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
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
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
Hyperfine Interactions
Isomer Shift
Quadrupole Splitting
Magnetic Splitting
Electron Density
Electric Field Gradient
Magnetic Hyperfine Field
B = 10 T
57Fe Mössbauer spectra
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
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.
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
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
Magnetic structure of FeAs
Polarized neutron scattering resultsE. E. Rodriguez et al., Phys. Rev. B 83, 134438 (2011)
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
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
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.
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.
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.