Dynamics of a fractal set of first-order magnetic phase transitions in frustrated ${\mathrm{Lu}}_2{\mathrm{CoMnO}}_6$

The axial next-nearest-neighbor Ising model predicts a fractal (infinite) set of phases with incommensurate wave vectors that are separated by first-order phase boundaries. This complexity results from a simple frustration condition between nearest- and next-nearest-neighbor interactions along a chain of Ising spins. Using x-ray photon correlation spectroscopy (XPCS), we investigate the surprising antiferromagnetic dynamics that emerge from such a complex phase diagram over a wide range of temperatures. We present XPCS measurements of the frustrated magnetic chain compound ${\mathrm{Lu}}_2{\mathrm{CoMnO}}_6$ and Monte Carlo simulations. Incommensurate magnetic Bragg peaks slide towards commensurate “up-up-down-down” spin order with decreasing temperature and increasing time. Both simulation and experiment support a counterintuitive “upside-down” temperature dependence of the magnetic dynamics: at higher temperatures in the region of first-order phase boundaries, slower dynamics are observed where the speckle maintains its coherence. At the lowest temperatures, where part of the sample adopts commensurate order, the dynamics speed up and result in fast decoherence.

Figure 1

(a) Structure of ${\mathrm{Lu}}_2{\mathrm{CoMnO}}_6$ with spins (arrows) and Lu atoms omitted. (b) Incommensurate and commensurate Bragg peaks, shown with their respective reciprocal space wave vector. (c) Experimental setup of a resonant XPCS experiment, with the $c$ axis normal to the illuminated sample face.

Figure 2

Center of mass (CoM) of (a) CM and (b) ICM peaks at 35 K shown in detector pixels (1 pixel = $7\times {10}^{-5}$ Å${}^{-1}$). The color denotes the relative position in time over 1.8 h. Insets show the Bragg peak, with the red dot indicating the center of mass. White hash marks denote 20-pixel intervals.

Figure 3

(a) Waterfall plot (right) showing the cross section of a $\pi$ ICM Bragg peak at 35 K vs time, where the cross section is integrated over the red line out defined on the left. (b) Similar waterfall plot for 24 K. Normalized autocorrelation function $(g^{\left(2\right)}-1)$ vs time for (c) the CM peak at [0, 0, 1/2] and (d) ICM peak at $[0.0087,-0.0042,0.489]$ and $[0.0168,-0.006,0.4888]$ at 35 K. All data are shown for the Co $L_3$ edge with $\pi$ polarization. The data at 55 K are above $T_N$ and thus represent the $\left[001\right]$ structural peak in the first harmonic of the x-ray beam.

Figure 4

(a) Monte Carlo simulations of the ICM AFM wave vector $Q$ vs $T$, obtained by slowly cooling to $T=0$ and then heating. The inset shows the magnetic model with nearest- and next-nearest-neighbor magnetic interactions. (b) Calculated spin autocorrelation function $A\left(t\right)$ at fixed $Q=0.25\times 2\pi /c$ vs time for varying $T$. Time $t$ is shown in units of Monte Carlo sweep (MCS).