Permanent magnet applications

Journal of Magnetism and Magnetic Materials 248 (2002) 441–456

Topical review

Permanent magnet applications

J.M.D. Coey*

Physics Department, Trinity College, Dublin 2, Ireland

Received 24 April 2002

Abstract

Rare-earth permanent magnets are ideally suited to generate magnetic fields comparable to their spontaneous

polarization JS: Near-square hysteresis loops and large values of the coercivity and anisotropy fields greatly simplifymagnet design, as each magnet block is effectively transparent to the magnetic fields produced elsewhere in the magnet

assembly. The fields generated by compact and efficient magnet structures requiring no continuous expenditure of

energy can be static or variable, uniform or nonuniform. Permanent magnets are fully competitive with electromagnets

for fields up to 2T, and fields as high as to 5T can be produced in a small volume. When a field with a rapid spatial

variation is required, permanent magnets may offer the only practicable solution. Both permanent magnet structures

and the uses to which they are put are reviewed, classifying the magnet applications in terms of the nature of the field,

the effect on the magnet and the physical effect exploited. r 2002 Elsevier Science B.V. All rights reserved.

PACS: 07.55.Db; 75.50.Ww; 75.60�d; 85.70�w

Keywords: Rare-earth permanent magnets; Magnetic flux sources; Variable magnetic fields; Permanent magnetic allocations; Halbach

cylinders; Couplings; Bearings; Magnetic separation; Motors; Actuators

1. Introduction

Permanent magnets are unique in their ability todeliver magnetic flux into the airgap of a magneticcircuit without any continuous expenditure ofenergy [1]. The flux density may be uniform ornonuniform, steady or time varying. Magnetapplications can also be classified by their influ-ence on the magnet or by the physical effect that isbeing exploited. A summary of magnet applica-tions is provided in Table 1. Although the list isquite extensive, permanent magnets are really justbeginning to be appreciated and exploited. On

account of their versatility and economy, perma-nent magnets are finding numerous new applica-tions, besides replacing electromagnets for manypurposes.We first expand briefly on the different physical

effects mentioned in the Table. A steady uniformfield may be used to generate torque C or alignexisting magnetic moments m since C ¼ m .B: Thecorresponding quantum phenomenon is Zeemanspliting of atomic or nuclear energy levels.Particles of charge q moving through the uniformfield with velocity v are deflected by the Lorentzforce F ¼ qv .B; which causes them to move in ahelix in free space with the cyclotron frequencyfc ¼ eB=2pme; 28GHz/T for an electron. Whenthe electrons are confined to a conductor of length

*Tel.: +353-1-6081470; fax: +353-1-6711759.

E-mail address: [email protected] (J.M.D. Coey).

0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 3 3 5 - 9

L aligned perpendicular to the field, as in thearmature of a motor or actuator, they constitute acurrent I ; and the Lorentz force leads to thefamiliar expression F ¼ BIL: Conversely, movinga conductor through the field produces an inducedemf given by Faraday’s law e ¼ �dF=dt where Fis the flux threading the circuit of which theconductor forms a part.Spatially nonuniform fields offer another series

of potentially useful effects. They exert a force on amagnetic moment given by the energy gradient,F ¼ =ðm .BÞ: They also exert nonuniform forceson charged particles, which can be used to focusion or electron beams or to generate intenseelectromagnetic radiation in a synchrotron wig-gler. The ability of rare-earth permanent magnetsto generate complex flux patterns with rapidspatial variation (=B > 100T/m) is unsurpassedby any electromagnetic device. The Amperiansurface current equivalent to a magnet withJSE1T is 800 kAm�1. Solenoids, whether resistiveor superconducting, have to be several centimetersin diameter to accommodate the requisite Ampere-turns, whereas blocks of rare-earth or ferritemagnets of any size can be assembled in anydesired orientation as close to each other asnecessary.Variable or time-varying fields can be produced

by displacing or rotating the magnets, or bymoving soft iron in the magnetic circuit. Theymay induce an emf according to Faraday’s law

and exert forces on the resulting Eddy currents in aconductor. Alternatively, they may be used toswitch on or measure continuously the othereffects of a field, for example, in a magnetizationmeasurement.Viewed from the standpoint of the permanent

magnet, the applications are classified as static ordynamic according to whether the working pointof the magnet in the second quadrant of thehysteresis loop is fixed or moving. Its positiondepends on the magnitude of the H-field to whichthe magnet is subjected, which depends in turn onthe magnet shape, the airgap and the fieldsgenerated by any electric currents flowing in thevicinity. On account of their square loops, orientedferrite and rare-earth magnets are well-suited fordynamic applications that involve changing fluxdensity in the magnet. Ferrites and bondedmetallic magnets also minimize Eddy currentlosses. The working point changes wheneverpermanent magnets move relative to each other,when the airgap changes or if there are time-varying currents. In the former cases, there ismechanical recoil when the working point movesalong the loop as the airgap changes from anarrow one to a wider one during operation. In thelatter case, the recoil is active because the magnetsin motors and similar devices are subject to an H-field during operation as a result of currents in thecopper windings. The field is greatest at startup, orin the stalled condition. Provided m0Hc exceeds Br;

Table 1

Summary of permanent magnet applications

Field Magnetic effect Type Examples

Uniform Zeeman splitting Static Magnetic resonance imaging

Torque Static Alignment of magnetic powder

Hall effect, magnetoresistance Static Sensors, read-heads

Force on conductor Dynamic Motors, actuators, loudspeakers

Induced emf Dynamic Generators, microphones

Nonuniform Force on charged particles Static Beam control, radiation sources (microwave, uv; X-ray)Force on magnet Dynamic Bearings, couplings, Maglev

Force on paramagnet Dynamic Mineral separation

Time varying Varying field Dynamic Magnetometers

Force on iron Dynamic Switchable clamps, holding magnets

Eddy currents Dynamic Metal separation, brakes

J.M.D. Coey / Journal of Magnetism and Magnetic Materials 248 (2002) 441–456442

it is possible to drive the working point momenta-rily into the third quadrant of the B:H loopwithout demagnetizing the permanent magnet.The intrinsic coercivity iHc may be as importanta figure of merit as the energy product ðBHÞmax inthis type of application.The properties of some typical magnet grades

are summarized in Table 2. Magnets nowadays areusually squat cylinders with a demagnetizingfactor NE1

2; because the working point then

corresponds to maximum energy product [1]. Asthe energy product of permanent magnets hasincreased, there has been a trend towards minia-turization and moving-magnet designs. Permanentmagnet devices have become smaller and lighter.The number of parts is reduced, for example, byshifting the magnets of a brushless DC motor tothe rotor and moulding the magnets together withthe shaft and gear in one piece. Moving magnetshave low inertia, and the stationary windings canbe thermally heat-sunk. The benefit of permanentmagnets in small magnetic circuits can be appre-ciated by comparing a small disk-shaped magnetwith a coil having the same magnetic moment. Adisk of diameter 8mm and height 2mm made of amaterial with magnetization M ¼ 1MA/m hasmagnetic moment mE0:1Am2. An equivalent coilof the same diameter would require an impossible2000A turns.An overall breakdown of permanent magnet

applications is given in Fig. 1. Hard ferritesaccount for 55% of the market by value, rare-earth magnets are at 35%, and most of theremainder is alnico. In volume terms, globalproduction averages to about 80 g of hard ferrite

and 1 g of rare-earth magnet for everyone onEarth.Motors and actuators account for most of the

magnets produced. Electrical machines can run attemperatures in excess of 1001C, and there is anongoing effort to develop new materials that canbe used up to 4001C [3]. Magnetization andcoercivity naturally decline as the Curie point isapproached; the temperature coefficients of thesequantities around ambient temperature are listedin Table 3. The maximum temperatures at which

Table 2

Characteristics of typical commercial-oriented magnets

Br (T) JS (T) iHc

(kAm�1)BHc

(kAm�1)

ðBHÞmax(kJm�3)

SrFe12O19 0.41 0.47 275 265 34

Alnico 1.25 1.40 54 52 43

SmCo5 0.88 0.95 1700 660 150

Sm2Co17n 1.08 1.15 800 800 220

Nd2Fe14B 1.28 1.54 1000 900 300

n Intergrown with 1:5 phase.

Fig. 1. Summary of permanent magnet applications.

Table 3

Temperature coefficients and maximum operating temperatures

for permanent magnets

TC (1C) dMS=dT (%) dHc=dT (%) Tmax (1C)

SrFe12O19 450 �0.20 0.40 300

Alnico 800 �0.02 0.03 500

SmCo5 720 �0.04 �0.20 250

Sm2Co17n 820 �0.03 �0.20 350

Nd2Fe14B 310 �0.13 �0.60 120

n Intergrown with 1:5 phase.

J.M.D. Coey / Journal of Magnetism and Magnetic Materials 248 (2002) 441–456 443

typical magnets can safely be used are alsoindicated in the table.

2. Applications

An account of the main applications is nowgiven, with emphasis on permanent magnetstructures as flux sources [4–6]. When blocks ofrare-earth or ferrite magnets are placed in contact,the field of one magnet does not significantlyperturb the magnetization of its neighbours,because the longitudinal susceptibility is zero fora square hysteresis loop and the transversesusceptibility MS=Ha is only of order 0.1, sincethe anisotropy field Ha is much greater than themagnetization (Table 4). The directions of magne-tization of two blocks of SmCo5 in contact withtheir easy directions perpendicular, for example,will deviate by less than a degree from the easy

directions. A consequence of the rigidity of themagnetization is that the superposition of fluxproduced by rare-earth permanent magnets islinear, and the magnetic material is effectivelytransparent, behaving like vacuum with perme-ability m0: Transparency and rigidity greatlysimplify the design of magnetic circuits [2].Theflux density in the airgap BgðrÞ scales with, but isnot limited by the remnant polarization of themagnet material;

BgðrÞ ¼ KðrÞBrðrÞ:

Here, KðrÞ is the geometric constant of themagnetic circuit; when K > 1; the circuit achievesflux concentration [4].

2.1. Flux sources

(a) Uniform fields: The magnetic field producedby a point dipole of moment m (Am2) is quite

Table 4

Intrinsic magnetic properties of phases used in permanent magnet manufacture

Compound TC (1C) Ms (MAm�1) Js (T) K1 (MJm�3) Ha (MAm�1) J2s =4m0 (kJm�3)

BaFe12O19 Hexagonal 450 0.38 0.47 0.25 1.1 44

SmCo5 Hexagonal 720 0.84 1.05 17 32 219

Sm2Co17 Rhombohedral 827 1.04 1.30 3.3 5.1 336

Nd2Fe14B Tetragonal 312 1.29 1.61 4.9 6.1 516

Sm2Fe17N3 Rhombohedral 476 1.23 1.54 8.6 11.2 472

Fig. 2. Comparison of the magnetic field pattern produced: (a) by a point dipole of moment m; and (b) a line dipole with moment l perunit length.


nonuniform (Fig. 2a). In polar coordinates

Hr ¼ 2m cos y=4pr3; Hy ¼ m sin y=4pr3;

Hf ¼ 0 ð1Þ

so the magnitude and direction of H depend bothon r and y: The field due to an extended line dipoleof moment l (Am) is different

Hr ¼ lcos y=2pr3; Hy ¼ lsin y=2pr3;

Hf ¼ 0 ð2Þ

so the magnitude of H ; OðHr2 þ Hy2 þ Hf2 Þ; isactually independent of y; its direction makes anangle Z ¼ 2y with the orientation of the magnet(Fig. 2b).By assembling long cylindrical magnet segments

around a hollow bore it is possible to create a fieldwhich is uniform within a certain region of spaceand zero elsewhere [4–6]. Choosing the orientationof each segment appropriately, the fields will alladd at the centre. In the transverse field designshown in Fig. 3a, the outer surface will be anequipotential provided t=r ¼ O2� 1; in which casethe flux density in the airgap is 0:293Br [2].Multiples of this field can be obtained by nestingsimilar structures inside each other. Shimming to

compensate any imperfections in the magnets orassembly is possible by placing appropriatecompensating dipoles in the corners. Open cylin-ders or permanent magnets with iron yokes(Fig. 3b) provides highly uniform fields (betterthan one part in 105) which may be used formagnetic resonance imaging. Permanent magnetflux sources supply fields of order 0.3 T in whole-body scanners. Fields are lower than those ofcompeting superconducting solenoids, but there isno need for any cryogenic installation. Nuclearmagnetic resonance spectrometers with permanentmagnets flux sources are finding applications forquality control in the food, polymer and construc-tion industries.Fig. 3c shows a different design where the

direction of magnetization of any segment is atan angle Z ¼ 2y’ from the vertical axis. Accordingto Eq. (2), all segments now contribute tocreate a uniform field across the airgap in thevertical direction. Unlike the structure of Fig. 3a,the radii r1 and r2 can take any values withoutcreating a stray field outside the cylinder.The device is commonly known as a Halbachcylinder, although it was suggested earlier byMallinson [7]. The flux density in the airgap of a

Fig. 3. Cross-section of some permanent magnet structures which generate a uniform magnetic field in the direction shown by the

hollow arrow. Magnets are unshaded; the shaded material is soft-iron.


long cylinder is

B ¼ Br lnðr2=r1Þ; ð3Þ

where r1 and r2 are the inner and outer radii. Inpractice, it is convenient to assemble the devicefrom n trapezoidal segments, as illustrated inFig. 3d for n ¼ 8: In that case, an extra factor½sinð2p=nÞ�=ð2p=nÞ must be included on the right-hand side of Eq. (3). Furthermore, the cylindersare never infinitely long; the length is typicallycomparable to the diameter, so the geometricconstant K is reduced by an amount DK ¼ðz=2Þ½1=z0 � 1=zi� þ ln½ðz þ z0Þ=ðz þ ziÞ� where z isthe distance from the centre, z0 ¼ ðz2 þ r20Þ

1=2 andzi ¼ ðz2 þ r2i Þ

1=2 [8]. For example, the flux densityat the centre of an octagonal cylinder withr1 ¼ 12mm, r2 ¼ 40mm and length 80mm madeof a grade of Nd–Fe–B having Br ¼ 1:20T isBg ¼ 1:25T, compared to the value of 1.44 Tcalculated from Eq. (3). Here is an example of anironless magnetic circuit with K > 1; illustratingthe idea of magnetic flux concentration. It is alsopossible to introduce iron into the airgap toenhance the field at the centre (Fig. 3e).Large cylindrical magnets of the Halbach-type

weighing several tonnes are used for magneticannealing of wafers up to 200mm in diameter in afield of E1T for the manufacture of spin valveread heads and magnetic random-access mem-ories.Assemblies composed of pairs of magnetized

wedges allow great flexibility in the shape of thecavity while offering efficiencies comparable tothose of Halbach cylinders [9]. A differentsimplification of the basic structure employstransversely magnetized cylindrical rods, as shownin Fig. 3e [10] This allows both longitudinal andtransverse access to the cavity. The geometricalconstant at the centre for a set of n rods which arejust touching is

K ¼ ðn=2Þsin2ðp=nÞ: ð4Þ

By increasing n; the central region in which thefield is uniform is enlarged, but the magnitude ofthe field itself is reduced.The limit to the fields that can be generated

using permanent magnets is about 5T, which hasrecently been achieved in a tiny cavity in a

spherical magnet structure [11]. The limit is set inpart by the coercivity of the material. The verticalsegments in Fig. 3 are subject to a reverse H-fieldequal to the field in the bore. But there is also apractical size limitation imposed by the exponen-tial increase in dimension of Eq. (3). Admitting amaterial existed with Br ¼ 1:5T and m0Hc ¼ 5T,the diameter required to achieve 5 T in a 25mmbore is 700mm. Such a structure 400mm highwould weight about a tonne.(b) Nonuniform fields: The cylindrical configura-

tions of Fig. 3 may be modified to produce avariety of nonuniform fields such as quadrupolefields, particularly useful for charged-particlebeam control [12]. Higher multipole fields thandipole are obtained by having the orientation ofthe magnets in the ring vary as Z ¼ ð1þ ðn=2ÞÞy;where n ¼ 2 for a dipole field, n ¼ 4 for aquadrupole and so on. The field at the centre ofthe quadrupole is zero, but whenever the particlebeam deviates it experiences an increasing fieldwhich causes its trajectory to curve back to thecentre. Coaxial dipole rings known as ‘‘magne-trons’’ are used in sputtering systems to increasethe ionization of the plasma near the target byextending the paths of the electrons into helicesaround the field lines. The magnets in an ion pumphave a similar function. The magnetrons indomestic microwave ovens are devices whereelectrons emit cyclotron radiation as they movein trajectories determined by the field of a ferritering magnet.A variant of the normal multipole Halbach

configuration is the external Halbach configura-tion where the orientation Z varies as ð1� ðn=2ÞÞyUThe multipole field is then produced outside thecylinder. The case of n ¼ 2 (uniform magnetiza-tion) produces a dipole field outside the cylinder,and zero field in the bore. The case n ¼ 4;illustrated in Fig. 4c, produces a quadrupole fieldoutside the cylinder and zero field inside. Theexternal Halbach designs are useful for the rotorsof permanent magnet electric motors.Other arrangements of cylindrical magnets

produce a uniform magnetic field gradient alonga particular direction (Fig. 4d). Field gradients areespecially useful for exerting forces on othermagnets.


Another type of permanent magnet structurecreates an nonuniform magnetic field along theaxis of the magnet, which is the direction ofmotion of a charged particle beam [2]. Microwavepower tubes such as the travelling wave tube aredesigned to keep the electrons moving in a narrowbeam over the length of the tube and focussingthem at the end while coupling energy from anexternal coil. The design with SmCo5 magnetsgenerating a periodic axial field in Fig. 5a iscompact, and uses no power. One period of thestructure in Fig. 5a generates an axial fieldgradient, known as a cusp field. Uses of cuspfields include the stabilization of molten metalflows. Fields of alternating direction are also usedin magnetic water treatment.Insertion devices for generating intense beams

of hard radiation (uv and X-ray) from energetic

electron beams in synchrotron sources create aperiodic transverse field. These devices are knownas wigglers, since they cause the electrons to travelin a sinuous path. Similar structures are used infree-electron lasers. A design including segmentsmagnetized in the parallel direction to concentratethe flux is shown in Fig. 5b.(c) Variable fields: Fields can be varied by

changing the airgap, or by some movement of themagnets or iron in a structure with respect to eachother. The working point is displaced as themagnets move so these devices involve mechanicalrecoil. A simple type of variable flux source is aswitchable magnet (Fig. 6). These are often used inholding devices, where a strong force is exerted ona piece of ferrous metal in contact with themagnet. The working point shifts from the opencircuit point to the remanence point where H ¼ 0

Fig. 4. Cross-section of some permanent magnet structures which generate non-uniform magnetic fields (a), (b) quadrupole fields,

(c) an external quadrupole field, and (d) a field gradient.


as the circuit is closed. The maximum force F thatcan be exerted at the face of a magnet of area Am

where the flux density is Br is given by

F=Am ¼ B2r=2m0: ð5Þ

Forces of up to 40N cm�2 can be achieved forBr ¼ 1T.Simple force applications in catches and closures

consume large amounts of sintered ferrite. Bonded

ferrite magnetized in strips of alternating polarityis widely used for fixing signs and light objects tosteel panels such as refrigerator doors.To create a uniform variable field, two Halbach

cylinders of the type shown in Fig. 3 with the sameradius can be nested inside each other as shown inFig. 7a. Then by rotating them through an angle7a about their common axis, a variable field2 cos a Br lnðr2=rlÞ is generated. No torque wouldbe needed to rotate two ideal Halbach cylinders,but in practice some torque arises from thesegmented structure and end effects [13].Another solution (Fig. 7b) is to rotate the rods

in the device of Fig. 3f [14]. By gearing a manglewith an even number of rods so that the alternaterods rotate clockwise and anticlockwise though anangle a; the field varies as Bmax cos a: Furthersimplification is possible with a magnetic mirror, ahorizontal sheet of soft iron containing the axis ofsymmetry which produces an inverted image of themagnets, and halves the number required [2]. Thetorque needed to vary the field in a mangleincreases with decreasing number of rods. Avariable field gradient can also be obtained in themangle [14]. A movable axial field gradient can beobtained with nonuniformly magnetized rods [15].

Fig. 5. Periodic flux sources: (a) a magnet for a microwave

travelling-wave tube and (b) a wiggler magnet used to generate

intense electromagnetic radiation from an electron beam.

Fig. 6. Two design for switchable permanent magnets.


These permanent magnet variable flux sourcesare compact and particularly convenient touse since they can be driven by stepping orservomotors and they have none of the highpower and cooling requirements of a comparableelectromagnet. A typical commercial flux source ofthe design shown in Fig. 7a uses 20 kg of Nd–Fe–Bmagnets to generate a fields up to 2.0 T in a25mm bore. Rotating or alternating fields canbe generated by rotating the magnets continu-ously.A variable flux source can also be made from a

uniformly magnetized magnet ring with a hole (then ¼ 2 external Halbach cylinder) and a movableiron sheath (Fig. 7c). When the sheath fully coversthe cylinder, flux is confined within the bore, wherepreviously it was zero [16].Permanent magnet variable flux sources are

expected to displace resistive electromagnets togenerate fields of up to about 2.0 T, but theycannot compete with superconducting solenoids inthe higher field range.

2.2. Couplings and bearings

Permanent magnets are useful for couplingrotary or linear motion when no contact betweenmembers is allowed [17]. Fig. 8 illustrates thedesign of two magnetic bearings, a simple rotarycoupling, and a magnetic gear. Forces dependquadratically on the remanence of the magnets, soit is advantageous to select material with a largepolarization. If the coupling slips, the magnetsmay be subjected to a substantial reverse field, sohigh coercivity is also needed. Rare-earth magnetsare ideal. The maximum torque can be varied byadjusting the airgap, and values of order 10Nmmay be achieved in couplings a few centimeters indimension.Magnetic bearings are simple, cheap and reli-

able. They are best suited to high-speed rotarysuspensions, in flywheels or turbopumps forexample. Linear suspensions have been tested inprototype magnetically levitated transportationsystems. The simplest bearings are made of two

Fig. 7. Permanent magnet variable flux sources: (a) a double Halbach cylinder, (b) a four-rod magnetic mangle, and (c) an external

dipole ring with a movable iron sheath.


ring-shaped magnets in repulsion (Fig. 8b and c).Some configurations provide radial restoring forceprovided the axis is prevented from shifting ortwisting. Others support a load in the axialdirection, but must be prevented from moving inthe radial direction. The linear magnetic bearingsprovide levitation along a track, but lateralconstraint is required. It is impracticable to equipa great length of track with permanent magnets, soinstead levitation may be provided by repulsionfrom Eddy currents generated in a track ofaluminium plates, or by attraction of the magnetson the vehicle to a suspended iron rail.It is a feature of bearings made entirely of

permanent magnets that a mechanical constraint(or active electromagnetic support) is generallyrequired in one direction. Unfortunately, it isimpossible to design a static field configurationwhich will draw a small magnet towards a fixedpoint in space. The field near such a point wouldhave to satisfy the condition that dB=dx; dB=dy

and dB=dz are all negative, which contradictsMaxwell’s equation = .B ¼ 0: The impossibility of

stable magnetostatic levitation of a magnet at apoint is known as Earnshaw’s theorem.Stable levitation is possible, however, when

there is another component, specifically a dia-magnet or superconductor, which creates anupright image of the permanent magnet. As themagnet moves away from a position of unstableequilibrium, there is a repulsive restoring force asit approaches its image (Fig. 9). The maximumrepulsive force for perfect flux expulsion from asuperconductor (susceptibility w ¼ �1) is given byEq. (5). Normal diamagnets, with wE� 10�4 to�10�5, produce much weaker images, but they canbe used in conjunction with permanent magnets tostabilize a metastable point of levitation for asmall magnet.Greater repulsive forces could be achieved using

superconducting ‘permanent magnets’. These areusually blocks of melt-textured high-temperaturesuperconductor, in which the trapped flux densityBr can be as high as 14.4 T [18]. Huge forces, oforder 108Nm�2 (tonnes per square centimeter),are envisagable, but major drawbacks are the

Fig. 8. Some magnetic bearings and couplings: (a) is a linear bearing, (b) and (c) are rotary bearings, (d) is a face-type coupling and

(e) is a magnetic gear.


difficulty in establishing the flux in the super-conductor, and the need for cooling.

2.3. Magnetic separation

Magnetic separation is a technology based onnonuniform or time-varying magnetic fields whichaffords great economic and social benefits. Whenthe moment m is induced by a field in material ofvolume V and susceptibility w; the force is

F ¼ ð1=2Þm0wVrðH2Þ: ð6Þ

To separate ferrous and nonferrous scrap or toselect minerals from crushed ore on the basis oftheir magnetic susceptibility it is sufficient to useopen gradient magnetic separation where materialtumbles through a region where there is a strongmagnetic field gradient. A gradient of 100Tm�1

produces separation forces of order 108Nm�3.High-gradient magnetic separation is suitable

for capturing weakly paramagnetic material suchas red blood cells. Here, a liquid containing theparamagnetic solids in suspension passes througha tube filled with a fine ferromagnetic mesh or steelwool which distorts the flux pattern in an appliedfield, creating local field gradients as high as105 Tm�1 where separation forces can reach1011Nm�3. The paramagnetic material remainsstuck to the wires until the external field isswitched off, when it may be flushed out of thesystem. Switchable permanent magnets can beused to create the field.A different principle is employed in electromag-

netic separation to sort nonferrous metal such asaluminium cans from nonmetallic material in astream of refuse (Fig. 10). A fast-moving conveyor

belt carries the rubbish over a static or rotatingdrum with embedded ferrite or rare-earth magnets.The relative velocity of the magnets and the refusemay be 50ms�1. Eddy currents induced in themetal create a repulsive field, and the metal isthrown off the end of the belt in a differentdirection to the nonmetallic waste. In electromag-netic separation, deflection depends on the ratio ofconductivity to density, so it is possible to separatemetals such as aluminium, brass and copper.

2.4. Sensors

Magnetic sensors are based on detecting avarying field in an airgap using a Hall effect ormagnetoresistance probe which delivers a voltageproportional to B: Magnetic position and speedsensors are used in automobile system controls,where they offer reliable noncontact sensing in ahostile environment involving dirt, vibration andhigh temperatures. Angular position sensors builtinto electronically commutated motors can besimple Hall or magnetoresistance sensors whichdetect the stray field produced by a multipolerotor.

2.5. Motors and actuators

Motors and actuators whose operation dependson permanent magnets are produced in hugequantities, >108 per year. A household whichowned two or three motors 50 years ago may nowpossess a hundred, in domestic appliances, audio,video and computer equipment, clocks, watches,toys and the car. Most of these are small DCpermanent magnet motors. The high-energy

Fig. 9. Images of a permanent magnet in: (a) a soft ferromagnet and (b) a superconductor or strong diamagnet.


product high anisotropy of the rare-earth perma-nent magnets makes it possible to realize compact,low-inertia, high-torque devices—stepper motors,actuators, brushless DC motors—which are themeans for electronically regulated motion control.Ferrites are produced in huge quantities forlow-cost motors for consumer products, includingautomobiles. DC servomotors are found inmachine tools, robots and other industrial ma-chinery. Permanent magnets can also be usedto advantage in large industrial drives, bringingsavings in weight, energy and material costs.The ability to fabricate ferrite or rare-earthmagnets in any desired shape has led to many

permutations on a few basic electrical machinedesigns.An actuator is an electromechanical device with

a limited linear or angular displacement [19]. Thedefinition encompasses loudspeakers, micro-phones, moving-coil meters, print-head actuators,disk-drive head actuators, actuators for industrialrobots, pneumatic pumps, car door locks, noiseand vibration control using antiphase displace-ment and many others. Usually, the airgap is fixed,and the working is dynamic due to the H-fieldproduced by current windings. Actuators tend tobe rather simple mechanical structures delivering aforce directly to move a load. Three basic

Fig. 10. Electromagnetic separation with permanent magnets.


configurations are moving-coil, moving-magnetand moving-iron.Moving-coil loudspeakers have been built with

permanent magnets for over 50 years. Flux isdirected into a radial airgap where the voice coil issuspended, attached to a light, rigid cone. Theforce on the coil is proportional to the flux densityin the airgap Bg; and the acoustic power varies asB2g; which is maximized by operating near the

ðBHÞmax point of the magnet. Good results areobtained when Bg exceeds about 0.5 T, and themass of the voice coil is less than a gram. Designswith cheap flat ferrite ring magnets are inefficientas there is much flux leakage. Efficient moving-magnet designs are feasible using Nd–Fe–B, wherea cylindrical magnet is glued to the cone and astationary drive-coil surrounds it.A large class of voice-coil actuators are similar

in principle to a loudspeaker. Rapid dynamicresponse is assured by the low mass of the voicecoil assembly and the low inductance of the coil inthe airgap. A common planar configuration usedfor head positioning in computer hard-disk drivesis shown in Fig. 11. Here a flat coil is attached to alever which allows it to swing in a limited arcbetween two pairs of rare-earth magnets. Thedesign requires Nd–Fe–B with the highest possible

energy product (>400 kJm�3). Access time atconstant acceleration a is proportional to 1=Oa;hence to 1=OBg: High-grade Nd–Fe–B is also usedin the actuators in laser compact-disc players. It isremarkable that various types of voice–coil actua-tors account for about 40% of Nd–Fe–B produc-tion (Fig. 1).Moving-magnet actuators may be of the linear

or rotating variety. They offer low inertia and noflying leads. Linear reciprocating actuators with astroke of several millimeters are used in pumpsoperating at frequencies of order 50Hz, designedto correspond to the resonant frequency of themechanical system. Rotary actuators can beregarded as electric motors with restricted travel.Moving iron actuators likewise may be linear orrotary. Reed switches, where two flat soft ironreeds are drawn into contact by a magnetic field,can be activated with a solenoid, or simply bymoving a magnet.A vast range of motors can be designed with

magnets, their power ranging from microwatts forwristwatch motors, to hundreds of kilowatts forindustrial drives [20]. A common DC motor designis shown in Fig. 12a. The permanent magnet onthe fixed outer section, known as the stator, createsa field at the windings of the rotor. A mechanical

Fig. 11. A flat voice-coil actuator for a personal-computer disk drive.


commutator with brushes distributes current tothe windings in such a way that the torque on therotor is always in the same sense. Conversely, thedevice will also function as a generator, producingan emf U if it is driven at an angular velocity o: Ina DC servomotor, the torque or the angularvelocity is controlled by modifying the appliedvoltage. Simple velocity control is based onmonitoring the back-emf U ; but more sophisti-cated control systems use a tachogenerator(a small DC motor coupled to the drive shaft) ora precise position encoder to generate the voltagefed back to control the output power.The motor design may be modified, as shown in

Fig. 12b, to eliminate the mechanical commutatorwhich is a source of wear and sparking. In thebrushless DC motor, the magnets are situated onthe rotor, and the armature windings, now locatedon the stator, are energized in an appropriatesequence by means of power electronics. Electro-nically commutated motors are reliable and theyare particularly suited to high-speed operation,o > 30 c/s (>1000 rpm). Position sensors form anintegral part of the device since the winding to beenergized depends on the position of the rotor.One limitation is the maximum working tem-

perature of high remanence grades of Nd–Fe–Band ferrite which cannot match the runningtemperatures of many classical induction motors(Table 4). For special applications, this problemcan be solved by using new, high-temperaturegrades of Sm–Co [3]

By unrolling the armature, a linear motor isobtained. Flattening the rotor into a disk producesa pancake motor. The low moment of inertiameans that high angular accelerations are possible,especially when Nd–Fe–B is used for the magnets.They may be embedded in the rotor so as toconcentrate the air-gap flux.A stepping motor turns through a fixed angle

when one of the windings is energized by a suitableelectronic control circuit. Designs may incorporatea ring magnet with many poles around thecircumference. These can be fabricated frompolymer-bonded ferrite by injection mouldingand they are then pulse-magnetized using a specialfixture. A common design of hybrid permanent-magnet stepper motor makes 200 steps perrevolution, a 1.81 step size. With suitable control,it will proceed in half-steps of 0.91. Tiny two-polestepper motors using bonded Sm–Co magnets areused in clocks and watches.

2.6. Miscellaneous

A host of magnetic water treatment devices aremarketed throughout the world for domestic andindustrial use which serve to inhibit limescaledeposits in pipework carrying hard water. Theyappear to influence the structure and morphologyof the calcium carbonate precipitate, altering thecalcite:aragonite ratio or the manner of calcitenucleation [21–23]. Other reports exist of amagnetic field effect on precipitation of inorganic

Fig. 12. DC motor designs: (a) brush motor with magnets on the stator and (b) brushless motor with magnets on the rotor.


salts from supersaturated solution [24], the rate ofelectrodeposition of metals [25] and electropoly-merization [26]. Permanent magnet devices areused extensively in the Chines oil industry tocontrol wax formation from heavy crude oil [27].The reality of some of these effects seems to be inlittle doubt, but a convincing theory or explana-tion is often lacking. If these processes wereproperly understood, it may be possible torationally design new permanent magnet devicesfor maximum effect in a range of industrialprocesses.

3. Conclusions

The burgeoning range of permanent magnetapplications in electrical engineering has beenmade possible by the discovery of new magneticmaterials and their continual improvement. Weare near the end of the exponential growth ofenergy product of conventional magnets.Although a further doubling of ðBHÞmax to800 kJm�3 might be possible in due course, furtherprogress is constrained by the intrinsic magneticproperties of any material known to ordermagnetically at room temperature. Superconduct-ing permanent magnets may find a use in futurefor niche applications.There is no prospect of permanent magnet

applications stagnating in future. The utility ofmodern permanent magnets has barely begun tobe appreciated. There are good prospects forinnovative applications, especially if the propertiesof cost-effective magnet grades can be tailored tonew requirements such as thermal stability orhigh-temperature operation. One prediction is thatthe electromagnet is technically obsolete, andlikely to be superseded for many purposes bypermanent magnet variable flux sources whichhave great advantages of compactness and inde-pendence of large power supplies or coolingrequirements.Products like cordless electric tools or personal

stereos owe their existence to advanced permanentmagnets. One may expect that other new consumerproducts will appear which exploit their benefits.The fact that such a large proportion of the rare-

earth magnet market depends on a single applica-tion, miniature voice-coil actuators for hard-discdrives, suggests not so much that the market isvulnerable to changes in the shape of personalcomputers and home electronics as that it iscapable of great expansion as a few more massapplications emerge. The electric automobile is oneof the products which could transform the scale ofindustrial applications of permanent magnets.

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Permanent magnet applications

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