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Peculiar magnetism of the FeAs – grand parent of Peculiar magnetism of the FeAs – grand parent of the iron-based superconductorsthe iron-based superconductors
A. Błachowski1, K. Ruebenbauer1, J. Żukrowski2, and Z. Bukowski3
1 Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, Cracow, Poland
2 Department of Solid State Physics, Faculty of Physics and Applied Computer Science,AGH University of Science and Technology, Cracow, Poland
3 Institute of Low Temperature and Structure Research, Polish Academy of Sciences,Wrocław, Poland
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This work was supported by the National Science Center of Poland, Grant DEC-2011/03/B/ST3/00446
XVI KKN - XVI National Conference on SuperconductivityOctober 7-12, 2013: Zakopane, Poland
Seminarium Instytutu Fizyki UP, Kraków, 25 października 2013 r. (piątek): sala 513: 9.35
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Mössbauer Spectroscopy Laboratory at MSDInstitute of Physics, Pedagogical University
Cracow, Poland
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Contents
Introduction to Mössbauer spectroscopy Phase diagram of the Fe-As system and structure of the FeAs Magnetic order in FeAs studied by polarized neutron scattering Mössbauer spectroscopy results:
-------------------------------------------------------------------------------------------------------------------------------------- - Hyperfine magnetic fields – and hyperfine field spirals
- Electron density on iron nuclei and electric quadrupole interactions
- Recoilless fraction and magneto-elastic effects
- Anisotropy of the recoilless fraction
- Spectra in the external magnetic field
- High temperature behavior -------------------------------------------------------------------------------------------------------------------------------------- Reference:
A. Błachowski, K. Ruebenbauer, J. Żukrowski, and Z. Bukowski, J. Alloys Comp. 582, 167 (2014) www.elektron.up.krakow.pl/feas2.pdf
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Conclusions
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Mössbauer Spectroscopy
Ecv
E
1 mm/s 48 neV
-ray energy is modulated by the Doppler effect due to the source motion vs. absorber
Mössbauer spectrum
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Hyperfine Interactions
Isomer Shift
Quadrupole Splitting
Magnetic Splitting
Electron Density
Electric Field Gradient
Magnetic Hyperfine Field
B = 10 T
57Fe Mössbauer spectra
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Electric Field Gradient + Magnetic Hyperfine Field
= 0°
= 90°
B = 10 T
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A bit of formalism
Relevant hyperfine Hamiltonian:
Choice of the “convenient” reference frame:
Transition and parameter dependence of the Hamiltonians:
. ) ( : ) (
: pure : : )(
21)()(
23)(
BSBA
II
ggQee
pg
pe
HHHH
M1
. : 0 : : )12(2
:
23
10
3
10
3
1
0x
1IIIH
jiij
iiiijjiijij
iiiN
ijjiij
xx
UUUUUU
E
c
II
eQA
SBE
cgA
. ) sin cos ( sin cos : )12(4
: ) ( 3
: : )( : || || || provided 10
: : 0 : : )( )(
213
3
133
0
3
10
22
21
2230
232332211
33
22113
1321
1321
IIII
1IIIIIH
bbBBBRb
VRUR
BbVE
c
II
eQA
SbE
cgA
BVVV
V
VV
V
VVVVV
iiiQ
iiiNQ
zz
yyxx
iiiiiijij
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Lattice dynamics and transition intensity corrections:
. has oneconst )(For
: )( )( )( sin ] )'( exp[
: / :
1
: 1,0', with |' '|| |
2
0 0 1
)1('
)1(
00''
111011
*1010
*11
*1011
1C
C
C
f
ddfdMMidα
g
ggg
gg
ggg
MMMMMM
kkMkMMM'
MMMM
egeg
Thermal ellipsoid for FeAs:
. 1 )Re( : 0 )Re( and 1
0 : ] sinsin exp[ ~ )(
11111121
1121
22112233222
gggg
bbbbbbqf
For such axial ellipsoid aligned with the Cartesian quantization axes one has single anisotropy parameter.For the present case ellipsoid is flattened along y-axis.
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Spiral structure of the magnetic hyperfine field
. )(sin )(cos ! )!(
!exp )(
1 00
L
l
l
m
mmllmPmml
lBB
Parameterization of the spiral field:
www.elektron.up.krakow.pl/mosgraf-2009
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Iron-arsenic phase diagram
Landolt-Börnstein New Series IV/5
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Structure of FeAs
1. Orthorhombic structure2. The Pnma symmetry group3. Arrows show Pna21 distortion4. Quantization axes: abc - xyz5. All FeFe atoms are equivalent within Pnma6. Thermal ellipsoid is flattened along b-axis
Orientation of magnetic spirals
[0 k+1/2 0] iron and [0 k 0] iron
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p-T phase diagram of FeAs
J. R. Jeffries et al., Phys. Rev. B 83, 134520 (2011)
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Magnetic structure of FeAs
Polarized neutron scattering resultsE. E. Rodriguez et al., Phys. Rev. B 83, 134438 (2011)
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Low temperature spectra of FeAs
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Anisotropy of the hyperfine magnetic fields (spiral projections onto a-b plane) in FeAsLeft column shows [0 k+1/2 0] iron, right column shows [0 k 0] iron.
Ba and Bb - iron hyperfine field components along the a-axis and b-axis, respectively.
Orientation of the EFG and
hyperfine magnetic field in the main crystal axes
Average hyperfine fields <B> for
[0 k+1/2 0] and [0 k 0] irons.
Tc - transition temperature - static critical exponent
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FeAs
Spectral shift S and
quadrupole coupling constant AQ versus temperature
for [0 k+1/2 0] iron and [0 k 0] iron.
Line at 72 K separate magnetically ordered region from paramagnetic region.
Relative recoilless fraction <f>/<f0> versus temperature
Green points correspond to magnetically ordered region. Red point is the normalization point.
Inset shows relative spectral area RSA plotted versus temperature.
. 1
RSA1 0
0
C
n
n
N
NN
C
)1(88.0
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Anisotropy of the recoilless fraction - FeAs
Anisotropy disappears in the magnetic region
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Spectra in the external field anti-parallel to the beam - FeAs
Model 1 (different electron densities) is preferred, as for Model 2 one obtains unphysical diamagnetic „susceptibility”.
There is significant anisotropy of the „susceptibility” evenhigh above transition temperature.
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High temperature spectra of FeAs
Model 1
Saturation of the recoilless fraction anisotropy above RT is an indication of the onset of the quasi-harmonic behavior.
Arsenic starts to evaporate at 1000 K and under vacuum leading to the Fe2As phase – irreversible process.
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Conclusions
The iron hyperfine field along the electronic spin spiral varies enormously in amplitudein the magnetically ordered region. The pattern resembles symmetry of 3d electrons in the a-b plane with the significant distortion caused by the arsenic bonding p electrons.
Another unusual feature is strong coupling between magnetism and lattice dynamics i.e. very strong phonon-magnon interaction.
Static critical exponents suggest some underlying transition leading to the magnetic order. Due to the lack of the structural changes one can envisage some subtle order-disorder transition with very small latent heat and hysteresis driven by the itinerant charge/spin ordering.
The sample starts to loose arsenic at about 1000 K under vacuum, what might be explanation for the specific heat anomaly observed at high temperature.