Hysteresis

Definition and Overview

Basic Concept

Hysteresis: lagging response of magnetization (M) in ferromagnetic materials to applied magnetic field (H). Magnetic flux density (B) does not retrace same path when H varies cyclically. Nonlinear, path-dependent behavior.

Historical Context

Term introduced by Sir James Alfred Ewing, 1881. Early studies on iron and steel magnetic properties. Foundation for magnetic materials science and electrical engineering.

Physical Origin

Arises from domain wall motion, magnetic domain rotation, and energy barriers. Intrinsic material defects and microstructure cause irreversible magnetization changes.

"Hysteresis is the memory effect of magnetic materials, crucial for permanent magnetism and transformer design." -- C.P. Bean

Magnetization Process

Initial Magnetization Curve

Starting from demagnetized state, magnetization increases with H, domains align, walls move. Curve nonlinear, saturates at high H (saturation magnetization, Ms).

Domain Wall Movement

Primary mechanism at low fields. Domain walls shift to increase aligned domains. Impeded by defects, inclusions, grain boundaries.

Rotation of Magnetic Moments

At higher fields, domain rotation dominates. Magnetic moments rotate towards field direction overcoming anisotropy energy barriers.

B-H Curve Characteristics

Definition

B-H curve: plot of magnetic flux density (B) versus magnetic field strength (H). Illustrates magnetization and hysteresis behavior.

Hysteresis Loop

Closed loop formed during cyclic magnetization. Area proportional to energy loss per cycle. Key parameters: coercivity (Hc), remanence (Br), saturation (Bs).

Saturation

Maximum B reached when all domains fully aligned. Further increase in H produces negligible B change.

Magnetic Domains and Microstructure

Domain Concept

Ferromagnetic materials subdivided into domains with uniform magnetization. Minimize total magnetic energy by reducing stray fields.

Domain Wall Types

Bloch walls: magnetization rotates perpendicular to wall. Néel walls: magnetization rotates within plane. Wall type affects hysteresis properties.

Influence of Microstructure

Grain size, impurities, dislocations affect domain wall mobility. Fine grains increase coercivity; annealing reduces defects, lowers hysteresis loss.

Coercivity and Retentivity

Coercivity (Hc)

Magnetic field intensity required to reduce net magnetization to zero after saturation. Indicator of material's resistance to demagnetization.

Retentivity or Remanence (Br)

Residual magnetization after external field removed. Determines permanent magnet strength.

Classification by Coercivity

Soft magnetic materials: low Hc, used in transformers. Hard magnetic materials: high Hc, used in permanent magnets.

Energy Loss and Hysteresis Loop Area

Energy Dissipation

Energy loss per magnetization cycle equals area enclosed by hysteresis loop. Manifests as heat.

Quantitative Expression

Energy loss density (W) per cycle:

W = ∮ H dB

Integral of H over B for closed loop path.

Impact on Devices

Core loss in transformers, inductors. Minimizing hysteresis loss improves efficiency and reduces heating.

Types of Hysteresis

Magnetic Hysteresis

Classic lag of B behind H in ferromagnets. Exhibits irreversible domain processes.

Ferroelectric Hysteresis

Analogous behavior in ferroelectric materials with polarization versus electric field.

Other Forms

Mechanical hysteresis: stress-strain lag in ferromagnetic alloys. Thermal hysteresis: temperature-dependent magnetization lag.

Mathematical Models

Preisach Model

Phenomenological model representing hysteresis as superposition of elementary rectangular loops. Widely used for simulation.

Jiles-Atherton Model

Physical model based on domain wall motion and pinning. Parameters relate to material microstructure.

Mathematical Expression

dM/dH = (M_eq - M)/ (kδ) - c dM/dHwhere:M = magnetization,M_eq = equilibrium magnetization,k = pinning coefficient,c = reversibility coefficient,δ = direction of field change (+1 or -1) 

Applications of Hysteresis

Transformers and Inductors

Soft magnetic cores designed to minimize hysteresis loss, improve efficiency in power devices.

Permanent Magnets

Utilize high coercivity materials to retain magnetization for motors, sensors, data storage.

Magnetic Recording

Hysteresis enables data encoding via remanent magnetization states in recording media.

Magnetic Sensors

Exploitation of hysteresis properties in switches, memory elements, and spintronic devices.

Measurement Techniques

Vibrating Sample Magnetometer (VSM)

Measures magnetic moment by vibrating sample in uniform field. High sensitivity, dynamic measurement.

B-H Loop Tracer

Direct plotting of B-H curves using electronic circuits, useful in material characterization.

Magneto-Optical Kerr Effect (MOKE)

Optical technique detecting surface magnetization changes during hysteresis cycles.

Temperature Effects

Curie Temperature

Above critical temperature, ferromagnetism disappears; hysteresis vanishes.

Temperature Dependence of Coercivity

Hc decreases with rising temperature due to thermal agitation reducing anisotropy energy.

Thermal Activation of Domain Walls

Thermally assisted domain wall motion causes variation in hysteresis loop shape and area.

Recent Research and Developments

Nanostructured Magnetic Materials

Engineering domain sizes and boundaries at nanoscale to tailor hysteresis for improved performance.

Magnetocaloric Effect and Hysteresis

Studies on low hysteresis materials enhancing magnetic refrigeration efficiency.

Spintronics and Hysteresis Control

Manipulation of hysteresis loops via spin currents, enabling energy-efficient memory devices.

Advanced Modeling Techniques

Machine learning approaches to predict hysteresis behavior from microstructural data.

References

• Cullity, B.D., Graham, C.D., Introduction to Magnetic Materials, Wiley-IEEE Press, 2008, pp. 101-145.
• Jiles, D.C., Introduction to Magnetism and Magnetic Materials, 2nd ed., CRC Press, 1998, pp. 200-230.
• Preisach, F., Über die magnetische Nachwirkung, Zeitschrift für Physik, vol. 94, 1935, pp. 277-302.
• Chikazumi, S., Physics of Ferromagnetism, 2nd ed., Oxford University Press, 1997, pp. 320-370.
• Jiles, D.C., Atherton, D.L., Theory of ferromagnetic hysteresis, Journal of Magnetism and Magnetic Materials, vol. 61, 1986, pp. 48-60.