Single Crystal Neutron Diffraction. Single Crystal Neutron Diffraction. What What ‘‘s new?s new?

Arsen Gukasov, Laboratoire Léon Brillouin

CEA-CNRS, Saclay, France

Present state of SC Diffraction

Recent Applications of SC Diffraction

Polarized Neutron Diffraction

Spin density and local susceptibility

Polarization Analysis

Future Challenges

OUTLINEOUTLINE

Solids of Platon

waterearthfire air

5 Two-Dimensional Bravais Lattices

Hexagonal

Oblique Rectangular

Square

Two-Dimensional Bravais Lattices

a=b

Rectangular Rectangular Square Hexagonal

Two-Dimensional Bravais Lattices

a=b

Rectangular Rectangular Square Hexagonal

α=90° α=120°

Centered Bravais Lattices

a2

=0.5*arctng(1/2)* a1

a=b α=90°

Dmin

=0.5*Dmax

= a1

φ=arcsin(1/2)

Cmm

Cmm

P2

6mm

Two-Dimensional Space Groups

Cmm

P2

6mm

Square 2D Structures

P4 C4mm

14 3D Bravais Lattices

230 Space Groupes

Cannonball problem

The problem of close-packing of spheres was first mathematically analyzed by Thomas Harriot

around 1587,

after a question on piling cannonballs on ships was posed to him by Sir Walter Raleigh

on their expedition to America.

Cannonballs were usually piled in a rectangular or triangular wooden frame, forming a three-sided or four-sided pyramid. Both arrangements produce a face-centered cubic lattice –with different orientation to the ground.

FCC and HCP structures Density 0.74

Three-Dimensional Space Groups

2D Rectangular and 3D Orthorhombic Structures

P2mmPmmm

Tetragonal Rod Close Packings

The density is the same 0.7854.

P42

/mmcP4/mmm I41

/amd

Cubic Rod Close Packings

Density 0.5890

Pm3nI41

/amd

Density 0.6802

Rod Close Packings

P6/mmmThe density is 0.9069.

P4/mmmThe density is 0.7854.

FourierFourier

transform (transform (FTFT) and Diffraction pattern) and Diffraction pattern

s

=

FM (q)e-iqr

FourierFourier

transform (transform (FTFT) and Diffraction pattern) and Diffraction pattern

Lattice , and its FT :

Crystal 1 Molecule FT:

FT

of the crystal =Product of molecule FT and Rec. Latt. FT

Time of flight (TOF) neutron Diffraction from a single crystal

Multiple reflections sorted by Time-Of-Flight

SXD at ISIS, TOPAZ at SNS ESS Mag

Diffractometer

SINGLE COUNTER DIFFRACTIONSINGLE COUNTER DIFFRACTION

000

a*b*

-340

D

-140

sin(hkl )= /2Dhkl

0

50

10 0

150

2 0 0

2 50

3 0 0

-1.5° omega +1.5°

4-circles

4-

cercles : D9,D10, 6T2,5C2,TRICS(High resolution crystallography)

Bras levant : D3,D15, D23, 6T2, 5C1 (diffraction in extreme conditions)

First generation neutron diffractometers

UNPOLARISED NEUTRON DIFFRACTION UNPOLARISED NEUTRON DIFFRACTION 44--CIRCLESCIRCLES

Structure determination

Anharmonicity

Microcrystals

<0.05mm3 (PSD)

Epitaxial

layers(PSD)

DIFFRACTION USING PSDDIFFRACTION USING PSD

000

a*b*

-340

D

Diffraction conventionnelle:

-140

Diffraction using PSD :

Pre-project

Design

Realisation

Qualificatio n

Budget 380 k€ (50 kE Aquitaine R i )

33

• 256 position sensitive tubes(Ø ~ 1.2cm) 30b 3He efficiency 76% for 0.7Å �× 5height 47 cm �× 5•modular geometry:blocks of 16 paired tubes (2 tubes make one detector: less electronics and cables)

Opens to: 0.58Å measurements, more complex environments (HT), smaller samples, …

25

•

Berceau

équipé

de tables x,y,z•

Support X,Y,Z

•

λ

variables

( 2 Monok

avec foc

vert, 3 take- off)

•

Détecteur

2D

Take-off = 32° Take-off = 65°

S. GautrotV. KlosekM.H. Mathon

16 tubes L=100×2,54 cm P≈

12 bar

Conception (I. Goncharenko) : ~2004Construction : 2008-2009Operation started in march 2011

16 mars 2014 35

4f Magnetism and its Effects on Electronic Properties of Dy3

Ru4

Al12D.I. Gorbunov1,2*, M.S. Henriques3, A.V. Andreev1, A. Gukasov4, V. Petříček1, N.V. Baranov5, Y. Skourski6, V. Eigner1, M. Paukov2

4f Magnetism and its Effects on Electronic Properties of Dy3

Ru4

Al12D.I. Gorbunov1,2*, M.S. Henriques3, A.V. Andreev1, A. Gukasov4, V. Petříček1, N.V. Baranov5, Y. Skourski6, V. Eigner1, M. Paukov2

k=(1/2 0 1/2)

Minimum SC size for neutron studies?

a,b,c<10 A V>0.01mm3 (X-rays >0.0001mm3)

High resolution mode

1.36 m instead of 56 cm

•Pixels (2x2 mm) → résolution de 0.2°x0.2°

BiFeO3

, 0.7x0.7x4.10-2

mm3

CYCLOID WITH D=640 Ǻ

P [111]q1

Rotation plane : (-12-1) = P[111]

q1

Domain I

Domain IIP [1-11]

q1

Rotation plane : (121) = P’[1-11]

q1

P [111]

P [1-11]

q1

E

Neutron diffraction on thin films: what can we gain by using 2D detectors ?

20 22 24 26 281300

1400

1500

1600 1 0 +

Experiment Gaussian fit

1 0 -

Inte

nsity

(cou

nts/

60 s

ec)

(degrees)

(degrees)

2

(deg

rees

)

21 22 23 24 25 26 27 28

60

56

52

48

44

40

36100

120

140

160

180

(degrees)

2 (d

egre

es)

21 22 23 24 25 26 27 28

60

56

52

48

44

40

3620

40

60

80

100

120

Laplacian of Gaussian filtering

Cr 200 nm layer on Mg0

31,5 32,0 32,5 33,0

C r 0 0 2 rock ing sca n E xperim en t G auss ian fit

F W H M = 0 .23°

Inte

nsity

(u. a

rb.)

(degrees)

V=0.02mm3

UNPOLARISED NEUTRON DIFFRACTION UNPOLARISED NEUTRON DIFFRACTION NORMAL BEAM GEOMETRYNORMAL BEAM GEOMETRY

H, T phase diagramm

High pressure

photoexcitation

Diifuse

scattering (PSD)

6T2, Lifting counter mode

7.5 T + 40 mK

7.5 T +10 Gpa+40 mK

I.Mirebeau, I. N. Goncharenko, G. Dhalenne, A. Revcolevschi,Phys. Rev. Lett. 93, 187204 ( 2004).

Pi

=2.8 GPa; Pu

=0

Pi

=2.0 GPa; Pu

=0.3 GPa along 111

Pi

=2.4 GPa; Pu

=0.3 GPa along 011

T=0.14K

Tb2

Ti2

O7

a spin liquid single crystalunder pressure and applied field

Mapping of Spin ice

on the water ice

Oxygen

proton

If ferromagnetic

interactions, the ground configuration is «

two in –

two out

»

spins

Similar to ice ground state:«

two close –

two far

»

protons

with zero point entropy

Spin iceM.Harris, S Bramwell. Nature 399

(1999) 311 & A.P.Ramirez et al, Nature 399

(1999) 333

Cooling of Spin ice in field takes longer than without it

Double layered monopole structure in spin liquideA Sazonov, A Gukasov, I Mirebeau and P Bonville. Phys. Rev. B 85, 214420 (2012)

POLARIZED NEUTRON DIFFRACTIONPOLARIZED NEUTRON DIFFRACTION

M F HD

I+

I-

P0

parallel to H

P0

antiparallel

to H

R = I+ / I - = ( FN

+FM

) 2 / ( FN

- FM

) 2

R 1+4

FM

(q)=

FN

(q)

R = ( 1+ ) 2 / ( 1-

) 2, where = FM

/ FN

PND APPLICATIONSPND APPLICATIONS

Spin Densities

Magnetic structure refinement

Local Susceptibility Parameters (LSP)

Formfactors, L/S ratio

5C1 polarised neutron diffractometer (LLB)5C1 polarised neutron diffractometer (LLB)

monitor

samplecryomagnet 8T

lifting counter

magnetic guides

Heuslerpolarising

monochrom

ator

magnetic guides

cryoflipper

SPIN DENSITY OF SPIN DENSITY OF Mn(dca)2(pym)H2OMn(dca)2(pym)H2O

-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

�

� ��

� �

� �� �

�

��

�

M

n1

M

n2

N

7

C

8

C

5

C

7

H

1

C

6

H

2

O

1

N

8

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

N 4

N 5

N 6

C 3C

4M

nM

n�

�

��

�

�� �

�

��

�

pym=N2(CH)4 (pirimidine) dca=N(CN)2 (dicianamide)

Bulk magnetisation Mi (r)=ij j

NONNON--COLLINEAR SPIN DENSITIES COLLINEAR SPIN DENSITIES

H

Mz

HMz

H

Mz

Mx

I± F 2 N

±2(PP0 *FFM ) FN

+ FM

2

I± F 2 N

±2FMz FN

+ FM

2

F. Wang; A Gukasov et al., PRL, 2003 ORIGIN OF THE FIELD INDUCED METALIC STATE OF (La0.4

Pr0.6) 1.2

Sr1.8

Mn2

O

77

ANISOTROPIC SYSTEMS UNDER MAGNETIC FIELDANISOTROPIC SYSTEMS UNDER MAGNETIC FIELD

ANISOTROPIC SUSCEPTIBILITIESANISOTROPIC SUSCEPTIBILITIES

Bulk magnetisation Mi (r)=ij j

332322131211

ij

The number of independent components of ij is determined by the crystal symmetry class:

cubic groups 1 parameter all uniaxial

groups 2 parameters

Orthorhombic 3 ... Monoclinic 4 ... Triclinic 6

ANISOTROPIC SUSCEPTIBILITIESANISOTROPIC SUSCEPTIBILITIES

M

H

330001100011

ij

CUBIC, 11 = 22 = 33

M

H

110001100011

ij

ANISOTROPIC BULK SUSCEPTIBILITYANISOTROPIC BULK SUSCEPTIBILITY

UNIAXIAL 11 = 22 < 3

MMi

= a

aij

j

LOCAL SUSCEPTIBILITIESLOCAL SUSCEPTIBILITIES

I±

N 2 ±2FN

(PP0 *

aij

jj

) + |aij

jj

|2

I

N 2

2 P0z

N

Mz

+Mz2

R = I+ / I -, CHILSQ (CCSL)

A Gukasov

and P J Brown, J Phys C, 14, 8831, 2002

Magnetic monopoles

270 K 1 T, 100 FR

H // 111

MAGNETIC ELLIPSOIDS in TbTi

H II [111]

100 K 1 T, 100 FR

MAGNETIC ELLIPSOIDS in TbTi

H II [111]

50 K 1 T, 100 FR

MAGNETIC ELLIPSOIDS in TbTi

H II [111]

10 K 1 T, 150 FR

MAGNETIC ELLIPSOIDS in TbTi

H II [111]

5 K 1 T, 150 FR

MAGNETIC ELLIPSOIDS in TbTi

H II [111]

Ising

versus XYanisotropy

“as seen”

by PND. H. Cao, A. Gukasov

et al. PRL 103, 056402 (2009)

Can we measure ASPs on Powder samples?

powder Tb2Sn2O7 on Super-6T2, (measuring time 200 sec)

100k 5T

2k 5T

24°

Can we measure ASPs on Powder samples?

powder Tb2Sn2O7100k 5T

2k 5T

Can we measure ASPs on Powder samples?

CHILSQ program in CCSL (P J Brown)

Can we measure ASPs with upolarized neutrons?

Extinction rule for pyrochlore impose (00h)=4n

Im

(200)~χ12 Ising or XY behavior

Im

(400)~χ11 Heisenberg behavior

PND PROVIDESPND PROVIDES

Spin Densities

Magnetic structure refinement

Atomic Susceptibility Parameters

Non-collinear Magnetization Densities ?

Rectangular 2D Space GroupRectangular 2D Space Group

Pmm

Rectangular 2D Space Group Rectangular 2D Space Group PmmPmm

Pmm

Neutron beam

Laser

H

Optical Fiber

0P

crista l

PhotoPhoto--excitation setup at 5C1 diffractometerexcitation setup at 5C1 diffractometer

S. Decurtins et al. Inorg. Chem. 24 (1985) 2174

~ 514 nm

Light Induced Excited Spin State Trapping Light Induced Excited Spin State Trapping (LIESST) in (LIESST) in Fe(ptz)Fe(ptz)66

](BF](BF44

))22

0.00 2.00 4.00 6.00 8.00 10.00

4.00

2.00

0.00

2.00

4.00

6.00

8.00

0.00

2.00

-0.20-0.18-0.16-0.14-0.12-0.10-0.08-0.06-0.04-0.02-0.020.000.020.040.060.080.100.120.140.160.180.20

a

b

Very

Intense

Polarized Neutron DIFFRACTOMETER (5C1) at LLB

project started in 2006

+25 °

-5 °

M F

25°x90°

0.7 rad

VIP

Neutron DIFFRACTOMETER (5C1) deliverd in 2010

WISH diffractometer, ISIS TS2WISH diffractometer, ISIS TS2

85

• 256 position sensitive tubes(Ø ~ 1.2cm) 30b 3He efficiency 76% for 0.7Å �× 5height 47 cm �× 5•modular geometry:blocks of 16 paired tubes (2 tubes make one detector: less electronics and cables)

Opens to: 0.58Å measurements, more complex environments (HT), smaller samples, …

25

LAUE DIFFRACTOMETERS LAUE DIFFRACTOMETERS

Advantages:

Large angular covering (9 rad) High Luminosity, Small crystals Problems:

High Background, hkl overlapping,

Specrum Normalisation, Wavelength dependent corrections

SPIN DENSITY ON LIGANDS OSPIN DENSITY ON LIGANDS O22--

AND FORMFACTOR AND FORMFACTOR OF OF RuRu

in Sr2RuO4in Sr2RuO4

xy

t2g

A Gukasov, M Braden, R J Papoular, S Nakatsuji and Y Maeno PRL, 89, 087202-1, 2002

ANOMALOUS SPIN DENSITY ON OXYGEN IN Ca(Sr)ANOMALOUS SPIN DENSITY ON OXYGEN IN Ca(Sr)22

RuORuO44

Ru4+ 0.36(1)μB O2-

0.070(2)μB

19%

of Ru

Diffuse Scattering in Tb2

Ti2

O7

at 160mK

2D cuts in BZ with step δ= (0.25,-0.25,0) along the [1-10] axis

001

002

003

110

220

-1-10-2-20

2 0 0 3 1 0-0-2 0-1-3 0

001

002

003

160mK, H=0T 160mK, H=4T

Tb2Ti2O7 H II[1-10], [hhl] cut

160mK, H=1T

002

110-1-10

-1-10 110

002

00-2

111

Data Treatment (II)

Final peak extraction using Res. Parameters

Corrections (efficiency, Lorenz etc.)

I (hkl) , FR(hkl)

Evolution of Tb Anisotropy in TbMnOEvolution of Tb Anisotropy in TbMnO33

. .

200 K

150 K

100 K

75 K

Crystal Structure of LadderCrystal Structure of Ladder--Chain Compound SrChain Compound Sr1414

CuCu2424

OO4141

; ;

(h k l ) chain reflections

The = c1 /c2 =0.698(8)≈

0.7close to the commensurate value =7/10.

Sublattice

CuO2

a=11.4698, b=13.3527, c1

=2.7268 ( Amma)

( h k 0.7*l ) ladder

reflections

(hk0) common reflections of both

Sublattice

Sr2

Cu2

O3 a=11.4698, b=13.3527, c2

=3.9235 (Fmmm)

Reciprocal Reciprocal ––space viewspace view CuO2

Amma : k+l =2n

Sr2

Cu2

O3 Fmmm

: k, l=2n

Reciprocal Reciprocal ––space viewspace view CuO2

Amma : k+l =2n

Sr2

Cu2

O3 Fmmm

: k, l=2n

satellite (composite) reflections from interaction of lad-ch

Crystal Structure of LadderCrystal Structure of Ladder--Chain Compound SrChain Compound Sr1414

CuCu2424

OO4141

; ;

Crystal of cylindrical shape of about 4x3x2.5 mm3

~20 mm3

Measured reflections

1172, indep. 688., obs. (I ≥

3 s(I)) 502

hkl0 hk0m (hkl±1) (hkl±2)

R F2 6.25 3.11 11.86 36.66

*1c)(*b*a*

2c*1c*b*ahklmq mlkhmlkh

SrSr1414

CuCu2424

OO4141

, Super, Super--Space Group refinement Space Group refinement

J Etrillard, A Gukasov, M Braden. Physica C 403, 2004 and Phys Rev B 69, 214426, 2004