Physical meaning of Spin-Orbit-Coupling matrix elements

[CMG]

Hi,

I did a Spin-orbit coupling included calculation and got the "Spin-Orbit-Coupling matrix elements" output in the OUTCAR as following:

Ion: 1
l= 1
0.0000000 -0.9361646 -0.9375252
-0.9361646 0.0000000 -0.9335295
-0.9375252 -0.9335295 0.0000000
l= 2
0.0000000 -0.0032798 0.0000000 -0.0038162 -0.0099388
-0.0032798 0.0000000 -0.0092811 -0.0034199 -0.0032864
0.0000000 -0.0092811 0.0000000 -0.0083653 0.0000000
-0.0038162 -0.0034199 -0.0083653 0.0000000 -0.0011943
-0.0099388 -0.0032864 0.0000000 -0.0011943 0.0000000
l= 3
0.0000000 -0.0076429 0.0000000 0.0000000 0.0000000 -0.0082498 -0.0463040
-0.0076429 0.0000000 -0.0125139 0.0000000 -0.0109340 -0.0227420 -0.0061167
0.0000000 -0.0125139 0.0000000 -0.0300528 -0.0062111 -0.0123419 0.0000000
0.0000000 0.0000000 -0.0300528 0.0000000 -0.0335391 0.0000000 0.0000000
0.0000000 -0.0109340 -0.0062111 -0.0335391 0.0000000 -0.0135615 0.0000000
-0.0082498 -0.0227420 -0.0123419 0.0000000 -0.0135615 0.0000000 -0.0080843
-0.0463040 -0.0061167 0.0000000 0.0000000 0.0000000 -0.0080843 0.0000000


I'm wondering if anyone could kindly explain what' the physical meaning of the matrix? Any reference elaborate on that?

Thanks,
Wei

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