Ferromagnetic resonance

Ferromagnetic resonance,orFMR,is coupling between anelectromagnetic waveand themagnetizationof 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) 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 thepolarizationof the wave must match the orientation of the magnetization.

This effect can be used for various applications such asspectroscopictechniques or conception ofmicrowavedevices.

The FMRspectroscopictechnique is used to probe themagnetizationofferromagneticmaterials. It is a standard tool for probingspin wavesand spin dynamics. FMR is very broadly similar toelectron paramagnetic resonance(EPR), and also somewhat similar tonuclear magnetic resonance(NMR), except that FMR probes the sample magnetization resulting from themagnetic momentsof dipolar-coupled but unpairedelectrons,while NMR probes the magnetic moment ofatomic nucleithat 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 asresonance isolatorsorcirculators.

History[edit]

Ferromagnetic resonance was experimentally discovered byV. K. Arkad'yevwhen he observed theabsorptionofUHFradiation byferromagnetic materialsin 1911. A qualitative explanation of FMR along with an explanation of the results from Arkad'yev was offered up byYa. G. Dorfmanin 1923, when he suggested that theopticaltransitions due toZeemansplitting could provide a way to study ferromagnetic structure.

A 1935 paper published byLev LandauandEvgeny Lifshitzpredicted the existence of ferromagnetic resonance of theLarmor precession,which was independently verified in experiments by J. H. E. Griffiths (UK) andE. K. Zavoiskij(USSR) in 1946.^[1]^[2]^[3]

Description[edit]

FMR arises from the precessional motion of the (usually quite large) magnetization $\scriptstyle {\vec {M}}$ of a ferromagnetic material in an external magnetic field $\scriptstyle {\vec {H}}$ .The magnetic field exerts atorqueon the sample magnetization which causes the magnetic moments in the sample toprecess.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 amicrowave resonant cavitywith anelectromagnet.The resonant cavity is fixed at a frequency in thesuper high frequencyband. 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 themagnetic fieldis 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 theKittelformula:^[4]

f={\frac {\gamma }{2\pi }}{\sqrt {B(B+\mu _{0}M)}}

where $M$ is the magnetization of the ferromagnet and $\gamma$ is thegyromagnetic ratio.^[5]

References[edit]

^J. H. E. Griffiths (1946). "Anomalous high-frequency resistance of ferromagnetic metals".Nature.158(4019): 670–671.Bibcode:1946Natur.158..670G.doi:10.1038/158670a0.S2CID 4143499.
^Zavoisky, E.(1946). "Spin magnetic resonance in the decimeter-wave region".Fizicheskiĭ Zhurnal.10.
^Zavoisky, E.(1946). "Paramagnetic absorption in some salts in perpendicular magnetic fields".Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki.16(7): 603–606.
^Kittel, Charles; (2004).Introduction to Solid State Physics(8th ed.). Wiley.ISBN 047141526X
^Kittel, Charles (15 January 1948). "On the Theory of Ferromagnetic Resonance Absorption".Physical Review.73(2): 155–161.Bibcode:1948PhRv...73..155K.doi:10.1103/PhysRev.73.155.

External links[edit]

Calculation of some important resonance fields
Spatially resolved ferromagnetic resonance technique
Ferromagnetic Resonance (FMR)(Wolfgang Kuch, Freie Universität Berlin)

[1] J. H. E. Griffiths (1946). "Anomalous high-frequency resistance of ferromagnetic metals".Nature.158(4019): 670–671.Bibcode:1946Natur.158..670G.doi:10.1038/158670a0.S2CID 4143499.

[2] Zavoisky, E.(1946). "Spin magnetic resonance in the decimeter-wave region".Fizicheskiĭ Zhurnal.10.

[3] Zavoisky, E.(1946). "Paramagnetic absorption in some salts in perpendicular magnetic fields".Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki.16(7): 603–606.

[4] Kittel, Charles; (2004).Introduction to Solid State Physics(8th ed.). Wiley.ISBN 047141526X

[5] Kittel, Charles (15 January 1948). "On the Theory of Ferromagnetic Resonance Absorption".Physical Review.73(2): 155–161.Bibcode:1948PhRv...73..155K.doi:10.1103/PhysRev.73.155.

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Ferromagnetic resonance

History[edit]

Description[edit]

See also[edit]

References[edit]

Further reading[edit]

External links[edit]