Saturation and coherence properties of three-magnon nonlinear processes

Araújo, Cid B. de; Rezende, S. M.

doi:10.1103/physrevb.9.3074

Cited by 15 publications

(18 citation statements)

References 8 publications

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“…However, the confluent process itself has no threshold condition; the BEC magnon pairs k 0 ,−k 0 with any value of n k0 will create k =0 magnons. This is in contrast to the so-called subsidiary resonance instability process 15,17 in which the three-magnon splitting process occurs only if the microwave field exceeds a critical value. The amplitude of the k = 0 mode is maximum at the resonance condition 0 =2 k0 , which in the experiments of Ref.…”

Section: ͑9͒mentioning

confidence: 64%

Theory of microwave superradiance from a Bose-Einstein condensate of magnons

Rezende

2009

Phys. Rev. B

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We show that the nearly uniform mode generated by the confluence of Bose-Einstein condensate ͑BEC͒ magnon pairs produced by microwave radiation in a film of yttrium iron garnet ͑YIG͒ is a coherent magnon state. This state corresponds to a macroscopic precessing magnetization which emits a superradiant microwave signal as a result of the cooperative action of the spins. The theory explains quantitatively recent experimental observations of microwave emission from a BEC of magnons in a YIG film when the driving power exceeds a critical value.In a recent series of papers Demokritov et al. 1-3 reported the experimental observation of quasiequilibrium Bose-Einstein condensation ͑BEC͒ of magnons at room temperature in films of yttrium iron garnet ͑YIG͒ driven by microwave radiation. When magnetized in the plane these films have a dispersion relation ͑frequency k versus wave vector k͒ for magnons propagating along the field that exhibits a minimum frequency k0 =2f min at k 0 ϳ 10 5 cm −1 . Magnon pairs with opposite wave vectors pumped parametrically in large numbers by the microwave field are redistributed over the spectrum creating a hot magnon gas that remains decoupled from the lattice for some time due to the relatively slow spin-lattice relaxation. The experiments show that if the microwave power exceeds a certain threshold value the intensity of the light scattered by magnon with frequency k0 increases by orders of magnitude indicating the formation of a Bose-Einstein condensate. [1][2][3] We have shown 4 that the cooperative action in an interacting magnon gas in a YIG film creates a coherent magnon state at k0 when the magnon population exceeds a critical density. The coherent state corresponds to a macroscopic precessing magnetization providing theoretical support for the experimentally observed Bose-Einstein condensate of magnons. Since the wavelength of the associated spin wave is on the order of 10 −5 cm, the direct microwave radiation from the BEC is negligible. However, as observed by Dzyapko et al.,5 if the applied in-plane static field has a value such that the frequency of the k Ϸ 0 magnon is 0 =2 k0 , a microwave radiation is generated by k Ϸ 0 magnons created by pairs of BEC magnons k 0 ,−k 0 through a three-magnon confluent process. The k Ϸ 0 value is necessary for emission because the wave number of electromagnetic radiation with frequency of 1.5 GHz, as in the experiments, 5 is k =2 / f Ϸ 0.3 cm −1 . In this Rapid Communication we show that the k Ϸ 0 magnons created by the BEC are coherent magnons states, which correspond to a nearly uniform magnetization precessing with frequency 0 and generating a microwave signal. The microwave emitted by the collective action of the spins is identified with superradiance. We show that this process occurs when the driving microwave power exceeds a critical value and that the theoretical results for the emitted signal power agree very well with the experimental data. 5 The term superradiance was introduced by Dicke 6 in 1954 to designate the type of spontaneous ...

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Section: ͑9͒mentioning

confidence: 64%

Theory of microwave superradiance from a Bose-Einstein condensate of magnons

Rezende

2009

Phys. Rev. B

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“…In this Brief Report, we study in more detail the quantum nature of the spin waves excited by the dc current near threshold. The formalism used is the same employed to study quantum coherence in spin waves driven by microwave fields 14 and in laser systems. 15 We consider a ferromagnetic film of thickness d traversed by a direct current with spin-polarized electrons.…”

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confidence: 99%

“…14,15 The other parameters are ␦ =3/ 2͑u k 2 + v k 2 ͒, u k and v k are the coefficients of the Bogoliubov transformation relating the collective spin deviation operators to the normal mode spin-wave operators, N is the number of spins S in the sample, and T k is the coefficient arising from the surface dipolar and anisotropy contributions to the four-magnon interaction. For the magnetization perpendicular to the film plane one has 12 u k =1, v k = 0, and…”

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confidence: 99%

Quantum coherence in spin-torque nano-oscillators

Rezende

2010

Phys. Rev. B

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We study the quantum coherence properties of spin waves in a ferromagnetic thin film driven by a dc current in a spin-torque nano-oscillator. We show that if the current barely exceeds the threshold value the driven magnon states are not coherent and exhibit pronounced thermal noise. Only when the current exceeds the threshold value by a certain amount that depends on the material parameters and temperature of the nanostructure the microwave oscillation will exhibit quantum coherence.

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“…As in the previous studies of the perpendicular (5) and parallel pumping ( 6 ) , we a r e mainly interested in the properties around the threshold. The study applies to a cubic ferromagnetic insulator, elastically isotropic, with low anisotropy and saturated along one of the [loo] …”

mentioning

confidence: 99%

“…and bl, b a r e the magnetoelastic constants (reference (7)). 2 The t e r m H describes the interaction with the heat bath (references (5,6)) and B can be put in the form where g which is described by the frequencies UJ and operators R . This t e r m is introduced to incorporate the relaxation and fluctuations in a consistent quantum way without the usual procedure of doing the substitution w k-wk + iqk which leads to a violation of the boson-type commutation rules of the magnon operators.…”

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confidence: 99%

Quantum theory of the parametric excitation of magnons by phonon pumping

Araujo

1975

Physica Status Solidi (b)

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We give a theoretical account of the quantum properties of the magnon states generated by phonon pumping (1 to 3) in terms of the coherent-magnon-states representation (4 to 6). As in the previous studies of the perpendicular (5) and parallel pumping ( 6 ) , we a r e mainly interested in the properties around the threshold. The study applies to a cubic ferromagnetic insulator, elastically isotropic, with low anisotropy and saturated along one of the [loo]

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Saturation and coherence properties of three-magnon nonlinear processes

Cited by 15 publications

References 8 publications

Theory of microwave superradiance from a Bose-Einstein condensate of magnons

Theory of microwave superradiance from a Bose-Einstein condensate of magnons

Quantum coherence in spin-torque nano-oscillators

Quantum theory of the parametric excitation of magnons by phonon pumping

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