Magnetostructural transition, metamagnetism, and magnetic phase coexistence in Co${}_{10}$Ge${}_3$O${}_{16}$

Co${}_{10}$Ge${}_3$O${}_{16}$ crystallizes in an intergrowth structure featuring alternating layers of spinel and rock salt. Variable-temperature powder synchrotron x-ray and neutron diffraction, magnetometry, and heat capacity experiments reveal a magnetostructural transition at $T_{\mathrm{N}}=203$ K. This rhombohedral-to-monoclinic transition involves a slight elongation of the CoO${}_6$ octahedra along the apical axis. Below $T_{\mathrm{N}}$, the application of a large magnetic field causes a reorientation of the Co${}^{2+}$ Ising spins. This metamagnetic transition is first order as evidenced by a latent heat observed in temperature-dependent measurements. This transition is initially seen at $T=180$ K as a broad upturn in the $M$–$H$ near $H_{\mathrm{C}}=3.9$ T. The upturn sharpens into a kink at $T=120$ K and a “butterfly” shape emerges, with the transition causing hysteresis at high fields while linear and reversible behavior persists at low fields. $H_{\mathrm{C}}$ decreases as temperature is lowered and the loops at positive and negative fields merge beneath $T=20$ K. The antiferromagnetism is described by $k_{\mathrm{M}}=\left(00\frac{1}{2}\right)$ and below $T=20$ K a small uncompensated component with $k_{\mathrm{M}}=\left(000\right)$ spontaneously emerges. Despite the Curie-Weiss analysis and ionic radius indicating the Co${}^{2+}$ is in its high-spin state, the low-temperature $M$–$H$ trends toward saturation at $M_{\mathrm{S}}=1.0$ ${\mu }_{\mathrm{B}}$/Co. We conclude that the field-induced state is a ferrimagnet, rather than a $S=1/2$ ferromagnet. The unusual $H$–$T$ phase diagram is discussed with reference to other metamagnets and Co(II) systems.

Figure 1

Schematic crystal structure of Co${}_{10}$Ge${}_3$O${}_{16}$. This is the low-temperature $C2/m$ structure which has the same topology as the high-temperature $R\overline{3}m$, but a smaller unit cell. The spinel layer, with tetrahedral Ge${}^{4+}$, is in the middle and is sandwiched between rock-salt-like slabs of edge-sharing Ge${}^{4+}$ and Co${}^{2+}$ octahedra. The sphere colors correspond to maroon, Ge; blue, Co; and orange, O.

Figure 2

Temperature evolution of a powder synchrotron x-ray diffraction peak through the magnetostructural transition of Co${}_{10}$Ge${}_3$O${}_{16}$. The top panel shows the $T=300$ K data and fit for the $R\overline{3}m$ (208) peak. An intensity contour plot is displayed in the center panel to illustrate the splitting of the peak as temperature is lowered through $T_{\mathrm{N}}=203$ K. The bottom panel presents the $T=90$ K data and fit for the $C2/m$ (222) and ($40\overline{4}$) peaks.

Figure 3

Powder synchrotron x-ray diffraction and Rietveld refinement for Co${}_{10}$Ge${}_3$O${}_{16}$ at $T=100$ K using a monoclinic $C2/m$ model. The low-temperature monoclinic cell was determined through pattern indexing and its atom positions were derived from the high-temperature $R\overline{3}m$ model using group-subgroup theory. The small residual and good refinement figures of merit support the validity of the model.

Figure 4

Structural parameters for Co${}_{10}$Ge${}_3$O${}_{16}$ as a function of temperature, as determined by Rietveld refinement of powder synchrotron x-ray diffraction data. The dashed line indicates the phase boundary between the high-temperature $R\overline{3}m$ and low-temperature $C2/m$ structures. The $R\overline{3}m$ and $C2/m$ parameters are shown by the red and navy symbols, respectively, while the volume is displayed as the black squares. The arrows indicate the labeling axes.

Figure 5

Magnetic susceptibility as a function of temperature for Co${}_{10}$Ge${}_3$O${}_{16}$. The data were collected under $H=0.1$, 1, and 5 T using a ZFC-FC procedure.

Figure 6

Magnetization versus field sweeps for Co${}_{10}$Ge${}_3$O${}_{16}$ at different temperatures. The data for each temperature are offset by 5 T increments along the $x$ axis to facilitate visualization. The virgin curve for the $T=1.8$ K trace is dashed to distinguish it from the loop. Dashed black lines are provided to establish the graph origin for each data set.

Figure 7

A field-induced first-order phase transition at low temperature in Co${}_{10}$Ge${}_3$O${}_{16}$. The zero-field cooled (ZFC) trace is greater than the field-cooled (FC) for $7<T<30$ K. This is a result of thermal hysteresis between the FC data collected on heating and cooling, with the curves offset by 11 K at the largest point.

Figure 8

Heat capacity for Co${}_{10}$Ge${}_3$O${}_{16}$. The top panel displays the heat capacity collected under different magnetic fields, while the bottom shows the heat capacity normalized by temperature. An anomaly is observed at $T=203$ K, corresponding to the magnetostructural phase transition. This transition temperature is lowered to $T=199$ K with the application of $H=7$ T. A small upturn in $C_{\mathrm{p}}$/$T$ is seen below 15 K and is suppressed by magnetic field.

Figure 9

Powder neutron diffraction for Co${}_{10}$Ge${}_3$O${}_{16}$ at different temperatures. Magnetic Bragg reflections of $k_{\mathrm{M}}=\left(00\frac{1}{2}\right)$ emerge beneath $T_{\mathrm{N}}=203$ K. The peak positions of the nuclear and $k_{\mathrm{M}}=\left(00\frac{1}{2}\right)$ magnetic phases are shown in the panel above the patterns, colored red and black, respectively. The $T=5$ and 100 K patterns are quite similar, however a close look reveals a new magnetic peak at $Q=0.65$ Å${}^{-1}$, the (001) nuclear position, as well as additional magnetic intensity at other nuclear reflections, which is consistent with the onset of an additional $k_{\mathrm{M}}=\left(000\right)$. This development occurs for $T<20$ K and is associated with the uncompensated magnetism that is observed concomitantly. Each panel displays data from a separate detector bank with different resolution.

Figure 10

Structural and magnetic $H$–$T$ phase diagram for Co${}_{10}$Ge${}_3$O${}_{16}$. The contour plot of $\text{log}(dM/dH)$, taken from the first quadrant of the $M$–$H$ plot, demonstrates the development of ferrimagnetism (FiM). Magnetometry and neutron diffraction experiments revealed the spontaneous emergence of FiM for $T<20$ K. The phase boundary between antiferromagnetism (AFM) and paramagnetism (PM) was observed in both the magnetic and heat capacity data. The indicated crystal structure space groups were solved by refinement of powder synchrotron x-ray diffraction. The FiM phase must have a different nuclear structure than the AFM phase because the transition between them is first order. The solid and dashed lines indicate first- and second-order nature, respectively.