Temperature dependence of spin-dependent tunneling conductance of magnetic tunnel junctions with half-metallic $\mathrm{C}{\mathrm{o}}_2\mathrm{MnSi}$ electrodes

In order to elucidate the origin of the temperature ($T$) dependence of spin-dependent tunneling conductance ($G$) of magnetic tunnel junctions (MTJs), we experimentally investigated the $T$ dependence of $G$ for the parallel and antiparallel magnetization alignments, $G_{\mathrm{P}}$ and $G_{\mathrm{AP}}$, of high-quality $\mathrm{C}{\mathrm{o}}_2\mathrm{MnSi}$ (CMS)/MgO/CMS MTJs having systematically varied spin polarizations ($P$) at 4.2 K by varying the Mn composition $\alpha$ in $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{Si}$ electrodes that exhibited giant tunneling magnetoresistance ratios. Results showed that $G_{\mathrm{P}}$ normalized by its value at 4.2 K exhibited a notable, nonmonotonic $T$ dependence although its variation with $T$ was significantly smaller than that of $G_{\mathrm{AP}}$ normalized by its value at 4.2 K, indicating that an analysis of the experimental $G_{\mathrm{P}}\left(T\right)$ is critical to revealing the origin of the $T$ dependence of $G$. By analyzing the experimental $G_{\mathrm{P}}\left(T\right)$, we clarified that both spin-flip inelastic tunneling via a thermally excited magnon and spin-conserving elastic tunneling in which $P$ decays with increasing $T$ play key roles. The experimental $G_{\mathrm{AP}}\left(T\right)$, including its stronger $T$ dependence for higher $P$ at 4.2 K, was also consistently explained with this model. Our findings provide a unified picture for understanding the origin of the $T$ dependence of $G$ of MTJs with a wide range of $P$, including MTJs with high $P$ close to a half-metallic value.

Figure 1

Schematic diagram of the layer structure of $\mathrm{C}{\mathrm{o}}_{50}\mathrm{F}{\mathrm{e}}_{50}$ (CoFe)-buffered $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{\beta }$ (CMS)/MgO/CMS MTJ (CMS MTJ) consisting of (from the substrate side) MgO buffer (10 nm)/CoFe buffer (30 nm)/CMS lower electrode (3 nm)/MgO barrier (1.4–3.2 nm)/CMS upper electrode (3 nm)/CoFe (1.1 nm)/$\mathrm{I}{\mathrm{r}}_{22}\mathrm{M}{\mathrm{n}}_{78}$ (10 nm)/Ru cap (5 nm), grown on a MgO(001) single-crystal substrate.

Figure 2

Typical dependence of $R_{\mathrm{P}}A,R_{\mathrm{AP}}A$, and TMR ratio on MgO barrier thickness ($t_{\mathrm{MgO}}$) at 290 K for CMS MTJs with $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{1.30}\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes fabricated on a $20\times 20\mathrm{m}{\mathrm{m}}^2$ substrate over a $t_{\mathrm{MgO}}$ range from 2.2 to 3.1 nm, where $A$ is the nominal junction area of $10\times 10\mu {\mathrm{m}}^2$. The MgO tunnel barrier had a wedge structure, and its nominal thickness was varied from 1.4 to 3.2 nm on each $20\times 20\mathrm{m}{\mathrm{m}}^2$ substrate by linearly moving the shutter during the deposition by electron-beam evaporation.

Figure 3

(a) Typical temperature dependence of $G_{\mathrm{P}}/A$ and $G_{\mathrm{AP}}/A$ of a CMS MTJ with Mn-rich $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{1.30}\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes and $t_{\mathrm{MgO}}=2.65\mathrm{nm}$ from 4.2 to 290 K showing TMR ratios of $2010\%$ at 4.2 K and $335\%$ at 290 K, where $G_{\mathrm{P}}$ and $G_{\mathrm{AP}}$ are the tunneling conductances for the parallel and antiparallel magnetization alignments between the lower and upper electrodes, and $A$ is the nominal junction area of $10\times 10\mu {\mathrm{m}}^2$. The bias voltage was 2 mV. (b) Resulting $T$ dependence of the TMR ratio.

Figure 4

(a) Normalized $G_{\mathrm{P}}$ and (b) $G_{\mathrm{AP}}$ as a function of $T$ from 4.2 to 290 K for CMS MTJs with various $\alpha$ ranging from Mn-deficient $\alpha =0.73$ to Mn-rich $\alpha =1.30$ in $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes, where $G_{\mathrm{P}}$ and $G_{\mathrm{AP}}$ are normalized by the respective values at 4.2 K. The data of $\alpha =1.30\mathrm{MTJ}$ are the same as those shown in Fig. 3.

Figure 5

Dependence of (a) the characteristic temperature $T_2$ and (b) the maximum decrease in the normalized $G_{\mathrm{P}}$ ($G_{\mathrm{P},\mathrm{N}}$) at $T_2$, defined as $\mathrm{\Delta }{G}_{\mathrm{P},\mathrm{N}}\left(T_2\right)=G_{\mathrm{P},\mathrm{N}}\left(T_2\right)-1$, on the tunneling spin polarization at 4.2 K, $P$(4.2 K). The straight lines are guides for the eye.

Figure 6

Fitting curves of the extended Zhang model (solid lines) [Eq. (7)] for the experimental $G_{\mathrm{P}}\left(T\right)$ normalized by the respective values at 4. 2 K of the CMS MTJs with $\alpha =0.73$ (open triangles), 1.24 (open squares), and 1.30 (open circles) in $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes. The experimental data of $G_{\mathrm{P}}\left(T\right)$ are the same as shown in Fig. 4. The data of the normalized $G_{\mathrm{P}}\left(T\right)$ for $\alpha =0.73$ and 1.24 have respective offsets of $+0.02$ and $+0.01$.

Figure 7

(a) Variations with $T$ from the values at $T=0\mathrm{K}$ of the elastic tunneling term $\mathrm{\Delta }{G}_{\mathrm{P},\mathrm{N},\mathrm{el}}\left(T\right)$ [Eq. (8)] and the inelastic tunneling term $\mathrm{\Delta }{G}_{\mathrm{P},\mathrm{N},\mathrm{in}}\left(T\right)$ [Eq. (7c)] obtained by fitting the experimental $G_{\mathrm{P},\mathrm{N}}$($T$) by the extended Zhang model for CMS MTJs with $\alpha =0.73$ (dotted line), 1.24 (dashed line), and 1.30 (solid line). (b) Absolute values of the derivatives of $G_{\mathrm{P},\mathrm{N},\mathrm{el}}\left(T\right)$ and derivatives of $G_{\mathrm{P},\mathrm{N},\mathrm{in}}\left(T\right)$ for the CMS MTJs with $\alpha =0.73$ to 1.30. The intersection of the $-d{G}_{\mathrm{P},\mathrm{N},\mathrm{el}}\left(T\right)/dT$ and $d{G}_{\mathrm{P},\mathrm{N},\mathrm{in}}\left(T\right)/dT$ lines for each α in (b) determines $T_2$ to be 162 K for $\alpha =0.73$, 227 K for $\alpha =1.24$, and 237 K for $\alpha =1.30$. The triangles, squares, and circles shown in (a) are the $\mathrm{\Delta }{G}_{\mathrm{P},\mathrm{N},\mathrm{in}}\left(T_2\right)$ and $\mathrm{\Delta }{G}_{\mathrm{P},\mathrm{N},\mathrm{el}}\left(T_2\right)$ values for the $\alpha =0.73$, 1.24 and 1.30 MTJs, respectively.

Figure 8

Experimental $G_{\mathrm{P}}\left(T\right)$ normalized by its value at 4.2 K, $G_{\mathrm{P}}\left(T\right)/G_{\mathrm{P}}$(4.2 K), of the $t_{\mathrm{MgO}}=2.31\mathrm{nm}$ CMS MTJ with $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{1.24}\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes ($\alpha =1.24$; open circles) along with that of the $t_{\mathrm{MgO}}=2.69\mathrm{nm}$ CMS MTJ ($\alpha =1.24$; open squares) for comparison. These two MTJs were prepared with the same device fabrication process on the same epitaxial layer structure. The fitting curve of the extended Zhang model for the $t_{\mathrm{MgO}}=2.31\mathrm{nm}$ CMS MTJ is also shown along with that for the $t_{\mathrm{MgO}}=2.69\mathrm{nm}$ CMS MTJ for comparison. The experimental $G_{\mathrm{P},\mathrm{N}}$($T$) data and fitting curve of the extended Zhang model for the $t_{\mathrm{MgO}}=2.69\mathrm{nm}$ MTJ ($\alpha =1.24$) are the same as those shown in Fig. 6. The data of the $G_{\mathrm{P},\mathrm{N}}\left(T\right)$ for the $t_{\mathrm{MgO}}=2.69\mathrm{nm}$ MTJ have an offset of $+0.01$.

Figure 9

(a) Comparison of fitting curves for $G_{\mathrm{AP}}\left(T\right)$ normalized by the value at 4.2 K of the CMS MTJ with $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{1.30}\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes ($\alpha =1.30$) by the original Zhang model (dashed-dotted line), the extended Zhang model (solid line), and the Shang model (dashed line). The experimental data (open circles) are the same as those of $\alpha =1.30$ shown in Figs. 3 and 4. The experimental $G_{\mathrm{AP},\mathrm{N}}\left(T\right)$ data with the fitting curves of the extended Zhang and Shang models have respective offsets of +0.5 and +1.0. (b) Decomposition of the variation of the experimental $G_{\mathrm{AP},\mathrm{N}}\left(T\right)$ of $\alpha =1.30$ CMS MTJ into two components by fitting with the extended Zhang model: One is the inelastic tunneling term $\mathrm{\Delta }{G}_{\mathrm{AP},\mathrm{N},\mathrm{in}}\left(T\right)$ [Eq. (12c)], and the other is the elastic tunneling term $\mathrm{\Delta }{G}_{\mathrm{AP},\mathrm{N},\mathrm{el}}\left(T\right)$ [Eq. (12b)].

Figure 10

Fitting curves (solid lines) for the experimental $G_{\mathrm{AP}}\left(T\right)$ normalized by the respective values at 4.2 K by the extended Zhang model [Eq. (12)] for the CMS MTJs with various $\alpha$ in $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes. The experimental $G_{\mathrm{AP},\mathrm{N}}\left(T\right)$ are the same as shown in Fig. 4 and are shown as open triangles, open squares, and open circles for $\alpha =0.73$, 1.24, and 1.30, respectively. The normalized $G_{\mathrm{AP}}\left(T\right)$ for $\alpha =1.24$ and 1.30 have respective offsets of $+0.5$ and $+1.0$.

Figure 11

(a) Dependence of the coefficient $B_{\mathrm{AP}}=2P_0^2/\left(1-P_0^2\right)$, the parameter $1/\xi =\left(1+P_0^2\right)/\left(1-P_0^2\right)$, and the product $a·f$(290 K) on Mn composition $\alpha$ in $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes, where these values are normalized by the respective values for $\alpha =0.73$. (b) Dependence of the parameter ${\gamma }_{\mathrm{AP}}=G_{\mathrm{AP}}\left(290\mathrm{K}\right)/G_{\mathrm{AP}}\left(4.2\mathrm{K}\right)$ on $1/\xi$ for CMS MTJs with $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.84}$ electrodes (open circles). Dependence of ${\gamma }_{\mathrm{AP}}$ on $1/\xi$ for CMS MTJs with $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.96}$ electrodes reported in Ref. [12] are also plotted (solid and open triangles), where solid triangles are for $\alpha$ being smaller than a certain critical $\alpha$ value, ${\alpha }_{\mathrm{c}}$, for $\mathrm{C}{\mathrm{o}}_2\mathrm{M}{\mathrm{n}}_{\alpha }\mathrm{S}{\mathrm{i}}_{0.96}$ electrodes, and open triangles are for $\alpha$ being larger than ${\alpha }_{\mathrm{c}}$ [12].