Magnetic domain growth in geometrically frustrated Ising antiferromagnets ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Nb}}_2{\mathrm{O}}_6$ $(x=0 \text{and} 0.004)$ as seen via time-resolved neutron diffraction measurements

We have investigated anomalously slow magnetic domain growth in an antiferromagnetic (AF) phase of isosceles triangular lattice Ising antiferromagnets ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Nb}}_2{\mathrm{O}}_6$ with $x=0$ and 0.004, by means of time-resolved neutron diffraction measurements. Applying the multi-profile-deconvolution analysis to the observed diffraction profiles, we have revealed that time evolutions of spin correlation lengths along the $a$ and $b$ axes, ${\xi }_a$ and ${\xi }_b$, are well described by a power-law scaling form of ${\xi }_{0\alpha }+L_{\alpha }{(t/{\tau }_{\alpha })}^n$ $\left(\alpha =a,b\right)$ with a universal growth exponent of $n=0.2$. The characteristic time scale of the domain growth, ${\tau }_{\alpha }$, was found to exhibit Arrhenius-type temperature dependence in the AF phase. A comparison between the results of the $x=0$ and 0.004 samples has revealed that the nonmagnetic substitution significantly reduces the initial correlation length, ${\xi }_{0\alpha }$, and the activation energy in the Arrhenius-type temperature dependence of ${\tau }_{\alpha }$. We have also found that magnetic domain growth in a magnetic-field-induced ferrimagnetic phase also follows the power law with the growth exponent of $n=0.2$. On the basis of these results, we have concluded that the existence of ferromagnetic Ising spin chains running along the $c$ axis and the geometrical spin frustration in the $ab$ plane are the keys to the domain growth kinetics in this system. The former and the latter govern the characteristic time scale and the growth exponent, respectively.

Figure 1

(a) $H_{\left|\right|c}\text{−}T$ magnetic phase diagram of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ (redrawn from Ref. [14]). Open and filled circles denote the critical fields determined by $H$-increasing and decreasing processes, respectively. (b) A schematic diagram showing the magnetic structure in the AF phase and the A/D-type domain walls. Open and filled circles denote the 1D ferromagnetic chains with up and down spins, respectively. Orange circles indicate the “isolated” spin chains at which in-plane exchange interactions are canceled out. (c) A schematic diagram showing the magnetic structure in the FR phase and the A'/C'-type domain walls. Orange circles indicate the 1D spin chains with up (down) spins at which the sum of the in-plane exchange energy, $(-)2J_1{\mathbf{S}}_r·{\mathbf{S}}_{r+b}$, is canceled out by the Zeeman energy of $-(+)g{\mu }_{\mathrm{B}}{\mathbf{S}}_r·\mathbf{H},$ at $H\sim H_s$ [11].

Figure 2

(a) A schematic drawing of the reciprocal lattice map of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ and the tracks of the resolution functions in the scans for the determination of $S\left(\mathbf{q}\right)$ in the AF phase. [(b)–(e)] The neutron diffraction profiles of the $1\frac{1}{2}0$ magnetic reflection measured by the reciprocal lattice scans along (b) $h$ and (c) $k$ directions and (d) the $\omega$ scan and (e) the $\omega \text{−}2\theta$ scan at $T=1.7$ K in the AF phase, at $t\sim 3\times {10}^4$ s, using the $x=0$ sample. Solid, dotted, and dashed lines show the results of the MPD analyses in which the functional form of $S\left(\mathbf{q}\right)$ is assumed to be Eq. (3), Lorentzian and Gaussian, respectively.

Figure 3

Comparisons of the magnetic diffraction profiles at $t=240$ and $2.9\times {10}^4$ s, for (a) the $\left(0\frac{1}{2}0\right)$ reflection measured along the $h$ direction and (b) the $\left(3\frac{1}{2}0\right)$ reflection measured along the $k$ direction, in the AF phase of the $x=0$ sample. Note that the diffraction profiles at $t=2.9\times {10}^4$ s along the $h$ and $k$ directions were actually measured with 32k and 36k monitor, respectively. The intensities and errors are normalized to the data measured with 8000 and 9000 monitor.

Figure 4

The time evolutions of the spin correlation lengths along the (a) $a$ and (b) $b$ directions in the AF phase of the $x=0$ sample, and those along the (c) $a$ and (d) $b$ directions in the AF phase of the $x=0.004$ sample. Solid lines denote the power law fitting with $n=0.2$. Double-logarithmic plots of ${\xi }_{\alpha }\left(t\right)-{\xi }_{0\alpha }$ as functions of $t/{\tilde{\tau }}_{\alpha }$ in (e) $x=0$ and (f) 0.004 samples.

Figure 5

Comparisons between the temperature dependencies of (a) ${\tilde{\tau }}_a$, (b) ${\xi }_{0a}$, (c) ${\tilde{\tau }}_b$, and (d) ${\xi }_{0b}$ in the AF phase of the $x=0$ and 0.004 samples.

Figure 6

The neutron diffraction profiles measured along the (a) $h$ and (b) $k$ directions at $H=1300$ Oe, $T=1.2$ K, and $t\sim 2\times {10}^4$ s using the $x=0$ sample. The results of the MPD analysis with Eq. (3) are shown by solid lines. The time evolutions of (c) ${\xi }_a$ and (d) ${\xi }_b$ measured at $T=1.2$ K under applied magnetic fields of $H=1000$ and 1300 Oe. Solid and dotted lines denote the power law fitting with $n=0.2$.