Electronic transport in magnetically ordered ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films

${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films exhibit antiferromagnetic or ferromagnetic behavior depending on the carbon doping level $x$. We report a detailed electronic-transport study of films prepared with different $x$. All films exhibit metallic behavior of the temperature-dependent resistivity $\rho \left(T\right)$ with a logarithmic increase towards low temperatures attributed to the structural disorder and the accompanied scattering of conduction electrons by two-level systems. Below $1\mathrm{K}$, the Kondo-type behavior $\rho \left(T\right)\sim -\ln T$ shows a crossover to Fermi-liquid behavior $\rho \sim -T^2$ independent of the type of magnetic order. The magnetoelectronic properties such as Hall effect and magnetoresistance show clear differences characteristic for the different magnetically ordered phases, i.e., antiferromagnetic vs ferromagnetic.

Figure 1

$\theta \text{−}2\theta$ x-ray scans ($\mathrm{Cu}{K}_{\alpha }$ radiation) of $100\mathrm{nm}$ thick ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films.

Figure 2

Scanning electron micrographs of two ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ fims of (a) $30\mathrm{nm}$ and (b) $400\mathrm{nm}$ thickness.

Figure 3

(a) Magnetization $M\left(T\right)$ of two $100\mathrm{nm}$ ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films in an applied field of $10\mathrm{mT}$. Inset shows a plot $M$ vs ${(T∕T_C)}^{3∕2}$ $(T_C=350\mathrm{K})$ for $x=0.8$ with the solid line indicating a linear behavior due to ferromagnetic spin waves. (b) Magnetic hysteresis loops of ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ with the magnetic field $B$ applied parallel (solid line) and perpendicularly (dashed line) to the film plane.

Figure 4

(Color online) Resistivity $\rho$ vs temperature $T$ for $100\mathrm{nm}$ thick ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films with different carbon concentrations $x$. Solid line for $x=0.8$ shows a calculation of $\rho \left(T\right)$ according to Eq. (2).

Figure 5

Concentration dependence of (a) minimum resistivity ${\rho }_{\min }$, (b) resistance ratio $\mathrm{RRR}=\rho$ $\left(270\mathrm{K}\right)∕{\rho }_{\min }$, and (c) slope $\alpha$ of the logarithmic behavior $\Delta \rho ∕{\rho }_{\min }=\alpha \ln (T∕T_{\min })$ at low $T$ for $100\mathrm{nm}$ thick films. RRR data point for $x=0$ in (b) represents the average over two samples. Solid lines serve as guides to the eye.

Figure 6

(Color online) Low-temperature behavior of $\rho \left(T\right)$ for ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films with (a) $x=0$ and (b) $x=0.2$. Dashed-dotted lines indicate a behavior $\rho \sim T^2$ [Eq. (4)] and solid line indicates a behavior described by Eq. (5).

Figure 7

(Color online) (a) Semilogarithmic plot of the excess resistivity $\Delta \rho =\rho \left(T\right)-{\rho }_{\min }$ for ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_x$ films with $x⩾0.4$. (b) Semilogarithmic plot of the excess resistivity $\Delta \rho$ for ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ films of different film thickness $d$. Solid lines show a behavior $\Delta \rho \sim -\ln T$.

Figure 8

(Color online) Semilogarithmic plot of $\rho \left(T\right)$ for a $165\mathrm{nm}$ ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ film (Table , sample i) in various applied magnetic fields $B$ applied perpendicularly to the film plane. Dashed-dotted lines indicate a linear dependence of constant slope.

Figure 9

(Color online) Semilogarithmic plot of the low-temperature resistivity $\rho (T,B)$ in zero field (closed symbols) and in $5\mathrm{T}$ (open symbols) with respect to the low temperature resistivity ${\rho }_{\min }\left(B\right)=\rho (T_{\min },B)$ for (a) ${\mathrm{Mn}}_5{\mathrm{Si}}_3$ and (b) ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ films. Solid lines indicate a behavior $\sim -\ln T$. Insets show $\rho (T,B)-{\rho }_{\min }\left(B\right)$ vs $T^2$ where the dashed-dotted lines indicate a behavior $\sim -T^2$.

Figure 10

(Color online) Relative magnetoresistance $\mathrm{MR}=[\rho \left(B\right)-\rho \left(0\right)]∕\rho \left(0\right)$ vs applied magnetic field $B$ for (a) antiferromagnetic ${\mathrm{Mn}}_5{\mathrm{Si}}_3$ and (b) ferromagnetic ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ films. Inset shows the $\mathrm{MR}(B_{\parallel }\phantom{)}$ for ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ after subtraction of the linear “background” indicated by the dashed line in (b).

Figure 11

(Color online) Hall resistivity ${\rho }_{\text{Hall}}\left(B\right)-{\rho }_{\text{Hall}}\left(0\right)$ vs applied magnetic field $B$ for antiferromagnetic ${\mathrm{Mn}}_5{\mathrm{Si}}_3$ (ten times) and ferromagnetic ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ films $(d=100\mathrm{nm})$. Inset shows the Hall resistivity for ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ at high fields. Dash-dotted lines indicate a linear behavior.