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Jx support the following features:

J in momentum space.

MFT is a linear response calculation and can be performed in momentum space. Therefore, MFT can compute short and long-term interactions in moment space, without multiple real space supercells calculations.

Fe metal Jij profile
The calculated Jij for bcc Fe as a function of interatomic distance.

J coupling matrix (Orbital resolved interactions)

A useful feature of MFT is to calculate the orbitally decomposed magnetic response function. It means that a magnetic coupling constant is extended to a matrix. If we consider d orbital system, for example, each magnetic atom has five magnetic orbitals and the magnetic coupling J12 (in between atom 1 and atom 2) is expressed by a 5X5 matrix J12.

NiO J<sub>12</sub> matrix
The calculated second neighbor J12 along the z axis for AFM-G type NiO. The super exchange between eg orbital is clear shown in orbital resolved MFT.

Local axis redefinition for orbital resolved J

In practice, a difficulty in analyzing magnetic materials arises from the absence of well-defined global coordinate axis. A typical example is the distorted oxides in which the local x,y,z coordinate at one site is not the same at another. When one tries to calculate the orbital-dependent magnetic coupling, this ambiguity can cause annoying problems. With this motivation, Jx provides functionality for the user to re-define the local coordinates.

CrO2 orbital redefinition
(a) Jx provides the option to re-define the local coordinate (x′ , y′ , z′) being different from the original (x, y, z) = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]. One needs to specify x′ and z′ which is equivalent to specifying two Euler angles. (b) The calculated magnetic couplings of CrO2 in which the local coordinates of two Cr sites are not identical due to the structural distortion. The red and blue lines represent the orbital decomposed couplings before and after the redefinition of the axis, respectively. It is clearly seen that, by defining the proper local coordinates, the magnetic interaction is well described in between the t2g orbital moments.

Support mulitple Tight-binding Hamiltonian

Basically, any tight-binding style Hamiltonian could be utilized for Jx. Currently we support following interfaces: