DMI Study Materials
Is large enough by a few ? magnitudes, which sets the characteristic length scale for the edge tilting [28]. Alternatively, in [28] the condition is justified when the system has sufficiently large anisotropy to avoid the formation of cycloids. Furthermore, we notice that the ratio of D and the critical magnitude ${D}_{c}=4\sqrt{{{AK}}_{{\rm{u}}}}/\pi $ is around 1.1, thus the constant arising from integrating equation (11) should tend to zero, as shown in [28]. This condition can also be seen as a significantly large DMI Study Materials cycloid period. If the length L of the system is increased the formation of cycloids would be favoured [44]. With the simplified evaluation of T at the boundary it is straightforward to apply the shooting method. An alternative calculation to obtain general solutions of equations (11) and (12), as employed in [44], requires a more careful analysis of the boundary conditions. Depending on the chirality of the system, which can be observed from the simulations, we fix the condition ${\rm{\Theta }}(-L/2)=\arcsin (\mp {\rm{\Delta }}/\xi )$ and vary dT(-L/ 2)/dx until finding a solution that satisfies ${\rm{\Theta }}(L/2)\,=\arcsin (\pm {\rm{\Delta }}/\xi )$. The upper sign + refers to the interfacial case and the Exam Dumps bottom sign—to the bulk DMI case. In figures 1(a) and (b) we compare results from the theory and simulations of the one-dimensional problem, for systems with interfacial (Cnv) and bulk (T) DMI, respectively.