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The Curie temperature is the transition temperature above which a ferromagnetic material loses spontaneous magnetization. A hot conducting planetary core can generate a magnetic field through dynamo action without behaving as a permanent magnet. The blocking temperature at which a mineral records crustal remanence also depends on its relaxation timescale and need not equal its Curie temperature.

A hard magnetic material strongly resists reversal of its magnetization, giving high coercivity and useful remanence for permanent magnets. The relevant hardness is magnetic, not a mechanical strength rating.

A magnet is a material object or current arrangement that produces a magnetic field. Permanent magnets retain magnetization, while electromagnets use a supplied electric current in a winding.

Magnetic hysteresis means that a material's magnetization depends on its field history as well as the present applied field. A closed quasistatic magnetic cycle dissipates energy per unit volume equal to its $H$–$B$ loop area. It is relevant to remanence in permanent magnets and core losses in electrical transformers.

A permanent magnet retains a substantial magnetization without an applied coil electric current. In a ferromagnetic material this reflects microscopic magnetic moments, magnetic domains and their resistance to rearrangement. The history-dependent relation between applied field and magnetization gives magnetic hysteresis, remanence and coercivity. A soft core used in an electromagnet or electrical transformer is chosen for easy magnetization and small hysteretic loss; a permanent-magnet material must resist demagnetization.^[ref]

The macroscopic fields obeyin magnetostatics. The magnetization can be represented by equivalent bound currents,Thus both permanent magnetic matter and free coil electric currents generate a magnetic field. Its magnetic field lines form continuous loops; apparent north and south poles are not isolated magnetic charges.

In a long ideal solenoid, $H\simeq nI$. A linear core would give $B\simeq {\mu }_0{\mu }_{r}nI$, until saturation or other nonlinear effects invalidate a constant magnetic permeability. In a finite magnetic circuit, air gaps and demagnetizing fields affect the field strongly: because the gap has low magnetic permeability, it often needs most of the available magnetomotive force. A permanent magnet can have a nonzero internal $\mathbf{H}$ even when ${\mathbf{J}}_f=0$, because its boundaries create a demagnetizing field. Hence setting $\mathbf{H}=0$ merely because there is no free coil electric current is generally incorrect.

Magnetization and field response. A magnetic material contains microscopic magnetic moments associated with electron spin and orbital motion. The magnetization $\mathbf{M}$ is magnetic dipole moment per unit volume. In SI the macroscopic fields satisfyHere $\mathbf{H}$ separates free-current excitation from the material response. A uniform isotropic linear material has $\mathbf{M}={\chi }_m\mathbf{H}$, givingThis constant scalar magnetic permeability model is useful only within its linear range. Crystals can have a susceptibility tensor; strongly magnetic materials depend on field and magnetic history. For a finite specimen the internal $\mathbf{H}$ also includes its demagnetizing field. In a uniformly magnetized ellipsoid, $H_{\mathrm{int}}=H_{\mathrm{applied}}-N_{d}M$ along a principal axis, so sample shape affects the apparent susceptibility.

Diamagnetic and paramagnetic response. Diamagnetism is a weak negative susceptibility caused by induced orbital response opposing the applied field. It occurs in all matter but can be masked by larger positive contributions. Closed-shell materials such as bismuth or many organic compounds show it clearly. Ordinary diamagnetism is often only weakly temperature dependent; superconducting flux exclusion is a separate collective phenomenon and is not described by an arbitrarily small negative susceptibility.

Paramagnetism arises when available magnetic moments partially align with a field. Thermal disorder prevents complete alignment at weak fields. For independent localized moments of magnitude $m$, the classical weak-field result iswhere the second expression uses $B\simeq {\mu }_{0}H$ in a weakly magnetic sample. Thus localized moments obey a Curie law in this regime. Quantum angular momentum changes the coefficient to the appropriate $J(J+1)$ expression and gives saturation at strong field. Conduction electrons instead exhibit Pauli paramagnetism: only states near the Fermi surface can change spin populations, so a degenerate gas has a nearly temperature-independent response. Its orbital diamagnetism must also be included for a full metallic susceptibility.

Collective magnetic order. Exchange interactions can favor parallel alignment, producing ferromagnetism below the Curie temperature. Iron, cobalt and nickel are familiar examples. A material may contain regions of spontaneous magnetization, or magnetic domains, while having little net external moment because the domains point in different directions. Applied fields move domain walls and rotate moments; at large fields the magnetization approaches saturation. Pinning and energy barriers make this process hysteretic. Remanence is the magnetization left after removing the driving field, and coercivity measures the reverse field needed to bring the chosen response back to zero.

The area of a closed $B$–$H$ loop is the energy dissipated per unit volume per quasistatic cycle, $\oint HdB$, with positive dissipated magnitude. Consequently the magnetic permeability is neither one universal constant nor enough information to describe a ferromagnet: differential magnetic permeability $dB/dH$, saturation and hysteresis all matter. Above the ordering temperature the spontaneous moment disappears, and a Curie–Weiss law is often an appropriate approximate paramagnetic description away from the critical region.

In antiferromagnetism, ordered opposing sublattices have equal moments and cancel macroscopically in the ideal compensated case. The order disappears above the Néel temperature. In ferrimagnetism, opposing sublattices have unequal moments and leave a net magnetization. Ferrites combine ferrimagnetic response with relatively high electrical resistivity, making them valuable when eddy-current losses would be substantial in a metallic core.

Electromagnets and engineering choice. A coil supplies free-current magnetomotive force $NI$. For a simple uniform magnetic path, Ampère's law gives $H\ell \simeq NI$ and flux $\Phi \simeq \mu ANI/\ell$. A high-magnetic permeability soft magnetic core concentrates flux and reduces the current required for a given field. With an air gap $g$,Even a short gap can dominate the magnetic reluctance. The approximate attractive force across one uniform gap is $F\simeq B^{2}A/(2{\mu }_0)$, obtained from the field energy, with fringing neglected.

Soft magnetic materials have small coercivity and narrow hysteresis loops; they suit relays, electrical transformer cores and controllable electromagnets. Hard magnetic materials retain their magnetization and suit permanent magnets. Laminating metallic cores breaks large eddy-current loops; ferrites are useful at higher frequencies because of their resistivity. Increasing current cannot increase $B$ indefinitely through the linear formula: core saturation, coil heating and leakage limit performance. A good design selects material for the field amplitude, switching frequency and acceptable loss, rather than simply choosing the largest quoted magnetic permeability.

A permanent magnet retains magnetization after the applied magnetizing magnetic field is removed. Its working magnetic field persists without a driving electric current in a winding.