Magnetism and Magnetic Materials

Introduction to Magnetism

Magnetism is a quantum mechanical phenomenon arising from two sources: electron spin (intrinsic angular momentum, s=1/2) and orbital angular momentum of electrons around nuclei. Classical electromagnetism cannot account for the existence of permanent magnets—Bohr-van Leeuwen theorem proves that thermal equilibrium magnetisation is always zero in purely classical physics; magnetism is fundamentally quantum. The magnetic moment of an atom combines spin and orbital contributions via the total angular momentum J and Landé g-factor. Exchange interactions—arising from Coulomb electrostatics combined with the Pauli exclusion principle (which depends on spin)—determine whether neighbouring spins align ferromagnetically (parallel, J>0) or antiferromagnetically (antiparallel, J<0).

Magnetic materials underpin modern technology: permanent magnets in electric motors (EV drivetrains use ~2 kg NdFeB magnets), speakers, generators, and MRI machines; soft magnetic cores in transformers and inductors; magnetic recording in hard disk drives; and emerging spintronic devices exploiting electron spin as an information carrier. The global permanent magnet market exceeds $20 billion annually and is critical for the energy transition—wind turbines and electric vehicles both rely heavily on rare-earth permanent magnets. Understanding and engineering magnetic materials from atomic exchange interactions to mesoscale domain structures is the domain of modern magnetism research.

Types of Magnetic Order

Ferromagnetism and Antiferromagnetism

Ferromagnetism (Fe, Co, Ni, Gd, and alloys): below Curie temperature T_C (Fe: 1043 K, Co: 1388 K, Ni: 627 K), spontaneous parallel spin alignment produces macroscopic magnetisation through positive exchange interaction J>0 in Heisenberg model H = -J*sum(S_i·S_j). Mean-field (Weiss) theory predicts T_C = zJS(S+1)/(3k_B) (z=coordination number)—qualitatively correct but overestimates T_C by ignoring fluctuations. Magnetic domains—regions of uniform magnetisation separated by domain walls (Bloch walls for 180° rotation through bulk, Néel walls at surfaces)—form to minimise total magnetostatic energy, explaining demagnetised state of unmagnetised ferromagnets. Antiferromagnetism: neighbouring spins antiparallel (MnO, NiO, Cr, FeO)—zero net magnetisation but ordered below Néel temperature T_N; detectable by neutron diffraction (neutrons interact with both nuclear and magnetic moments), spin-wave (magnon) spectroscopy, and exchange bias in ferromagnet/antiferromagnet bilayers. Ferrimagnetism (Fe3O4, ferrites, garnets): two antiparallel sublattices with unequal moments give net magnetisation—traditional transformer and antenna core materials.

Magnetic Anisotropy and Hysteresis

Magnetic anisotropy—preference for magnetisation along specific crystallographic directions—determines coercive field, hysteresis loop shape, and suitability for hard (permanent magnet) or soft (transformer core) applications. Magnetocrystalline anisotropy energy for uniaxial material: E_a = K_u * sin^2(theta) (K_u = uniaxial anisotropy constant; theta = angle from easy axis)—high K_u gives large coercive field. Shape anisotropy (demagnetisation energy): elongated particles favour magnetisation along long axis. Surface/interface anisotropy (Néel): in thin films and multilayers, broken symmetry at interfaces contributes perpendicular magnetic anisotropy (PMA) enabling out-of-plane magnetisation critical for high-density magnetic recording (perpendicular recording, 2005 onward in hard disks). Hysteresis loss (area enclosed by B-H loop) represents energy dissipated per cycle in AC applications—minimised in soft magnets (Fe-Si transformer steel, amorphous ribbons, nanocrystalline FINEMET) by grain orientation, composition, and nanostructure control reducing coercivity to <1 Oe while maintaining high saturation magnetisation.

Permanent Magnets

Rare-Earth Permanent Magnets

NdFeB (Nd2Fe14B) permanent magnets—discovered by Sagawa (Sumitomo) and Croat (GM) in 1984—have the highest energy product (BH)_max ~400-500 kJ/m^3, ~10× older AlNiCo and ferrite magnets—enabling compact, lightweight electric motors and generators. The large magnetocrystalline anisotropy arises from Nd crystal field acting on 4f electrons; the high saturation magnetisation from Fe sublattice; Curie temperature 585 K limits operations above ~80°C without Dy/Tb substitution. SmCo5 and Sm2Co17 magnets: higher Curie temperature (~1000 K) and corrosion resistance for aerospace and high-temperature motors; less affected by heavy rare earth supply chain concerns than NdFeB. Critical material supply chain vulnerability: 85% of NdFeB production and >90% of raw rare earth element mining (Nd, Pr, Dy, Tb) concentrated in China, driving recycling research (urban mining from end-of-life EV and wind turbine magnets) and alternative reduced-rare-earth or Fe-N permanent magnet development programmes worldwide.

Spintronics and Magnetic Devices

Spintronics uses electron spin degree of freedom alongside (or instead of) charge to process and store information—potentially reducing energy consumption and enabling non-volatile memory. Giant magnetoresistance (GMR Nobel 2007), tunnelling magnetoresistance (TMR), spin-transfer torque (STT), spin-orbit torque (SOT), and voltage-controlled magnetic anisotropy (VCMA) are the physical phenomena underlying spintronic devices. STT-MRAM commercialised by Everspin (~2016) and embedded in Samsung/TSMC nodes as cache replacement; SOT-MRAM under development for faster switching without read-disturb issues. Racetrack memory (Parkin IBM concept): magnetic domain walls carrying bit information driven along ferromagnetic nanowire tracks by current-driven spin torques—3D stacked tracks potentially enabling much higher density than conventional MRAM. Magnonic logic: information encoded in spin wave (magnon) phase or amplitude rather than charge current—potentially coherent, low-dissipation signal processing beyond GHz frequencies.

Examples and Applications

Example 1: MRI Superconducting Magnets

Clinical MRI scanners use superconducting solenoid magnets (NbTi wire, 1.5–3 T; NbTiN or NbSn for 7T) cooled by liquid helium to 4 K generating highly homogeneous static fields over 50 cm bore. Shimming—additional small superconducting or resistive correction coils eliminating field inhomogeneities—achieves B0 uniformity below 1 ppm over the imaging volume. Gradient coils (switched at kHz rates, up to 80 mT/m amplitude) encode spatial information via frequency and phase; the acoustic noise of MRI from Lorentz force vibration of gradient coils in the main field can reach 130 dB requiring acoustic shielding. Helium-free MRI using cryocoolers (Siemens MAGNETOM Free.Max 0.55T, United Imaging 3T) eliminates liquid helium dependency—critical for global health as helium supply tightens. High-temperature superconductor (HTS, REBCO) MRI magnets operating at 20-40 K from cryocoolers represent the frontier—enabling higher fields (11.7T human whole-body MRI at CEA Neurospin) without the complexity and cost of liquid helium cryostats.

Example 2: Magnetic Recording Physics

Hard disk drives (HDDs) store data as magnetic domains in thin polycrystalline CoCrPt-oxide perpendicular recording media—grains ~5-8 nm diameter, each grain a single domain, ~20 grains per bit for signal/noise above threshold. Read heads use tunnelling magnetoresistance (TMR) sensors with CoFeB-MgO-CoFeB junctions delivering >600% TMR ratio at room temperature—resolution below 10 nm. Write heads use trailing-edge pole focusing field using high-moment soft magnetic pole (CoFe) with ~800 kA/m saturation. Heat-assisted magnetic recording (HAMR, Seagate deployment 2020+): laser spot heats media locally above Curie temperature enabling writing on ultra-high anisotropy FePt L10 media (K_u ~7×10^6 J/m^3), reducing thermal stability concerns at sub-5 nm grain sizes needed for >4 Tbit/inch^2 density. Microwave-assisted magnetic recording (MAMR): spin-transfer oscillator generating near-field microwave assists in reducing coercive field without heating, alternative to HAMR—Western Digital EAMR (energy-assisted) approach. Cloud data centres use ~5 billion HDDs globally storing ~10 zettabytes of data.

Example 3: Magnetic Skyrmions

Magnetic skyrmions—topologically protected whirling spin textures with vortex-like magnetic structure characterised by topological charge Q=-1—are nanoscale (~10-100 nm) quasiparticles in chiral magnets stabilised by Dzyaloshinskii-Moriya interaction (DMI: antisymmetric exchange from spin-orbit coupling at interfaces or in non-centrosymmetric crystals). Skyrmions were first observed in bulk MnSi by neutron scattering (2009) and in thin films by Lorentz TEM (Heinze et al. 2011). Room-temperature skyrmions in Pt/Co/MgO multilayers and Fe/Ir(111) surfaces were discovered 2013-2016. Interest for memory: skyrmions can be nucleated, annihilated, and driven along nanowire tracks by spin-orbit torques at ultralow current densities (~10^6 A/m^2 versus 10^12 A/m^2 for domain walls in simple ferromagnets)—potential for extremely energy-efficient racetrack memory. Anti-skyrmions (opposite topological charge) and higher-order skyrmion textures (biskyrmions, skyrmionium) in D2d symmetry materials expand the topological spin texture zoo observable by quantitative Lorentz TEM differential phase contrast imaging.

Example 4: Magnetic Refrigeration

Magnetocaloric effect (MCE): a magnetic material heats when adiabatically magnetised (spins align, reducing magnetic entropy, raising temperature to conserve total entropy) and cools when demagnetised—the basis for magnetic refrigeration, an alternative to vapour compression refrigeration without HFC refrigerants and compressors. Gadolinium has the largest MCE near room temperature at its TC=294 K (delta T_ad ~3-5 K at 5 T). Giant MCE materials: La(Fe,Si)13 compounds (first-order magnetic transition with delta T_ad ~15 K at 1 T due to coupled structural-magnetic transition); Mn-Fe-P-Si (magnetocaloric efficiency competitive for near-room-temperature heat pumps); Heusler alloy Ni-Mn-X (metamagnetic shape-memory materials). Active magnetic regenerator (AMR) cycle using layered magnetocaloric material beds in oscillating field achieves temperature spans of 40-80 K. Commercial magnetic refrigerators at demonstration/pre-commercial stage: Cooltech Applications (France), Astronautics Corp (USA). If scaled, magnetic refrigeration could eliminate ~7% of global electricity use currently consumed by vapour compression cooling while eliminating refrigerant GHG emissions.

Example 5: Antiferromagnetic Spintronics

Antiferromagnetic (AFM) materials—long ignored for spintronics because they appeared magnetically silent (zero net moment)—are now recognised as storing information in their Néel order parameter (sublattice magnetisation direction) detectable by anisotropic magnetoresistance and the spin Hall magnetoresistance. AFM spintronics advantages: THz-frequency spin dynamics (10× faster than ferromagnets); insensitivity to stray fields; no stray field disturbance of neighbouring bits; and abundant materials (MnN, Mn2Au, CuMnAs are room-temperature AFMs controllable by spin-orbit torques). Electrical switching of Néel order in CuMnAs and Mn2Au thin films by current pulses was demonstrated 2016-2019—enabling non-volatile rewritable AFM memory. AFM magnons in NiO coupled to heavy metal (Pt) spin Hall layers transmit spin current over nm distances—spin Seebeck effect and spin pumping in AFM/NM bilayers demonstrate electrical readout of AFM magnon dynamics. Altermagnets—recently identified third class of collinear magnetic order with zero net moment but spin-split electronic bands (not due to SOC) found in RuO2, MnTe—may combine advantages of ferro and antiferromagnets for spintronics.

Example 6: Magnetic Nanoparticles in Medicine

Superparamagnetic iron oxide nanoparticles (SPIONs, ~5-20 nm Fe3O4 or gamma-Fe2O3) have no remanence at room temperature—aggregation-free in biological media—yet respond strongly to AC and DC magnetic fields for medical applications. MRI contrast agents: SPIONs shorten T2 relaxation time of nearby water protons, creating dark contrast regions in T2-weighted images—FDA-approved agents (Feridex, Combidex for lymph node staging) were withdrawn but newer generation ultrasmall SPIONs (USPIO) and clustered SPIONs are in clinical trials. Magnetic hyperthermia: AC field (~100 kHz, ~20 mT) drives SPION loss mechanism (Néel relaxation: magnetisation reversal; Brownian relaxation: particle rotation viscous loss)—heating tumour tissue to 42-45°C (selective thermosensitisation of cancer cells without harming surrounding tissue). MagForce AG conducted first clinical magnetic hyperthermia treatments for glioblastoma (Phase II, Berlin 2010)—injecting magnetite nanofluid directly into tumour then applying AC field. Magnetic drug targeting: drug-loaded SPION aggregates directed to tumour sites by external permanent magnet gradients, reducing systemic drug distribution and side effects.

Example 7: Magneto-Optics

Magneto-optical effects—changes in optical properties of materials in the presence of magnetic fields—enable both scientific characterisation and practical applications. Faraday effect: rotation of linear polarisation plane of transmitted light proportional to magnetic field component along propagation (Verdet constant V: theta = V*B*l)—used in optical isolators preventing laser back-reflection (Tb3Ga5O12 garnet crystals), and as current sensors measuring field from current-carrying conductors at high voltage. Magneto-optical Kerr effect (MOKE): rotation of reflected light polarisation by magnetised surface—MOKE magnetometry measures hysteresis loops of thin magnetic films with monolayer sensitivity, and time-resolved MOKE (pump-probe, femtosecond lasers) measures ultrafast demagnetisation dynamics (~100 fs timescale from laser-excited hot electrons—discovered by Beaurepaire et al. 1996 challenging spin-lattice relaxation models). MOKE microscopy images magnetic domain structures with optical resolution. X-ray magnetic circular dichroism (XMCD): differential absorption of left/right circularly polarised synchrotron X-rays by transition metal L-edges in magnetic materials yields element-specific spin and orbital moments (sum rules) and picosecond time-resolved magnetisation dynamics.

Example 8: Quantum Magnets and Spin Liquids

Geometrically frustrated quantum magnets—where competing exchange interactions cannot all be simultaneously satisfied—exhibit exotic ground states without conventional long-range order. Kagome lattice antiferromagnets (Herbertsmithite ZnCu3(OH)6Cl2): perfect geometric frustration suppresses ordering to T→0; neutron scattering reveals gapless continuum of fractionalised spin-1/2 spinon excitations rather than magnon quasiparticles—hallmark of Z2 quantum spin liquid (QSL) ground state. Kitaev honeycomb model (exactly solvable): bond-direction-dependent Ising interactions on honeycomb lattice produce fractionalized Majorana fermion + Z2 gauge flux excitations; alpha-RuCl3 is the leading candidate material—proximate Kitaev physics evidenced by continuum scattering and half-integer quantised thermal Hall coefficient possibly indicating non-Abelian anyons. Triangular lattice organic Mott insulators (kappa-(BEDT-TTF)2Cu2(CN)3, EtMe3Sb[Pd(dmit)2]2) exhibit spin liquid behaviour: no magnetic ordering to 30 mK despite J~250 K. Understanding QSLs guides routes to topological quantum memories and fractionalized excitations that may underpin fault-tolerant quantum computing.

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