Complex itinerant ferromagnetism in noncentrosymmetric Cr${}_{11}$Ge${}_{19}$

The noncentrosymmetric ferromagnet Cr${}_{11}$Ge${}_{19}$ has been investigated by electrical transport, AC and DC magnetization, heat capacity, x-ray diffraction, resonant ultrasound spectroscopy, and first principles electronic structure calculations. Complex itinerant ferromagnetism in this material is indicated by nonlinearity in conventional Arrott plots, unusual behavior of AC susceptibility, and a weak heat capacity anomaly near the Curie temperature (88 K). The inclusion of spin wave excitations was found to be important in modeling the low temperature heat capacity. The temperature dependence of the elastic moduli and lattice constants, including negative thermal expansion along the $c$ axis at low temperatures, indicates strong magneto-elastic coupling in this system. Calculations show strong evidence for itinerant ferromagnetism and suggest a noncollinear ground state may be expected.

Figure 1

The tetragonal Cr${}_{11}$Ge${}_{19}$ structure. (a) Arrangement of Cr and Ge atoms in the complex Nowotny chimney ladder structure emphasizing the long $c$ axis (52.321 Å). (b) A view down the $c$ axis. One turn of the Cr helix is emphasized on moving from 0, 1, 2, and 3 counterclockwise. (c) A perpendicular view showing a Ge helix within a Cr helix. The Cr atoms are shown as black (larger) balls, and the Ge atoms are shown as orange (smaller) balls.

Figure 2

Rietveld refinement of x-ray powder pattern of Cr${}_{11}$Ge${}_{19}$ collected at room temperature.

Figure 3

$M/H$ as a function of temperature measured at an applied field of $H$ $=$ 10 kOe. Inset shows the fit to the Curie-Weiss law.

Figure 4

(a) $M$ versus $H$ for ${\text{Cr}}_{11}{\text{Ge}}_{19}$ at indicated temperatures. The plots from 70 to 110 K are in the interval of every 5 K. (b) $M^2$ versus $H/M$ (Arrott plot) and (c) $M^4$ versus $H/M$ for ${\text{Cr}}_{11}{\text{Ge}}_{19}$ at indicated temperatures.

Figure 5

AC susceptibility of Cr${}_{11}$Ge${}_{19}$ as a function of temperature at indicated applied fields.

Figure 6

Temperature dependence of molar heat capacity of Cr${}_{11}$Ge${}_{19}$. Inset shows the low temperature fit of the heat capacity.

Figure 7

Heat capacity of Cr${}_{11}$Ge${}_{19}$ in ambient field and 50 kOe. The inset shows $\Delta C_p=C_p(H=0)-C_p(H=50\text{kOe})$.

Figure 8

Resistivity of Cr${}_{11}$Ge${}_{19}$ as a function of temperature. Inset shows the magnetoresistance.

Figure 9

Temperature dependence of lattice constants of Cr${}_{11}$Ge${}_{19}$. The lattice constants are normalized by dividing with values at 300 K.

Figure 10

Variation of elastic moduli (a) $C_{11}$ and (b) $C_{44}$ as a function of temperature.

Figure 11

Electronic density of states of Cr${}_{11}$Ge${}_{19}$ in (a) nonmagnetic state and (b) magnetic state.