Electronic transport in reactively sputtered Mn₃GaN films prepared under optimized nitrogen flow

Sputtering without N₂ flow results in the formation of Mn₃Ga with tetragonal structure. Figure 1(a) shows a symmetrical $\theta/2\theta$ x-ray scan of 25 nm Mn₃Ga deposited on MgO (001). The Bragg reflection observed at $2\theta = 51.23 ^{\circ}$ corresponds to a lattice plane distance d = 0.1783 nm. By comparison with previous studies we assign this peak to the (004) reflection of the tetragonal $D0_{22}$ phase of Mn₃Ga with a lattice constant c = 0.711–0.7133 nm along the growth direction [26–30]. Mn₃Ga is ferrimagnetic with an easy axis along the crystallographic c axis and a high Curie temperature of 730 K [28, 29].

Zoom In Zoom Out Reset image size

Supplying a flow Φ = 0.6 sccm N₂ results in a change of the x-ray diffraction diagram with a Bragg peak around 46.91^∘, see figure 1(b) for films deposited on MgO (001) substrates. The variation of the peak intensities from sample to sample is due to the different tilt angles to reduce the strong reflection from the single-crystalline substrate. We identify this peak as the (002) reflection from the cubic Mn₃GaN antiperovskite structure corresponding to a lattice constant c = 0.3874 nm along the growth direction in good agreement with bulk Mn₃GaN [31]. The epitaxial growth of the cubic antiperovskite phase is confirmed for Φ = 0.6 sccm by a φ-scan of the $\left\lbrace 311 \right\rbrace$ planes at 2θ = 82.55^∘ (d = 0.1172 nm) around the [001] surface normal, see inset figure 1(b). This results in a ratio c/a = 0.999 suggesting an almost perfect cubic lattice with negligible tetragonal distortion as reported earlier for a similar low deposition rate of 0.02 nm s⁻¹ [18]. Due to the large lattice mismatch of 8% between MgO (a = 0.4215 nm) and Mn₃GaN the film is fully relaxed. Increasing the N₂ flow leads to a shift of the (002) peak to lower scattering angles and to a gradual expansion of the Mn₃GaN lattice.

On MgO (111), Mn₃GaN grows along the $\left[ 111 \right]$ direction with a lattice plane distance d(111) = 0.2235 nm corresponding to a lattice constant c = 0.3871 nm, similar to the lattice constant for films grown on MgO(001).

In the following we focus on the resistivity measurements performed on films prepared under different N₂ gas flows. The temperature dependence of the resistivity ρ, figure 2(a), shows a metallic behavior for all films except for Φ = 3.0 sccm. $\rho(T)$ exhibits a broad and shallow kink around 270 K representing $T_\textrm{N}$ of the antiferromagnetic $\Gamma ^{5g}$ phase [10]. The residual resistivity at low temperatures increases with increasing N₂ gas flow. Note that the film with zero flow represents tetragonal Mn₃Ga with a different structure and should not be compared to the Mn₃GaN_x films. However, a similar metallic-like behavior with a smaller residual resistivity of 30 $\mu \Omega$cm was reported earlier for 240 nm thick films [30].

Zoom In Zoom Out Reset image size

Except for the film deposited with Φ = 1.0 sccm, $\rho(T)$ in figure 2(b) does not reach a temperature-independent value at low temperatures but instead increases again when cooling to below a temperature $T_\textrm{min}$, where $\rho(T_\textrm{min })$ is considered as the residual resistivity. For Φ = 1.0 sccm (blue squares) we do not observe an increase toward the lowest achievable temperature 1.8 K

The semi-logarithmic plot of $\Delta \rho = \rho(T)-\rho(T_\textrm{min})$ in figure 2(b) clearly shows that $\Delta \rho(T)$ follows a logarithmic temperature dependence $\Delta \rho(T) = \alpha\, \textrm{log}(T/T_\textrm{min})$ below $T_\textrm{min}$ with a negative slope $\alpha = \mathrm d\rho/\mathrm d\textrm{log}(T/T_\textrm{min})$. It is important to note that this logarithmic behavior does not depend on the magnetic field perpendicularly applied to the sample surface, see figure 2(c).

An earlier study on the electronic transport in ferromagnetic Mn₅Si₃C_x films revealed a similar dependence of the low-temperature resisitvity behavior on the carbon concentration [32]. The logarithmic increase of the resistivity towards lower temperatures was attributed to the scattering of conduction electrons by structural two-level systems (TLS) [33] and not to other quantum corrections like weak localization or enhanced electron-electron interaction. The latter are expected to change in a magnetic field [34], in contrast to the independence of the logarithmic slope α on an applied magnetic field as large as 6 T shown in figure 2(c).

The behavior can be theoretically described by an orbital Kondo effect that gives rise to a logarithmic $\rho(T)$ dependence around the Kondo temperature $T_\textrm{K}$ [35–38] as experimentally observed in ThAsSe and Ni_xNb$_{1-x}$ metallic glasses [39, 40]. The logarithmic increase of $\rho(T)$ toward low temperatures is due to the increasing coupling between dynamical scatterers and conduction electrons. For further details we refer to [32].

Therefore, we ascribe the logarithmic increase of $\rho(T)$ toward low temperatures of Mn₃GaN_x films to the presence of dynamical scatterers, e.g. atomic vacancies, displaced or interstitial atoms or atoms located in grain boundaries. We use the slope α and the temperature $T_\textrm{min}$ as indicators for the degree of structural disorder. The lower the slope and $T_\textrm{min}$, the higher the structural quality.

The characteristic parameters from x-ray diffraction and electronic transport are summarized in figure 3. Films prepared with $\Phi \approx$  1 sccm are characterized by the lowest residual resistance ρ_min, almost zero slope $-\alpha$, and highest residual resistance ratio RRR = $\rho(300\, \textrm{K})/\rho_\textrm{min}$. Results obtained on films grown with an optimized gas flow are discussed in the following.

Zoom In Zoom Out Reset image size

The previous data have been obtained while cooling the samples from 350 K down to 2 K. A different temperature dependence was observed when the samples were heated up from 2 K to 350 K. Figure 4(a) shows data of two films prepared under similar conditions on MgO (001) and (111) substrates. For both films, a broad hysteresis of the two datasets appears between 40 K and 140 K, which is stronger for the film deposited on MgO(111). In antiferromagnetic metals, a magnetic phase transition often gives rise to a sudden decrease of the resistivity with an inflexion point representing $T_\textrm{N}$, corresponding to a local minimum in the derivative $\mathrm d\rho/\mathrm dT$ [41]. In the present case, $\mathrm d\rho/\mathrm dT$ of the films (inset figure 4(a)) exhibits a broad step at $T_\textrm{N}$ = 270 K which we attribute to the Néel temperature of the antiferromagnetic $\Gamma ^{5g}$ phase mentioned before [10, 20]. The resistivity above $T_\textrm{N}$ is only weakly temperature dependent for $T \gt T_\textrm{N}$ so that only a broad step of $\mathrm d\rho/\mathrm dT$ survives at $T_\textrm{N}$.

Zoom In Zoom Out Reset image size

Furthermore, a local minimum appears in $\mathrm d\rho/\mathrm dT$ at a transition temperature $T^{\ast} \approx$ 120 K. The transition at $T^{\ast}$ was observed previously in Mn₃GaN films [22, 23] and was assigned to a ferromagnetic-like transition, presumably due to the coexistence of the $\Gamma ^{5g}$ phase and a M-1 phase of tetragonal symmetry and noncollinear and noncoplanar magnetic order. This coexistence was first discovered by neutron powder diffraction analysis below 109 K [5]. The M-1 phase of Mn₃GaN is particularly interesting because it has been recently suggested as a potential candidate for p-wave magnetic order, where inversion symmetry is broken but the combined translational and time-reversal symmetry is maintained [42]. However, earlier ac susceptibility measurements on Mn₃GaN indicated the formation of a spin-glass state below a freezing temperature around 133 K [43].

Therefore, we have investigated the thermal hysteresis of $\rho(T)$ of the sample on MgO(111) with the more pronounced hysteresis by performing resistivity measurements with different thermal cycles. Figure 4(b) shows the difference $\Delta \rho (T)$ between the resistivity measured while cooling from 140 K to a temperature $T_\textrm{cool}$ and subsequently heating up again to 140 K for various temperatures $T_\textrm{cool}$. $\Delta \rho (T)$ gradually grows with decreasing $T_\textrm{cool}$ and reaches a maximum for $T_\textrm{cool} \unicode{x2A7D}$ 20 K, see inset figure 4(b). Apparently, the phase transition in the resistivity is fully established only after cooling to temperatures to below 20 K. This suggests that the M-1 phase continuously develops while cooling over a wide temperature range by reformation of the $\Gamma^{5g}$ phase in agreement with the increasing M-1 phase fraction observed by neutron powder diffraction [5].

The two magnetic phases of Mn₃GaN_x film are also observed in magnetization measurements. As the magnetization of the thin films is very small, the SQUID magnetometer records strong fluctuations of the signal as soon as the magnetic moment m of the sample (film and substrate) vanishes, see raw data (open circles) around $m (T) \approx$  0 in figure 5. Therefore, we measured m of the bare substrate (black open symbols) and subtracted these data from the raw data. The magnetization $M (T)-M (300\,\textrm{K})$ of the film on MgO(111) increases continuously with decreasing temperature in the $\Gamma ^\textrm{5g}$ phase below 300 K. Below ≈ 100 K, we observe a steeper rise of the magnetization toward lower temperatures which we attribute to the additional contribution from the M-1 phase below $T^{\ast}$. An increase of 30 mµ_B/f.u. corresponds to 0.01 µ_B/Mn, much smaller than 0.2 µ_B/Mn and 0.08 µ_B/Mn previously reported for bulk and thin film Mn₃GaN, respectively, which is presumably due to the smaller M-1 phase fraction in the present case [5, 23].

Zoom In Zoom Out Reset image size

In the two-phase region below $T^{\ast} \approx$  120 K we observe an AHE, see figure 6, where the insets show the saturation value at µ₀H = 2 T. Because of the small AHE for the 50 nm film (figure 6(a)) we subtracted the linear-in-field contribution $\rho_{yx}^0 = R_\textrm{H} \mu_0H$ arising from the ordinary Hall effect and obtain $\rho_{yx}^\textrm{A} = \rho_{yx} - \rho_{yx}^0 = 0.036\, \mu\Omega \textrm{cm}$ and $R_\textrm{H} = 0.9 \times 10^{-4} \textrm{cm}^3$/As at 50 K. The temperature below which the AHE emerges agrees with the transition temperature $T^{\ast}$ determined from the $\rho(T)$ behavior, figure 4. Similar to the temperature dependence of $\rho(T)$ (figure 4) we observe a strong thermal hysteresis of ρ_yx(2 T) between cooling down and heating up the sample, see inset figure 6(b). Below 40 K both data sets merge in agreement with the saturation of $\Delta \rho_\textrm{max}$ in figure 4(b). The occurrence of a AHE below $T^{\ast}$ confirms that the phase transition at $T^{\ast}$ is of magnetic origin, possibly coupled to a change of the crystalline structure. However, the fact that the AHE does not vanish in the M-1 phase below $T^{\ast}$ requires additional tilting or disordering of the magnetic moments to break the combined translational and time-reversal symmetry that would otherwise prevent an AHE in the perfectly ordered M-1 phase.

Zoom In Zoom Out Reset image size

For $T \gt$  120 K, only the comparatively small ordinary Hall effect appears. This is in line with the fact that for cubic and structurally relaxed antiperovskite Mn₃GaN with $\Gamma ^{5g}$ magnetic structure no AHE is expected [14, 15].

Finally, we mention that for the ferrimagnetic Mn₃Ga film ($\Phi = 0)$ we observe an AHE with a broad hysteresis and a coercivity $\mu_0H_c \approx$ 2 T that barely shrinks between 50 K and 300 K due to the high $T_\textrm{C}$ = 730 K [28, 29], similar to results previously reported for 240 nm thick films on Mg (001) substrates [30].

Mn₃GaN is known to exhibit a distortion of the cubic lattice by 0.4% when the temperature changes across $T_\textrm{N}$ [20, 31, 44]. For resolving this lattice distortion in the Mn₃GaN_x films we performed x-ray diffraction at various temperatures close to $T_\textrm{N}$.

Figures 7(a) and (b) show the (002) and (111) Bragg reflections of Mn₃GaN for films deposited on MgO(001) and amorphous SiO₂, respectively. In both cases, the Bragg reflections shift to higher diffraction angles with increasing temperature corresponding to a decrease of the lattice parameter along the surface normal. From the temperature dependence of the lattice parameters d(002) and d(111), figure 7(c), a strong compression of the crystalline lattice along the surface normal is observed between 275 K and 300 K. We attribute this compression to the transition from the antiferromagnetic $\Gamma ^{5g}$ phase to the paramagnetic phase above $T_\textrm{N}$ and the strong coupling between the crystalline lattice and the magnetic order. Note that this temperature dependence is opposite to what is expected from the usually observed thermal expansion for solid materials. We mention that similar results have been obtained for Mn₃GaN_x films deposited under optimized conditions on other substrates like Si (100) and diamond. For the film on SiO₂, a compression of $\unicode{x2A7E}$ 0.4% similar to the result for bulk Mn₃GaN is observed. The apparently smaller compression of 0.1% for the film on MgO(001) is due to the slightly reduced transition temperature $T_\textrm{N}$ and the inaccessibility of lower temperatures in the experimental setup in ambient air.

Zoom In Zoom Out Reset image size

The structural phase transition accompanied with the magnetic phase transition is also observed as a pronounced step in $\rho(T)$ for the thickest film deposited on SiO₂, figure 7(d), with a thermal hysteresis of similar magnitude as observed for the lattice distortion, figure 7(c). We did not observe a clear dependence on the applied magnetic field except that the transition takes place at different temperatures in subsequent thermal cycles possibly due to supercooling/superheating effects in a regime of metastable states.