hall effect experiment theory

• Electromagnetism

Hall Effect

Hall effect is a process in which a transverse electric field is developed in a solid material when the material carrying an electric current is placed in a magnetic field that is perpendicular to the current. The Hall effect was discovered by Edwin Herbert Hall in 1879. In this article, let us learn about the Hall effect in detail.

Principle of Hall effect

The principle of the Hall effect states that when a current-carrying conductor or a semiconductor is introduced to a perpendicular magnetic field, a voltage can be measured at the right angle to the current path. This effect of obtaining a measurable voltage is known as the Hall effect.

When a conductive plate is connected to a circuit with a battery, then a current starts flowing. The charge carriers will follow a linear path from one end of the plate to the other end. The motion of charge carriers results in the production of magnetic fields. When a magnet is placed near the plate, the magnetic field of the charge carriers is distorted. This upsets the straight flow of the charge carriers. The force which upsets the direction of flow of charge carriers is known as Lorentz force .

Due to the distortion in the magnetic field of the charge carriers, the negatively charged electrons will be deflected to one side of the plate and positively charged holes to the other side. A potential difference, known as the Hall voltage will be generated between both sides of the plate which can be measured using a metre.

The Hall voltage represented as V H is given by the formula:

I is the current flowing through the sensor

B is the magnetic field strength

q is the charge

n is the number of charge carriers per unit volume

d is the thickness of the sensor.

Similar Reading:

Hall Coefficient

The Hall coefficient R H is mathematically expressed as

Where j is the current density of the carrier electron, Ey is the induced electric field and B is the magnetic strength. The hall coefficient is positive if the number of positive charges is more than the negative charges. Similarly, it is negative when electrons are more than holes.

Applications of Hall Effect

Hall effect principle is employed in the following cases:

• Magnetic field sensing equipment
• For the measurement of direct current, Hall effect Tong Tester is used.
• It is used in phase angle measurement
• Proximity detectors
• Hall effect Sensors and Probes
• Linear or Angular displacement transducers
• For detecting wheel speed and accordingly assist the anti-lock braking system.

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Frequently Asked Questions – FAQs

Name one practical use of hall effect..

Hall effect is used to determine if a substance is a semiconductor or an insulator. The nature of the charge carriers can be measured.

How is Hall potential developed?

When a current-carrying conductor is in the presence of a transverse magnetic field, the magnetic field exerts a deflecting force in the direction perpendicular to both magnetic field and drift velocity. This causes charges to shift from one surface to another thus creating a potential difference.

What is a Hall effect sensor?

A Hall effect sensor is a device that is used to measure the magnitude of a magnetic field.

In the Hall effect, the direction of the magnetic field and electric field are parallel to each other. True or False?

False. The magnetic field and electric field are perpendicular to each other.

Explain Lorentz Force.

Lorentz force is the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B.

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Hall Effect in Physics

The Hall effect is a phenomenon in physics that occurs when a magnetic field is applied perpendicular to the flow of current in a conductor or semiconductor. This results in the development of a transverse voltage, known as the Hall voltage, across the material. Understanding the Hall effect is crucial because it provides insights into the behavior of charge carriers in materials. The effect has significant implications in various fields, from fundamental physics to practical applications in electronic devices.

What Is the Hall Effect?

The Hall effect describes the generation of a voltage difference (Hall voltage) across an electrical conductor through which an electric current is flowing, when a magnetic field is applied perpendicular to the current. This effect was discovered by Edwin Hall in 1879 and is a critical tool in the study of electronic properties of materials.

Importance of the Hall Effect

The Hall effect is important because it allows for the determination of the type (positive or negative), density, and mobility of charge carriers in a material. It is particularly useful in the characterization of semiconductors and in the design of various electronic components and sensors.

American physicist Edwin Herbert Hall discovered the Hall effect in 1879 while working on his doctoral thesis at Johns Hopkins University. He observed that placing a current-carrying conductor in a perpendicular magnetic field generates a voltage across the conductor in a direction perpendicular to both the current and the magnetic field. This discovery provided a new way to probe the properties of conductors and semiconductors, significantly advancing the field of solid-state physics. Keep in mind, Hall’s observation occurred prior to the discovery of the electron.

Theory Behind the Hall Effect

The Lorentz force explains the Hall effect. The Lorentz force acts on the moving charge carriers in the presence of a magnetic field. When a current flows through a conductor in the presence of a perpendicular magnetic field, the charge carriers (electrons or holes) experience a force that is perpendicular to both the current direction and the magnetic field. Positive and negative charges move in opposite directions. Charge carriers accumulate on one side of the conductor, creating a voltage difference across the conductor, known as the Hall voltage.

Positive Charge Carriers

In situations involving metal wires, the charge carriers are electrons. In semiconductors, charge carriers can be holes (with electrons moving in the opposite direction). However, sometimes current involves positive charge carriers. Examples include:

• Ionic Conductors : In ionic conductors, the charge carriers are electrolytes , which are ions.
• Plasma : There are both electrons and free positive ions in plasma. Examples of environments involving plasma include stars, neon signs, and plasma televisions.
• Solid-State Materials : The primary charge carriers are ions with positive charges in certain ionic crystals or superconductors.

Hall Voltage Formula

Calculate the Hall voltage (VH) using the following formula:

V H = B · I / n · q · d

• B is the magnetic field strength (in Tesla, T),
• I is the current through the conductor (in Amperes, A),
• n is the charge carrier density (in carriers per cubic meter, m -3 ),
• q is the charge of the carriers (in Coulombs, C),
• d is the thickness of the conductor (in meters, m).

Example Problem

For example:

A copper strip of thickness 0.01cm is in a magnetic field of 0.5T. A current of 3 A flows through the strip. Given that the charge carrier density in copper is approximately 8.5×10 28  m −3 and the charge of an electron is 1.6×10 −19  C, calculate the Hall voltage.

• Convert Thickness to Meters: 𝑑 = 0.01 cm = 0.01×10 −2  m = 1×10 −4  m
• Identify Given Values: 𝐵 = 0.5 T 𝐼 = 3 A 𝑛 = 8.5×1028 m −3 𝑞 = 1.6×10 −19  C
• Plug the Values into the Hall Voltage Formula: 𝑉 𝐻 = 𝐵⋅𝐼 / 𝑛⋅𝑞⋅𝑑 = 0.5 T ⋅ 3 A / 8.5×10 28  m −3 ⋅ 1.6×10 −19  C ⋅ 1×10 −4  m
• Calculate the Denominator: 𝑛⋅𝑞⋅𝑑 = 8.5×10 28 ⋅ 1.6×10 −19 ⋅ 1×10 −4 𝑛⋅𝑞⋅𝑑 = 8.5×1.6×10 28−19−4 𝑛⋅𝑞⋅𝑑=13.6 × 10 5
• Calculate the Hall Voltage: 𝑉 𝐻 = 0.5 ⋅ 3 / 13.6×10 5 𝑉 𝐻 = 1.5 / 13.6×10 5 𝑉 𝐻 = 1.10×10 −6  V V H ​= 1.10 μ V

Result: The Hall voltage across the copper strip is 1.10 𝜇V.

The Hall Coefficient

The Hall coefficient (R H ) is a fundamental parameter that characterizes the Hall effect in a material. It is the ratio of the induced electric field (Hall voltage) to the product of the current density and the applied magnetic field. Mathematically, the Hall coefficient is:

R H = E H / J · B​​

• E H ​ is the Hall electric field,
• J is the current density,
• B is the magnetic field.

The Hall coefficient provides information about the type and density of charge carriers in the material. For a material with positive charge carriers (holes or cations ), the Hall coefficient is positive, and for negative charge carriers (electrons or anions), it is negative.

Using the Right-Hand Rule with the Hall Effect

The right-hand rule is a simple mnemonic for determining the direction of the Hall voltage. According to this rule, if you point the thumb of your right hand in the direction of the current and your index finger in the direction of the magnetic field, your middle finger (perpendicular to both the thumb and index finger) points in the direction of the induced Hall voltage.

What Is a Hall Effect Sensor?

A Hall effect sensor is a transducer that varies its output voltage in response to changes in the magnetic field. These sensors are used to detect the presence, absence, or strength of a magnetic field. They are commonly used in applications such as:

• Automotive Ignition Systems : For determining the position of the crankshaft or camshaft.
• Proximity Sensors : For detecting the proximity of objects in automated systems.
• Speed Detection : In tachometers and anti-lock braking systems (ABS).
• Current Sensing : In power supplies and battery management systems.
• Nondestructive Testing : Sensors detect defects and irregularities, with applications in crack detection and thickness measurements.

Hall Effect Controllers and Joysticks

Hall effect controllers and joysticks utilize Hall sensors for detecting the position of a control stick or lever. Unlike traditional potentiometers, Hall effect sensors do not suffer from mechanical wear and tear. Thus, they offer more reliable and longer-lasting performance. These controllers find use in various applications, including gaming, aviation, and industrial control systems.

Applications of the Hall Effect

The Hall effect has numerous applications, including:

• Hall Effect Sensors : These devices use the Hall effect to measure magnetic field strength. They are popular in automotive, industrial, and consumer electronics for applications like current sensing, position sensing, and speed detection. The sensors also find use in blood flow meters and magnetically activated implants (e.g., cochlear implants) in medicine and biology.
• Magnetic Field Measurement : The Hall effect determines the strength and direction of magnetic fields in various scientific and industrial applications.
• Semiconductor Characterization : The Hall effect determines the carrier concentration, mobility, and type in semiconductors, which is essential for designing and optimizing electronic devices.
• Space Exploration : Hall effect thrusters are ion thrusters for spacecraft propulsion. The Hall effect also measures properties of plasma in space environments.

Additionally, the effect is important in fusion research and in understand star formation.

Quantum Hall Effect

The quantum Hall effect occurs in two-dimensional electron systems subjected to low temperatures and strong magnetic fields. A characteristic of the quantum Hall effect is the quantization of the Hall conductance in integer multiples of a fundamental constant. This discovery was made by Klaus von Klitzing in 1980.

Spin Hall Effect

The spin Hall effect is a phenomenon where an electric current flowing through a material with strong spin-orbit coupling generates a transverse spin current, leading to spin accumulation on the material’s edges. This effect is essential for spintronics, a field of study that develops electronic devices based on electron spin rather than charge.

Experimental Setup for Measuring the Hall Effect

Measuring the Hall effect involves a set-up for observing the transverse voltage generated across a material when an electric current flows through it in the presence of a perpendicular magnetic field. Here’s a detailed description of the experimental setup and procedure:

Experimental Setup

• Hall Bar Sample : A rectangular strip of the material (conductor or semiconductor). The dimensions of the sample should be well-defined, especially the thickness (𝑑).
• Constant Current Source : A DC power supply that provides a stable and known current (𝐼) through the Hall bar sample.
• Magnetic Field Source : Typically an electromagnet or a permanent magnet capable of generating a uniform magnetic field (𝐵) perpendicular to the current flow in the sample. Make sure the strength of the magnetic field is adjustable and measurable.
• Voltmeter : Use a sensitive voltmeter or a digital multimeter for measuring the Hall voltage (𝑉 𝐻 ) across the sample. Connect the voltmeter to the sides of the Hall bar where the voltage develops.
• Positioning Apparatus : Use clamps or other equipment that secures the Hall bar sample in place and ensures that the magnetic field is perpendicular to the current flow.
• Temperature Control (Optional) : If the experiment requires measurements at different temperatures, include a temperature-controlled environment or a heating/cooling apparatus.
• Cut the sample into a rectangular strip with well-defined dimensions.
• Attach electrical contacts to the ends of the sample for the current and to the sides for measuring the Hall voltage.
• Connect the sample to the constant current source, ensuring that the current flows uniformly through the length of the Hall bar.
• Connect the voltmeter across the sides of the sample.
• Place the sample in the magnetic field generated by the electromagnet or permanent magnet.
• Ensure that the magnetic field is perpendicular to the plane of the Hall bar sample and the direction of the current.
• Adjust and measure the strength of the magnetic field using a gaussmeter or a similar device.
• Turn on the current source and set the desired current (𝐼) through the Hall bar.
• With the magnetic field applied, read the Hall voltage (𝑉 𝐻 ) from the voltmeter. This voltage is the potential difference across the width of the sample due to the Hall effect.
• Repeat the measurements for different values of the magnetic field strength (𝐵) and current (𝐼) to study the dependence of the Hall voltage on these parameters.
• Optionally, repeat the measurements at different temperatures if temperature control is available.

Data Analysis

• Using the measured Hall voltage (𝑉 𝐻 ​), current (𝐼), magnetic field strength (𝐵), and thickness of the sample (𝑑), calculate the Hall coefficient (𝑅 𝐻​ ) using the formula: 𝑅𝐻 = 𝑉 𝐻 ⋅𝑑 / 𝐼⋅𝐵​
• The sign of the Hall coefficient indicates the type of charge carriers: positive (𝑅 𝐻 > 0) for holes and negative (𝑅 𝐻 < 0) for electrons.
• Use the magnitude of 𝑅 𝐻 for calculating the charge carrier density (𝑛) using the relationship: 𝑛 = 1 / 𝑅 𝐻 ⋅𝑞​ where 𝑞 is the charge of the carrier (e.g., 1.6×10 −19  C for electrons).
• Calculate the mobility (𝜇) of the charge carriers if the conductivity (𝜎) of the material is known: 𝜇 = 𝜎 / 𝑛⋅𝑞​
• Braiding, C. R.; Wardle, M. (2012). “The Hall effect in star formation”. Monthly Notices of the Royal Astronomical Society . 422 (1): 261. doi: 10.1111/j.1365-2966.2012.20601.x
• Hall, Edwin (1879). “On a New Action of the Magnet on Electric Currents”. American Journal of Mathematics . 2 (3): 287–92. doi: 10.2307/2369245
• Karplus, R.; Luttinger, J. M. (1954). “Hall Effect in Ferromagnetics”. Phys. Rev . 95 (5): 1154–1160. doi: 10.1103/PhysRev.95.1154
• Ohgaki, Takeshi; Ohashi, Naoki; et al. (2008). “Positive Hall coefficients obtained from contact misplacement on evident n-type ZnO films and crystals”. Journal of Materials Research . 23 (9): 2293. doi: 10.1557/JMR.2008.0300
• Ramsden, Edward (2011). Hall-Effect Sensors: Theory and Application . Elsevier. ISBN 978-0-08-052374-3.

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Hall Effect

The Hall effect occurs when a magnetic field is applied at a right angle to an electric current flowing through a conductor. As a result, a voltage is created across the conductor, perpendicular to both the electric current and the magnetic field.

This phenomenon demonstrates how electric and magnetic fields can influence the movement of charged particles in a material. By studying the Hall effect, scientists can learn important information about the charge carriers, such as electrons, within the material.

This effect was discovered by American Physicist Edwin Hall in 1879.

When an electric current flows through a conductor, electrons move along its length in the opposite direction of the current. When a magnetic field is applied perpendicular to this current, something interesting happens. Each electron feels a force called the Lorentz force, which pushes it sideways, perpendicular to both the current direction and the magnetic field lines .

This sideways push is key to understanding the Hall Effect. Imagine electrons moving through a conductor because of an electric field that drives them forward. When a magnetic field is added, it exerts a sideways force on the electrons, making them move to one side of the conductor. As electrons gather on one side, they create a negative charge buildup, leaving a positive charge on the other side. This separation of charges creates an electric field inside the conductor that opposes further electron movement.

This process continues until the electric force from the charge buildup balances the magnetic force from the Lorentz force. The result is a stable situation where the forces are balanced, and a voltage, called the Hall voltage, is generated across the conductor.

In the previous section, we saw how Hall voltage is generated. The following expression gives its value:

• V H is the Hall voltage
• I x is the current flowing through the conductor
• B z is the applied magnetic field
• n is the number of charge carriers per unit volume
• e is the value of the electric charge
• t is the thickness of the conductor

Hall Coefficient

The Hall coefficient is a fundamental parameter in understanding the behavior of charge carriers in materials subjected to a magnetic field. It is defined as the ratio of the Hall voltage to the product of the applied magnetic field, current density, and sample thickness. Mathematically, the Hall coefficient is given by

• R H is the Hall coefficient
• E y is the electric field due to the Hall effect
• j x is the current density

The Hall coefficient provides crucial insights into the material’s electronic properties. Its interpretation extends beyond a mere numerical value. It reflects the density and mobility of charge carriers within the material.

Applications

• Magnetic Field Sensing Equipment: Used to measure magnetic fields accurately in various applications, including scientific research and industrial processes.
• Current Sensors: Enables the measurement of electrical currents without direct contact, enhancing safety and reliability in electrical systems.
• Voltage Sensors: Utilized to measure voltages accurately across different systems, ensuring precise monitoring and control.
• Magneto-Resistive Sensors: Detects changes in magnetic fields by measuring resistance, commonly used in data storage devices, automotive applications, and more.

Aside, Hall effect can determine the carrier concentration, mobility, and conductivity of semiconductors.

Example Problems

Problem 1 : A thin rectangular metal plate of thickness 1 cm is subjected to a magnetic field of strength B = 0.5 T. When a current of I = 2 A flows through the plate, a Hall voltage of V H = 0.1 V is measured. Calculate the charge carrier density in the metal.

The Hall voltage can be calculated using the formula:

Rearranging the formula for n, we get:

Given data:

• B z = 0.5 T
• V H = 0.1 V
• t = 1 cm = 0.01 m (converted to meters)

Substituting the values, we get:

The charge carrier density of the metal is 6.25 x 10 21 m – 3 .

• Hall Effect – Hyperphysics.phy-astr.gsu.edu
• The Hall Effect – Courses.lumenlearning.com
• What is the Hall Effect? – Melexis.com
• The Hall Effect – Phys.libretexts.org

Article was last reviewed on Tuesday, July 23, 2024

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by Chris Woodford . Last updated: June 7, 2024.

Photo: A Hall-effect sensor (indicated by the white arrow) helps to measure the rotational position of this old floppy disk motor. More about this in a moment...

What is the Hall effect?

Photo: You can't see a magnetic field, but you can measure it with the Hall effect. Photo by courtesy of Wikimedia Commons .

“ If the current of electricity in a fixed conductor is itself attracted by a magnet, the current should be drawn to one side of the wire... ” Edwin Hall , 1879

How does the Hall effect work?

Which way do they go.

Artwork: Charged particles moving in a magnetic field experience a force (the Lorentz force) that changes their direction, giving rise to the Hall effect. You can use Fleming's left-hand rule (motor rule) to figure out the direction of the force providing you remember that the rule applies to conventional current (a flow of positive charges) and the field flows from north to south. In this example, if we have a flow of electrons into the page, the conventional current flows out of the page (so that's the direction in which your second finger should point). If the field flows from left to right (first finger), our thumb tells us the electrons will move upward.

Using the Hall effect

Photo: 1) A typical silicon Hall-effect sensor. It looks very much like a transistor —hardly surprising since it's made in a similar way. Photo by explainthatstuff.com. 2) A Hall-effect probe used by NASA in the mid-1960s. Photo by courtesy of NASA Glenn Research Center (NASA-GRC) .

What are Hall-effect sensors used for?

Photo: This small brushless DC motor from an old floppy-disk drive has three Hall-effect sensors (indicated by red circles) positioned around its edge, which detect the motion of the motor's rotor (a rotating permanent magnet) above them (not shown on this photo). The sensors are not much to look at, as you can see from the closeup photo on the right!

Artwork: How a typical Hall sensor is packaged. Magnetic fields can be very small, so we need our detectors to be as sensitive as possible, and here's one way to achieve that. The Hall chip itself (green, 17) is mounted on an iron carrier plate (gray, 16) sandwiched inside two molded plastic sections (gray, 11, 12). The chip is wired by leads (19) to terminal pins (blue) by which it can be connected into a circuit. But the really important parts are two soft iron "flux concentrators" (orange, 15, 21), which make the device very much more sensitive. When you place a magnet (22) near the sensor, these concentrators allow the magnetic flux (the "density" of magnetism produced by the magnetic field) to flow around a continuous loop through the Hall chip, producing either a positive or negative voltage. If the magnet slides over to the other side of the sensor, it produces the opposite voltage. Artwork from US Patent 3,845,445: Modular Hall Effect Device by Roland Braun et al, IBM Corporation, October 29, 1974, courtesy of US Patent and Trademark Office.

If you liked this article...

Don't want to read our articles try listening instead, find out more, you might also like these articles....

• Researchers Simplify Switching for Quantum Electronics by Edd Gent. IEEE Spectrum, October 30, 2023. What is the quantum Hall effect... and what use is it?
• Graphene Magnetic Sensor Hundred Times More Sensitive Than Silicon by Dexter Johnson. IEEE Spectrum, June 26, 2015. German researchers develop magnetic Hall effect sensors based on graphene.
• How Do You Measure the Magnetic Field? by Rhett Allain. Wired, January 21, 2014. Comparing traditional compasses with Hall-effect sensors found in a smartphone.
• [PDF] The discovery of the Hall effect by G.S. Leadstone, Physics Education, Volume 14, 1979. How Hall discovered his effect and figured out what it meant by challenging some of the earlier work by James Clerk Maxwell.

More technical

• The Vertical Hall-Effect Device by R. S. Popovic, IEEE Electron Device Letters, Vol.5, No.9, pp.357–358, Sept. 1984, doi: 10.1109/EDL.1984.25945.

Papers by Edwin Hall

• On a New Action of the Magnet on Electric Currents by Edwin H. Hall, American Journal of Mathematics, Vol. 2, No. 3 (Sep., 1879), pp. 287–292. Hall's original paper.
• An Explanation of Hall's Phenomenon by Edwin H. Hall, Science, Vol. 3, No. 60 (Mar. 28, 1884), pp. 386–387. Hall's own description and explanation of his original experiment.
• A Theory of the Hall Effect and the Related Effect for Several Metals by Edwin H. Hall, PNAS USA, Vol. 9, No. 2 (Feb. 15, 1923), pp. 41–46. One of Hall's later papers.
• Hall-Effect Sensors: Theory and Applications by Edward Ramsden. Newnes, 2006. Covers the physics behind Hall-effect sensors and how to incorporate them into practical circuits. Includes coverage of proximity sensors, current-sensors, and speed-and-timing sensors. Also has a handy glossary and list of suppliers.
• Hall-Effect Devices by R. S. Popović. Institute of Physics, 2004. A somewhat bigger and more detailed book, but covering similar ground with a mixture of theory, practical circuits, and everyday applications.
• The Hall Effect and Its Applications by C. Chien (ed). Plenum Press, 1980/Springer, 2013. A reissue of the proceedings of a 1979 symposium at Johns Hopkins University, on November 13, 1979 to commemorate the 100th anniversary of Hall's discovery.
• The Hall Effect in Metals and Alloys by Colin Hurd. Springer 1972/2012. A modern reissue of a 1970s introduction.

Practical projects

• Door Activated LED Lighting using Hall Effect Sensors : Woody1189 wires up his closet with a Hall-effect sensor so it lights up automatically when he opens the door!
• Electric Bike Hub Motor—How to Replace a Hall-effect Sensor : Jeremy Nash explains what a Hall-effect sensor does in a brushless motor—and how to replace the sensor when it fails.
• How to make a magnet polarity detection circuit : Thomas Kim shows us how to make a magnet detector based on a Hall-effect sensor extracted from a laptop cooler fan.
• US Patent 3,845,445A: Modular hall effect device by R. Braun et al, IBM, October 29, 1974. The concentrating, modular Hall effect device illustrated above.
• US Patent 3,845,445A: Hall element device with depletion region protection barrier by R. Popovic, Siemens, May 29, 1990. A Hall element that can be incorporated into an integrated circuit that's designed to be stable over a long lifetime.

Text copyright © Chris Woodford 2009, 2020. All rights reserved. Full copyright notice and terms of use .

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Nanoscale Device Characterization Division

Hall effect measurements introduction.

The objective of this Web site is twofold: (1) to describe the Hall measurement technique for determining the carrier density and mobility in semiconductor materials and (2) to initiate an electronic interaction forum where workers interested in the Hall effect can exchange ideas and information. The following pages will lead the reader through an introductory description of the Hall measurement technique, covering basic principles, equipment, and recommended procedures.

The importance of the Hall effect is supported by the need to determine accurately carrier density, electrical resistivity, and the mobility of carriers in semiconductors. The Hall effect provides a relatively simple method for doing this. Because of its simplicity, low cost, and fast turnaround time, it is an indispensable characterization technique in the semiconductor industry and in research laboratories. Furthermore, two Nobel prizes (1985, 1998) are based upon the Hall effect.

The history of the Hall effect begins in 1879 when Edwin H. Hall discovered that a small transverse voltage appeared across a current-carrying thin metal strip in an applied magnetic field. Until that time, electrical measurements provided only the carrier density-mobility product, and the separation of these two important physical quantities had to rely on other difficult measurements. The discovery of the Hall effect enabled a direct measure of the carrier density. The polarity of this transverse Hall voltage proved that it is in fact electrons that are physically moving in an electric current. Development of the technique has since led to a mature and practical tool, which today is used routinely for characterizing the electrical properties and quality of almost all of the semiconductor materials used by industry and in research labs throughout the world.

Notice of Online Archive: This page is no longer being updated and remains online for informational and historical purposes only.

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Hall effect, what it shows:.

When a magnetic field is applied perpendicular to a conductor carrying current, a potential difference is observed between points on opposite sides of the conductor. This happens because the magnetic field deflects the moving electrons (Lorentz force) to the edge of the conductor and the altered charge distribution generates a transverse electric field.

How it works:

The conductor is a small bar (11mm × 2mm × 2mm) of germanium (p-type?). Current (18 mA) is made to flow down the length of the bar by a 3 volt potential difference. Two pointed screws are used to pick up the transverse voltage across the bar. In the absence of a magnetic field, these points would be at the same potential, but due to the fact that they are not exactly opposite each other, there is a small (5½ mV) potential difference between them. Upon inserting the sample in a magnetic field (provided by a 2500 gauss "magnetron magnet"), the potential increases to +24½ mV. When the magnetic field is reversed (simply flip the sample over), the potential difference is -13½ mV. The change in potential is 38 mV and we deduce the Hall Voltage to be half of that, or 19 mV.

Setting it up:

The germanium sample and digital voltmeter can be shown on a document camera. The current is provided by two 1½ volt batteries in series.

The effect was discovered in 1879 by E.H. Hall. In those days no one understood the mechanism of conduction in metals. A complete understanding of the Hall effect came only with the quantum theory of metals, about 50 years after Hall's discovery.

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Hall effect

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• BCcampus Publishing - The Hall Effect
• Core - The Hall effect - an important diagnostic tool
• Engineering LibreTexts - Hall Effect
• Christian-Albrechts-Universität zu Kiel - Departments of the Faculty of Engineering - The Hall Effect
• The Department of Physics at the University of Toronto - The Hall Effect
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• National Center for Biotechnology Information - PubMed Central - Hall Effect Imaging
• University of Central Florida Pressbooks - University Physics Volume 2 - The Hall Effect
• The National High Magnetic Field Laboratory - Magnetic Academy - Hall Effect
• Hall effect - Student Encyclopedia (Ages 11 and up)

Hall effect , development of a transverse electric field in a solid material when it carries an electric current and is placed in a magnetic field that is perpendicular to the current. This phenomenon was discovered in 1879 by the U.S. physicist Edwin Herbert Hall. The electric field, or Hall field, is a result of the force that the magnetic field exerts on the moving positive or negative particles that constitute the electric current. Whether the current is a movement of positive particles, negative particles in the opposite direction, or a mixture of the two, a perpendicular magnetic field displaces the moving electric charges in the same direction sideways at right angles to both the magnetic field and the direction of current flow. The accumulation of charge on one side of the conductor leaves the other side oppositely charged and produces a difference of potential. An appropriate meter may detect this difference as a positive or negative voltage. The sign of this Hall voltage determines whether positive or negative charges are carrying the current.

In metals, the Hall voltages are generally negative, indicating that the electric current is composed of moving negative charges, or electrons. The Hall voltage is positive, however, for a few metals such as beryllium , zinc , and cadmium , indicating that these metals conduct electric currents by the movement of positively charged carriers called holes . In semiconductors, in which the current consists of a movement of positive holes in one direction and electrons in the opposite direction, the sign of the Hall voltage shows which type of charge carrier predominates. The Hall effect can be used also to measure the density of current carriers, their freedom of movement, or mobility , as well as to detect the presence of a current on a magnetic field.

The Hall voltage that develops across a conductor is directly proportional to the current, to the magnetic field, and to the nature of the particular conducting material itself; the Hall voltage is inversely proportional to the thickness of the material in the direction of the magnetic field. Because various materials have different Hall coefficients, they develop different Hall voltages under the same conditions of size, electric current, and magnetic field. Hall coefficients may be determined experimentally and may vary with temperature .

What is a Hall Effect in Metals and Semiconductor

Hall Effect was introduced by an American Physicist Edwin H.Hall in the year 1879. It is based on the measurement of the electromagnetic field. It is also named as ordinary Hall Effect. When a current-carrying conductor is perpendicular to a magnetic field, a voltage generated is measured at right angles to the current path. Where current flow is similar to that of liquid flowing in a pipe. Firstly it was applied in the classification of chemical samples. Secondly, it was applicable in Hall Effect Sensor where it was used to measure DC fields of the magnet, where the sensor is kept stationary.

Principle of Hall Effect

Hall Effect is defined as the difference in voltage generated across a current-carrying conductor, is transverse to an electrical current in the conductor and an applied magnetic field perpendicular to the current.

Hall Effect = induced electric field / current density * the applied magnetic field –(1)

Theory of Hall Effect

Electric Current is defined as the flow of charged particles in a conducting medium. The charges that are flowing can either be Negative charged – Electrons ‘e- ‘/ Positive charged – Holes ‘+’.

Consider a thin conducting plate of length L and connect both ends of a plate with a battery. Where one end is connected from the positive end of a battery to one end of the plate and another end is connected from the negative end of a battery to another end of the plate. Now we observe that currently starts flowing from negative charge to the positive end of the plate. Due to this movement, a magnetic field is generated.

Lorentz Force

For instance, if we place a magnetic bare nearby the conductor the magnetic field will disturb the magnetic field of charge carriers. This force which distorts the direction of charge carriers is known as Lorentz force.

Due to this, the electrons will move to one end of the plate and holes will move to another end of the plate. Here Hall voltage is measured between two sides of plates with a multimeter . This effect is also known as the Hall Effect. Where the current is directly proportional to deflected electrons in turn proportional to the potential difference between both plates.

Larger the current larger is the deflected electrons and hence we can observe the high potential difference between the plates.

Hall Voltage is directly proportional to the electric current and applied magnetic field.

VH = I B / q n d —– ( 2 )

I – Current flowing in Sensor B – Magnetic Field Strength q – Charge n – charge carriers per unit volume d – Thickness of the sensor

Derivation of Hall Coefficient

Let current IX is current density, JX times the correctional area of the conductor wt.

IX = JX wt = n q vx w t ———-( 3 )

According to Ohms law, if current increases the field also increases. Which is given as

JX = σ EX , ————( 4 )

Where σ = conductivity of the material in the conductor.

On considering the above example of placing a magnetic bar right angle to the conductor we know that it experience Lorentz force. When a steady state is reached there will be no flow of charge in any direction which can be represented as,

EY = Vx Bz , ————–( 5 )

EY – electric field / Hall field in the y-direction

Bz – magnetic field in the z-direction

VH = – ∫0w EY day = – Ey w ———-( 6 )

VH = – ( (1/n q ) IX Bz ) / t , ———– ( 7 )

Where RH = 1/nq ———— ( 8 )

Units of Hall Effect: m3 /C

Hall Mobility

µ p or µ n = σ n R H ———— ( 9 )

Hall mobility is defined as µ p or µ n is conductivity due to electrons and holes.

Magnetic Flux Density

It is defined as the amount of magnetic flux in an area taken right angles to the magnetic flux’s direction.

B = VH d / RH I ——– ( 1 0 )

Hall Effect in Metals and Semiconductor

According to the electric field and magnetic field the charge carriers which are moving in the medium experience some resistance because of scattering between carriers and impurities, along with carriers and atoms of material which are undergoing vibration. Hence each carrier scatters and loses its energy. Which can be represented by the following equation

F retarded  = – mv/t , ————– ( 1 1 )

t = average time between scattering events

According to Newtons seconds law ,

M (dv/dt )= ( q ( E + v * B ) – m v) / t ——( 1 2 )

m= mass of the carrier

When a steady state occurs the parameter’ v ‘ will be neglected

If ’B’ is along z-coordinate we can obtain a set of ’ v ‘ equations

vx = ( qT Ex) / m + (qt BZ vy ) / m ———– ( 1 3 )

vy = (qT Ey ) / m – (qt BZ vx) / m ———— ( 1 4 )

vz = qT Ez / m ———- ( 1 5 )

We know that Jx = n q vx ————— ( 1 6 )

Substituting in the above equations we can modify it as

Jx = ( σ/ ( 1 + (wc t)2)) ( Ex + wc t Ey ) ———– ( 1 7 )

J y = ( σ * ( Ey – wc t Ex ) / ( 1 + (wc t)2 ) ———- ( 1 8 )

Jz = σ Ez ———— ( 1 9 )

We know that

σ n q2 t / m ———– ( 2 0 )

σ = conductivity

t = relaxation time

wc q Bz / m ————– ( 2 1 )

wc = cyclotron frequency

Cyclotron Frequency is defined as in a magnetic field frequency of rotation of a charge. Which is the strength of the field.

Which can be explained in the following cases to know if it is not strong and/or “t” is short

Case (i) : If wc t << 1

It indicates a weak field limit

Case (ii) : If wc t >> 1

It indicates a strong field limit.

The advantages of the hall-effect include the following.

• Speed of operation is high i.e, 100 kHz
• Loop of operations
• Capacity to measure large current
• It can measure Zero speed.

Disadvantages

The disadvantages of the hall-effect include the following.

• It cannot measure the flow of current greater than 10cm
• There is a large effect of temperature on carriers, which is directly proportional
• Even in the absence of a magnetic field small voltage is observed when electrodes are at centered.

Applications of Hall Effect

The applications of the hall-effect include the following.

• Magnetic Field senor
• Used for multiplication
• For direct current measuring, it uses Hall Effect Tong Tester
• We can measure phase angles
• We can also measure Linear displacements transducer
• Spacecraft propulsion
• Power supply sensing

 Thus, the Hall Effect is based on the Electro-magnetic principle. Here we have seen the derivation of Hall Coefficient, also Hall Effect in Metals and Semiconductors . Here is a question, How is Hall Effect applicable in Zero speed operation?

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Physical Review B

Covering condensed matter and materials physics.

• Collections
• Editorial Team

Emergence of giant orbital Hall and tunable spin Hall effects in centrosymmetric transition metal dichalcogenides

Pratik sahu, jatin kumar bidika, bubunu biswal, s. satpathy, and b. r. k. nanda, phys. rev. b 110 , 054403 – published 1 august 2024.

• No Citing Articles
• Supplemental Material
• INTRODUCTION
• BASIC FORMALISM AND COMPUTATIONAL METHOD
• MAGNETIC MOMENTS AND ANOMALOUS HALL…
• ORBITAL AND SPIN HALL CONDUCTIVITIES
• SUMMARY AND OUTLOOK
• ACKNOWLEDGMENTS

We demonstrate the formation of orbital and spin Hall effects (OHE/SHE) in the 1T phase of nonmagnetic transition metal dichalcogenides. With the aid of density functional theory calculations and model Hamiltonian studies on M X 2 ( M = Pt, Pd; and X = S, Se, and Te), we show an intrinsic orbital Hall conductivity ( ∼ 10 3 ℏ / e Ω − 1 cm − 1 ), which primarily emerges due to the orbital texture around the valleys in the momentum space. The robust spin-orbit coupling in these systems induces a sizable SHE out of OHE. Furthermore, to resemble the typical experimental setups, where the magnetic overlayers produce a proximity magnetic field, we examine the effect of magnetic field on OHE and SHE and showed that the latter can be doubled in these class of compounds. With a giant OHE and tunable SHE, the 1T-TMDs are promising candidates for spin and orbital driven quantum devices such as SOT-MRAM, spin nano-oscillators, spin logic devices, etc., and to carry out spin-charge conversion experiments for fundamental research.

• Received 14 May 2024
• Revised 13 July 2024
• Accepted 22 July 2024

DOI: https://doi.org/10.1103/PhysRevB.110.054403

©2024 American Physical Society

Physics Subject Headings (PhySH)

• Research Areas
• Physical Systems

Authors & Affiliations

• 1 Center for Atomistic Modelling and Materials Design, Indian Institute of Technology Madras , Chennai 600036, India
• 2 Condensed Matter Theory and Computational Lab, Department of Physics, Indian Institute of Technology Madras , Chennai 600036, India
• 3 Department of Physics and Astronomy, University of Missouri , Columbia, Missouri 65211, USA
• * Contact author: [email protected]
• † Contact author: [email protected]
• ‡ Contact author: [email protected]

Article Text (Subscription Required)

Supplemental material (subscription required), references (subscription required).

Vol. 110, Iss. 5 — 1 August 2024

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A schematic diagram illustrating orbital and spin Hall effect, where the electric field is applied along the x axis, and the orbital/spin current is produced along the y axis. Vertical arrows represent spins, while the circles indicate orbital magnetization.

(a) Crystal structure of the 3D TMDs in the centrosymmetric 1 T phase, top and side views (left and right, respectively). (b) Comparison of the band structures of PtSe 2 obtained from the DFT and tight binding methods in the presence of SOC and without the magnetic field ( B = 0 ). (c) Partial densities of state (PDOS), indicating Pt(d) and Se(p) to be the important orbitals near the Fermi energy. (d) Tight-binding band structure in the presence of both the magnetic field and SOC. The colored spin-split bands are not spin pure due to the SOC term, which mixes the two spins. Note that the hole pocket at Γ and the electron pockets at K as well as along the H − A line are the dominant contributors to the Hall conductivities due to the energy denominator in the Kubo expressions. (e) Sketch of the Brillouin zone.

Momentum space distribution of (a) orbital moment and (b) spin moment for B z = 0.1  eV in PtSe 2 in the k z = 0 plane. The units are in Bohr magneton ( μ B ). The moments are prominent around the K and the Γ points on this plane, contributing a principal amount to the SHC/OHC. Panels (c) and (d) show the total orbital and spin moments (BZ sum) as a function of the magnetic field. Without a magnetic field, the net moments, as well as the moments everywhere in the BZ, are zero due to the existence of both the inversion and the time reversal symmetry.

Anomalous Hall conductivity in PtSe 2 in the presence of the magnetic field. (a) Berry curvature Ω z ( k ⃗ ) (units of Å 2 ), defined as the sum of ∑ n Ω n k ⃗ z over the occupied bands n , on the k z = 0 plane with the scaled magnetic field μ B B 0 / ℏ ≡ B z = 0.1  eV. (b) Different components of the AHC in units of ℏ / e Ω − 1 cm − 1 as a function of the magnetic field.

(a) Orbital and (b) spin Hall conductivity for PtSe 2 , with B = 0 , as a function of the Fermi energy. (c) and (d) Orbital and spin Berry curvature sums Ω y x z , orb / spin ( k ⃗ ) , defined as the sum over occupied bands of the corresponding Berry curvature at a specific k ⃗ point, in units of Å 2 in the k z = 0 plane for the case E F = 0 . Contours of constant OBC/SBC values are shown in Panels (c) and (d). We note that while the SBC (d) preserves the sixfold rotational symmetry of the crytal, it is broken in the case of OBC (c). This is attributed to the distortion of the hybridized orbitals due to the electric field.

Orbital and spin Berry curvature sums along the high symmetry lines for PtSe 2 .

Orbital, spin, and anomalous Hall conductivities for PtSe 2 as a function of the magnetic field. Note that the magnitude of the OHC is by far the largest as compared to the other two, and of course the AHC is nonzero only when a magnetic field is present. The conductivities are in units of ℏ / e Ω − 1 cm − 1 .

(a) Dependence of the OHC and SHC for PtSe 2 (units of ℏ / e Ω − 1 cm − 1 ) on the SOC strength λ . Here, B z = 0 . (b) The same as a function of the magnetic field but with λ = 0 . The SHC is zero, if both λ and B z are zero.

Magnitudes of the OHC (left) and the SHC (right) as a function of the applied magnetic field for several TMD compounds.

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