Magnetic materials - a term commonly used for materials which exhibit strong magnetic properties, such as ferromagnetic or ferrimagnetic, further broadly classified as magnetically soft, hard, or semi-hard.¹⁾ The “soft-hard” naming convention is related to the ease of magnetisation rather than to the mechanical properties.

Magnetic hard drives rely on many types of magnetic and non-magnetic materials

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However, in general all materials are “magnetic” but they respond in various ways to magnetic field, depending on their atomic structure and ambient conditions, or at least do not significantly obstruct magnetic field. In that sense, even vacuum is “magnetic” because magnetic field can propagate through it and by definition²⁾ its magnetic permeability $μ_0$ is a universal physical constant in the SI system of units.³⁾

On the other hand, antiferromagnetic materials have internally ordered magnetic structure, but such that does not produce large values of susceptibility (i.e. appears to be “non-magnetic”). Yet, these materials find use in special magnetic applications such as magnetoresistive sensors in magnetic hard drives.⁴⁾

Magnetic field can be completely expelled from a superconducting body (Meissner effect) but this happens due to the induced surface electric currents, rather than magnetic response as such. However, from the outside, type I superconductors behave as if they were perfect diamagnets, with permeability of zero (comparing to vacuum which has permeability of unity).⁵⁾

Efficient energy transformation relies on electrical steels (soft magnetic materials) ^{Marvin L. Daniels, Public domain}

Brushless DC motor with ferrite magnets in the outer rotor and electrical steel and copper windings in the inner stator

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Magnetic properties of all pure chemical elements of practical importance were measured, with at least an order-of-magnitude accuracy (see the large illustration with the periodic table below). The elements can be broadly classified into diamagnetic and paramagnetic (weak magnetic properties) and ferromagnetic (strong magnetic properties). At room temperature only three elements are ferromagnetic: iron, cobalt, and nickel.

However, pure elements are rarely used because of their magnetic properties (but they can be used for other reasons, like for instance copper for making electric wires or noble gases for providing protective chemical atmosphere).

From engineering viewpoint, metal alloys and chemical compounds, even made from non-ferromagnetic elements, can exhibit very strong magnetic effects, which need to be optimised or tailored, by many means: chemical composition, mechanical forming, thermal processing (annealing), with or without magnetic field, etc.

Periodic table of elements, with magnetic properties⁶⁾ (at very low temperatures, and also high pressure, many elements become superconducting and hence strongly diamagnetic)

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Molar magnetic susceptibility of chemical elements at room temperature⁷⁾

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There are several ways in which materials can respond, and these different types of response are described by various types of magnetism:

• ferromagnetism
• ferrimagnetism
• antiferromagnetism
• paramagnetism
• diamagnetism
• superparamagnetism
• helimagnetism
• spin glass
• metamagnetism
• sperimagnetism
• micromagnetism
• frustrated magnetism

A wide range of materials is widely used in engineering applications, both “magnetic” and “non-magnetic”:

• soft magnetic materials
• hard magnetic materials
• semi-hard magnetic materials
• magnetorheological materials (ferrofluids and ferroelastomers)
• non-magnetic materials
• antiferromagnetic

These are described below.

Soft magnetic materials or rather “magnetically soft materials” are used in energy generation and transformation, mechanical force generation, and signal processing such as sensing and transmission.

A family of B-H loops (hysteresis loops) at various amplitudes of AC excitation, for grain-oriented electrical steel magnetised at 50 Hz

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The “softness” in the name refers to their magnetic response (ferromagnetism or ferrimagnetism), as they can be easily magnetised and demagnetised (especially when compared to “hard” materials). The B-H loop is narrow, so that the coercivity values are low. For example the standard IEC 60404-1 defines magnetically soft materials as such that have coercivity H_c below 1000 A/m.⁸⁾

Soft magnetic materials are used extensively in conversion of electric energy, both: to a different level (transformer) as well as to a different form (motor, generator). The largest power transformers can have magnetic cores weighting several hundreds tons.

Under AC conditions, maximum power converted by a magnetic core is a function of the level of flux density (the higher magnetic saturation the better) and magnetic losses (the lower the better). In low-frequency applications the saturation is the limiting factor. But in high frequency applications it is the loss, so magnetic cores may need to operate significantly below the saturation limit to avoid thermal damage.

Also, it is typically advantageous that magnetic permeability is as high as possible, especially in magnetic shielding applications, but also for high-sensitivity of sensors and transducers.

There are several groups of materials, and their use is dictated typically by the cost of a given solution.

For soft magnetic materials, the image below shows the summary of four types of characteristics: saturation, permeability, frequency range, and relative cost.

Overview of properties of soft magnetic materials: saturation, permeability, frequency range, material cost¹⁰⁾

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Optimum operating point P for a permanent magnet is where the product B and H reaches maximum BH_max¹¹⁾

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Hard magnetic materials or rather “magnetically hard materials” exhibit large coercivity H_c > 100 kA/m.¹²⁾

Once magnetised, they retain a significant amount of magnetic energy and become strong sources of magnetic field, without any need for power supply, so they are also referred to as permanent magnets or simply “magnets”.

The energy density of a magnet is proportional to the values of coercivity and remanence. The highest energy magnets such as NdFeB have mostly linear part of the B-H curve in the second quadrant, and the optimum operating point is such that the product B·H reaches the maximum (BHmax), as illustrated in the graph.

Because of the high coercivity of permanent magnets, there is a considerable difference in the B-H and J-H hysteresis loops. For the same reason, there are two values of coercivity _BH_c and _JH_c.

Magnets are used as sources of magnetic field, with three main areas of application:

• generation of mechanical force by attracting or repelling other magnets, electromagnets, or magnetic materials
• main source of magnetic field for electric motors, generators, and electromagnetic actuators
• auxiliary biasing magnetic field for sensors and transducers

Typical NdFeB magnets

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Typical ferrite magnets

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Overview of properties of hard magnetic materials: remanence, coercivity, temperature range, material cost¹³⁾

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Materials are classified as “semi-hard” mostly on the basis of their coercivity, with a range intermediate between the soft (the lower the better) and hard (the higher the better).

However, from a wider perspective, it is the specific mode of use of a given material that defines the classification.¹⁴⁾ There are three main types of applications for semi-hard magnetic materials:

• Low-density information storage (e.g. anti-theft device)
• High-density information storage (e.g. magnetic hard drive)
• Mechanical force generation or transmission (e.g. electropermanent magnet)

Overview of properties of semi-hard magnetic materials: remanence, coercivity, and energy density¹⁵⁾

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Electromagnetic detection coils in an anti-theft system, installed by the entrance/exit of a shop

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Retail of consumer products involves the risk of theft, especially with respect to smaller and expensive products such as consumer electronics or clothing. Electromagnetic phenomena are used in several technical implementations of anti-theft systems, which have to be of very low cost and reliable over significant distance to a detector (up to 2 m).¹⁶⁾

Anti-theft device storing just one bit of information; built into a sticker (top and bottom view)

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One such application involves semi-hard materials. Two strips of metal are packaged together in a low-cost tag, one is magnetically soft, the other is semi-hard, so that it can be magnetised without the use of excessive energy, and it will retain the magnetised state - therefore the information about the change of the state remains recorded.

The size of the strips of metal is such that they respond with a resonance, to a high-frequency electromagnetic field (e.g. 58 kHz). After the purchase, the checkout operator can run the tag over a strong magnetic field (magnet or electromagnet) and magnetise (or demagnetise) the semi-permanent strip. This alters the resonance point of the tag, such that the detection coils do not detect the resonance any more.¹⁷⁾

The tags must be cheap, because they are single-use only (and remain attached to the sold items), and their cost must be born by the retailer.

“Low-density” applies here, because effectively just one bit of information is stored - before/after the tag was processed as “sold”.

Hard drive is a high-density information storage device

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High-density information storage is used for digital applications in magnetic hard drives and magnetic tapes. In the past also magnetic cassettes (audio), floppy drives, and magneto-optic drives were used, but these were superseded by other solutions. Semi-hard materials are used in all such magnetic storage devices.

A layer of a semi-hard material is deposited on a suitable substrate (rigid for disks, flexible for tapes). The magnetic layer can be magnetised locally by a suitable recording head, and it is designed to retain the state of the local magnetisation, so that the reading head can read out the magnetic state and translate it into digital information (0 or 1).

The amount of information stored is directly proportional to the density of recording - the higher the density the more information can be stored with the same size of device, hence “high-density” is an appropriate name.

Currently, hard drive technology allows storing around 1 TB of data per 1 inch² (or 6.5 cm²), using semi-hard materials such as Co-Cr-Pt.^18)19)20)

For future applications the semi-hard materials are also going to be used (in magnetic recording), but complexity of technology is expected to increase, because of the superparamagnetic limit.²¹⁾

Cross-section view through a perpendicular recording hard disk structure (made from CoCrPt-SiO₂): a) diagram, b) TEM image^{22) Y. Zhang, A. Shakil, H. Wang, X. Li, H. Tang, A.A. Polycarpou, Nature, Scientific Reports, CC-BY-4.0}

TEM planar (top) views of the magnetic recording layer (CoCrPt-SiO₂)^{23) Y. Zhang, A. Shakil, H. Wang, X. Li, H. Tang, A.A. Polycarpou, Nature, Scientific Reports, CC-BY-4.0}

Semi-hard materials can be also used to transfer or generate mechanical forces.

One of the most basic applications is the needle of an ordinary magnetic compass.²⁴⁾ The needle cannot be made from a “soft” magnetic material because it has to remain magnetised, even if medium magnetic fields appear for some time in the vicinity. On the other hand, the needle cannot be made from a very strong magnet, such that it is not attracted to weakly magnetic materials.

There are also industrial application of semi-hard materials. Electropermanent magnets are used in lifting of ferromagnetic loads. Such lifts are safer than ordinary electromagnets because continuous supply of electricity is not required for generation of continuous force.

In certain applications such as mechanical couplings and clutches which require control of the amount of torque, semi-hard materials can be used as the magnetically active elements whose “remagnetisation” by continuous displacement against a permanent magnet provides a controlled amount of torque, due to mechanical forces arising from the work done on hysteresis loss of the active element. Such devices are used for example in the heads mounting caps on bottles in industrial quantities.²⁵⁾²⁶⁾

Ferrofluid on a flat surface, with strong magnet underneath

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Ferrofluids or magnetorheological liquids are made by suspending solid magnetic particles in a liquid. Appropriate formulation is required in order to prevent the particles from clumping together under the application of magnetic field, and this can be achieved for example by electrostatic forces, or by using surfacant (surface active coating).²⁷⁾

Industrial applications of ferrofluids are limited to very niche applications, additionally limited by the long-term stability of such liquids. Typically low viscosity, low vapour pressure, and high chemical inertness are desirable features for carrier liquid, surfacant and magnetic particles. Ferrofluids based on ferrite, with magnetisation up to 0.1 T can be achieved with approximately 25% volume ratio of ferrite particles to carrier fluid.²⁸⁾

However, they found use for example in controllable shock absorbers in some cars. The mechanical response can be adjusted by application of magnetic field which changes the effective viscosity of the liquid.

Magnetic domains observed with the Bitter method ^{Copyright © Xin Tong Xu}

The Bitter method of observations of magnetic domains relies on the application of effective ferrofluid with very low density of magnetic particles.²⁹⁾

The particles are attracted to the location of stray field correlated to the location of domains and domain walls and visualise their location and orientation. This technique can be used with the “wet” method with the fluid present, or with the “dry” method after the liquid is evaporated.³⁰⁾

For large domains, for example as in grain-oriented electrical steel a portable device such as magnetic domain viewer can be used.³¹⁾

Similar techniques are employed in magnetic non-destructive testing, in which spray-on liquids are used for detection of cracks in ferromagnetic structures. Stray magnetic field is produced for example by application of a magnetising yoke with a permanent magnet.

Magnetorheological elastomer - rubber block filled with magnetic particles

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Magnetorheological elastomers are elastomers (polymers) with embedded magnetic particles.³²⁾

Such approach is utilised in bonded magnets which use polymer as the bonding agent. It is a fairly inexpensive method employed for making low-cost fridge magnets, with injection or compression moulding process. It is possible to dispose such sheet of magnet on a mechanically flexible substrate, thus achieving a flexible magnet. The energy density of such magnets is low, because the magnetic particles cannot be packed to a similar density as for example in the sintering process used for high energy density magnets. Therefore, the achievable magnetic forces are low and usable only for non-critical applications in consumer products.

For magnetically soft materials, the magnetic permeability of such composite material is proportional to the ratio of magnetic particles to the non-magnetic matrix, and it is quite low, less than 100 for typically investigated materials.³³⁾

Industrial applications for such materials are limited, even though there are attempts at applying the materials to electromagnetic actuators.³⁴⁾ They can be also used for sensing applications where mechanical flexibility is required.³⁵⁾

In a common language, “non-magnetic” are those materials which do not exhibit strong magnetic response - they have low relative permeability μ_r, very close to unity, or susceptibility close to zero (similar to vacuum).³⁶⁾

In engineering applications the permeability of such materials is typically assumed to be unity (same as vacuum), with negligible error.³⁷⁾ Diamagnets, paramagnets and antiferromagnets are utilised for their lack of magnetic response (non-magnetic). Antiferromagnets are used in some magnetic sensors such as spin valves for their magnetic properties.

Permeabilities of magnetic materials (e.g. ferromagnets) are much higher than non-magnetic materials (e.g. vacuum, diamagnets and paramagnets)

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All substances exhibit the diamagnetic effect due to orbital motion of electrons. They are always repelled from the applied magnetic field, but the effect is very small⁴²⁾, with the forces negligible in engineering applications. However, it can be demonstrated that a piece of diamagnetic pyrolytic graphite can levitate above a magnet.⁴³⁾

Nevertheless, these forces are too small to be useful for industrial or engineering applications. Therefore, typical diamagnets are treated as “non-magnetic”.

Permanent magnet levitating above a superconductor placed in a liquid nitrogen ^{Copyright © CERN, Piotr Traczyk}

Superconductors are said to be perfect diamagnets, but the mechanism is different, because the macroscopic surface currents are responsible for repelling the magnetic field.⁴⁴⁾

Magnetic permeability of superconductors is zero (compared to 1 of vacuum's) and the repulsion is strong enough to levitate relatively large amount of mass. However, this property of superconductors is rarely used, because much stronger forces can be achieved from electromagnetic effects, by passing current through the superconducting wire or coil.

Superconductors can be used for shielding of magnetic field, because the expel magnetic field from their inside.⁴⁵⁾

The diamagnetic contribution is masked in some materials by the paramagnetic effect, which concentrates the applied field and produces force which always attracts, regardless the polarity of the magnetic field.⁴⁶⁾

The paramagnetic effect is somewhat stronger than diamagnetism, but still for most practical applications can be neglected, and the material can be treated as “non-magnetic”.

However, all magnetic materials become paramagnetic at sufficiently high temperatures (above Curie temperature).^47)48)49) Therefore, in the vicinity of the critical temperature the material can be at the transition for example between ferromagnetic and paramagnetic state and the forces will change proportionally to the magnetic state of the material.

Antiferromagnets have two opposing magnetic sub-lattices

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Antiferromagnets are materials in which there are two magnetic sub-lattices which exactly oppose each other. Internally their are magnetically ordered, but the magnetic contributions cancel each other and on the outside the material is indistinguishable from a paramagnet.⁵⁰⁾

Because they are ordered, at sufficiently high temperature (Néel temperature)⁵¹⁾ they undergo a transition to an ordinary paramagnetic state. In either magnetic state, the permeability and forces are small and thus for most engineering applications the materials are “non-magnetic”.

However, the antiferromagnetic state can be utilised in some magnetic sensors such as spin valves, either by directly employing an antiferromagnetic layer, or by creating a similar behaviour by spacing ferromagnetic layers by a precise amount.⁵²⁾

Pure vacuum is devoid of any matter which could provide additional response to magnetic field.

Magnetic field in “nonmagnetic” vacuum can bend the path of moving electrons ^{by M. Białek, Wikimedia Commons, CC-BY-SA-3.0}

However, magnetic field penetrates vacuum, and the ratio between the resultant magnetic flux density B and the applied magnetic field strength H is known as the magnetic constant or permeability of vacuum $μ_0$ = 4·π·10^-7 H/m, with the relative magnetic permeability of exactly 1.

The magnetic field penetrates the vacuum in a lossless way.

There is no force between the vacuum and the magnetic field and therefore by the same token as for the paramagnets and diamagnets, the vacuum is treated as “non-magnetic” in magnetic circuits.

• Types of magnetism
• Superconductivity