NEGF method for the non-collinear DFT

OpenMX Ver. 3.9 supports the NEGF method coupled with the non-collinear DFT method, which can be regarded as a full implementation of NEGF within NC-DFT. The spin-orbit coupling, the DFT+$U$ method, and the constraint schemes to control direction of spin and orbital magnetic moments supported for NC-DFT are all compatible with the implementation of the NEGF method. Thus, it is expected that a wide variety of problems can be treated, such as transport through magnetic domains with spiral magnetic structure. The usage of the functionality is the same as that for the collinear DFT case.

As an example, we show a result for zigzag graphene nanoribbon calculated by the NEGF method coupled with NC-DFT in Fig. 46. It is assumed that spin moments at the zigzag edges align upward and rightward in the left and right leads, respectively. Those calculations were performed by the conventional NC band structure method with the constraint scheme as the step 1. Then, any constraint was not applied in the calculation of the step 2. After getting the SCF convergence in the step 2, it is found that the spin direction gradually rotates in the central region as shown in Fig. 46(a). The calculations can be traced by input files 'Lead-L-8ZGNR-NC.dat', 'Lead-R-8ZGNR-NC.dat', and 'NEGF-8ZGNR-NC.dat' stored in the directory 'work/negf_example'. Also, you will find another example for input files of a gold chain in the same directory.

Figure: (a) Zigzag graphene nanoribbon with non-collinear spin direction represented by arrow. The length of the arrow corresponds to magnitude of the spin moment. In the calculations of the step 1, the constraint scheme to control spin direction was applied so that spin moments at the zigzag edges can align upward and rightward in the left and right leads, respectively. (b) Transmission of electron through the channel region C shown in Fig. 46(a).