Dynamic approach to finite-temperature magnetic phase transitions in the extended ${J}_{1}\ensuremath{-}{J}_{2}$ model with vacancy order

Dynamic approach to finite-temperature magnetic phase transitions in the extended $J_{1} - J_{2}$ model with vacancy order

N. J. Zhou, B. Zheng, and J. H. Dai

Phys. Rev. E 87, 022113 – Published 13 February 2013

Abstract

The recently discovered iron-based superconductors $A$ $_{y}$ Fe $_{2 - x}$ Se $_{2}$ ( $A = K$ , Rb, Cs, Tl) show a long-range antiferromagnetic order with an unexpectedly high transition temperature $T_{N} \sim 550$ K and a unique $\sqrt{5} \times \sqrt{5}$ vacancy order. Taking the extended $J_{1}$ - $J_{2}$ model as a minimal model, we investigate the finite-temperature magnetic phase transitions in a square lattice with a $\sqrt{5} \times \sqrt{5}$ vacancy superstructure by using large-scale Monte Carlo simulations. By the parallel tempering technique, the block spin checkerboard and stripe antiferromagnetic states are detected to be the ground states for three representative sets of model parameters. The short-time dynamic approach is applied to accurately determine the critical temperature as well as the static and dynamic exponents. Our results indicate that the dramatic enhancement of the critical temperature as observed in experiments should be mainly due to a combination of the vacancy order and the block lattice contraction.

Received 10 September 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022113

Authors & Affiliations

N. J. Zhou^1,*, B. Zheng², and J. H. Dai¹

¹Department of Physics, Hangzhou Normal University, Hangzhou 310036, People's Republic of China
²Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China

^*zhounengji@hznu.edu.cn

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Vol. 87, Iss. 2 — February 2013

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Figure 1
The magnetic structure of $A$ $_{y}$ Fe $_{2 - x}$ Se $_{2}$ from the top is displayed. In the upper panel, the solid squares connecting the circles indicate the fundamental blocks with four Fe atoms at the corners. The proposed magnetic couplings $(J_{1}, J_{1}^{'})$ with solid lines and $(J_{2}, J_{2}^{'})$ with dashed lines represent the NN and NNN couplings, respectively. In the lower panel, two magnetic configurations, the block spin checkerboard and stripelike antiferromagnetic states, are shown by open ( $S_{i} = 1$ ) and solid circles ( $S_{i} = - 1$ ).Reuse & Permissions
Figure 2
(a) The second moment of the pseudomagnetization in the parallel tempering process is displayed for different sets of model parameters. The dashed line represents constant $M^{(2)} (t) = 1$ . (b) Dynamic relaxation of the pseudomagnetization is plotted for different temperatures. For clarity, the curves at $K_{c}$ with different lattice sizes are shifted down. Dashed lines indicate power-law fits.Reuse & Permissions
Figure 3
(a) The logarithmic derivative of the pseudomagnetization $M (t, τ)$ is displayed at $K_{c}$ for case I (stars) and case II (open squares). Dashed lines represent power-law fits, and solid lines indicate the fits with power-law correction. (b) The Binder cumulant $U (t)$ is plotted with solid lines on a double-log scale for different lattice sizes $L = 250, 500$ , and 1000 (from above). According to Eq. (9), data collapse is demonstrated at a fixed lattice size $L = 500$ . Open circles and triangles correspond to $L = 250$ and 1000, respectively.Reuse & Permissions
Figure 4
(a) The spatial correlation function $C (r, t)$ is displayed on a log-log scale. Data collapse is demonstrated at a fixed $t = 20 480$ MCS. Open circles, open triangles, stars, solid circles, and solid squares correspond to $t = 20, 80, 320, 1280$ , and 5120, respectively. In the inset, the scaling function $\tilde{C} (s) s^{0.25}$ is shown on a linear-log scale. For clarity, the curve of case II is shifted right. (b) Dynamic relaxation of $χ (t)$ and $S (t)$ are plotted with solid lines for case I. Dashed lines represent power-law fits.Reuse & Permissions
Figure 5
(a) The scaling function $\tilde{A} (t / t^{'})$ against $ξ (t) / ξ (t^{'})$ is displayed for cases I and II on a double-log scale. According to Eq. (10), data collapse is observed for different waiting time $t^{'}$ . (b) The time evolution of $M (t)$ is plotted for cases I and II with an initial magnetization $m_{0} = 0.01$ . The lattice size is $L = 1000$ . In both panels (a) and (b), dashed lines show power-law fits.Reuse & Permissions
Figure 6
(a) $M (t)$ in case III is plotted for different temperatures. For clarity, the curve at $K_{c}$ is shifted down. Dashed line shows a power-law fit. (b) The square lattice with a $\sqrt{5} \times \sqrt{5}$ vacancy superstructure and the bathroom-tile lattice are shown within the dashed squares. The same topological structure is revealed.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Dynamic approach to finite-temperature magnetic phase transitions in the extended $J_{1} - J_{2}$ model with vacancy order

N. J. Zhou, B. Zheng, and J. H. Dai

Phys. Rev. E 87, 022113 – Published 13 February 2013

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Physical Review E

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Dynamic approach to finite-temperature magnetic phase transitions in the extended J1−J2 model with vacancy order

N. J. Zhou, B. Zheng, and J. H. Dai

Phys. Rev. E 87, 022113 – Published 13 February 2013

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Dynamic approach to finite-temperature magnetic phase transitions in the extended $J_{1} - J_{2}$ model with vacancy order