Ferromagnetic resonance, or FMR, is coupling between an

electromagnetic wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...

and the

magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quanti ...

of a medium through which it passes. This coupling induces a significant loss of power of the wave. The power is absorbed by the precessing magnetization (

Larmor precession Sir Joseph Larmor (; 11 July 1857 – 19 May 1942) was an Irish mathematician and physicist who made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter. His most influential work was ...

) of the material and lost as heat. For this coupling to occur, the frequency of the incident wave must be equal to the precession frequency of the magnetization (Larmor frequency) and the polarization of the wave must match the orientation of the magnetization. This effect can be used for various applications such as spectroscopic techniques or conception of

microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...

devices. The FMR spectroscopic technique is used to probe the

ferromagnetic Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagne ...

materials. It is a standard tool for probing spin waves and spin dynamics. FMR is very broadly similar to

electron paramagnetic resonance Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spin ...

(EPR), and also somewhat similar to

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

(NMR), except that FMR probes the sample magnetization resulting from the

magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

s of dipolar-coupled but unpaired

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

s, while NMR probes the magnetic moment of

atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. Aft ...

that are screened by the atomic or molecular orbitals surrounding such nuclei of non-zero nuclear spin. The FMR resonance is also the basis of various high-frequency electronic devices, such as resonance isolators or

circulator In electrical engineering, a circulator is a passivity (engineering), passive, non-Reciprocity (electrical networks), reciprocal three- or four-port (circuit theory), port device that only allows a microwave or radio frequency, radio-frequency ...

History

Ferromagnetic resonance was experimentally discovered by V. K. Arkad'yev when he observed the absorption of

UHF Ultra high frequency (UHF) is the ITU designation for radio frequencies in the range between 300 megahertz (MHz) and 3 gigahertz (GHz), also known as the decimetre band as the wavelengths range from one meter to one tenth of a meter ...

radiation by

ferromagnetic material Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromag ...

s in 1911. A qualitative explanation of FMR along with an explanation of the results from Arkad'yev was offered up by Ya. G. Dorfman in 1923, when he suggested that the

optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...

transitions due to Zeeman splitting could provide a way to study ferromagnetic structure. A 1935 paper published by

Lev Landau Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and ma ...

and

Evgeny Lifshitz Evgeny Mikhailovich Lifshitz (; ; 21 February 1915 – 29 October 1985) was a leading Soviet physicist and brother of the physicist Ilya Lifshitz. Work Born into a Ukrainian Jewish family in Kharkov, Kharkov Governorate, Russian Empire (now K ...

predicted the existence of ferromagnetic resonance of the

, which was independently verified in experiments by J. H. E. Griffiths (UK) and E. K. Zavoiskij (USSR) in 1946.

Description

FMR arises from the precessional motion of the (usually quite large) magnetization

\scriptstyle\vec

of a ferromagnetic material in an external magnetic field

\scriptstyle\vec

. The magnetic field exerts a

torque In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...

on the sample magnetization which causes the magnetic moments in the sample to

precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In ot ...

. The precession frequency of the magnetization depends on the orientation of the material, the strength of the magnetic field, as well as the macroscopic magnetization of the sample; the effective precession frequency of the ferromagnet is much lower in value from the precession frequency observed for free electrons in EPR. Moreover, linewidths of absorption peaks can be greatly affected both by dipolar-narrowing and exchange-broadening (quantum) effects. Furthermore, not all absorption peaks observed in FMR are caused by the precession of the magnetic moments of electrons in the ferromagnet. Thus, the theoretical analysis of FMR spectra is far more complex than that of EPR or NMR spectra. The basic setup for an FMR experiment is a microwave resonant cavity with an

electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire (likely copper) wound into a electromagnetic coil, coil. A current through the wire creates a magnetic ...

. The resonant cavity is fixed at a frequency in the

super high frequency Super high frequency (SHF) is the ITU designation for radio frequencies (RF) in the range between 3 and 30 gigahertz (GHz). This band of frequencies is also known as the centimetre band or centimetre wave as the wavelengths range from one ...

band. A detector is placed at the end of the cavity to detect the microwaves. The magnetic sample is placed between the poles of the electromagnet and the

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

is swept while the resonant absorption intensity of the microwaves is detected. When the magnetization precession frequency and the resonant cavity frequency are the same, absorption increases sharply which is indicated by a decrease in the intensity at the detector. Furthermore, the resonant absorption of microwave energy causes local heating of the ferromagnet. In samples with local magnetic parameters varying on the nanometer scale this effect is used for spatial dependent spectroscopy investigations. The resonant frequency of a film with parallel applied external field

B

is given by the

Kittel 220px, A kittel A ''kittel'' ( ) is a white linen or cotton robe worn by some religious Ashkenazi Jews on holidays, in the synagogue or at home when leading the Passover seder. Grooms sometimes wear kittels. It is also customary for Jews to be ...

formula: :

f = \frac  \sqrt

where

M

is the magnetization of the ferromagnet and

\gamma

is the

gyromagnetic ratio In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...

References

External links

* *
Ferromagnetic Resonance (FMR)
(Wolfgang Kuch, Freie Universität Berlin) {{Branches of spectroscopy Spectroscopy Magnetic ordering

History

Description

See also

References

Further reading

External links