Nanoscale thermoelectrical detection of magnetic domain wall propagation

In magnetic nanowires with perpendicular magnetic anisotropy (PMA) magnetic domain walls (DWs) are narrow and can move rapidly driven by current induced torques. This enables important applications like high-density memories for which the precise detection of the position and motion of a propagating DW is of utmost interest. Today's DW detection tools are often limited in resolution, require complex instrumentation, or can only be applied on specific materials. Here we show that the anomalous Nernst effect provides a simple and powerful tool to precisely track the position and motion of a single DW propagating in a PMA nanowire. We detect field and current driven DW propagation in both metallic heterostructures and dilute magnetic semiconductors over a broad temperature range. The demonstrated spatial accuracy below 20 nm is comparable to the DW width in typical metallic PMA systems.

Figure 1

Principle of ANE-based DW detection: (a) AHE DW detection by probe current $I$ inside a Hall cross. (b) ANE DW detection in a PMA wire: a transverse temperature gradient $\nabla T_y$ generates an ANE voltage $V_{\mathrm{ANE}}$ along the wire depending on $x_{\mathrm{DW}}$. (c) False color electron micrograph of CoFeB nanowire (green) with Pt contacts and heater line (brown). The wire $l$ length between the contacts is 6.4 µm. The wire is 600 nm wide. A 200-nm-wide notch is situated at the center. (d) Color map of the simulated temperature distribution for electrical heating with $P_{\mathrm{heat}}=5.1\mathrm{mW}$. (e) The temperature profile along the dashed line in the simulation. The temperature drops from 435 K at the heater to 297 K at the CoFeB wire where an edge-to-edge temperature drop of 45 mK is calculated (marked in the inset by arrows). (f) ANE reversal loops from full negative to positive saturation. $V_{\mathrm{ANE}}$ is plotted vs $B_{\mathrm{app}}$. The black curve shows data of a CoFeB wire at room temperature and $P_{\mathrm{heat}}=7.4\mathrm{mW}$. The red curve shows (GaMn)(AsP) data taken at $T=65.5\mathrm{K}$ and $P_{\mathrm{heat}}=0.75\mathrm{mW}$. (g) Pinning of a propagating DW at the notch of a CoFeB device. $V_{\mathrm{ANE}}$ at $P_{\mathrm{heat}}=5.1\mathrm{mW}$ plotted as a function of $B_{\mathrm{app}}$ for a sweep from $-200\mathrm{mT}$ to positive fields at a sweep rate of 8.3 mT/s. The plateau at $V_{\mathrm{ANE}}=0$ results from pinning of a propagating DW at the notch. Inset: MFM image of a pinned DW at the notch. The two contrasts correspond to opposite $m_z$ on either side of the notch.

Figure 2

ANE detection of MFM controlled DW propagation in a CoFeB nanowire. (a) Scheme of MFM controlled DW propagation as an MFM tip is scanned across the wire. The stray field of the magnetic MFM tip nucleates a reversed domain and propagates the DW ahead of the tip. (b) ANE measurement of tip induced DW propagation at $B_{\mathrm{app}}=0,P_{\mathrm{heat}}=7.3\mathrm{mW}$, and MFM tip $x$ velocity of 25 nm/s. Top panel shows wire geometry relative to tip position. Plateaus indicate stepwise DW motion between pinning sites. The wide plateau near the center corresponds to pinning at the notch. (c) and (d) Details of plateaus indicated by arrows in (b) plotted with corresponding colors for data and arrows. (e) ANE measurement of tip induced DW propagation at applied fields of $B_{\mathrm{app}}=-4.0\mathrm{mT}$ (blue), 3.7 mT (red), and 8.3 mT (black). $P_{\mathrm{heat}}=5.1\mathrm{mW}$. Tip $x\mathrm{velocity}=30\mathrm{nm}/\mathrm{s}$. For higher fields parallel to the tip field the DW propagates ahead of the tip. For $B_{\mathrm{app}}=8.3\mathrm{mT}$ pinning only occurs at the notch.

Figure 3

ANE DW detection in a (GaMn)(AsP) microwire. (a) False color electron micrograph of the device with microwire colored in green, Pt heater line in brown, and Au nucleation strip line in blue. (b) ANE measurement during field induced DW propagation. Normalized $V_{\mathrm{ANE}}$ vs $B_{\mathrm{app}}$ at $P_{\mathrm{heat}}=0.5\mathrm{mW}$ and sweep rate of 0.25 mT/s. At $B_{\mathrm{app}}\cong 0.05\mathrm{mT}$ a DW is nucleated (blue arrow). Plateaus result from pinning at intrinsic unintentional pinning sites. Inset: MOKE microscope images corresponding to the three pinned DW states marked (i)–(iii). (c) ANE measurement of spin torque induced DW propagation at $B_{\mathrm{app}}=0$. ANE data is taken after application of 1 µs pulses of current density $j$ as indicated. For high current density high DW velocities up to 30 m/s are found. For lower current density DW propagation is hindered by pinning at various nonintentional pinning sites.