BL Practice: BL08W, Cheiron2009

Spin moment determination of ferro- or ferrimagnetic materials
using magnetic Compton scattering
Yoshiharu Sakurai and Masayoshi Itou
Japan Synchrotron Radiation Research Institute

1. Introduction to Compton scattering and magnetic Compton scattering(1) Compton Scattering [1]Most students remember learning the Compton effect, i.e. the effect ofCompton scattering, from an introductory textbook on quantum ideas. The Compton
effect, the increase in the wavelength, i.e. the decrease in the energy, of X-rays andgamma-rays on being scattered by material objects, clearly demonstrates that X-rays
and gamma-rays have a particle nature and these particles, the photons, behave likematerials particles in collisions with electrons in material objects. Considering acollision between a photon and an electron, conservation laws for energy andmomentum lead to a simple result for the energy shift (ΔE) of a photon by Compton
scattering,h 2 q 2 hq ⋅ p+,(1)2mm
where p is the electron momentum before scattering, q the scattering vector, m theelectron mass. The first term corresponds to the fixed shift in energy only depending on
the scattering geometry, and the second term is a Doppler shift that depends on theΔE =component of the electron momentum p along the scattering vector q. Therefore, theCompton-scattered X-ray line is broadened by moving electrons (see Fig.1). Under animpulse approximation, the line shape is in proportion to the so-called Compton profile,J(pz),J ( p z ) = ∫∫ n( p x , p y , p z )dp x dp y ,(2)where n(px, py, pz) is the probability distribution of the electron momenta in materialobject and the z direction is taken along the scattering vector q. The Compton profile
can be normalized to the total number of electrons N in the material object,∫ J ( p )dp = N .
zz(3)5e+7Compton Scattered
X-raysCounts4e+7

CeRh3B2

Fluorescent
X-rays3e+72e+7Elastic
Peak

1e+70050

100

150200

X-ray Energy (keV)

Fig.1: X-ray energy spectrum from CeRh3B2 measured by a Ge-SSD
with a scattering angle of 168 degrees. The incident X-ray energy is175 keV at Elastic Peak and the Compton scattered X-ray line at 105
keV is broadened by Doppler-shift in collision between the photons
and moving electrons.
(2) Magnetic Compton Scattering [2]When the X-rays are circularly polarized and the material object is a ferro- or

ferromagnetic material, the Compton-scattered X-ray line shape is proportional to thescattering cross section,d 2σ= C ⋅ J ( p z ) + C mag ⋅ PC ⋅ S ⋅ (k cos θ + k')J mag ( p z ) ,dΩdω

(4)where PC is the degree of circular polarization of X-rays, S the spin direction, k (k’) thewavevector of incident (scattered) x-rays, θ the scattering angle. C and Cmag areconstants. The first term corresponds to the eq.(2) and the second term is the magnetic
term which includes the magnetic Compton profile Jmag(pz),[]J mag ( p z ) = ∫∫ nup (p) − ndown (p) dpx dp y
p = ( px , p y , pz ),(5)where nup(p) and ndown(p) are the probability distribution of the electron momenta for
up-spin electrons and down-spin electrons in a ferromagnetic material. The magnetic
Compton profile can be normalized to the difference in the numbers of up-spin anddown-spin electrons, i.e spin moment μspin (μB) for g=2,

∫Jmag( pz )dpz = ∫∫∫ nup (p)dpx dp y dpz −∫∫∫ ndown(p)dpx dp y dpz= N up − N down.

(6)= μ spin ( μ B )The second term in eq.(4) can be isolated by changing the degree of circularpolarization of incident X-rays Pc or changing the spin direction S in a ferromagnet.
Usually, the spin direction is changed by external magnetic field for isolating themagnetic term. Figure 2 shows spectra of Compton scattered X-rays from apolycrystalline Fe with different spin directions (Positive and Negative), together withthe difference between the Positive and Negative spectra (Difference), i.e. magnetic
Compton profile.

2e+62e+5Fe

Positive
NegativeDifference

CountsMag. Effect = 2.09 %,20 min. , R.T.

1e+6

1e+501800

2000

2200

02400

Channel No.

Fig.2: Spectra of Compton scattered X-rays from Fe with positiveand negative spin directions, together with the difference spectrum(magnetic Compton profile) between them.

2. Spin moment determination [3]In order to determine the absolute spin moment in a sample, the magnetic

effect R is defined by the following equation,
I+ −I−,(7)
I+ +I+
where I+ and I- are the integrated intensity of Compton scattered X-ray spectra
measured when the spin direction, i.e. the direction of external magnetic field, is parallelR=(+) and anti-paralell (-) to the scattering vector. On the other, using eqs.(3), (4) and (6),I + − I − = 2Cmag ⋅ PC ⋅ S ⋅ (k cosθ + k ' ) ∫ J mag ( pz )dpz
= 2Cmag ⋅ PC ⋅ S ⋅ (k cosθ + k ' ) ⋅ μ spin ,(8)I + + I − = 2C ∫ J ( pz )dpz = 2C ⋅ N ,and thus the magnetic effect R is given by,⎛μ ⎞R = A⎜⎜ spin ⎟⎟ ,
⎝ N ⎠

(9)

where μspin is the spin moment and N the total number of electrons, again. Once thecoefficient A is given, the spin moment can be determined from the experimentally
determined magnetic effect R through eq.(9) since the total number of electrons N isknown. The coefficient A is usually determined by measurement on a well-characterized
ferromagnet, such as Fe, in which its spin moment is already known. Figure 3 shows the0.10500.060.5

Ni

40
30

0.4
0.30.2

200.1

10090

0.095-0.1
100 105 110 115 120

IP(ω) - IN(ω)0.08

IP(ω) + IN(ω)

FeCo

X-ray Energy, ω (keV)

0.04

Ni
SrRuO30.00-0.02-0.005

CeRh3B20.000

500
0.0400
300

-0.5

200

CeRh3B2

100090-1.095

IP(ω) - IN(ω)

0.02

La0.8Sr0.2MnO3IP(ω) + IN(ω)

Spin moment / Total Number of Electrons

relationship between the experimentally obtained R and μspin/N for Fe, Co, Ni, LSMO
and SRO in which their spin moments are determined by other methods.

100 105 110 115 120

X-ray Energy, ω (keV)

0.005 0.010 0.015
Magnetic Effect, R

0.020

Fig.3: Relationship between the magnetic effect R and mspin/N forFe, Co, Ni, LSMO and SRO in which their spin moments aredetermined by other methods.

3. Experimental Setup: Magnetic Compton Scattering Spectrometer
Figure 4 show the magnetic Compton scattering spectrometer at theBL08Wbeamline. The spectrometer consists of a 3T-superconducting magnet, a sample
cryo-cooler and a 10-element Ge SSD. The superconducting magnet can reverse themagnetic field in few seconds between -2.5 T and +2.5T and the cryo-cooler can holdthe sample at a temperature between 5 K and R.T. The incident X-rays are ellipticallypolarized and their energy is 175 keV. Compton scattered X-rays from a sample aredetected by the 10-element Ge SSD at a scattering angle of 178 degrees.

Incident X-rays:
175 – 275 keV,
Elliptical Polarization
Sample Environments:
H = 0T - 3T
T = 5K - RT

3T-Superconducting

Magnet10-element
Ge-SSD
Cryocooler

HX-rays
SampleFig.4: Magnetic Compton scattering spectrometer at BL08W

4. PracticeIn the beamline practice (BL08W), we measure three ferromagnetic samples,
Fe, Ni and CeRh3B2.
Firstly, we measure polycrystalline samples of Fe and Ni at room temperature.
The aim of this experiment is to see that the magnitude of magnetic effect depends onthe value of spin moment. The spin moments on Fe and Ni are 2.083 μB and 0.512 μB
from other measurements.
Secondly, we measure a single crystal of CeRh3B2 at 10 K. The aim is to seethat the magnetic effect is negative due to the presence of significant orbital moment inthis Ce compound [3].

5. References[1] see, X-ray Compton Scattering, eds M. J. Cooper et al., Oxford University Press
2004.
[2] N. Sakai, J. Appl. Crystallogr. 29 (1996) 81.
[3] Y. Sakurai, M. Itou, J. Tamura-Okada, S. Nanao, A. Thamizhavel, Y. Inada,A. Galatanu, E. Yamamoto and Y. Onuki, J. Phys.: Condens. Matter 15 (2003)
S2183.