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

Mössbauer Spectroscopy Laboratory at MSDInstitute of Physics, Pedagogical University

Cracow, Poland

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

Electric Field Gradient + Magnetic Hyperfine Field

= 0°

= 90°

B = 10 T

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

Iron-arsenic phase diagram

Landolt-Börnstein New Series IV/5

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

p-T phase diagram of FeAs

J. R. Jeffries et al., Phys. Rev. B 83, 134520 (2011)

Magnetic structure of FeAs

Polarized neutron scattering resultsE. E. Rodriguez et al., Phys. Rev. B 83, 134438 (2011)

Low temperature spectra of FeAs

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

Anisotropy of the recoilless fraction - FeAs

Anisotropy disappears in the magnetic region

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.