Exponents for sound attenuation near critical points in solids

Murata, Kenneth K.

doi:10.1103/physrevb.13.4015

Cited by 64 publications

(15 citation statements)

References 17 publications

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“…Then the singular part of the response function W obeys the scaling relation This type of singularity in the ultrasonic attenuation, which we shall also call Murata-Iro-Schwabl behaviour, has been so far obtained by neglecting the energy density fields [3,4] and it is believed to take place in magnetic metals [1,2]. Note, however, that the coefficient W2 in this limit is equal to 2(g -wfCs) 2 to be compared with 2g 2 in the model where the coupling to the energy fields has been neglected [4].…”

Section: General Expressionsmentioning

confidence: 99%

“…It is supposed to be described by the theories [3][4][5] in which the sound wave is assumed to couple to two critical spin fluctuations. The sound attenuation coefficient is proportional then to the imaginary part of the four-spin response function and the critical exponent characterising its divergence is found to be zv+α, where z is the dynamical critical exponent, v is the exponent of the correlation length and a is the exponent of the specific heat.…”

Section: Introductionmentioning

confidence: 99%

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Theory of Critical Sound Attenuation in Ising-Type Magnets

Pawlak

2000

Acta Phys. Pol. A

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The critical behaviour of sound attenuation has been studied in an elastically isotropic Ising system above the critical point on the basis of a complete stochastic model including both spin-energy and lattice-energy modes linearly coupled to the longitudinal sound mode. The effect of spin-lattice relaxation on the ultrasonic attenuation is investigated. The crossover between Kawasaki behaviour and Murata-Iro-Schwabl behaviour is studied as dependent on the values of ultrasonic frequency, reduced temperature, relaxation times, etc. A new high-frequency regime is discussed in the magnetic systems. This new regime corresponds to an adiabatic sound propagation and is very similar to the ones in binary mixture and liquid helium. A new frequency-dependent specific heat being the harmonic average of the bare lattice and critical spin specific heats is introduced. It was shown that such specific heat describes the process of equilibration between spin and lattice subsystems and includes the most important features of critical sound attenuation.

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Section: General Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of Critical Sound Attenuation in Ising-Type Magnets

Pawlak

2000

Acta Phys. Pol. A

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“…Asymptotically i.e. for ω, t -> 0 strong singularity term always dominates [3,10] It is rather unexpected that a similar singularity dominates also for high frequencies, ώ = 1, where This new behaviour can be obtained from the asymptotic behaviour by simple replacement α -> -α and Φ -+ Φ-1 . The weak singularity term, can be dominant for t > only if there exists a frequency window ω = ΓS/CS Γ, with the crossover reduced temperature t c ross α ( Γ)1/(z^-α) This regime is believed to take place in magnetic insulators [1,2].…”

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confidence: 99%

“…The crossover between insulator-like behaviour t -2 α a n d In typical ultrasonic experiments near the magnetic phase transition temperature we observe strong anomalies of sound attenuation in magnetic metals such as some rare-earth metals, whereas in magnetic insulators only very weak anomaly is observed [1,2]. Many theories have been proposed to describe the strong anomaly in various substances [3][4][5][6]. They assume that the sound mode is coupled to two spin fluctuations above Τ .…”

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Spin-Lattice Relaxation Effects in Critical Sound Propagation

Pawlak

1997

Acta Phys. Pol. A

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The nonasymptotic critical properties of sound propagation are studied in compressible Ising system above Τ. In the present paper we analyse a model where in addition to the coupling to two order-parameter fluctuations tle sound mode couples linearly to the fluctuations of spin-energy and lattice-energy densities. Both subsystems exchange energy with the rate determined by the bare spin-lattice relaxation time: The total energy may be conserved or not. The crossover between insulator-like behaviour t -2 α a n d In typical ultrasonic experiments near the magnetic phase transition temperature we observe strong anomalies of sound attenuation in magnetic metals such as some rare-earth metals, whereas in magnetic insulators only very weak anomaly is observed [1,2]. Many theories have been proposed to describe the strong anomaly in various substances [3][4][5][6]. They assume that the sound mode is coupled to two spin fluctuations above Τ . On the other hand, the weak anomalies have been qualitatively explained by postulating the dominance of the linear coupling to the spin-energy density [7]. In our recent study we have investigated a model where both couplings were present [8]. Inn this paper we present more extensive discussion of the problem including also the lattice energy mode and transfer of energy between spin and lattice subsystems. We consider the acoustic phonon Q coupled to the scalar spin S and to the fluctuations of energy of spin and lattice subsystems. The Hamiltonian of the elastically isotropic system may be specified as (449) m e t a l -l i k e b e h a v i o u r t i t -( z v ± α ) i n u l t r a s o n i c a t t e n u a t i o n i s i n v e s t i g a t e d

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Ultrasonic investigation of the phase transitions in NH4Cl1–xBrx Mixed Crystals

Gotoc

Fujimura

Kamiyoshi

1978

Phys. Stat. Sol. (a)

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Studying the critical phenomena accompanying the order‐disorder phase transition (β‐δ, β‐γ) in NH4Cl1–xBrx mixed crystals especially at multicritical points, the velocity and the attenuation of the longitudinal sound wave at 10 MHz propagating along the [100] direction are measured as a function of mole fraction (x = 0 to 1) and of temperature (310 to 200 K). A large critical softening of velocity is observed in the disordered β‐phase of both β‐δ and β‐γ transitions. The results indicate that the fluctuations of two order parameters corresponding to the δ‐ and γ‐phases have a mutual interaction through elastic strain. The critical softening is expressed by a simple power low: [V(∞)‐V(0)]/V(∞) = A[(T – T0)/T] q. The critical index, q, varies with x. The fluctuations of the two order parameters in the disordered β‐phase are enhanced near the triple point, and are suppressed near the tricritical point.

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Exponents for sound attenuation near critical points in solids

Cited by 64 publications

References 17 publications

Theory of Critical Sound Attenuation in Ising-Type Magnets

Theory of Critical Sound Attenuation in Ising-Type Magnets

Spin-Lattice Relaxation Effects in Critical Sound Propagation

Ultrasonic investigation of the phase transitions in NH4Cl1–xBrx Mixed Crystals

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