Defect-induced short-range-order from a spin-ice related state in deformed pyrochlore ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$

Recently, we observed a kagome-ice-like partial ferromagnetic order with coexisting fluctuation in a deformed pyrochlore structure ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$. Here, we show that when lattice defects are present, the remaining fluctuating spins in this material further freeze at lower temperatures below $T<T_g=4\mathrm{K}$ after it initially freezes into the partial ferromagnetic order near $T_C=10\mathrm{K}$. This low-temperature transition is glasslike requiring an extremely slow relaxation process in ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$. Enhanced disorder in ${\left({\mathrm{Co}}_{1-x}{\mathrm{Al}}_x\right)}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ leads to a short-range order for the fluctuating spins. This result can be considered as an interesting analogy to the low-temperature anomaly in defect-containing pure and doped water ice, especially in the light of its relevance to the problem of residual entropy in ice-water or spin-ice transition.

Figure 1

(Color online) (a) $M\text{−}H$ hysteresis loop appeared at $2\mathrm{K}$ for a polycrystalline ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ sample. (b) Remanent magnetization at $2\mathrm{K}$ after removing a $5\mathrm{T}$ field. $M_r$ showed a slow decay following the equation $M_r=0.035e^{-(t∕\tau )}-0.03\ln t+0.80$ with a large time constant $\tau =1020\mathrm{s}$. The inset plot depicts the quick increase of $\tau$ below $4\mathrm{K}$.

Figure 2

(Color online) Temperature dependence of specific heat $C_p\left(T\right)$. The squares and open circles represent data for polycrystalline ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ and ${\left({\mathrm{Co}}_{0.9}{\mathrm{Al}}_{0.1}\right)}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$, respectively, at zero field; the filled circles are data for ${\left({\mathrm{Co}}_{0.9}{\mathrm{Al}}_{0.1}\right)}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ under a magnetic field of $0.5\mathrm{T}$. The inset plot is an enlarged view of the low-temperature section for ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$.

Figure 3

(Color online) Temperature dependences of dc susceptibilities measured at $50\mathrm{Oe}$ under field-cooling (open symbols) and zero-field-cooling (filled symbols) conditions, respectively.

Figure 4

(Color online) Temperature dependences of ac susceptibilities at various frequencies for [(a) and (b), respectively] single crystal and polycrystalline ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ and (c) polycrystalline ${\left({\mathrm{Co}}_{0.9}{\mathrm{Al}}_{0.1}\right)}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$).

Figure 5

(Color online) Frequency dependence of the imaginary part of ac susceptibility at various temperatures for (a) polycrystalline ${\mathrm{Co}}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$ and (b) ${\left({\mathrm{Co}}_{0.9}{\mathrm{Al}}_{0.1}\right)}_2{\left(\mathrm{O}\mathrm{H}\right)}_3\mathrm{Cl}$, respectively.

Figure 6

(Color online) (a) Neutron diffraction intensity patterns for ${\left({\mathrm{Co}}_{0.9}{\mathrm{Al}}_{0.1}\right)}_2{\left(\mathrm{O}\mathrm{D}\right)}_3\mathrm{Cl}$ at low temperatures. Besides the magnetic reflection peaks developing below $T_C$, a diffused scattering at low angles as indicated by the arrow emerged below $T<4\mathrm{K}$. (b) The difference between the diffraction intensities and a fitted base line of the intensities of $6\mathrm{K}$ is plotted, respectively.