NEW parameter `easy_axis` or `spin_axis` should be added to modify the easy axis of magnetization in `noncolin=0 lspinorb=1 nspin=4` case

Background

Now the noncolin=0 lspinorb=1 case in ABACUS let the mag moment is constrained along the Z direction, which means that the mag moment can be only set to up or down along Z axis.

This kind of implementation largely limit the power of ABACUS. Given the magnetic moment is limited to the Z direction have been implemented now, it can be eaily found that the magnetic moment can be limited to any direction indeed. I sugguest that there should be a new parameter to set the easy axis of magnetic moment in the SOC colinear calculation, which is important in magnetic calculations.

Thus, a 3d vector parameter in xyz coordinates called easy_axis or spin_axis could be added to define the direction of magnetic moments to be limited.

This case is not as complicated as the constrained spin polarized case which contrained atoms one by one. The parameter noncolin=0 lspinorb=1 is still not changed which means that all the magnetic moments are constrained along one same line. Just add a direction which can be modified by users.

One can refer to the implementation of vasp SAXIS - VASP Wiki and VASP中的非线性磁性计算总结

SAXIS= sx sy sz !global spin quantisation axis|default：0+ 0 1

Now the noncolin=0 lspinorb=1 case is:

The Constraint DFT for collinear spin polarized calculations does not consider the case of noncolin=0 lspinorb=1 nspin=4 :

Describe the solution you'd like

Provide a 3d vector parameter to modify the global spin quantisation axis in noncolin=0 lspinorb=1 nspin=4 case.

Task list only for developers

[ ] Notice possible changes of behavior
[ ] Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

No response

Notice any changes of core modules (Reminder only for developers)

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Notice Possible Changes of Core Modules (Reminder only for developers)

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Additional Context

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Task list for Issue attackers (only for developers)

[ ] Review and understand the proposed feature and its importance.
[ ] Research on the existing solutions and relevant research articles/resources.
[ ] Discuss with the team to evaluate the feasibility of implementing the feature.
[ ] Create a design document outlining the proposed solution and implementation details.
[ ] Get feedback from the team on the design document.
[ ] Develop the feature following the agreed design.
[ ] Write unit tests and integration tests for the feature.
[ ] Update the documentation to include the new feature.
[ ] Perform code review and address any issues.
[ ] Merge the feature into the main branch.
[ ] Monitor for any issues or bugs reported by users after the feature is released.
[ ] Address any issues or bugs reported by users and continuously improve the feature.

deepmodeling / abacus-develop