~ Beamline Practice ~BL39XU (Magnetic Materials Beamline)
1st and 2nd October 2013
Beamline scientists:
Motohiro Suzuki (JASRI/SPring-8, Leader of MCD team)Naomi Kawamura (JASRI/SPring-8)
Masaichiro Mizumaki (JASRI/SPring-8)
Title:
Handling of X-ray polarization and application to X-ray magnetic circulardichroism spectroscopy
Abstract:
X-ray magnetic circular dichroism (XMCD) is X-ray absorption spectroscopy using
circular polarized X-rays. This is a powerful technique to investigate magnetic
materials, providing element specificity, electronic-shell selectivity, andangular-momentum sensitivity. XMCD experiments in the hard X-ray region (> 4
keV) require no ultra-high vacuum condition and are particularly useful to study
magnetism under multiple extreme conditions (high magnetic field, low temperature,and high pressure). In the practice, you will learn how to tune several devices at thebeamline, the unduator, double-crystal monochromator, and X-ray phase plate, togenerate a circularly polarized X-ray beam. You will take some XMCD data bystatic and polarization-modulation techniques to know that how the modulation
technique is useful for improving the data quality. A practice of the sum-ruleanalysis to determine the magnetic moments from the measured XMCD spectra will
be performed.

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Time Table:
09:30 – 09:45
09:45 – 11:45
11:45 – 13:00
13:00 – 14:50
14:50 – 15:10
15:10 – 16:45
16:45 – 17:00

Introduction of BL39XU
Controlling beamline optics (measurement of undulator spectrum
and polarization using a simple polarimeter)
Lunch
X-ray magnetic circular dichroism measurement
Rest
Sum-rule analysis
Summary-2-

Beamline:
BL39XU is a hard X-ray beamline covering X-ray energy of 5 – 37 keV.[1,2] Main
optical components consist of the undulator, double-crystal monochromator,
X-ray phase retarder, and higher-harmonics reduction mirror. Layout of thecomponents of BL39XU is shown in figure 1.

Figure 1. The layout of the optical components at BL39XU.

Undulator:
The light source of BL39XU is an in-vacuum undulator.[3] This undulator
provides with extremely high-brilliance X-rays linearly polarized in thehorizontal plane. The small X-ray source size and low divergence is perfectlycompatible with X-ray diffractive phase retarder [4] for handling the polarization
states. Table 1 summarizes the parameters of the undulator.
Table 1. BL39XU undulator source parameters.
Total length /Period /Number of period

4.5 m /32 mm /140

Minimum gap /Kmax

8 mm /2.46

Tunable energy range (1st, 3rd and 5th)

5 – 70 keVPeak brilliance

1.4 × 1020 photons/s/mrad2/mm2/0.1%b.w./100 mA

Total power /Power density

11 kW (K = 2.3) /470 kW/mrad2

Polarization

Horizontal-3-

Let’s calculate the 1st harmonic energy of the undulator !
Photon energy of the nth-harmonic undulator radiation is given by[5]  K 2  
E n = 9.50nE  λu 1 +

2

 

−1

2
B

(eV),

where,
K = 93.37 B p λu

is a dimensionless parameter, called “deflection parameter” or “K value”.
Parameters for the BL39XU undulator are:(a) Bp = 0.820 (T) for ID gap = 8 mm(b) Bp = 0.013 (T) for ID gap = 50 mm.
Please calculate the K value and the energy of the first harmonic E1 for thecases (a) and (b) using values of the beam energy of the storage ring, EB = 8(GeV) and periodic length of the undulator, λu = 0.032 m.

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Let’s measure the undulator spectra !
The undulator spectrum depends on the gap value (also, the K parameter).
The energy of the maximum intensity (peak energy) is changeable bychanging the gap value. Here, we investigate the relationship between the
gap value G (mm) and peak energy E (keV).
Gap value: G (mm)Peak energy: E (keV)

10
15
20
25
30
The relation of the peak energy E (keV) and the gap value G (mm) can beapproximated by,(1)

where ξ, K0 and EGFO are the parameters dependent on the characteristics of
the undulator (period and strength of the magnets) and the electron beamenergy of the storage ring. We determine these parameters by a least-square
fitting of our result.

ξ (mm) =K0 =EGFO (keV) =In SPring-8 users are allowed to change the undulator gap anytime,
without giving any influence of the stored electron beam (independent
tuning of undulator). At BL39XU the undulator gap is tuned to follow the
X-ray energy determined by the monochromator at each energy point whilea spectral scan. As a result, very smooth incident X-ray (I0) spectrum isobtainable as if using a white source. This feature is important to record an
EXAFS or XMCD spectrum in a wide energy range.

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Let’s derive the relation between ID gap and photon energy (equation (1)) !
The photon energy of the nth harmonic is described by the equation[5]  K 2  
E n = 9.50nE  λu 1 +

2

 

−1

2
B

(eV).

The dependence of the K value on the ID gap G can be approximated by.

Please derive Eq. (1) from these equations above.

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Put a graph of the undulator spectrum.

Put a graph of the relation between G (mm) and E (keV).

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X-ray phase retarder (XPR):
The diamond X-ray phase retarder (XPR) provides us with a freedom of the
X-ray polarization: the XPR is used to convert horizontal linear polarization of thesource into either circular, vertical, or elliptical polarization.[4] At BL39XU a highrate of circular polarization of PC > 0.9 is achieved over the wide energy range of
5–16 keV with the use of synthetic diamond crystals of appropriate thicknesses.

Let’s change the X-ray polarization !
An XPR can generate a phase-retardation between σ and π polarization
components of the incident X-ray. Polarization states are controllable bychanging the offset angle ∆θ (crystal angle measured from the Bragg
condition). The offset angle ∆θ for circular (±π/2 retardation) or verticalpolarization (±π retardation) depends on the X-ray energy (wavelength), thethickness of the XPR crystal, and the reflection plane; the phase retardation
δ generated by an XPR is given by [4]π  re Re(Fh Fh ) λ3 sin 2θ B 
δ =− 
⋅ t,
2  π 2V 2
∆θ

2

(2)

where,* Classical electron radius re = 2.8179 × 10-15 (m)* Crystal structure factor Re(FhFh) = 255.648121(for diamond 220 reflection)* Unit cell volume V = 45.385 (Å3) (for diamond crystal).
θB represents the Bragg angle, and t the path length of X-rays in the crystal.
When δ = ±π/2 (±π) circularly (vertically) polarized X-rays are generated.
X-ray polarization state can be determined using a simple polarimeter,
which consists of a Kapton scatter and two scintillation counters as shown infigure 2. When non-polarization component is negligible, the degree of
linear polarization is determined by
I − Ix,(3)
PL = yIy + Ix
where, Iy and Ix represent X-ray intensities scattered vertically andhorizontally, respectively. In this case, PL = 1, 0, and -1 means horizontally
linear, circularly, and vertically linear polarization, respectively.
Here, we measure PL at several X-ray energies using the simple
polarimeter. Moreover, we determine the condition of generating circularly-8-and vertically polarized X-rays by analyzing our result.
Thickness of a diamond XPR: t0 (mm) =E (keV)∆θC (arcsec)∆θV (arcsec)

6.5
7.5
8.5

Figure 2. Configuration of the simple polarimeter system.

Put a graph of the result of XPR θ scan.

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Let’s calculate the optimum offset angles for vertical and circularpolarizations !
Again, the phase shift δ at the offset angle ∆θ is described by the following
equationπ  re Re(Fh Fh ) λ3 sin 2θ B 
δ =− 
⋅ t
2  π 2V 2
∆θ

2

(2)'.

Basic parameters are shown as follows:* Classical electron radius re = 2.8179 × 10-15 (m)* Crystal structure factor Re(FhFh) = 255.648121(for diamond 220 reflection)* Unit cell volume V = 45.385 (Å3) (for diamond crystal)(a) Please confirm that the following equation can be derived from Eq. (2)':(2)''(Be careful about unit system !)(b) Please calculate the offset angles ∆θC and ∆θV at which vertical (δ = π)and circular (δ = π/2) polarizations are respectively generated, for X-ray
energies of 6.5, 7.5, and 8.5 keV.
Thickness of a diamond XPR: t0 (mm) =E (keV)∆θC (arcsec)

6.5
7.5
8.5

- 10 -∆θV (arcsec)

Let’s derive the relation between the optimum offset angle and photon
energy !
Please derive the relation between the offset angle ∆θ allowing vertical or
circular polarization and photon energy E, from Eq. (2).

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X-ray magnetic circular dichroism (XMCD):
X-ray magnetic circular dichroism (XMCD) is defined as a difference in the
X-ray absorption coefficients of the sample between for right- and left-circularly
polarized X-rays. XMCD is a powerful tool to study the electronic and magnetic
states of the ferromagnetic materials.[6, 7] In particular, its element-specific featureprovides us with detailed information for the magnetic properties.[8]The XMCD spectrometer consists of the magnet and X-ray detectors. The
electromagnet and superconducting magnet are available at BL39XU. In XMCD
measurement in the transmission mode, two ionization chambers are placed
before and after the sample to monitor the incident (I0) and transmitted (I) X-ray
intensities. In the fluorescence mode, a Si drift detector (SDD) is usually used tomonitor the fluorescence X-ray intensity from the sample, instead of the I
ionization chamber. An XMCD spectrum is obtained from the X-ray absorption
coefficients measured for both X-ray helicities at each energy point.

Figure 3. The XMCD spectrometer using the electromagnet.

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Let’s measure the XMCD spectrum !
Here, we measure XMCD spectra in MnPt3 and CoPt3 alloys using ahelicity-reversal (static) method. If the sample shape is lump or foil, youmust pay attention to the direction of the magnetic field applied so as to
avoid the demagnetizing effect; magnetic field should be applied in plane
for a foil sample. For fine powder samples, it does not matter which
direction magnetic field is applied. The XMCD spectra are measured by thetransmission-mode using two ionization chambers.

Measurement condition
Applied magnetic field: H (T)=Sample:Sample thickness: t (µm) =Gain of current amplifier: I0 @ 10
Energy range: E (keV) =Flipping times / Counting time:/ I1 @ 10~/

sec

Put a graph of the XMCD spectrum measured by helicity-reversal method.

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Helicity-modulation XMCD measurement:
To improve the accuracy of XMCD measurement, the helicity-modulation
technique [9] was developed. This technique allows a detection of dichroic signalsof the order of 0.01% with a good signal-to-noise ratio. Extremely high-quality
XMCD spectra are obtainable in a short acquisition time.
The helicity-modulation technique requires a combination of fast switching of
the X-ray helicity and a phase-sensitive (lock-in) detection system. Block diagramof the helicity-modulation technique is shown in figure 4.

Figure 4. The block diagram of the helicity-modulation technique.

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Let’s experience the helicity-modulation technique !
Here, we record an XMCD spectrum of the same MnPt3 and CoPt3 alloys
using the helicity-modulation method in the same condition of thehelicity-reversal method. Then we compare the obtained spectra using thedifferent methods, with respect to the statistic accuracy, signal-to-noise ratio,
and the acquisition time.

Measurement condition
Applied magnetic field: H (T)=Sample:Sample thickness: t (µm) =Gain of current amplifier: I0 @ 10
Energy range: E (keV) =Modulation frequency: f (Hz) =/ I1 @ 10~

Accumulation times:

Put a graph of the XMCD spectrum measured by helicity-modulation method.

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Origin of XMCD effects:
The origin of XMCD effects is explained using a simple model for opticaltransitions from the 2p core levels to the nd valence states, which corresponds to
the X-ray absorption at the L2 and L3 edges in 3d, 4d, and 5d transition metals.
The 2p core levels have a large spin-orbit interaction (~10 eV for 3d, ~100 eV for 4d,
and ~1 keV for 5d transition metals) and the core hole states are split into the 2p1/2(L2 edge) and 2p3/2 (L3 edge) levels. The nd valence states are assumed to split into
the majority and minority spin bands due to the exchange interaction, and in thefollowing, we assume for simplicity that the majority band is fully occupied andthe minority band is partially filled (i.e. there are some empty states above theFermi energy).
Photoabsorption process basically originates from the electric dipole (E1)transition. In this case, the orbital angular momentum between the initial andfinal states changes by ∆l = l’ – l = ±1, and the spin angular momentum s and its
magnetic quantum number ms are conserved (∆s = s’ – s = 0, ∆ms = ms‘– ms = 0)
according to the selection rules. When circular polarized X-rays with the photon
helicity of σ = ±ħ enters a magnetic material along the direction parallel to themagnetization, the magnetic orbital quantum number changes by ∆ml = ml‘ – ml =±1. The relative transition probabilities for the 2p→nd transitions can be calculatedusing the Clebsh-Gordan coefficients as shown in figure 5 (transition probabilities
are proportional to square of the Clebsh-Gordan coefficients). According to the
Fermi's golden rule, the relative transition intensity is proportional to the productof the transition probability and the density of state of the nd empty state. The
XMCD signal, therefore, arises if imbalances in the spin or orbital density of states
between major and minority bands in the final nd state are present.

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Figure 5. A simple picture of the relative transition probabilities for 2p→5dtransitions. In this diagram, it is assumed that the majority spin states
are completely filled.

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The magneto-optical sum-rules:
P. Carra and B. T. Thole derived important formulas for XMCD spectra basedon a localized model [10,11]. These formulas are called the magneto-optical
sum-rules, and the expressions are described as follows:∫ dω (µ − µ )+−j+ + j−ρ≡∫ dω (µ + µ + µ )
+

−

0

=

1 l (l + 1) + 2 − c(c + 1)
LZ
2 l (l + 1)(4l + 2 − n )j+ + j−c +1∫ dω (µ − µ ) − c ∫ dω (µ − µ )
+

d≡ j

−

+

−

j−

+

∫ dω (µ + µ + µ )+−0

j+ + j−l (l + 1) − 2 − c(c + 1)
l (l + 1)[l (l + 1) + 2c(c + 1) + 4] − 3(c − 1) (c + 2 )SZ +TZ
3c(4l + 2 − n )6lc(l + 1)(4l + 2 − n )2=2where, µ denotes the absorption coefficient. c and l denote the orbital quantum
numbers of a core hole and an excited state, respectively. (4l + 2 – n) denotes thenumber of holes in the valence shell. The suffixes j± = c ±1/2 mean the absorption
edge corresponding to the core states. <Lz> and <Sz> denote the expectation
values of the z component of the orbital and spin momentum operators,
respectively. z is taken along the quantization axis, which is parallel to the photon
wave vector. <Tz> denotes the expectation value of the magnetic dipole operator,
which reflects some aspheric nature of the spin moment due either to ananisotropic charge distribution around the absorbing atom, or spin-orbit
interaction.
For 2p→nd transitions (corresponding to L3 and L2 edges), c = 1 (2p) and l = 2(nd) are assigned in the equations above. Here, we define the following values,µ ≡ µ0 = (µ+ + µ-)/2, ∆µ ≡ (µ+-µ-) and nh ≡ 4 l+ 2 – n, and the following equations
are obtained:ρ≡∫ (∆µ )dωL3 + L 2∫ (µ )dω

=

3
LZ
2nh

L3 + L 2d≡∫ (∆µ )dω − 2 ∫ (∆µ )dωL3L2∫ (µ )dω=

1(2 SZ + 7 TZ )nh

L3 + L 2

These formulas allow us to calculate the value of the orbital angularmomentum <Lz> and the spin angular momentum <Sz> separately from the- 18 -

experimental results. Basically, the value of <Tz> term is smaller than the <Sz>term in most practical cases, in which the spin-orbit coupling in the final nd states
are negligibly small. However, <Tz> value is not always negligible compared to<Sz> in case of low crystal symmetry [12,13]. In case of the sample with a cubic
symmetry, <Tz> value is negligible [14]. Application of sum-rules is one of themost useful tools provided by XMCD spectroscopy.

Let’s apply the sum-rules to the experimental results !
Here, we apply the sum-rules to the experimental results for Pt in MnPt3
and CoPt3, and obtain <Lz> and <Sz> values. The required values to obtain<Lz> and <Sz> are integrals of the white-line parts at the L3,2 edges, integralsof the XMCD profiles at the L3,2 edges, and the number of holes, nh. All thevalues except for nh can be determined experimentally. There are several
ways to obtain the white-line integrals: (1) to assume a background function(transition to continuous levels), for example, an arctangent function, a step
function, etc., (2) to use an experimental XAS spectrum in a full-filled d-levelmaterial such as Au or materials including Au atoms. For nh, literature
values reported by band calculations are often used. The orbital and spin
magnetic moments are given by the relations, mL = −µB<Lz> and mS = −2µB
<Sz>, where µB denotes the Bohr magneton. Finally, you obtain the orbitaland spin magnetic moments of the target Pt atoms in MnPt3 and CoPt3.
Sum-rule analysis:nh =<Tz> =

Material <Lz>/<Sz> <Lz> mL (µB) <Sz> mS (µB) mL + mS (µB) Ref. (µB)
MnPt3

0.26 [16]CoPt3

0.26 [17]- 19 -

References:[1] See URL: http://www.spring8.or.jp/en/users/current_user/bl/beamline/BLtable/[2] H. Maruyama et al.: J. Synchrotron Rad. 6 (1999) 1133.
[3] T. Hara et al.: J. Synchrotron Rad. 5 (1998) 403.
[4] K. Hirano and H. Maruyama: Jpn. J. Appl. Phys. 36 (1997) L1272.
[5] H. Kitamura, J. Synchrotron Rad. 7 (2000) 121.
[6] N. Ishimatsu et al.: J. Phys. Soc. Jpn. 76 (2007) 064703.
[7] N. Kawamura et al.: J. Phys. Soc. Jpn. 76 (2007) 074716.
[8] A good example is given in : A. Koizumi et al.: Phys. Rev. B61 (2000) R14909.
[9] M. Suzuki et al.: Jpn. J. Appl. Phys. 37 (1998) L1488.
[10] B. T. Thole et al., Phys. Rev. Lett. 68 (1992) 1943.
[11] P. Carra et al., Phys. Rev. Lett. 70 (1993) 694.
[12] J. Vogel et al., Phys. Rev. B55 (1997) 3663.
[13] W. Grange et al., Phys. Rev. B58 (1998) 6298.
[14] R. Wu and A. J. Freeman, Phys. Rev. Lett. 73 (1994) 1994.
[15] W. Grange et al., Phys. Rev. B58 (1998) 6298.
[16] B. Antonini et al., Phys. Rev. 187 (1969) 611.
[17] F. Menzinger and A. Paoletti, Phys. Rev. 143 (1966) 365.

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