deg 2 ( )

Laboratory for Neutron Scattering Paul Scherrer Institut

Symmetry, magnetism and phase coexistence in superconducting iron chalcogenides AyFe2-xSe2 (A=K, Cs, Rb)

A diffraction view on the crystal structures, antiferromagnetic ordering and intrinsic phase separation in alkali-metal iron chalcogenides.

J. Phys.: Condens. Matter 24 435701 (2012); 23 156003 (2011); Phys. Rev. B 86, 174107 (2012); 83, 144410 (2011)

1 Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen, Switzerland

2 Laboratory for Developments and Methods, Paul Scherrer Institute, Switzerland

3 ESRF, BP220, 38043 Grenoble, France

4 Swiss-Norwegian Beam Lines at ESRF, France

5 Warsaw Univ Technol, Fac Chem, PL-00664 Warsaw, Poland

I4/mmm->I4/m with 4 arm k-star.

10 independent distortion modes: 2 order + 8 displacive The satellite reflections of phase A are indicated

by arrows for the stars {k

1

}={[2/5,1/5,1]} and {k

2

}

={[1/5,2/5,1]} by solid and dashed lines. The indexing is given in the average cell I4/mmm

E

1

Distortions for Fe in (ab) plane Dominant mode:

order

Fe displacements exaggerated for better visibility

E

2

Displacements

Fe Se

Cs Fe

Calculated by ISODISTORT stokes.byu.edu/isotropy.html

Vladimir Pomjakushin ¹ , Ekaterina Pomjakushina ² , Anna Krzton-Maziopa ^2,5 , Kazimierz Conder ² , Alexey Bosak ³ , Dmitry Chernyshov ⁴ and Volodymir Svitlyk ⁴

200B

200 0010 0010B

a

200

110 110B

200B Cs Fe Se0.8 1.6 2

0 1 0 0 0

1 0

0 _B

2 3 x 2

3 x

0.5 0.5 10_B 0.6 0.2 10

0.60.210 0.50.510_B

Rods of minority phase B. Log scale.

Origin: in plane 2D ordering of alkali- earth. Also 4 twins

-0.04 -0.02 0.00 0.02 0.04 (20L)B

(H010)B

Phase separation as seen by:

Single crystal synchrotron x-ray Powder neutron diffraction

Two metrically different phases: main AFM vacancy ordered (A) and vacancy free (B)

A has two twins in (ab) B has two four 100-twins

A

A A

A A B

B

Summary:

The ground state of the crystal is an intrinsically phase-separated state with two distinct-by-symmetry phases. The main phase has the iron vacancy ordered √5×√5 superstructure (I4/m space group) with AFM ordered Fe spins. The minority phase does not have √5×√5-type of ordering and has a smaller in-plane lattice constant a and larger tetragonal c-axis and can be well described by assuming the parent average vacancy disordered structure (I4/mmm space group) with the refined stoichiometry Rb0.60(5)(Fe1.10(5)Se)2. The minority phase amounts to 8–10% mass fraction. The minority phase merges with the main vacancy ordered phase on heating above the phase separation temperature TP = 475 K. The spatial dimensions of the phase domains strongly increase above TP from 1000 to >2500 Å due to the integration of the regions of the main phase that were separated by the second phase at low temperatures.

Using the arguments of commensurability and detailed analysis of twinning patterns, we augment the previous findings by quantifying the intergrowth state, consisting of the tetragonal phase with ordered Fe vacancies and the minor disordered phase.

Compared to the main phase, the minor one is compressed in the tetragonal a-b plane and expanded along the c direction; a set of modulated Bragg rods evidences a planar disorder. Fourfold splitting of the rods and main Bragg peaks implies a rotational twinning; close inspection of the lattice metric indicates that the symmetry of the minor phase is not higher than monoclinic, with a deviation from the orthogonal basis of ∼0.25°.

B phase rocking curves show small monoclinic distortion.

Temperature evolution of phase separation

A B

“Single” phase

20 40 60 80 100 120 140

0.0 0.2 0.4 0.6 0.8 1.0 1.2

55 60 65 70

0.0 0.2

(321)

(110)(002)

104 Neutron counts

2θ (deg)

Rb_yFe_2-xSe₂ HRPT λ=1.886 !

(101)/ (503)

(240) (200)A (213)A

Differential scanning calorimetry (DSC) signal as a function of temperature. Three peaks are observed: the largest at Ts = 535 K corresponds to the structure phase transition due to the vacancy ordering, T

N

and T

P

are related to AFM ordering and phase separation, respectively.

300 350 400 450 500 550

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

T_S T_N T_P

521 507 T_onset=466

535 518

DSC signal (arb.units)

Temperature (K) T_peak=480

0 0.2 0.4 0.6 0.8 1

o-Fe

0.4 0.6 0.8 1

o-Rb

3000 350 400 450 500 550

0.5 1 1.5 2 2.5

T ( K) MFe(µB)

Fe2 (16i) Fe1 (4d)

Rb2 (2a) Rb1 (8h)

TN TS

TP

phase A

Fe occupancies vacancy

Fe magnetic moment, µ

B 90

95 100

F1(%)

2 4 6 8

F2(%)

300 350 400 450 500 550

1000 1500 2000 2500 3000

T ( K)

L(

˚A)

TN TS

TP

Fraction phase A

Fraction phase B

Contribution of the minority in-plane compressed phase B (refined in the average crystal structure I4/mmm ) is shown by red curve.

Temperature evolution of phase separation

spatial domain sizes

100-rotational twinning

Crystal structure

Cs Fe

Se

122 I4/mmm average structure X

y

Fe

2-x

Se

I4/m vacancy ordered√5×√5 structure. Ideal order at x=0.4

Fe vacancy

A= 2a+b B= a+ 2b C=c

Basis transfomation

Cs

(8h) (x,y,0) (2a) (0,0,0)

Fe (4d) (½,0,¼) (16i) (x,y,z) Se (4e) (½, ½,z)

(16i) (x,y,z)

“vacancy”

(2a) (0,0,0)

(4d) (0, ½, ¼)

(4e) (0,0,z)

Position splitting Structure transition details

0 2 4 6 8 10 12 1.950 2.000 2.050 2.100

Some projections

T= 300K

For ideal vacancy order Cs

2

Fe

4

Se

5

= Cs

0.8

Fe

1.6

Se

2

really: A

y

Fe

x

Se

2

y=0.7-0.85, x=1.60-1.75

Fe Se

Mesh: phase A Mesh: phase B

A

B

B

Log scale.

Log scale.

T= 424K T= 485K T= 495K

T= 500K T= 500K T= 500K T= 500K

½½L rod

½½L

½½L