c ******************************************************************************
c
c TRIQS: a Toolbox for Research in Interacting Quantum Systems
c
c Copyright (C) 2011 by L. Pourovskii, V. Vildosola, C. Martins, M. Aichhorn
c
c TRIQS is free software: you can redistribute it and/or modify it under the
c terms of the GNU General Public License as published by the Free Software
c Foundation, either version 3 of the License, or (at your option) any later
c version.
c
c TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
c WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
c FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
c details.
c
c You should have received a copy of the GNU General Public License along with
c TRIQS. If not, see .
c
c *****************************************************************************/
SUBROUTINE setsym
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine sets up the symmetry matrices of the structure %%
C %% and the local rotation matrices for each atom of the system. %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
USE common_data
USE factorial
USE file_names
USE prnt
USE reps
USE symm
IMPLICIT NONE
C
COMPLEX(KIND=8), DIMENSION(:,:), ALLOCATABLE :: tmp_rot, spinrot
COMPLEX(KIND=8), DIMENSION(:,:),ALLOCATABLE :: tmat
COMPLEX(KIND=8), DIMENSION(:,:,:),ALLOCATABLE :: tmp_dmat
REAL(KIND=8) :: factor
INTEGER :: l, isym, mmax, nrefl, i, m, isrt, lms
INTEGER :: lm, is, is1
INTEGER :: iatom, imu, iatomref
REAL(KIND=8) :: det
REAL(KIND=8), DIMENSION(:),ALLOCATABLE :: bufreal
COMPLEX(KIND=8), DIMENSION(:),ALLOCATABLE :: bufcomp
COMPLEX(KIND=8), DIMENSION(:,:),ALLOCATABLE :: tmpcomp
COMPLEX(KIND=8), DIMENSION(1:2,1:2) :: spmt
C
C
WRITE(buf,'(a)')'======================================='
CALL printout(0)
WRITE(buf,'(a)')'Symmetry operations of the system'
CALL printout(1)
C
C ===========================================
C Reading of the symmetry file case.dmftsym :
C ===========================================
CALL setfact(170)
READ(iusym,*)nsym
WRITE(buf,'(a,i4)')'Number of Symmetries = ',nsym
CALL printout(0)
CALL printout(0)
C nsym = total number of symmetry operations for the structure
lsym=lmax
nlmsym=2*lsym+1
C lsym = maximal orbital number for the symmetry
C nlmsym = maximal size of the representation for the symmetry
ALLOCATE(srot(nsym))
DO isym=1,nsym
ALLOCATE(srot(isym)%perm(natom))
READ(iusym,*)srot(isym)%perm
ENDDO
C srot = table of symop elements from to 1 to nsym.
C the field srot(isym)%perm = the table of permutation for the isym symmetry (table from 1 to natom)
C srot(isym)%perm(iatom) = R[isym](iatom) = image by R[isym] fo iatom
WRITE(buf,'(a)')'Properties of the symmetry operations :'
CALL printout(0)
WRITE(buf,'(a)') ' alpha, beta, gamma are their Euler angles.'
CALL printout(0)
WRITE(buf,'(a)') ' iprop is the value of their determinant.'
CALL printout(0)
CALL printout(0)
WRITE(buf,'(a)')' SYM.OP. alpha beta gamma iprop'
CALL printout(0)
DO isym=1,nsym
READ(iusym,'()')
READ(iusym,'()')
READ(iusym,'(3(f6.1),i3)') srot(isym)%a, srot(isym)%b,
& srot(isym)%g, srot(isym)%iprop
C Printing the matrices parameters in the file case.outdmftpr
WRITE(buf,'(i5,3F10.1,5x,i3)')isym,
& srot(isym)%a,srot(isym)%b,srot(isym)%g,srot(isym)%iprop
CALL printout(0)
srot(isym)%a=srot(isym)%a/180d0*Pi
srot(isym)%b=srot(isym)%b/180d0*Pi
srot(isym)%g=srot(isym)%g/180d0*Pi
C the field srot(isym)%a is linked to the Euler precession angle (alpha)
C the field srot(isym)%b is linked to the Euler nutation angle (beta)
C the field srot(isym)%c is linked to the Euler intrinsic rotation angle (gamma)
C They are read in case.dmftsym in degree and are then transformed into radians
C the field sort(isym)% iprop = value of the transformation determinant (1 or -1),
C determines if there is an inversion in the transformation
READ(iusym,*)(srot(isym)%krotm(1:3,i),i=1,3)
srot(isym)%krotm(1:3,1:3)=
& TRANSPOSE(srot(isym)%krotm(1:3,1:3))
C the field srot(isym)%krotm = 3x3 matrices of rotation associated to the transformation (R[isym]).
C (without the global inversion). The matrix was multiplied by the value of iprop before being written in case.dmftsym.
C This reading line was chosen to be consistent with the writing line in rotmat_dmft (in SRC_lapw2)
ENDDO
C
C =============================================================
C Determination of the properties for each symmetry operation :
C =============================================================
C
C Creation of the rotational matrices for each orbital :
C ------------------------------------------------------
DO isym=1,nsym
ALLOCATE(srot(isym)%rotl(-lsym:lsym,-lsym:lsym,lsym))
srot(isym)%rotl=0.d0
ALLOCATE(tmat(1:2*lsym+1,1:2*lsym+1))
DO l=1,lsym
C Use of the subroutine dmat to compute the the rotational matrix
C associated to the isym symmetry operation in a (2*l+1) space :
CALL dmat(l,srot(isym)%a,srot(isym)%b,srot(isym)%g,
& REAL(srot(isym)%iprop,KIND=8),tmat,2*lsym+1)
srot(isym)%rotl(-l:l,-l:l,l)=tmat(1:2*l+1,1:2*l+1)
C srot(isym)%rotl = table of the rotationnal matrices of the symmetry operation
C for the different l orbital (from 1 to lsym), in the usual complex basis : dmat = D(R[isym])_l
C srot(isym)%rotl = D(R[isym])_{lm}
ENDDO
DEALLOCATE(tmat)
C
C
C Determination of the fields timeinv and phase (if SP+SO computations):
C ----------------------------------------------------------------------
C If the calculation is spin-polarized with spin-orbit, the magnetic spacegroup of the
C system is of type III (black-and-white type). The operation must then be classified
C according to their keeping the z-axis invariant or not.
C
C srot(isym)%timeinv = boolean indicating if a time reversal operation is required
IF(ifSP.AND.ifSO) THEN
det=srot(isym)%krotm(1,1)*srot(isym)%krotm(2,2)-
- srot(isym)%krotm(1,2)*srot(isym)%krotm(2,1)
C the value of det is cos(srot(isym)%b) even if the rotation is improper.
IF(det < 0.0d0) THEN
srot(isym)%timeinv=.TRUE.
C The direction of the magnetic moment is changed to its opposite ( srot(isym)%b=pi ),
C A time reversal operation is required.
srot(isym)%phase=srot(isym)%g-srot(isym)%a
C In this case, we define a phase factor for the off-diagonal term (up/dn term)
C which is srot(isym)%phase= g-a = 2pi+(alpha-gamma)
ELSE
srot(isym)%timeinv=.FALSE.
C The direction of the magnetic moment is unchanged ( srot(isym)%b=0 ),
C no time reversal operation is required.
srot(isym)%phase=srot(isym)%a+srot(isym)%g
C In this case, we define a phase factor for the off-diagonal term (up/dn term)
C which is srot(isym)%phase= a+g = 2pi-(alpha+gamma)
ENDIF
ELSE
C If the calculation is either spin-polarized without spin-orbit, or paramagnetic
C the magnetic spacegroup of the system is of type I (ordinary type). The operation
C are thus merely applied.
srot(isym)%timeinv=.FALSE.
srot(isym)%phase=0.d0
ENDIF ! End of the ifSP if-then-else
C
C
C Computation of the rotational matrices in each sort basis :
C -----------------------------------------------------------
ALLOCATE(srot(isym)%rotrep(lsym,nsort))
C
C Initialization of the srot(isym)%rotrep field
C This field is a table of size (lsym*nsort) which contains the rotation matrices
C of isym in the representation basis associated to each included orbital of each atom.
C srot(isym)%rotrep = D(R[isym])_{new_i}
DO isrt=1,nsort
DO l=1,lsym
ALLOCATE(srot(isym)%rotrep(l,isrt)%mat(1,1))
srot(isym)%rotrep(l,isrt)%mat(1,1)=0.d0
ENDDO
ENDDO
C
C Computation of the elements 'mat' in srot(isym)%rotrep(l,isrt)
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO l=1,lsym
C The considered orbital is not included, hence no computation
IF (lsort(l,isrt)==0) cycle
C The considered orbital is included
IF (reptrans(l,isrt)%ifmixing) THEN
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) )
C If this option is used, then ifSO=.TRUE. (because of the restriction in set_ang_trans.f)
C Moreover ifSP=.TRUE. (since ifSO => ifSP in this version)
DEALLOCATE(srot(isym)%rotrep(l,isrt)%mat)
ALLOCATE(srot(isym)%rotrep(l,isrt)%mat
& (1:2*(2*l+1),1:2*(2*l+1)))
ALLOCATE(tmp_rot(1:2*(2*l+1),1:2*(2*l+1)))
ALLOCATE(spinrot(1:2*(2*l+1),1:2*(2*l+1)))
spinrot=0.d0
C Computation of the full spinor rotation matrix associated to isym.
CALL spinrotmat(spinrot,isym,l)
C Computation of srot(isym)%rotrep(l,isrt)%mat
tmp_rot(1:2*(2*l+1),1:2*(2*l+1))=MATMUL(
& reptrans(l,isrt)%transmat(1:2*(2*l+1),1:2*(2*l+1)),
& spinrot(1:2*(2*l+1),1:2*(2*l+1)))
srot(isym)%rotrep(l,isrt)%mat(1:2*(2*l+1),1:2*(2*l+1))=
= MATMUL(tmp_rot(1:2*(2*l+1),1:2*(2*l+1)),
& TRANSPOSE(CONJG(reptrans(l,isrt)%transmat
& (1:2*(2*l+1),1:2*(2*l+1)))))
C the field srot(isym)%rotrep(l,isrt)%mat = (reptrans)*spinrot(l)*inverse(reptrans)
C or srot(isym)%rotrep = D(R[isym])_{new_i} = D(R[isym])_{lm}
C which is exactly the expression of the spinor rotation matrix in the new basis.
DEALLOCATE(tmp_rot)
DEALLOCATE(spinrot)
ELSE
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only)
DEALLOCATE(srot(isym)%rotrep(l,isrt)%mat)
ALLOCATE(srot(isym)%rotrep(l,isrt)%mat(-l:l,-l:l))
ALLOCATE(tmp_rot(-l:l,-l:l))
C Computation of srot(isym)%rotrep(l,isrt)%mat
tmp_rot(-l:l,-l:l)=MATMUL(
& reptrans(l,isrt)%transmat(-l:l,-l:l),
& srot(isym)%rotl(-l:l,-l:l,l))
srot(isym)%rotrep(l,isrt)%mat(-l:l,-l:l)=
= MATMUL(tmp_rot(-l:l,-l:l),
& TRANSPOSE(CONJG(reptrans(l,isrt)%transmat(-l:l,-l:l))))
C the field srot(isym)%rotrep(l,isrt)%mat = (reptrans)*rotl*inverse(reptrans)
C or srot(isym)%rotrep = D(R[isym])_{new_i} = D(R[isym])_{lm}
C which is exactly the expression of the rotation matrix for the up/up block in the new basis.
DEALLOCATE(tmp_rot)
ENDIF
ENDDO ! End of the l loop
ENDDO ! End of the isrt loop
ENDDO ! End of the isym loop
C
C
C =============================================================
C Printing the matrix parameters in the file fort.17 for test :
C =============================================================
DO isym=1,nsym
WRITE(17,'()')
WRITE(17,'(a,i3)')' Sym. op.: ',isym
DO i =1,3
ALLOCATE(bufreal(3))
bufreal(1:3)=srot(isym)%krotm(i,1:3)
WRITE(17,'(3f10.4)') bufreal
DEALLOCATE(bufreal)
ENDDO
WRITE(17,'(a,3f8.1,i4)')'a, b, g, iprop =',
& srot(isym)%a*180d0/Pi,srot(isym)%b*180d0/Pi,
& srot(isym)%g*180d0/Pi,srot(isym)%iprop
C Printing the data relative to SP option
IF (ifSP) THEN
WRITE(17,*)'If DIR. magn. mom. is inverted :'
& ,srot(isym)%timeinv
WRITE(17,*)'phase = ',srot(isym)%phase
ENDIF
C Printing the rotational matrices for each orbital number l.
WRITE(17,'()')
DO l=1,lsym
WRITE(17,'(a,a,i2)')'Rotation matrix ',
& 'D(R[isym])_{lm} for l = ',l
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=srot(isym)%rotl(m,-l:l,l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDDO
C Printing the matrices rotrep(l,isrt)%mat
WRITE(17,'()')
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO l=1,lsym
IF (lsort(l,isrt)==0) cycle
WRITE(17,'(a,i2,a,i2)')'Representation for isrt = ',
& isrt,' and l= ',l
IF (reptrans(l,isrt)%ifmixing) THEN
DO m=1,2*(2*l+1)
ALLOCATE(bufcomp(1:2*(2*l+1)))
bufcomp(1:2*(2*l+1))=
& srot(isym)%rotrep(l,isrt)%mat(m,1:2*(2*l+1))
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ELSE
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=
& srot(isym)%rotrep(l,isrt)%mat(m,-l:l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDIF
ENDDO
ENDDO
ENDDO
C
C
C =================================================================================
C Applying time-reversal operator if the system is spin-polarized with Spin Orbit :
C =================================================================================
C
C If the calculation is spin-polarized with spin-orbit, the magnetic spacegroup of the compound
C is of type III (black-and-white). The symmetry operations which reverse the z-axis must be
C multiplied by the time-reversal operator.
C If spin-orbit is not taken into account, all the field timeinv are .FALSE. and no time-reversal
C is applied, since the magnetic spacegroup of the compound is of type I (ordinary).
IF (ifSP) THEN
C The modification of srot(isym)%rotl is done for each isym
DO isym=1,nsym
DO l=1,lsym
IF (srot(isym)%timeinv) THEN
C The field srot(isym)%rotl is multiplied by the time-reversal operator in the complex basis.
ALLOCATE(tmpcomp(-l:l,-l:l))
tmpcomp(-l:l,-l:l)=
& srot(isym)%rotl(-l:l,-l:l,l)
CALL timeinv_op(tmpcomp,(2*l+1),l,0)
srot(isym)%rotl(-l:l,-l:l,l)=tmpcomp(-l:l,-l:l)
DEALLOCATE(tmpcomp)
C The field srot(isym)%phase must not be modified.
END IF
END DO
END DO
C
C The other modification are done for each (isrt,l) included.
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO l=1,lsym
C The considered orbital is not included, hence no computation
IF (lsort(l,isrt)==0) cycle
C If the basis representation needs a complete spinor rotation approach (matrices of size 2*(2*l+1) )
IF (reptrans(l,isrt)%ifmixing) THEN
DO isym=1,nsym
IF (srot(isym)%timeinv) THEN
C The field srot(isym)%rotrep(l,isrt)%mat is multiplied by the time-reversal operator in the corresponding basis of isrt.
CALL timeinv_op(srot(isym)%rotrep(l,isrt)%mat,
& 2*(2*l+1),l,isrt)
END IF
END DO ! End of the isym loop
C If the basis representation can be reduce to the up/up block (matrices of size (2*l+1) only)
ELSE
DO isym=1,nsym
IF (srot(isym)%timeinv) THEN
C The field srot(isym)%rotrep(l,isrt)%mat is multiplied by the time-reversal operator in the corresponding basis of isrt.
CALL timeinv_op(srot(isym)%rotrep(l,isrt)%mat,
& (2*l+1),l,isrt)
END IF
END DO ! End of the isym loop
END IF ! End of the ifmixing if-then-else
END DO ! End of the l loop
END DO ! End of the isrt loop
END IF ! End of the ifSP if-then-else
C
C
C ======================================================================
C Printing the time-reversal modification in the file fort.17 for test :
C ======================================================================
IF (ifSP.AND.ifSO) THEN
WRITE(17,'()')
WRITE(17,'(a)') '---With time-reversal operation---'
WRITE(17,'()')
C Printing the srot(isym) operations if necessary :
DO isym=1,nsym
IF (srot(isym)%timeinv) THEN
WRITE(17,'()')
WRITE(17,'(a,i3)')' Sym. op.: ',isym
C Printing the new rotational matrices for each orbital number l.
WRITE(17,'()')
DO l=1,lsym
WRITE(17,'(a,a,i2)')'T*Rotation matrix ',
& 'D(T.R[isym])_{lm} for l = ',l
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=srot(isym)%rotl(m,-l:l,l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDDO
C Printing the new matrices rotrep(l,isrt)%mat
WRITE(17,'()')
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO l=1,lsym
IF (lsort(l,isrt)==0) cycle
WRITE(17,'(a,i2,a,i2)')
& 'Representation for isrt = ',isrt,' and l= ',l
IF (reptrans(l,isrt)%ifmixing) THEN
DO m=1,2*(2*l+1)
ALLOCATE(bufcomp(1:2*(2*l+1)))
bufcomp(1:2*(2*l+1))=
& srot(isym)%rotrep(l,isrt)%mat(m,1:2*(2*l+1))
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ELSE
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=
& srot(isym)%rotrep(l,isrt)%mat(m,-l:l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
END DO
END IF
END DO
END DO
END IF
ENDDO
END IF
C
C
C ============================================================
C Creation of the global->local coordinate rotation matrices :
C ============================================================
ALLOCATE(rotloc(natom))
CALL printout(1)
WRITE(buf,'(a)')'-------------------------------------'
CALL printout(0)
WRITE(buf,'(a)')'Global-to-local-coordinates rotations'
CALL printout(1)
WRITE(buf,'(a)')'Properties of the symmetry operations :'
CALL printout(0)
WRITE(buf,'(a)') ' alpha, beta, gamma are their Euler angles.'
CALL printout(0)
WRITE(buf,'(a)') ' iprop is the value of their determinant.'
CALL printout(0)
CALL printout(0)
WRITE(buf,'(a)')' SORT alpha beta gamma iprop'
CALL printout(0)
READ(iusym,'()')
DO isrt=1,nsort
C Reading the data for the representative atom in case.dmftsym and printing them in case.outdmftpr :
C --------------------------------------------------------------------------------------------------
iatomref=SUM(nmult(0:isrt-1))+1
READ(iusym,'()')
DO i=1,3
ALLOCATE(bufreal(3))
READ(iusym,*) bufreal
rotloc(iatomref)%krotm(i,1:3)=bufreal(1:3)
DEALLOCATE(bufreal)
ENDDO
C the field rotloc(iatomref)%krotm = 3x3 matrices of rotation associated to the transformation Rloc
C Rloc = . The matrix was not multiplied by the value of iprop before being
C written in case.dmftsym (cf. SRC_lapw2/rotmat_dmft.f).
C rotloc(iatomref)%krotm can thus be either a proper or an improper rotation (with inversion).
C This reading line was chosen to be consistent with the writing line in rotmat_dmft (in SRC_lapw2)
READ(iusym,*)rotloc(iatomref)%a,rotloc(iatomref)%b,
& rotloc(iatomref)%g, rotloc(iatomref)%iprop
WRITE(buf,'(i5,3F10.1,5x,i3)')isrt,
& rotloc(iatomref)%a, rotloc(iatomref)%b,
& rotloc(iatomref)%g, rotloc(iatomref)%iprop
CALL printout(0)
rotloc(iatomref)%a=rotloc(iatomref)%a/180d0*Pi
rotloc(iatomref)%b=rotloc(iatomref)%b/180d0*Pi
rotloc(iatomref)%g=rotloc(iatomref)%g/180d0*Pi
C the field rotloc%a is linked to the Euler precession angle (alpha)
C the field rotloc%b is linked to the Euler nutation angle (beta)
C the field rotloc%c is linked to the Euler intrinsic rotation angle (gamma)
C They are read in case.dmftsym and printed in case.outdmftpr in degree and are then transformed into radians
C the field rotloc%iprop = value of the transformation determinant (should be 1 in almost all the cases),
C determines if there is an inversion in the transformation from global to local basis.
rotloc(iatomref)%krotm(1:3,1:3)=rotloc(iatomref)%iprop*
& rotloc(iatomref)%krotm(1:3,1:3)
C Now, the field rotloc(iatomref)%krotm described only the proper rotation associated to the transformation.
C
C Use of the subroutine dmat to compute the rotational matrix
C associated to the rotloc(iatomref) operation in a (2*l+1) orbital space :
ALLOCATE(tmat(1:2*lsym+1,1:2*lsym+1))
ALLOCATE(tmp_dmat(1:2*lsym+1,1:2*lsym+1,1:lsym))
DO l=1,lsym
tmat=0.d0
CALL dmat(l,rotloc(iatomref)%a,rotloc(iatomref)%b,
& rotloc(iatomref)%g,REAL(rotloc(iatomref)%iprop,KIND=8),
& tmat,2*lsym+1)
tmp_dmat(1:2*l+1,1:2*l+1,l)=tmat(1:2*l+1,1:2*l+1)
C tmp_dmat = D(Rloc)_{lm}
ENDDO
DEALLOCATE(tmat)
C
C
C Storing the rotloc matrix and initializing the other fields for all equivalent atoms :
C --------------------------------------------------------------------------------------
C All the equivalent atoms will have the same rotloc description. These data
C will be correctly redifined in the subroutine set_rotloc, where the action of the
C symmetry operation which transforms the representative atom in the considered one
C will be added.
DO imu=1,nmult(isrt)
iatom=SUM(nmult(0:isrt-1))+imu
IF(ifSP.AND.ifSO) THEN
C In this case, we have to consider the spinor rotation matrix associated to rotloc
C (the value of the Euler angle beta can be anything between 0 and Pi)
ALLOCATE(rotloc(iatom)%rotl(1:2*(2*lsym+1),
& 1:2*(2*lsym+1),lsym))
rotloc(iatom)%rotl=0.d0
DO l=1,lsym
C For each orbital (from l=0 to lsym)
C Calculation of the representation matrix of rotloc in the spin-space
C in agreement with Wien conventions used for the definition of spmt (in SRC_lapwdm/sym.f)
C Up/up and Dn/dn terms
factor=(rotloc(iatomref)%a+rotloc(iatomref)%g)/2.d0
spmt(1,1)=EXP(CMPLX(0.d0,factor))
& *DCOS(rotloc(iatomref)%b/2.d0)
spmt(2,2)=CONJG(spmt(1,1))
C Up/dn and Dn/up terms
factor=-(rotloc(iatomref)%a-rotloc(iatomref)%g)/2.d0
spmt(1,2)=EXP(CMPLX(0.d0,factor))
& *DSIN(rotloc(iatomref)%b/2.d0)
spmt(2,1)=-CONJG(spmt(1,2))
C Up/up block :
rotloc(iatom)%rotl(1:2*l+1,1:2*l+1,l)=
& spmt(1,1)*tmp_dmat(1:2*l+1,1:2*l+1,l)
C Dn/dn block :
rotloc(iatom)%rotl(2*l+2:2*(2*l+1),2*l+2:2*(2*l+1),l)=
& spmt(2,2)*tmp_dmat(1:2*l+1,1:2*l+1,l)
C Up/dn block :
rotloc(iatom)%rotl(1:2*l+1,2*l+2:2*(2*l+1),l)=
& spmt(1,2)*tmp_dmat(1:2*l+1,1:2*l+1,l)
C Dn/up block :
rotloc(iatom)%rotl(2*l+2:2*(2*l+1),1:2*l+1,l)=
& spmt(2,1)*tmp_dmat(1:2*l+1,1:2*l+1,l)
C The fields rotloc(iatom)%rotl now contain D(rotloc)_{lm}xD(rotloc)_{1/2}
ENDDO
ELSE
C In this case, we can consider the spatial rotation matrix only
C since each spin space is independent (paramagnetic or spin-polarized without SO computation)
ALLOCATE(rotloc(iatom)%rotl(-lsym:lsym,-lsym:lsym,lsym))
rotloc(iatom)%rotl=0.d0
DO l=1,lsym
rotloc(iatom)%rotl(-l:l,-l:l,l)=
= tmp_dmat(1:2*l+1,1:2*l+1,l)
C The fields rotloc(iatom)%rotl now contain D(rotloc)_{lm}
ENDDO
ENDIF
C The fields rotloc(iatom)%a,b and c will now contain the parameters linked to
C the Euler angles of the local rotation rotloc.
IF(imu.gt.1) THEN
rotloc(iatom)%a=rotloc(iatomref)%a
rotloc(iatom)%b=rotloc(iatomref)%b
rotloc(iatom)%g=rotloc(iatomref)%g
rotloc(iatom)%iprop=rotloc(iatomref)%iprop
rotloc(iatom)%krotm(1:3,1:3)=
= rotloc(iatomref)%krotm(1:3,1:3)
ENDIF
C The fields rotloc%phase, timeinv and srotnum are initialized to their
C default value.
rotloc(iatom)%phase=0.d0
rotloc(iatom)%timeinv=.FALSE.
rotloc(iatom)%srotnum=0
C the field rotloc(iatom)%srotnum and timeinv will be recalculated in set_rotloc.
ENDDO
DEALLOCATE(tmp_dmat)
ENDDO ! End of the isrt loop
C
C
C ====================================================================
C Printing the rotloc matrix parameters in the file fort.17 for test :
C ====================================================================
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO imu=1,nmult(isrt)
iatom=SUM(nmult(0:isrt-1))+imu
WRITE(17,'()')
WRITE(17,'(2(a,i3))')' SORT ',isrt,' IMU= ',imu
DO i=1,3
ALLOCATE(bufreal(3))
bufreal(1:3)=rotloc(iatom)%krotm(i,1:3)
WRITE(17,'(3f10.4)') bufreal
DEALLOCATE(bufreal)
ENDDO
WRITE(17,'(a,3f8.1,i4)')'a, b, g, iprop ==',
& rotloc(iatom)%a*180d0/Pi,rotloc(iatom)%b*180d0/Pi,
& rotloc(iatom)%g*180d0/Pi,rotloc(iatom)%iprop
C Printing the data relative to SP option
IF (ifSP) THEN
WRITE(17,*)'If DIR. magn. mom. is inverted :'
& ,rotloc(iatom)%timeinv
WRITE(17,*)'phase = ',rotloc(iatom)%phase
ENDIF
C Printing the rotloc matrices for each orbital number l.
WRITE(17,'()')
DO l=1,lsym
WRITE(17,'(a,a,i2)')'Rotation matrix ',
& 'D(R[isym])_{lm} for l = ',l
IF(ifSP.AND.ifSO) THEN
DO m=1,2*(2*l+1)
ALLOCATE(bufcomp(1:2*(2*l+1)))
bufcomp(1:2*(2*l+1))=rotloc(iatom)%rotl(m,1:2*(2*l+1),l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ELSE
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=rotloc(iatom)%rotl(m,-l:l,l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDIF
ENDDO
ENDDO
ENDDO
C
C
C ==================================================================================
C Computation of the true local rotation matrices for each non representative atom :
C ==================================================================================
CALL set_rotloc
C
C
C ====================================================================
C Printing the rotloc matrix parameters in the file fort.17 for test :
C ====================================================================
DO isrt=1,nsort
IF (notinclude(isrt)) cycle
DO imu=1,nmult(isrt)
iatom=SUM(nmult(0:isrt-1))+imu
WRITE(17,'()')
WRITE(17,'(2(a,i3))')' SORT ',isrt,' IMU= ',imu
DO i=1,3
ALLOCATE(bufreal(3))
bufreal(1:3)=rotloc(iatom)%krotm(i,1:3)
WRITE(17,'(3f10.4)') bufreal
DEALLOCATE(bufreal)
ENDDO
WRITE(17,'(a,3f8.1,i4)')'a, b, g, iprop ==',
& rotloc(iatom)%a*180d0/Pi,rotloc(iatom)%b*180d0/Pi,
& rotloc(iatom)%g*180d0/Pi,rotloc(iatom)%iprop
C Printing the data relative to SP option
IF (ifSP) THEN
WRITE(17,*)'If DIR. magn. mom. is inverted :'
& ,rotloc(iatom)%timeinv
WRITE(17,*)'phase = ',rotloc(iatom)%phase
ENDIF
C Printing the rotloc matrices for each orbital number l.
WRITE(17,'()')
DO l=1,lsym
WRITE(17,'(a,a,i2)')'Rotation matrix ',
& 'D(R[isym])_{lm} for l = ',l
IF(ifSP.AND.ifSO) THEN
DO m=1,2*(2*l+1)
ALLOCATE(bufcomp(1:2*(2*l+1)))
bufcomp(1:2*(2*l+1))=rotloc(iatom)%rotl(m,1:2*(2*l+1),l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ELSE
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=rotloc(iatom)%rotl(m,-l:l,l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDIF
ENDDO
C Printing the matrices rotrep(l)%mat
WRITE(17,'()')
DO l=1,lsym
IF (lsort(l,isrt)==0) cycle
WRITE(17,'(a,i2)')'Representation for l= ',l
IF (ifSP.AND.ifSO) THEN
DO m=1,2*(2*l+1)
ALLOCATE(bufcomp(1:2*(2*l+1)))
bufcomp(1:2*(2*l+1))=
& rotloc(iatom)%rotrep(l)%mat(m,1:2*(2*l+1))
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ELSE
DO m=-l,l
ALLOCATE(bufcomp(-l:l))
bufcomp(-l:l)=
& rotloc(iatom)%rotrep(l)%mat(m,-l:l)
WRITE(17,'(7(2f7.3,x))') bufcomp
DEALLOCATE(bufcomp)
ENDDO
ENDIF
ENDDO
ENDDO
ENDDO
C
RETURN
END
Subroutine dmat(l,a,b,c,det,DD,length)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine computes the inverse of the matrix of the %%
C %% representation of size (2*l+1) associated to the rotation %%
C %% described by (a,b,c) angles in Euler description and with %%
C %% determinant det. %%
C %% The obtained matrix is put in the variable DD. %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
IMPLICIT REAL*8 (A-H,O-Z)
INTEGER l,m,n,ifac,length
COMPLEX*16 izero,imag, dd
dimension DD(length,length)
imag=(0d0,1d0)
izero=(0d0,0d0)
pi=acos(-1d0)
do m=-l,l
do n=-l,l
call d_matrix(l,m,n,b,dm)
if (det.lt.-0.5) then
dd(l+m+1,n+l+1)=(-1)**l*cdexp(imag*n*a)
& *cdexp(imag*m*c)*dm
else
dd(l+m+1,n+l+1)=cdexp(imag*n*a)
& *cdexp(imag*m*c)*dm
end if
3 format(2I3,2f10.6)
end do
end do
do j=1,2*l+1
end do
5 format(7(2f6.3,1X))
end
Subroutine d_matrix(l,m,n,b,dm)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine is called by the subroutine dmat to compute the %%
C %% the value of the coefficient dm. %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
IMPLICIT REAL*8 (A-H,O-Z)
INTEGER l,m,n,t
sum=0d0
f1=dfloat(ifac(l+m)*ifac(l-m))/
& dfloat(ifac(l+n)*ifac(l-n))
do t=0,2*l
if ((l-m-t).ge.0.AND.(l-n-t).ge.0.AND.(t+n+m).ge.0) then
C general factor
f2=dfloat(ifac(l+n)*ifac(l-n))/dfloat(ifac(l-m-t)
& *ifac(m+n+t)*ifac(l-n-t)*ifac(t))
C factor with sin(b/2)
if ((2*l-m-n-2*t).eq.0) then
f3=1.
else
f3=(sin(b/2))**(2*l-m-n-2*t)
end if
C factor with cos(b/2)
if ((2*t+n+m).eq.0) then
f4=1.
else
f4=(cos(b/2))**(2*t+n+m)
end if
! write(12,*)f1,f2,f3,f4
sum=sum+(-1)**(l-m-t)*f2*f3*f4
end if
end do
dm=sqrt(f1)*sum
end
Integer Function ifac(n)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine computes the factorial of the number n %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definiton of the variables :
C ----------------------------
if (n.eq.0) then
ifac=1
else
ifac=1
do j=1,n
ifac=ifac*j
end do
end if
end
SUBROUTINE spinrotmat(spinrot,isym,l)
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C %% %%
C %% This subroutine sets up the complete spinor rotation matrix %%
C %% associated to the symmetry operation isym for the orbital l. %%
C %% %%
C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C Definition of the variables :
C -----------------------------
USE common_data
USE symm
IMPLICIT NONE
INTEGER :: l,isym
COMPLEX(KIND=8) :: ephase, det
REAL(KIND=8) :: factor
COMPLEX(KIND=8), DIMENSION(1:2*(2*l+1),1:2*(2*l+1)) :: spinrot
COMPLEX(KIND=8), DIMENSION(1:2,1:2) :: spmt
C
spinrot=0.d0
C For a computation with spin polarized inputs :
IF (ifSP) THEN
IF (srot(isym)%timeinv) THEN
C In this case, the Euler angle Beta is Pi. The spinor rotation matrix is block-antidiagonal and
C the time reversal operation will be applied to keep the direction of the magnetization.
C Up/dn block :
factor=srot(isym)%phase/2.d0
C We remind that the field phase is (g-a) in this case.
C as a result, ephase = exp(+i(g-a)/2) = -exp(+i(alpha-gamma)/2)
C in good agreement with Wien conventions for the definition of this phase factor.
ephase=EXP(CMPLX(0.d0,factor))
spinrot(1:2*l+1,2*l+2:2*(2*l+1))=
= ephase*srot(isym)%rotl(-l:l,-l:l,l)
C Dn/up block :
ephase=-CONJG(ephase)
C now, ephase = -exp(+i(a-g)/2) = exp(-i(alpha-gamma)/2)
spinrot(2*l+2:2*(2*l+1),1:2*l+1)=
= ephase*srot(isym)%rotl(-l:l,-l:l,l)
ELSE
C In this case, the Euler angle Beta is 0. The spinor rotation matrix is block-diagonal and
C no time reversal operation will be applied.
C Up/up block :
factor=srot(isym)%phase/2.d0
C We remind that the field phase is (a+g) in this case.
C as a result, ephase = exp(+i(a+g)/2)=-exp(-i(alpha+gamma)/2)
C in good agreement with Wien conventions for the definition of this phase factor.
ephase=EXP(CMPLX(0.d0,factor))
spinrot(1:2*l+1,1:2*l+1)=
= ephase*srot(isym)%rotl(-l:l,-l:l,l)
C Dn/dn block :
ephase=CONJG(ephase)
C now, ephase = exp(-i(a+g)/2) = -exp(+i(alpha+gamma)/2)
spinrot(2*l+2:2*(2*l+1),2*l+2:2*(2*l+1))=
= ephase*srot(isym)%rotl(-l:l,-l:l,l)
ENDIF
ELSE
C For a computation with paramagnetic treatment input files. (not used in this version)
C
C In this case, there is no restriction on the value of the Euler angle beta.
C The general definition of a spinor rotation matrix is used.
C
C Calculation of the representation matrix of isym in the spin-space
C in agreement with Wien conventions used for the definition of spmt (in SRC_lapwdm/sym.f)
C Up/up and Dn/dn terms
factor=(srot(isym)%a+srot(isym)%g)/2.d0
spmt(1,1)=EXP(CMPLX(0.d0,factor))*DCOS(srot(isym)%b/2.d0)
spmt(2,2)=CONJG(spmt(1,1))
C Up/dn and Dn/up terms
factor=-(srot(isym)%a-srot(isym)%g)/2.d0
spmt(1,2)=EXP(CMPLX(0.d0,factor))*DSIN(srot(isym)%b/2.d0)
spmt(2,1)=-CONJG(spmt(1,2))
C Up/up block :
spinrot(1:2*l+1,1:2*l+1)=
& spmt(1,1)*srot(isym)%rotl(-l:l,-l:l,l)
C Dn/dn block :
spinrot(2*l+2:2*(2*l+1),2*l+2:2*(2*l+1))=
& spmt(2,2)*srot(isym)%rotl(-l:l,-l:l,l)
C Up/dn block :
spinrot(1:2*l+1,2*l+2:2*(2*l+1))=
& spmt(1,2)*srot(isym)%rotl(-l:l,-l:l,l)
C Dn/up block :
spinrot(2*l+2:2*(2*l+1),1:2*l+1)=
& spmt(2,1)*srot(isym)%rotl(-l:l,-l:l,l)
ENDIF
C
RETURN
END