Formation of Magnetic Microphases in Ca$_3$Co$_2$O$_6$

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Abstract

We study a frustrated quantum Ising model relevant for Ca$_3$Co$_2$O$_6$ that consists of a triangular lattice of weakly-coupled ferromagnetic (FM) chains. According to our quantum Monte Carlo simulations, the chains become FM and form a three-sublattice "up-up-down" structure for $T \leq T_\text{CI}$. In contrast, long-period spin-density-wave (SDW) {\it microphases} are stabilized along the chains for $T_\text{CI} < T < T_c$. Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca$_3$Co$_2$O$_6$. We also discuss implications of microphases for the related multiferroic compounds Ca$_3$CoMnO$_6$ and Lu$_2$MnCoO$_6$.

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Exchange Monte Carlo Method and Application to Spin Glass Simulations

Koji Nemoto, Koji Hukushima (1995)

We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional $\pm J$ Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

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Antiferromagnetism. The Triangular Ising Net

G. Wannier (1950)

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Theory of Electron Nematic Order in LaOFeAs

JiangPing Hu, Chen Fang, Wei-Feng Tsai … (2008)

We study a spin $S$ quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large $S$ and large $N$ methods, we show that this model exhibits a sequence of two phase transitions: from a high temperature symmetric phase to a narrow region of intermediate ``nematic'' phase, and then to a low temperature spin ordered phase. Identifying phases by their broken symmetries, these phases correspond precisely to the sequence of structural (tetragonal to monoclinic) and magnetic transitions that have been recently revealed in neutron scattering studies of LaOFeAs. The structural transition can thus be identified with the existence of incipient (``fluctuating'') magnetic order.