Anisotropic spin fluctuations

The recording of JlSR spectra 76 4.1. Anisotropic spin fluctuations 124... 

R525 J. Yang and G.-q. Zheng, Multiple Superconducting Gaps, Anisotropic Spin Fluctuations and Spin-Orbit Coupling in Iron-Pnictides , arXiv.org, e-Print Archive, Condensed Matter, 30 May 2012, U20, AvaU. URL http // arxiv.org/PS cache/arxiv/pdf/1205/1205.6589vl.pdf. 

For 0.04 < T < 100 K, the SLR showed a strong T-dependence, indicating that the compound was much more itinerant than previously known Ce-based HF compounds. The observed T-variation was considered to indicate anisotropic spin fluctuations near a magnetic ordering, arising from a layered crystal structure. Bulk superconductivity set in at 0.40 K, below which there was no coherence peak and the SLR followed a relationship, suggesting unconventional superconductivity with an anisotropic (line-node) energy gap. 

We have chosen an anisotropic spin-environment coupling, oc az. This is a realistic model, e.g., for many designs of solid-state qubits, where the different components of the spin are influenced by entirely different environmental degrees of freedom [10, 15, 4]. While our analysis can be generalized to account for multiple-directional fluctuating fields [20], here we focus on unidirectional fluctuations (along the 2 axis). 

From the anisotropic nature of the superconductivity (d- or p-wave) and the intimate relation between the superconductivity and magnetism, the origin of the attractive force is considered to be due to the antiferro- or ferromagnetic spin fluctuations in HF superconductors. 

Now we consider thermodynamic properties of the system described by the Hamiltonian (2.4.5) it is a generalized Hamiltonian of the isotropic Ashkin-Teller model100,101 expressed in terms of interactions between pairs of spins lattice site nm of a square lattice. Hamiltonian (2.4.5) differs from the known one in that it includes not only the contribution from the four-spin interaction (the term with the coefficient J3), but also the anisotropic contribution (the term with the coefficient J2) which accounts for cross interactions of spins a m and s m between neighboring lattice sites. This term is so structured that it vanishes if there are no fluctuation interactions between cr- and s-subsystems. As a result, with sufficiently small coefficients J2, we arrive at a typical phase diagram of the isotropic Ashkin-Teller model,101 102 limited by the plausible values of coefficients in Eq. (2.4.6). At J, > J3, the phase transition line... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

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