Magnetic damping in sputter-deposited $\mathrm{C}{\mathrm{o}}_2\mathrm{MnGe}$ Heusler compounds with $A2,B2$, and $L{2}_1$ orders: Experiment and theory

We show that very low values of the magnetic damping parameter can be achieved in sputter deposited polycrystalline films of $\mathrm{C}{\mathrm{o}}_2\mathrm{MnGe}$ annealed at relatively low temperatures ranging from 240 °C to 400 °C. Damping values as low as 0.0014 are obtained with an intrinsic value of 0.0010 after spin-pumping contributions are considered. Of importance to most applications is the low value of inhomogeneous linewidth that yields measured linewidths of 1.8 and 5.1 mT at 10 and 40 GHz, respectively. The damping parameter monotonically decreases as the $B2$ order of the films increases. This trend is reproduced and explained by ab initio calculations of the electronic structure and damping parameter. Here, the damping parameter is calculated as the structure evolves from $A2$ to $B2$ to $L{2}_1$ orders. The largest decrease in the damping parameter occurs during the $A2$ to $B2$ transition as the half-metallic phase becomes established.

Figure 1

(a) X-ray diffraction 2θ scans showing the emergence of the (220) and (400) peaks after being annealed at 240 °C and higher. (b) Schematic cross-section diagram of sample structure. (c) Temperature-dependent VSM magnetometry curve showing the irreversible increase in the magnetization at 240 °C due to crystallization. (d) Example of the magnetic moment vs thickness measured at 300 and 5 K. The $x$ intercept indicates the magnetic dead layer thickness.

Figure 2

The in-plane (black circles) and out-of-plane (blue diamonds) lattice constants as a function of annealing temperature indicating a tetragonal strain that increases with annealing temperature.

Figure 3

(a) The [100] texture was confirmed by 2D scans whereby 2θ-ω scans are taken at different tilt angles. (b) A plot of the 2θ-ω scan in the vicinity of the (311) peak. The presence of this peak indicates $L{2}_1$ order, which is seen only in thicker samples. (c) 2θ-ω scans showing the (002) and (004) peaks at different annealing temperatures. (d) The ratio of the peaks is proportional to amount of $B2$ order, which increases with annealing temperature.

Figure 4

(a) An example of the real (left) and imaginary (right) transmission signal S21 as the field is swept through the resonance. Fits of the data to the Polder susceptibility tensor are included as the line through the data. (b) Linewidth vs frequency plots used to determine the damping parameter for several 16-nm samples annealed at different temperatures. The error bars are from the fits to the Polder susceptibility.

Figure 5

The total density of states (tDOS) calculated at 0 K for selected ordering of $\mathrm{C}{\mathrm{o}}_2\mathrm{MnGe}$. Black lines and grey shaded areas correspond to DOS calculated within the ASA scheme, red lines stand for FP calculations. (a) is the tDOS for $A2$; panel (b) the intermediate phase along the $A2\to B2$ transition with 52% $B2$ ordering $\mathrm{[}x=0.76,y=0$, see Eq. (3) and the corresponding text]; (c) and (d) correspond to tDOS for B2 phase. (e) is the tDOS for the intermediate phase between $B2$ and $L{2}_1$ phases [60% $L{2}_1$ ordering, $x=1,y=0.3$, see Eq. (3) and the corresponding text]. (f) is the tDOS for $L{2}_1$ phase with the corresponding $\left(x=1,y=0.5\right)$ doublet.

Figure 6

(a) Measured spectroscopic $g$ factor vs the annealing temperature. (b) The calculated $g$ factors as the crystalline order evolves from $A2$ (left) to $B2$ (center) to $L{2}_1$ (right).

Figure 7

(a) Measured saturation magnetization (black circles) and effective magnetization (blue triangles) vs the annealing temperature for the 16-nm samples. (b) Measured effective magnetization vs annealing temperature for samples with various thickness. (c) Anisotropy energy density vs the reciprocal thickness for the 400 °C annealed samples used to determine the bulk and interfacial components of the anisotropy. (d) Calculated saturation magnetization as the crystalline order evolves from $A2$ (left) to $B2$ (center) to $L{2}_1$ (right).

Figure 8

(a) Measured damping parameter vs annealing temperature for samples with various thickness. (b) Calculated damping parameter at 300 (black) and 10 K (orange) as the crystalline order evolves from $A2$ (left) to $B2$ (center) to $L{2}_1$ (right). (c) Plot of the damping parameter vs the reciprocal thickness used to account for the spin-pumping contribution to the damping. The $y$ intercept corresponded to the intrinsic damping parameter. (d) Plot of the measured inhomogeneous linewidth vs annealing temperature for samples with various thickness.

Figure 9

Calculated damping parameter vs the density of states at the Fermi energy.

Figure 10

(a) Composition weighted sum of the spin-orbit parameter for Co and Mn $3d$ orbitals and Ge $4p$ orbitals, for the unit cell of CMG, as a function of degree of ordering. (b) Element specific value of Co and Mn $3d$ as well as Ge $4p$ spin-orbit parameter for different ordering of CMG.

Figure 11

(a) Damping parameter vs resistivity for samples annealed at different temperatures. (b) Damping parameter and resistivity of the 16-nm sample annealed at 400 °C as a function of measurement temperature from RT down to approximately 5 K.