Large-tunneling anisotropic magneto-Seebeck effect in a CoPt/MgO/Pt tunnel junction

We theoretically investigate the tunneling anisotropic magneto-Seebeck effect in a realistically modeled $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{Pt}$ tunnel junction using coherent transport calculations. For comparison we study the tunneling magneto-Seebeck effect in $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{CoPt}$ as well. We find that the magneto-Seebeck ratio of $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{Pt}$ exceeds that of $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{CoPt}$ for small barrier widths, reaching $175\%$ at room temperature. This provides a sharp contrast to the magnetoresistance, in which $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{CoPt}$ performs better by one order of magnitude for all barrier widths. Thus, by switching from two ferromagnetic layers to one (so that spin-orbit coupling alone governs the magnetic transport anisotropy), the magnetoresistance ratio diminishes while the magneto-Seebeck ratio remains comparable or improves considerably. We therefore demonstrate that magnetic tunability can increase when caused solely by spin-orbit coupling. This result sheds light on the role that spin-orbit coupling plays in magnetically tuning the properties of tunnel junctions.

Figure 1

(a) The anisotropic MTJ ($\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{Pt}$). A temperature gradient induces an open-circuit voltage across the contacts, known as the Seebeck effect. Rotating the magnetization of CoPt produces varying Seebeck coefficients, also called the tunneling anisotropic magneto-Seebeck (TAMS) effect. (b) The normal MTJ ($\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{CoPt}$), which exhibits the tunneling magneto-Seebeck (TMS) effect. (c) The TAMS and TMS ratios plotted vs temperature and barrier thickness. The TAMS ratio (blue/red) surpasses the TMS ratio (cyan/orange) at small barrier thicknesses at all temperatures. This provides a contrast to the behavior of the TMR and TAMR ratios (discussed in Fig. 5).

Figure 2

(a) Atomistic schematic of the $\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{Pt}$ tunnel junction at the interfaces. (b) Schematic depicting the simplest geometry pertinent to the Landauer-Büttiker formalism. Reflectionless contacts (depicted in gray) behave as thermal reservoirs, populated with carriers at a given Fermi level $\mu$ and temperature $T$. Carriers supplied from each contact proceed towards or away from the scattering region (S) via the left (L) and right (R) semi-infinite leads.

Figure 3

Various transport quantities plotted over the 2DBZ at the Fermi energy. (a) The number of Bloch states (NOBS) traveling towards the scattering region in the CoPt lead ($\varphi =0^{\circ }$). (b) The NOBS pertaining to the Pt lead. (c) The unitless transmission ($\mathcal{T}$) of the AMTJ, containing five MgO monolayers ($\varphi =0^{\circ }$). Sharp peaks known as “hot spots” result from unrealistically clean interfaces. (d) The same transmission rescaled with hot spots removed (${\mathcal{T}}^{*}$).

Figure 4

Visual representation of the magnetoresistance and magneto-Seebeck effects at 300 K for a four monolayer barrier thickness. Both $\mathsf{\text{T}}$ [Eq. (5)] and $\mathsf{\text{G}}$ [Eq. (8)] are plotted vs energy for both devices. The lighter curves correspond to $\mathsf{\text{T}}$ (unitless) while the darker curves represent $\mathsf{\text{G}}$ (${\mathrm{Ry}}^{-1}$). Only the magnetization directions yielding the high/low (blue/red) magnetoresistance states are shown. The energy integral of $\mathsf{\text{G}}$ (the area under a darker curve) gives the conductance up to a factor of $e^2/h$ [Eq. (6)]. The weighted center of $\mathsf{\text{G}}$ (a vertical dashed line) gives the Seebeck coefficient up to a factor of $e/hTG$ [Eq. (7)]. While the normal MTJ displays a larger variation in the integral of $\mathsf{\text{G}}$, the AMTJ exhibits a greater variation in the asymmetry of $\mathsf{\text{G}}$. The difference in Seebeck coefficients and corresponding magneto-Seebeck ratios are shown for comparison.

Figure 5

Normalized conductance vs magnetization direction, shown for various numbers of MgO monolayers (ML) in the barrier (top panel). TAMR ($\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{Pt}$, middle panel) and TMR ($\mathrm{CoPt}\text{/}\mathrm{MgO}\text{/}\mathrm{CoPt}$, bottom panel) ratio vs barrier thickness, plotted for various temperatures and included numbers of ${\mathbf{k}}_{\left|\right|}$ points. While the TAMR curve peaks at five MgO monolayers, the TMR curve saturates as barrier thickness increases. The TMR ratios exceed the TAMR ratios by one order of magnitude.

Figure 6

(a) The Seebeck coefficient vs temperature, plotted for both devices and all magnetization directions (four MgO monolayers). Both devices produce Seebeck coefficients of similar strength. In addition, both devices produce comparable differences in the Seebeck coefficient (b) and magneto-Seebeck ratios (c) for all barrier thicknesses simulated. Furthermore, the TAMS ratio surpasses the TMS ratio for small barrier thicknesses, in contrast to the magnetoresistance ratios [Figs. 5 and 5], which behave oppositely for all barrier thicknesses.