Author Correction: Spin-orbit-torque-induced magnetic domain wall motion in Ta/CoFe nanowires with sloped perpendicular magnetic anisotropy

Correction to: Scientific Reports 10.1038/s41598-017-02208-y, published online 17 May 2017

This Article contains typographical errors in Equation (8), where

$$E_{\mathrm{DM}}=D[m_{\mathrm{z}}(\partial m_{\mathrm{x}}/\partial x)-(\partial m_{\mathrm{z}}/\partial z)]$$

should read:

$$E_{\mathrm{DM}}=D[m_{\mathrm{z}}(\partial m_{\mathrm{x}}/\partial x)-(\partial m_{\mathrm{z}}/\partial x)]$$

In addition, equation (15)

$$\begin{array}{ll}{I}_1={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}({\sin }^2\theta ){\left(\frac{\partial f}{\partial x}\right)}^2\mathrm{d}x;\hfill & I_2={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}x({\sin }^2\theta )\mathrm{d}x;\hfill \\ I_3={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}{\sin }^2\theta \mathrm{d}x;\hfill & I_4={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\left(\frac{\partial f}{\partial x}\right)\sin \theta \mathrm{d}x;\hfill \\ I_5{\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}({\sin }^2\theta ){\left(\frac{\partial f}{\partial q}\right)}^2\mathrm{d}x;\hfill & I_6={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\sin \theta \cos \theta \mathrm{d}x;\hfill \\ I_7={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\left(\frac{\partial f}{\partial q}\right)\sin \theta \mathrm{d}x;\hfill & I_8={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\sqrt{ax+b-\frac{1}{2}{\mu }_0{M}_S^2}({\sin }^2\theta )\mathrm{d}x\hfill \end{array}$$

should read:

$$\begin{array}{ll}{I}_1={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}({\sin }^2\theta ){\left(\frac{\partial f}{\partial x}\right)}^2\mathrm{d}x;\hfill & I_2={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}x({\sin }^2\theta )\mathrm{d}x;\hfill \\ I_3={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}{\sin }^2\theta \mathrm{d}x;\hfill & I_4={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\left(\frac{\partial f}{\partial x}\right)\sin \theta \mathrm{d}x;\hfill \end{array}$$

$$\begin{array}{ll}{I}_5={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}({\sin }^2\theta ){\left(\frac{\partial f}{\partial q}\right)}^2\mathrm{d}x;\hfill & I_6={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\sin \theta \cos \theta \mathrm{d}x;\hfill \\ I_7={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\left(\frac{\partial f}{\partial q}\right)\sin \theta \mathrm{d}x;\hfill & I_8={\int }_{-\frac{L\mathrm{x}}{2}}^{\frac{L\mathrm{x}}{2}}\sqrt{ax+b-\frac{1}{2}{\mu }_0{M}_S^2}({\sin }^2\theta )\mathrm{d}x\hfill \end{array}$$