Spin-lattice relaxation within a dimerized Ising chain in a magnetic field

• Published in: Journal of applied physics 2014-07, Vol.116 (3)
• Main Authors: Erdem, Rıza, Gülpınar, Gül, Yalçın, Orhan, Pawlak, Andrzej
• Format: Article
• Language: English
• Subjects: Applied physics; Chains; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Coupling; COUPLING CONSTANTS; Critical point; Distortion; EQUILIBRIUM; FLUCTUATIONS; FREE ENERGY; ISING MODEL; MAGNETIC FIELDS; Mathematical analysis; Matrix methods; MUON SPIN RELAXATION; Parameters; Qualitative analysis; RELAXATION TIME; SPIN; SPIN-LATTICE RELAXATION; SYNCHROTRON RADIATION; TEMPERATURE DEPENDENCE; THERMODYNAMICS; Time constant; TIME DEPENDENCE; TRANSFER MATRIX METHOD; Variation; WAVELENGTHS; X-RAY DIFFRACTION; X-ray scattering
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.4890636

A qualitative study of the spin-lattice relaxation within a dimerized Ising chain in a magnetic field is presented. We have first determined the time dependence of the deviation of the lattice distortion parameter δΔ from the equilibrium state within framework of a technique combining the statistical equilibrium theory based on the transfer matrix method and the linear theory of irreversible thermodynamics. We have shown that the time dependence of the lattice distortion parameter is characterized by a single time constant (τ) which diverges around the critical point in both dimerized (Δ≠0) and uniform (Δ=0) phase regions. When the temperature and magnetic field are fixed to certain values, the time τ depends only on exchange coupling between the spins. It is a characteristic time associated with the long wavelength fluctuations of distortion. We have also taken into account the effects of spatial fluctuations on the relaxation time using the full Landau-Ginzburg free energy functional. We have found an explicit expression for the relaxation time as a function of temperature, coupling constant and wave vector (q) and shown that the critical mode corresponds to the case q=0. Finally, our results are found to be in good qualitative agreement with the results obtained in recent experimental study on synchrotron x-ray scattering and muon spin relaxation in diluted material Cu1−yMgyGeO3 where the composition y is very close to 0.0209. These results can be considered as natural extensions of some previous works on static aspects of the problem.