applied field.  This field is called demagnetization field (Hd).   Consequently, the total field inside the material is Htot=Ha-Hd < Ha, resulting in the apparent permeability (μapp) that is smaller than the true permeability of the material (μr):

 ${ \mu }_{ app }=\frac { { \mu }_{ r } }{ 1+\frac { N }{ 4\pi } \left( { \mu }_{ r }-1 \right) } \\$ (3)

where N  is the demagnetization factor of the inclusion in the direction of the applied field.   Demagnetization factors of several common shapes are shown in the table.  It immediately becomes clear that for spherical-like particles, N is about 4π/3, which leads to μapp » 3 even if μr >> 1.  The best choice is N=0, which are true for film (flake) and rod geometries.  Alternatively, it is to have multidomain particles where closure domain will minimize the magnetic poles and consequently minimize the demagnetization factor.  Furthermore, by bringing particles closer to introduce exchange coupling among particles will significantly reduce the effect due to the demagnetization factor.

Our researches in this area focus on the development of various nanostructured materials based on nanowires, nanofibers, nanoflakes, etc.