Browsing by Author "Pawlak, Andrzej"
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Item Critical Sound Propagation in Magnets(Nova Science Publishers, 2009) Pawlak, AndrzejThe critical dynamics of sound is a very interesting field in which we can test modern concepts of the phase transition theory such as the universality of critical exponents, scaling or the crossover to another universality class etc. It is the aim of the study to present a general theory of critical sound propagation, which takes also into account some important nonasymptotic effects. In metallic magnets the critical anomalies in the sound attenuation coefficient are of different types than in magnetic insulators.The difference in the critical exponents used to be explained by the occurrence of different kinds of magnetoelastic coupling in the two classes of magnets mentioned. We will show in this chapter that one should assume coexistence of both types of coupling in all magnets. A very important role is played by the ratio of the spin-lattice relaxation time to the characteristic time of spin fluctuations. It is a crucial parameter determining whether the sound attenuation coefficient reveals a strong or a weak singularity in a given material. After a short introduction the fundamental concepts of the phase transition theory such as critical exponents, the scaling and universality hypothesis etc are reviewed in Section 2 of this chapter. Section 3 presents the idea of critical slowing down, dynamic scaling as well as the presentation of the basic dynamic universality classes. In Section 4, the model describing the static behavior of acoustic degrees of freedom is investigated. The expressions for the adiabatic and the isothermal sound velocity are also derived. The phenomenological theory of critical sound propagation is presented in very intuitive way in Section 5, while Section 6 contains a detailed description of the dynamic model based on the coupled nonlinear Langevin equations of motion. Three basic regimes characterized by different critical exponents and scaling functions are distinguished in the sound attenuation coefficient. Crossover effects from the insulator-type regime to the metallic-type regime and to the high-frequency regime are demonstrated on the example of the ultrasonic data for MnF2. The concept of the effective sound attenuation exponent is introduced using the data reported for FeF2 and RbMnF3. The frequency dependent longitudinal sound velocity and its relation to the static quantities are discussed. Finally, the unsolved questions and future prospects in this field are outlined.Item Magnets: Types, Uses and Safety(Nova Science Publishers, 2012) Pawlak, AndrzejThe critical dynamics of sound is a very interesting field in which we can test modern concepts of the phase transition theory such as the universality of critical exponents, scaling or the crossover to another universality class etc. It is the aim of the study to present a general theory of critical sound propagation, which takes also into account some important nonasymptotic effects. In metallic magnets the critical anomalies in the sound attenuation coefficient are of different types than in magnetic insulators. The difference in the critical exponents used to be explained by the occurrence of different kinds of magnetoelastic coupling in the two classes of magnets mentioned. We will show in this chapter that one should assume coexistence of both types of coupling in all magnets. A very important role is played by the ratio of the spinlattice relaxation time to the characteristic time of spin fluctuations. It is a crucial parameter determining whether the sound attenuation coefficient reveals a strong or a weak singularity in a given material. After a short introduction the fundamental concepts of the phase transition theory such as critical exponents, the scaling and universality hypothesis etc are reviewed in Section 2 of this chapter. Section 3 presents the idea of critical slowing down, dynamic scaling as well as the presentation of the basic dynamic universality classes. In Section 4, the model describing the static behavior of acoustic degrees of freedom is investigated. The expressions for the adiabatic and the isothermal sound velocity are also derived. The phenomenological theory of critical sound propagation is presented in very intuitive way in Section 5, while Section 6 contains a detailed description of the dynamic model based on the coupled nonlinear Langevin equations of motion. Three basic regimes characterized by different critical exponents and scaling functions are distinguished in the sound attenuation coefficient. Crossover effects from the insulator-type regime to the metallic-type regime and to the highfrequency regime are demonstrated on the example of the ultrasonic data for MnF2. The concept of the effective sound attenuation exponent is introduced using the data reported for FeF2 and RbMnF3. The frequency dependent longitudinal sound velocity and its relation to the static quantities are discussed. Finally, the unsolved questions and future prospects in this field are outlined.Item Propagacja dźwięku w pobliżu przemiany fazowej(Wydawnictwo Naukowe UAM, 2004) Pawlak, Andrzej; Muzia, KatarzynaThe book deals with the theoretical studies of critical behaviour of ultrasonic wave attenuation and propagation velocity in magnets. The effect of spin-lattice relaxation on the ultrasonic attenuation and velocity is investigated on the basis of the stochastic model including the energy relaxation and the sound mode. A novel high frequency regime in the ultrasonic attenuation is predicted. The scaling functions are calculated in the one-loop approximation within the renormalisation group formalism. In the diffusive version of the model a detailed analysis of the connection between the heat conduction and sound propagation is studied. An overview of experimental and theoretical sound attenuation exponents is also given. The ultrasonic attenuation measurements in MnF2 are interpreted in terms of the theoretical model proposed.