Ab initio study of magneto-ionic mechanisms in ferromagnet/oxide multilayers

The application of gate voltages in heavy metal/ferromagnet/oxide multilayer stacks has been identified as one possible candidate to manipulate their anisotropy at will. However, this method has proven to show a wide variety of behaviors in terms of reversibility, depending on the nature of the metal/oxide interface and its degree of oxidation. In order to shed light on the microscopic mechanism governing the complex magneto-ionic behavior in $\text{Ta/CoFeB/}{\text{HfO}}_2$, we perform ab initio simulations on various setups comprising Fe/O and ${\text{Fe/HfO}}_2$ interfaces with different oxygen atom interfacial geometries. After the determination of the more stable interfacial configurations, we calculate the magnetocrystalline anisotropy energy on the different unit cell configurations and formulate a possible mechanism that well describes the recent experimental observations in $\text{Ta/CoFeB/}{\text{HfO}}_2$.

Figure 1

Sketch of the different interfacial configurations. Unit cells (I) and (II) represent Fe/O interfaces while unit cells (III) and (IV) represent the $\mathrm{Fe}/{\mathrm{HfO}}_2$ interfaces.

Figure 2

Magnetocrystalline anisotropy energy (MCAE) comparison of the pure $\mathrm{Fe}/{\mathrm{HfO}}_2$ interface [structures (III) and (IV)]. The $\theta$ angle of the spin quantization axis (SQA) from Eq. (2) is shown in the inset of (a). (a), (b) MCAE for the ground state of the $\mathrm{Fe}/{\mathrm{HfO}}_2$ unit cell with a frontal O-Fe distance of (a) $\mathrm{\Delta }{z}_{\text{(O-Fe)}}=5.76a_B$ (equilibrium) and (b) $\mathrm{\Delta }{z}_{\text{(O-Fe)}}=3.76a_B$ (shifted). $\mathrm{\Delta }{z}_{\text{(O-Fe)}}$ represents the interplanar distance of the interstitial oxygen species from the Fe surface (marked with the dashed line). (c) $\mathrm{Fe}/{\mathrm{HfO}}_2$ unit cell with frontal oxygen positioning. (d), (e) Ground state of the $\mathrm{Fe}/{\mathrm{HfO}}_2$ unit cell with interstitial interplanar O-Fe distance of (d) $\mathrm{\Delta }{z}_{\text{(O-Fe)}}=5.34a_B$ (equilibrium) and (e) $\mathrm{\Delta }{z}_{\text{(O-Fe)}}=3.34a_B$ (shifted). (f) $\mathrm{Fe}/{\mathrm{HfO}}_2$ unit cell with interstitial oxygen positioning. $K_1$ represents the value of the MCAE and is given by $E(\theta =0)-E(\theta =\pi /2)$.

Figure 3

Magnetocrystalline anisotropy energy (MCAE) [$\theta$ from Eq. (2)] in the $\mathrm{Fe}/{\mathrm{HfO}}_2$ setup shown with a shifted oxygen species at the interface. (a) MCAE of the mixed surface in its ground state. (b) MCAE of the mixed surface with a frontal O-Fe distance of $5.78a_B$. (c) Side view of the $\mathrm{Fe}/{\mathrm{HfO}}_2$ unit cell with the mixed setup. $\mathrm{\Delta }{z}_{\text{(O-Fe)}1}$ and $\mathrm{\Delta }{z}_{\text{(O-Fe)2}}$ denote the interplanar distance of the frontal and interstitial oxygen species from the Fe surface, respectively (marked with the dashed line).

Figure 4

Magnetocrystalline anisotropy energy (MCAE) as a function of the frontal and interstitial oxygen atom interplanar distances as depicted in Fig. 3. (a) Effect of frontal oxygen shifts ($\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}$ variable) while the interstitial oxygen is kept fixed at a distance $\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}=2.53a_B$ from the FM surface. (b) Effect of frontal oxygen shifts ($\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}$ variable) while the interstitial oxygen is kept fixed at a distance $\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}=1.96a_B$ from the FM surface. The initial interplanar distance of the frontal oxygen atoms is $\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}=6.94a_B$ in both (a) and (b).

Figure 5

(a) Energetic cost of shifting interstitial and frontal oxygen atoms in the mixed interface setup displayed in Fig. 3. The starting positions are $\mathrm{\Delta }{z}_{\text{(O-Fe)1}}=2.53a_B$ for the interstitial oxygen atom and $\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)2}=6.94a_B$ for the frontal oxygen atoms [i.e., the setup of Fig. 3]. (b) MCAE at different frontal oxygen positions $\mathrm{\Delta }{z}_{\text{(O-Fe)2}}$ represented in Fig. 3. The starting positions are $\mathrm{\Delta }{z}_{\left(\text{O-Fe}\right)1}=-0.08a_B$ for the interstitial oxygen atom and $\mathrm{\Delta }{z}_{\text{(O-Fe)2}}=6.94a_B$ for the frontal oxygen atoms [i.e., the setup of Fig. 3]. Positive values on the $y$ axis indicate that the system has IP magnetic anisotropy.

Figure 6

Hypothesis for the mechanism governing the different magneto-ionic regimes in CoFeB/${\mathrm{HfO}}_2$ multilayers. (a) Ground state of the system. (b) Irreversible magnetization switching via interstitial sites occupied by migrating oxygen species. (c) Reversible magnetization switching via frontal oxygen shifts. The bottom cartoon in all three panels represents the magnetization direction and the switching process.