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We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice coupling. For a square lattice it is shown that the plaquette formation is the most favourable form of static two-dimensional dimerization. We also demonstrate that such distortions may coexist with long range magnetic order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Towards low temperatures significant softening mainly of zone boundary phonons is found, especially around the $(pi,0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a magnetic pressure on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency towards shear instabilities of the lattice.
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Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter of the expansion is the ratio of the colored noise timescale to the precession period. In the process we obtain the Gilbert damping from the same expansion. We recover the known results, when the coefficients of the two terms are proportional to one another, in the white noise limit; and show how colored noise leads to situations where this simple relation breaks down, but what replaces it can be understood by the appropriate generalization of the fluctuation--dissipation theorem. Numerical simulations of the stochastic equations support the analytic approach. In particular we find that the equilibration time is about an order of magnitude longer than the timescale set by the colored noise for a wide range of values of the latter and we can identify the presence of nutation in the non-uniform way the magnetization approaches equilibrium.
Nematic orders emerge nearly universally in iron-based superconductors, but elucidating their origins is challenging because of intimate couplings between orbital and magnetic fluctuations. The iron-based ladder material BaFe2S3, which superconducts under pressure, exhibits antiferromagnetic order below TN ~ 117K and a weak resistivity anomaly at T* ~ 180K, whose nature remains elusive. Here we report angle-resolved magnetoresistance (MR) and elastoresistance (ER) measurements in BaFe2S3, which reveal distinct changes at T*. We find that MR anisotropy and ER nematic response are both suppressed near T*, implying that an orbital order promoting isotropic electronic states is stabilized at T*. Such an isotropic state below T* competes with the antiferromagnetic order, which is evidenced by the nonmonotonic temperature dependence of nematic fluctuations. In contrast to the cooperative nematic orders in spin and orbital channels in iron pnictides, the present competing orders can provide a new platform to identify the separate roles of orbital and magnetic fluctuations.
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