4 X-ray Dichroisms in Spherical Tensor and Green’s Function Formalism
85
4.1.2 Definition of Dichroisms
X-ray dichroism can be defined as the difference in the X-ray absorption cross section
measured for two orthogonal polarization states of the incident light. There exist different types of dichroism. Dichroism measurements can be classified according to
the type of polarization used for the measurements into linear and circular. Linear
dichroism (LD) is the difference measured with linearly polarized light, where in
most cases the polarization vector is set parallel and perpendicular to an orientation axis, while circular dichroism (CD) is the difference measured with circularly
polarized light (left handed and right handed).
Not all systems exhibit dichroism effects when the polarization of the light is
changed. Certain symmetry conditions regarding the interaction operator between
light and matter have to be satisfied for dichroism effects to occur, which brings us to
the second classification of dichroism types. Two symmetry operations are essential
for this classification:
– Time-reversal symmetry,
– Space inversion (also called parity).
Natural dichroism (ND) refers to dichroism effects that occur in non-magnetic
systems where time-reversal symmetry is conserved (i.e., the system is even under
time-reversal operation). Using linearly polarized light, one can measure X-ray natural linear dichroism (XNLD). On the other hand, using circularly polarized light,
one can measure X-ray natural circular dichroism (XNCD) only for systems that
do not have a centre of inversion (i.e., the system is of odd parity).
Magnetic dichroism (MD) relates to dichroism effects measured in magnetic
(ferro, ferri, or antiferromagnetic) systems where time-reversal symmetry is broken
either by spontaneous magnetic ordering in the sample or by the application of an
external magnetic field. X-ray magnetic linear dichroism (XMLD) is parity-even
and time-reversal even and non-reciprocal linear dichroism (NRLD) is parity-odd
and time-reversal odd. Using circularly polarized light, X-ray magnetic circular
dichroism (XMCD) and X-ray magneto-optical dichroism (XMχ D) effects can be
measured. The former is parity-even and time-reversal odd while the later is parityodd and time-reversal odd.
In magnetic materials, which will be discussed in this chapter, several cases are
possible:
– In the case of centrosymmetric crystals with ferro- or ferrimagnetic properties,
one can measure XMCD.
– In the case of centrosymmetric crystals with antiferromagnetic properties, XMLD
can be measured.
– In the case of magnetized, non-centrosymmetric crystals, XMχ D and NRLD can
be measured.
XMCD and XMLD measurements give, respectively, access to the average value
of M and M
2
of the local magnetization for the absorber. On the other hand,
85
4.1.2 Definition of Dichroisms
X-ray dichroism can be defined as the difference in the X-ray absorption cross section
measured for two orthogonal polarization states of the incident light. There exist different types of dichroism. Dichroism measurements can be classified according to
the type of polarization used for the measurements into linear and circular. Linear
dichroism (LD) is the difference measured with linearly polarized light, where in
most cases the polarization vector is set parallel and perpendicular to an orientation axis, while circular dichroism (CD) is the difference measured with circularly
polarized light (left handed and right handed).
Not all systems exhibit dichroism effects when the polarization of the light is
changed. Certain symmetry conditions regarding the interaction operator between
light and matter have to be satisfied for dichroism effects to occur, which brings us to
the second classification of dichroism types. Two symmetry operations are essential
for this classification:
– Time-reversal symmetry,
– Space inversion (also called parity).
Natural dichroism (ND) refers to dichroism effects that occur in non-magnetic
systems where time-reversal symmetry is conserved (i.e., the system is even under
time-reversal operation). Using linearly polarized light, one can measure X-ray natural linear dichroism (XNLD). On the other hand, using circularly polarized light,
one can measure X-ray natural circular dichroism (XNCD) only for systems that
do not have a centre of inversion (i.e., the system is of odd parity).
Magnetic dichroism (MD) relates to dichroism effects measured in magnetic
(ferro, ferri, or antiferromagnetic) systems where time-reversal symmetry is broken
either by spontaneous magnetic ordering in the sample or by the application of an
external magnetic field. X-ray magnetic linear dichroism (XMLD) is parity-even
and time-reversal even and non-reciprocal linear dichroism (NRLD) is parity-odd
and time-reversal odd. Using circularly polarized light, X-ray magnetic circular
dichroism (XMCD) and X-ray magneto-optical dichroism (XMχ D) effects can be
measured. The former is parity-even and time-reversal odd while the later is parityodd and time-reversal odd.
In magnetic materials, which will be discussed in this chapter, several cases are
possible:
– In the case of centrosymmetric crystals with ferro- or ferrimagnetic properties,
one can measure XMCD.
– In the case of centrosymmetric crystals with antiferromagnetic properties, XMLD
can be measured.
– In the case of magnetized, non-centrosymmetric crystals, XMχ D and NRLD can
be measured.
XMCD and XMLD measurements give, respectively, access to the average value
of M and M
2
of the local magnetization for the absorber. On the other hand,