Line data Source code
1 : MODULE m_anglso
2 : contains
3 576000 : COMPLEX FUNCTION anglso(theta,phi,l1,m1,is1,l2,m2,is2,compo)
4 : USE m_juDFT
5 : USE m_constants
6 : !
7 : ! calculates spin-orbit matrix for theta,phi =/= 0
8 : !
9 : IMPLICIT NONE
10 : ! ..
11 : ! .. Scalar Arguments ..
12 : INTEGER, INTENT(IN) :: is1,is2,l1,l2,m1,m2
13 : INTEGER, INTENT(IN),OPTIONAL :: compo
14 : REAL, INTENT(IN) :: theta,phi
15 : ! ..
16 : ! .. Local Scalars ..
17 : REAL sgm1,sgm2,xlz,xlpl,xlmn,angl_r,angl_i
18 : LOGICAL :: l_standard_euler_angles
19 :
20 576000 : anglso = CMPLX(0.0,0.0)
21 576000 : IF (l1.NE.l2) THEN
22 : RETURN
23 : ENDIF
24 : !
25 :
26 70800 : l_standard_euler_angles=.FALSE.
27 :
28 70800 : sgm1 = is1
29 70800 : sgm2 = is2
30 70800 : IF (l1.LT.0) THEN
31 0 : WRITE (oUnit,FMT=*) ' PROGRAM STOPS IN ANGLSO ( L < 0 ) .'
32 0 : WRITE (oUnit,FMT=*) ' L1 =',l1,' L2 =',l2
33 0 : CALL juDFT_error("ANGLSO (L <0 )",calledby="anglso")
34 70800 : ELSE IF ((ABS(m1).GT.l1) .OR. (ABS(m2).GT.l2)) THEN
35 0 : WRITE (oUnit,FMT=*) ' PROGRAM STOPS IN ANGLSO ( M < L OR L < M )'
36 0 : WRITE (oUnit,FMT=*) ' L1 =',l1,' L2 =',l2
37 0 : WRITE (oUnit,FMT=*) ' M1 =',m1,' M2 =',m2
38 0 : CALL juDFT_error("ANGLSO ( M < L OR L < M )",calledby="anglso")
39 70800 : ELSE IF ((is1.NE.-1.AND.is1.NE.1) .OR. (is2.NE.-1.AND.is2.NE.1)) THEN
40 0 : WRITE (oUnit,FMT=*) ' PROGRAM STOPS IN ANGLSO ( S >< +-1/2 ) .'
41 0 : WRITE (oUnit,FMT=*) ' S1 =',0.5*sgm1,' S2 =',0.5*sgm2
42 0 : CALL juDFT_error("ANGLSO ( S >< +-1/2 )",calledby ="anglso")
43 : END IF
44 : !
45 : ! lz,l+,l-
46 : !
47 70800 : xlz = 0.0
48 70800 : xlpl= 0.0
49 70800 : xlmn= 0.0
50 : ! is1.eq.is2-2 -> <-| |+> => l+
51 70800 : IF (m1.EQ.m2+1) THEN
52 4400 : xlpl = SQRT(REAL((l2-m2)* (l2+m2+1)))
53 : ! is1.eq.is2+2 -> <+| |-> => l-
54 66400 : ELSE IF (m1.EQ.m2-1) THEN
55 4400 : xlmn = SQRT(REAL((l2+m2)* (l2-m2+1)))
56 : ! is1.eq.is2 -> <+| |+> => lz
57 62000 : ELSE IF (m1.EQ.m2 ) THEN
58 4800 : xlz = m2
59 : END IF
60 :
61 70800 : IF(PRESENT(compo))THEN
62 : ! Used for the wannier-interpolation of SOC:
63 : ! wann_socmat_vec allow us to
64 : ! add SOC during the wannier-interpolation.
65 : ! Therefore, theta and phi are specified during the
66 : ! Wannier-interpolation step and not here.
67 : ! Therefore, write out only xlz, xlpl, and xlmn and RETURN
68 : ! afterwards, without using theta and phi.
69 : ! xlz, xlpl and xlmn are needed in subroutine wann_socmat_vec.F
70 0 : if(compo.eq.1)then
71 0 : anglso = CMPLX(xlz,0.0)
72 0 : elseif(compo.eq.2)then
73 0 : anglso = CMPLX(xlmn,0.0)
74 0 : elseif(compo.eq.3)then
75 0 : anglso = CMPLX(xlpl,0.0)
76 : else
77 0 : CALL juDFT_error("maucompo",calledby ="anglso")
78 : endif
79 0 : RETURN
80 : END IF
81 :
82 :
83 : !
84 : ! rotated spin-orbit angular matrix
85 : ! <1| |1> or <2| |2>
86 : !
87 :
88 : ! If l_standard_euler_angles is set to .false., the old version
89 : ! of this subroutine is used, which works fine if only MAE is
90 : ! needed. In the old version, theta and phi specify the direction
91 : ! of spin quantization. However, there remains the degree of freedom
92 : ! of rotation around the spin quantization direction. The new version
93 : ! of this subroutine, which is switched on by setting l_standard_euler_angles
94 : ! to true, rotates x, y and z axes first by phi around z counterclockwisely
95 : ! and then the resulting axes x', y' and z' by theta around y'
96 : ! counterclockwisely to obtain the final coordinate frame x'', y'' and z''.
97 : ! This new version is useful when one is interested also in the spin
98 : ! perpendicular to the spin quantization axis. The old version seems to be
99 : ! different from the new one as follows when theta and phi differ from zero:
100 : ! x''_old = -x''_new
101 : ! y''_old = -y''_new
102 : ! z''_old = z''
103 : ! If theta and phi are zero, there is no difference, leading thus to a
104 : ! discontinuous Euler transformation in the old version and a continuous
105 : ! transformation in the new version.
106 : ! Both versions do not differ for MAE, but if the standard Pauli matrix
107 : ! is used to obtain x or y components of spin, the spin is discontinuous
108 : ! in the old version as a function of theta and phi.
109 :
110 : IF(l_standard_euler_angles)THEN
111 :
112 : IF (is1.EQ.is2) THEN
113 : angl_r = isign(1,is1) * ( COS(theta)*xlz +&
114 : & 0.5*SIN(theta)*COS(phi)*(xlmn + xlpl) )
115 : angl_i = isign(1,is1)*0.5*SIN(theta)*SIN(phi)*(xlmn - xlpl)
116 : ! <1| |2>
117 : ELSEIF (is1.EQ.is2+2) THEN
118 : angl_r = - SIN(theta)*xlz + COS(phi)*(&
119 : & COS(theta/2.)**2 * xlmn - SIN(theta/2.)**2 * xlpl )
120 : angl_i = SIN(phi)*( &
121 : & COS(theta/2.)**2 * xlmn + SIN(theta/2.)**2 * xlpl )
122 : ! <2| |1>
123 : ELSEIF (is1.EQ.is2-2) THEN
124 : angl_r = - SIN(theta)*xlz + COS(phi)*(&
125 : & + COS(theta/2.)**2 * xlpl - SIN(theta/2.)**2 * xlmn )
126 : angl_i = SIN(phi)*( &
127 : & - COS(theta/2.)**2 * xlpl - SIN(theta/2.)**2 * xlmn )
128 : ELSE
129 : angl_r = 0.0
130 : angl_i = 0.0
131 : ENDIF
132 :
133 : ELSE
134 70800 : IF (is1.EQ.is2) THEN
135 : angl_r = isign(1,is1) * ( COS(theta)*xlz +&
136 35400 : & 0.5*SIN(theta)*COS(phi)*(xlmn + xlpl) )
137 35400 : angl_i = isign(1,is1)*0.5*SIN(theta)*SIN(phi)*(xlmn - xlpl)
138 : ! <1| |2>
139 35400 : ELSEIF (is1.EQ.is2+2) THEN
140 : angl_r = SIN(theta)*xlz + COS(phi)*(&
141 17700 : & - COS(theta/2.)**2 * xlmn + SIN(theta/2.)**2 * xlpl )
142 : angl_i = -SIN(phi)*( &
143 17700 : & COS(theta/2.)**2 * xlmn + SIN(theta/2.)**2 * xlpl )
144 : ! <2| |1>
145 17700 : ELSEIF (is1.EQ.is2-2) THEN
146 : angl_r = SIN(theta)*xlz + COS(phi)*(&
147 17700 : & - COS(theta/2.)**2 * xlpl + SIN(theta/2.)**2 * xlmn )
148 : angl_i = SIN(phi)*( &
149 17700 : & COS(theta/2.)**2 * xlpl + SIN(theta/2.)**2 * xlmn )
150 : ELSE
151 : angl_r = 0.0
152 : angl_i = 0.0
153 : ENDIF
154 : ENDIF
155 : !
156 70800 : anglso = CMPLX(angl_r,angl_i)
157 :
158 70800 : RETURN
159 : END FUNCTION anglso
160 : END MODULE m_anglso
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