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Lecture 3 continuation from Wednesday
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Dynamical Matrix -
Conduction electrons
Importance of el-ph
Matrix elements
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G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1991)
NiAl
Exp.
Thy
Confirmed by
H. Chou and S.M.Shapiro
Phys. Rev. B48, 16088
(1993)
50-50 compound
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b- phaseNi0.625 Al0.375
T = 0 KTheory
(using rigid band
approximation)
G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1992)
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Solid lines are theory, with a
fictitious temperature of 1000 K to
account for thermal and alloydisorder.
Symbols are experiment at RT, and
dashed line is experiment at 85 K.
S.M. Shapiro, Mat.Sci. Forum 56-58, 33 (1990)
and
S.M. Shapiro, B.X. Yand, G. Shirane, Y. Noda, and
L.E. Tanner, Phys. Rev. Lett. 62, 1298 (1989)
Ni0.625 Al0.375
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Xiangyang Huang, Claudia Bungaro, Vitaliy Godlevsky, and Karin M. Rabe
Phys. Rev. 65, 014108 (2001).
NiTi B2 T=0K
Unstable
phonons
Electronic
structure -
force constants
Many Phonon is Bzone are imaginary!!!(all first principlesnot a surprise perhaps, at this is for T=0)
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Problem with first principles (T=0) calculation of the bcc structure:It is unstable if the temperature effect is not included, as we saw
Can be stabilized by non-linear phonon couplings: 3 & 4 order (T=0 OK)Ye, Chen, Ho, Harmon and Lindgrd, PRL, 58, 1769 (1987)
A new way is presented above:By allowing atoms to be displaced from the (average) bcc positionsSelf-consistently calculate forces and mean-square displacementsin a 4x4x4 times larger super cell than the uinit one until convergence.Frozen glassy-like structure?This nicely illustrates the bcc problem by a direct FP calculation
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Calculated phonon spectra
T>TM
!N T=0 !N
Imaginary
Takes into account the temperature! Compare to T=0 calculations.
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Energy paths through the landscape
The Na story
Total energy calculation for structuralphase transformations
Y.Y. Ye, C.-T. Chan, K.-M. Ho and B. N. Harmon
The International Journal of Supercomputer Applications,
Volume 4, No. 3 Fall 1990, pp. 111-121.
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bcc
hcp
9R
Na - precise total energy calculations
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The bcc-hcp transition
requires
1. A shuffle of atomic planescorresponding to a T1 N-
point phonon, and
2. A shear (Bain strain) that
changes the basal plane
angle from 109.47o to 120o.
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bcc hcp
The minimum energy
path displays some
interesting physics.
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9R has slightly
lower barrier and
slightly lower totalenergy compared
to the hcp phase.
bcc
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TMS March 10, 2008
X-Ray Magnetic Circular Dichroism (XMCD)
For
Rare Earth Magnetic Materials
Toward a Quantitative Analysis
Bruce Harmon
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TMS March 10, 2008
First, a big thanks!
To
Karl Gschneidner
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TMS March 10, 2008
5dEF
RCPLCP
2p3/2
2p1/2
XRESXMCD
XRES and XMCD
L3
L2
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TMS March 10, 2008
Good Features of XMCD
for magnetism studies
1. Element specific(tune beam to core energy)
2. ~ Orbital specific(dipole selection rule)
3. No nuclear absorption(sometimes problem for neutrons)
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TMS March 10, 2008
History
Magnetic x-ray dichroism in gadolinium metal
P. Carra, B. N. Harmon, B. T. Thole, M. Altarelli, and G. A. Sawatzky
Phys. Rev. Lett. 66, 2495-2498 (1991)
L2 L3
G. Schtz, et. al., Z. Phys. B 73, 67 (1988).
THEORY
EXPERIMENTL2 L3
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TMS March 10, 2008
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TMS March 10, 2008
OrbitalXMCD SUM RULES
Spin
where X-ray circular dichroism and local magnetic fieldsP. Carra, B. T. Thole, M. Altarelli, and X. WangPhys. Rev. Lett. 70, 694-697 (1993)
X-ray circular dichroism as a probe of orbital magnetization
B. T. Thole, P. Carra, F. Sette, and G. van der LaanPhys. Rev. Lett. 68, 1943-1946 (1992)
Limitation of the Magnetic-Circular-Dichroism Spin Sum Rule for Transition Metals andImportance of the Magnetic Dipole Term
R. Wu and A. J. Freeman
Phys. Rev. Lett. 73, 1994-1997 (1994)
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TMS March 10, 2008
The Sum Rules work wonderfully for 3d-transition metals!
But they do not work for Rare Earth materials!
Why?
(Atomic model assumptions breakdown!)
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TMS March 10, 2008
2p position
4pr2R2(r) 5d
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TMS March 10, 2008
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TMS March 10, 2008
Solid State Effects
5d spin up wave function is contracted by4f-5d exchange interaction
Spin up Radial Matrix Elements (ME) are largerthan spin down
Energy dependent ME
Top of
d-bands
EF
4f
up2pdown
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TMS March 10, 2008
Trend of Exchange and S-O Energyof Heavy Rare-Earth 5d States
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TMS March 10, 2008
0
2
4
6
8
10
RNi2Ge
2
Theory - hcp
LIII
/LII
Tb Dy Ho Er TmGd
Experiment RNi2Ge
2
Theory - HCP
BRANCHINGR
ATIO
No-Spin Orbit
6
Branching Ratio L3/L2
Experiment vs. Theory
J. W. Kim, Y. Lee, D. Wermeille, B. Sieve, L. Tan, S.L. Budko, S. Law, P. C. Canfield, B. N. Harmon,and A. I. GoldmanPhys. Rev. B 72, 064403 (2005)
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TMS March 10, 2008
(Low T) Orthorhombic Monoclinic (High T)
Thebreaking of Ge(Si) bonds is responsible for loss of magnetism
Gd5Si2Ge2
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TMS March 10, 2008
Gd5Si2Ge2 : XMCD
* XMCD data at the Ge K and Gd L3 edges.* XMCD signal of Ge K-edge indicates that the Ge 4p states carry
magnetic polarization.
D. Haskel et al. PRL 98 247205 (2007)
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TMS March 10, 2008
Ge2
Gd
Si
Ge1
Orthorhombic Monoclinic
ba
Gd5Si2Ge2:spin density contours
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TMS March 10, 2008
The Er2
Fe17
Story
J. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki
Phys. Rev. B 69, 014427 (2004)
The Er2Fe17N2.4XMCDspectra were
taken at roomtemperature and at
50K. Large spectralchanges, and
quadrupole features
observed.
Er L3 edge
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TMS March 10, 2008
The Er2Fe17 StoryJ. Chaboy, H. Maruyama, N. Kawamura, and M. Suzuki
Phys. Rev. B 69, 014427 (2004)
The Er L2 spectra
changes sign with
temperature!
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TMS March 10, 2008
Calculated L3 for Er2Fe17Yongbin Lee
with E2 contribution added
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TMS March 10, 2008
Calculated L2 for Er2Fe17
with E2 contribution added
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TMS March 10, 2008
Goldman et. al. L3
Experiment
Yongbin
TheoryEr L3 edge normalized to peak
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
-15 -10 -5 0 5 10 15 20
Energy (eV)
NormalizedDic
hroism(
topeak)
T=300K
T=200K
T=125K
T=75K
Experiment
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TMS March 10, 2008
Goldman et. al. L2
Experiment
Yongbin
Er L2 edge peak normalized
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
-10 -5 0 5 10 15 20
Energy (eV)
NormalizedDichroism(
toPeak)
T=300K
T=200K
T=125K
T=75K
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TMS March 10, 2008
The qualitative agreement leaves
little doubt the physics is correct,but the quantitative agreement is
poor!
New results indicate enhanced
orbital polarization on Er and also
possibly on Fe can account for all
the differences.
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TMS March 10, 2008
Thank You
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TMS March 10, 2008
K. Takeda et al.,
J. Alloys Compd. 281, 50 (1998)