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spin wave wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 theory toggle theory subsection 1 1 magnetization 2 experimental observation 3 practical significance 4 see also 5 references 6 external links toggle the table of contents spin wave 11 languages azərbaycanca català deutsch español français 日本語 қазақша 한국어 polski русский tiếng việt edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia wave which propagates through a magnetic material this article includes a list of general references but lacks sufficient corresponding inline citations please help improve this article by introducing more precise citations december 2013 learn how and when to remove this message in condensed matter physics a spin wave is a propagating disturbance in the ordering of a magnetic material these low lying collective excitations occur in magnetic lattices with continuous symmetry from the equivalent quasiparticle point of view spin waves are known as magnons which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice as temperature is increased the thermal excitation of spin waves reduces a ferromagnet s spontaneous magnetization the energies of spin waves are typically only μev in keeping with typical curie points at room temperature and below theory edit an illustration of the precession of a spin wave with a wavelength that is eleven times the lattice constant about an applied magnetic field the projection of the magnetization of the same spin wave along the chain direction as a function of distance along the spin chain the simplest way of understanding spin waves is to consider the hamiltonian h displaystyle mathcal h for the heisenberg ferromagnet h 1 2 j i j s i s j g μ b i h s i displaystyle mathcal h frac 1 2 j sum _ i j mathbf s _ i cdot mathbf s _ j g mu _ rm b sum _ i mathbf h cdot mathbf s _ i where j is the exchange energy the operators s represent the spins at bravais lattice points g is the landé g factor μ b is the bohr magneton and h is the internal field which includes the external field plus any molecular field note that in the classical continuum case and in 1 1 dimensions the heisenberg ferromagnet equation has the form s t s s x x displaystyle mathbf s _ t mathbf s times mathbf s _ xx in 1 1 2 1 and 3 1 dimensions this equation admits several integrable and non integrable extensions like the landau lifshitz equation the ishimori equation and so on for a ferromagnet j 0 and the ground state of the hamiltonian 0 displaystyle 0 rangle is that in which all spins are aligned parallel with the field h that 0 displaystyle 0 rangle is an eigenstate of h displaystyle mathcal h can be verified by rewriting it in terms of the spin raising and spin lowering operators given by s s x i s y displaystyle s pm s x pm is y resulting in h 1 2 j i j s i z s j z g μ b h i s i z 1 4 j i j s i s j s i s j displaystyle mathcal h frac 1 2 j sum _ i j s_ i z s_ j z g mu _ rm b h sum _ i s_ i z frac 1 4 j sum _ i j s_ i s_ j s_ i s_ j where z has been taken as the direction of the magnetic field the spin lowering operator s annihilates the state with minimum projection of spin along the z axis while the spin raising operator s annihilates the ground state with maximum spin projection along the z axis since s i z 0 s 0 displaystyle s_ i z 0 rangle s 0 rangle for the maximally aligned state we find h 0 j s 2 g μ b h s n 0 displaystyle mathcal h 0 rangle left js 2 g mu _ rm b hs right n 0 rangle where n is the total number of bravais lattice sites the proposition that the ground state is an eigenstate of the hamiltonian is confirmed one might guess that the first excited state of the hamiltonian has one randomly selected spin at position i rotated so that s i z 1 s 1 1 displaystyle s_ i z 1 rangle s 1 1 rangle but in fact this arrangement of spins is not an eigenstate the reason is that such a state is transformed by the spin raising and lowering operators the operator s i displaystyle s_ i will increase the z projection of the spin at position i back to its low energy orientation but the operator s j displaystyle s_ j will lower the z projection of the spin at position j the combined effect of the two operators is therefore to propagate the rotated spin to a new position which is a hint that the correct eigenstate is a spin wave namely a superposition of states with one reduced spin the exchange energy penalty associated with changing the orientation of one spin is reduced by spreading the disturbance over a long wavelength the degree of misorientation of any two near neighbor spins is thereby minimized from this explanation one can see why the ising model magnet with discrete symmetry has no spin waves the notion of spreading a disturbance in the spin lattice over a long wavelength makes no sense when spins have only two possible orientations the existence of low energy excitations is related to the fact that in the absence of an external field the spin system has an infinite number of degenerate ground states with infinitesimally different spin orientations the existence of these ground states can be seen from the fact that the state 0 displaystyle 0 rangle does not have the full rotational symmetry of the hamiltonian h displaystyle mathcal h a phenomenon which is called spontaneous symmetry breaking magnetization edit an excitation in the middle of a grid of spins propagates by exchanging torque and thus angular momentum with its neighbours in this model the magnetization m n μ b g s v displaystyle m frac n mu _ rm b gs v where v is the volume the propagation of spin waves is described by the landau lifshitz equation of motion d m d t γ m h λ m m h m 2 displaystyle frac d mathbf m dt gamma mathbf m times mathbf h frac lambda mathbf m times mathbf m times mathbf h m 2 where γ is the gyromagnetic ratio and λ is the damping constant the cross products in this forbidding looking equation show that the propagation of spin waves is governed by the torques generated by internal and external fields an equivalent form is the landau lifshitz gilbert equation which replaces the final term by a more simple looking equivalent one the first term on the right hand side of the equation describes the precession of the magnetization under the influence of the applied field while the above mentioned final term describes how the magnetization vector spirals in towards the field direction as time progresses in metals the damping forces described by the constant λ are in many cases dominated by the eddy currents one important difference between phonons and magnons lies in their dispersion relations the dispersion relation for phonons is to first order linear in wavevector k namely ώ ck where ω is frequency and c is the velocity of sound magnons have a parabolic dispersion relation ώ ak 2 where the parameter a represents a spin stiffness the k 2 form is the third term of a taylor expansion of a cosine term in the energy expression originating from the s i s j dot product the underlying reason for the difference in dispersion relation is that the order parameter magnetization for the ground state in ferromagnets violates time reversal symmetry two adjacent spins in a solid with lattice constant a that participate in a mode with wavevector k have an angle between them equal to ka experimental observation edit spin waves are observed through several experimental methods inelastic neutron scattering inelastic light scattering brillouin scattering raman scattering and inelastic x ray scattering time resolved magneto optic kerr effect moke inelastic electron scattering spin resolved electron energy loss spectroscopy and spin wave resonance ferromagnetic resonance in inelastic neutron scattering the energy loss of a beam of neutrons that excite a magnon is measured typically as a function of scattering vector or equivalently momentum transfer temperature and external magnetic field inelastic neutron scattering measurements can determine the dispersion curve for magnons just as they can for phonons important inelastic neutron scattering facilities are present at the isis neutron source in oxfordshire uk the institut laue langevin in grenoble france the high flux isotope reactor at oak ridge national laboratory in tennessee usa and at the national institute of standards and technology in maryland usa brillouin scattering similarly measures the energy loss of photons usually at a convenient visible wavelength reflected from or transmitted through a magnetic material brillouin spectroscopy is similar to the more widely known raman scattering but probes a lower energy and has a superior energy resolution in order to be able to detect the mev energy of magnons time resolved moke microscopy measures the change in polarization of pulsed laser light reflected from a magnetic material a subtype of this method known as super nyquist sampling moke sns moke relies on undersampling of the coherent spin wave with the laser pulses ferromagnetic or antiferromagnetic resonance instead measures the absorption of microwaves incident on a magnetic material by spin waves typically as a function of angle temperature and applied field ferromagnetic resonance is a convenient laboratory method for determining the effect of magnetocrystalline anisotropy on the dispersion of spin waves one group at the max planck institute of microstructure physics in halle germany proved that by using spin polarized electron energy loss spectroscopy speels very high energy surface magnons can be excited this technique allows one to probe the dispersion of magnons in the ultrathin ferromagnetic films the first experiment was performed for a 5 ml fe film 1 with momentum resolution the magnon dispersion was explored for an 8 ml fcc co film on cu 001 and an 8 ml hcp co on w 110 respectively 2 the maximum magnon energy at the border of the surface brillouin zone was 240 mev practical significance edit when magnetoelectronic devices are operated at high frequencies the generation of spin waves can be an important energy loss mechanism spin wave generation limits the linewidths and therefore the quality factors q of ferrite components used in microwave devices the reciprocal of the lowest frequency of the characteristic spin waves of a magnetic material gives a time scale for the switching of a device based on that material see also edit magnonics holstein primakoff transformation spin engineering references edit plihal m mills d l kirschner j 1999 spin wave signature in the spin polarized electron energy loss spectrum in ultrathin fe film theory and experiment phys rev lett 82 12 2579 2582 bibcode 1999phrvl 82 2579p doi 10 1103 physrevlett 82 2579 vollmer r etzkorn m kumar p s anil ibach h kirschner j 29 september 2003 spin polarized electron energy loss spectroscopy of high energy large wave vector spin waves in ultrathin fcc co films on cu 001 pdf physical review letters 91 14 147201 bibcode 2003phrvl 91n7201v doi 10 1103 physrevlett 91 147201 pmid 14611549 anderson philip w 1997 concepts in solids lectures on the theory of solids repr ed singapore world scientific isbn 981 02 3231 4 anderson philip w 1997 basic notions of condensed matter physics cambridge mass perseus publishing isbn 0 201 32830 5 ashcroft neil w mermin n david 1977 solid state physics 27 repr ed new york holt rinehart and winston isbn 0 03 083993 9 chikazumi sōshin 1997 physics of ferromagnetism 2nd ed oxford oxford university press isbn 0 19 156985 2 external links edit spin waves the feynman lectures on physics list of labs performing brillouin scattering measurements retrieved from https en wikipedia org w index php title spin_wave oldid 1335293710 categories magnetic ordering waves hidden categories articles with short description short description is different from wikidata use american english from february 2019 all wikipedia articles written in american english articles lacking in text citations from december 2013 all articles lacking in text citations this page was last edited on 28 january 2026 at 12 23 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a 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