OSNS - Neutrons and X-rays in magnetism · 16th Oxford School on Neutron Scattering | Navid Qureshi THE EUROPEAN NEUTRON SOURCE Result: Diffraction pattern 0 20 40 60 80 100 120 140

$Page 1: OSNS - Neutrons and X-rays in magnetism · 16th Oxford School on Neutron Scattering | Navid Qureshi THE EUROPEAN NEUTRON SOURCE Result: Diffraction pattern 0 20 40 60 80 100 120 140$
I N S T I T U T L A U E L A N G E V I N

T H E E U R O P E A N N E U T R O N S O U R C E16th Oxford School on Neutron Scattering | Navid Qureshi

Navid Qureshi

Neutrons and X-rays in magnetism


MotivationProblem Method

simple magnetic structures and large magnetic moments

complex magnetic structures and/or small magnetic moments

spin density maps and non-spherical models

complex magnetic structures, cs separation and chiralities

separate nuclear/magnetic scattering and directional information

powder diffractionsingle-crystal

diffraction

flipping ratio method

spherical neutron polarimetry

longitudinal polarization

analysis


MotivationProblem Method

Complexity scale


Magnetic structuresPowder diffraction


Result: Diffraction pattern

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

Useful information lies in the

‣ position

‣ the intensity

‣ the shape and width

of the reflections.

Powder diffraction

Magnetic structures

Downsides:

‣ not always easy to find q

‣ superposition of peaks

‣ magnetic equivalents not equivalent


Result: Diffraction pattern

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

Useful information lies in the

‣ position

‣ the intensity

‣ the shape and width

of the reflections.

Powder diffraction

Magnetic structures

Downsides:

‣ not always easy to find q

‣ superposition of peaks

‣ magnetic equivalents not equivalent


Powder diffraction - ambiguity

Magnetic structures

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)

0 20 40 60 80 100 120 140 1600

50

100

150

200

250

300

350

400

450

500

550

2θ (deg)

Inte

nsity

(cou

nts)


Magnetic ordering in manganates

Magnetic structures

Radaelli et al., Phys. Rev. B 55 3015 (1997)

1. Different modulations for Mn3+ and Mn4+ sub lattices

2. Different moment directions for Mn3+ and Mn4+

3. Spin-flip domain boundaries in Mn3+ structure


Single crystal diffraction - 4-circle geometry

by adjusting 2𝜃, 𝜔, 𝜒 and 𝜙

the sample is put in reflection position

D10 (ILL)

single crystal on Al pin

Magnetic structures


Single crystal diffraction - Normal beam geometry

cryomagnets, pressure cells, … cannot be tilted much

→ confined to the scattering plane e.g. only (hk0) reflections

→ lifting counter able to reach l=1, 2…

Magnetic structures


Magnetic ordering in Ni3V2O8

Magnetic structures

Lawes et al., Phys. Rev. Lett. 95 087205 (2005)

Law

es e

t al

., P

hys.

Rev

. Le

tt.

93

247

201

(200

4)

complex cycloidal magnetic structure breaks inversion symmetry and induces macroscopic electric polarisation → multiferroic


Comparison: Powder vs. single crystal diffraction

Magnetic structures

‣ straightforward experiment

‣ Rietveld analysis (profile)

‣ no knowledge on structure required

‣ peak overlap

‣ loss of vectorial information

‣ requires knowledge on structure

‣ list of (hkl) and intensities

‣ peaks measured individually

‣ no loss of vectorial information

‣ Extinction ‣ magnetic domains


Comparison: Powder vs. single crystal diffraction

Magnetic structures

‣ straightforward experiment

‣ Rietveld analysis (profile)

‣ no knowledge on structure required

‣ peak overlap

‣ loss of vectorial information

‣ requires knowledge on structure

‣ list of (hkl) and intensities

‣ peaks measured individually

‣ no loss of vectorial information

‣ Extinction ‣ magnetic domains


Non-resonant magnetic X-ray diffraction

Magnetic structures

‣ At 1 keV magnetic scattering cross section is 3.8*10-6 smaller than Thomson scattering

‣ Only a few unpaired electrons contribute to magnetic scattering, while all electrons to Thomson scattering

‣ however, large flux largely compensates for small cross sections

‣ Magnetic scattering (and L/S) has different polarization dependence than Thomson scattering

‣ spin and orbital moment can be distinguished ‣ microfocussing down to 20 nm

Ohsumi and Arima, Advances in Physics: X 1 128 (2016)



Magnetic structures

Johnson et al., Phys. Rev. Lett. 107 137205 (2011)

- use of X-ray polarisation to deduce spin-rotation plane

- magnetic structure refinement to unpolarised neutron data



Magnetic structures

- microfocusing allows to probe individual magnetic domains

50 µm resolution

Johnson et al., Phys. Rev. Lett. 110 217206 (2011)


Resonant magnetic X-ray diffraction

Magnetic structures

‣ Tune the energy of the X-ray beam to an absorption edge

‣ Photon is absorbed and the system re-emits a photon with the same energy

‣ Element-specific information

‣ Combination of spectroscopy technique with Bragg scattering

Lee

et a

l., P

hys.

Rev

. Le

tt.

11

0 1

3720

3 (2

013)

‣ Ideal example: GdMn2O5

‣ Gd and Mn order

‣ Gd has huge neutron absorption cross section


Polarized neutronsWhy use them?

reference frame [100]-[001] scattering plane

neutron spin state can be different after scattering process depending on interaction

Rules:

1. Nuclear scattering is always a non-spin-flip process

2. Only the component contributes to magnetic scattering

3. The magnetic component contributes to spin-flip scattering

4. The magnetic component contributes to non-spin-flip scattering

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FM ? Pi<latexit sha1_base64="APSo68qE537ftvwOEreo89iOYIo=">AAACBnicbVDLSsNAFJ3UV62vqEsRBovgQkqigi4LgrgRKtgHNCVMppN26GQyzEyEErJy46+4caGIW7/BnX/jpI2grQcuHM65l3vvCQSjSjvOl1VaWFxaXimvVtbWNza37O2dlooTiUkTxyyWnQApwignTU01Ix0hCYoCRtrB6DL32/dEKhrzOz0WpBehAachxUgbybf3vQjpYRCmV5l/4wkixY/QyHzq21Wn5kwA54lbkCoo0PDtT68f4yQiXGOGlOq6jtC9FElNMSNZxUsUEQiP0IB0DeUoIqqXTt7I4KFR+jCMpSmu4UT9PZGiSKlxFJjO/EY16+Xif1430eFFL6VcJJpwPF0UJgzqGOaZwD6VBGs2NgRhSc2tEA+RRFib5ComBHf25XnSOqm5pzX39qxaPy7iKIM9cACOgAvOQR1cgwZoAgwewBN4Aa/Wo/VsvVnv09aSVczsgj+wPr4B/5aZYw==</latexit>

FM k Pi<latexit sha1_base64="Ba/cDunxuxaOM8rack20E/kw7Wo=">AAACCnicbVDLSsNAFJ3UV62vqEs3o0VwISVRQZcFQdwIFewDmhIm05t26OTBzEQoIWs3/oobF4q49Qvc+TdO2gjaeuDC4Zx7ufceL+ZMKsv6MkoLi0vLK+XVytr6xuaWub3TklEiKDRpxCPR8YgEzkJoKqY4dGIBJPA4tL3RZe6370FIFoV3ahxDLyCDkPmMEqUl19x3AqKGnp9eZe6NExNBOAf+IzYyl7lm1apZE+B5Yhekigo0XPPT6Uc0CSBUlBMpu7YVq15KhGKUQ1ZxEgkxoSMygK6mIQlA9tLJKxk+1Eof+5HQFSo8UX9PpCSQchx4ujO/Uc56ufif102Uf9FLWRgnCkI6XeQnHKsI57ngPhNAFR9rQqhg+lZMhzoOqnR6FR2CPfvyPGmd1OzTmn17Vq0fF3GU0R46QEfIRueojq5RAzURRQ/oCb2gV+PReDbejPdpa8koZnbRHxgf3yyDmyE=</latexit>


Spin densitiesFlipping ratio method

‣ sensitive technique used to derive spin density maps

‣ accurate allow a non-spherical model of the spin distribution

‣ accuracy due to interference term

E.g.:

unpolarized:

polarized:

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F 2N + F 2

M = 1.01F 2N

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(FN + FM )2 = F 2N + 2FNFM + F 2

M = 1.21F 2N

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flipping ratio: R =I+

I�=

1.21

0.81⇡ 1.25

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Leco

mte

et

al., A

CA T

rans

action

s (2

011)

significant population of and dz2 dx2�y2

spin density in double-bridged Cu complex


x and y within scattering plane z vertical

Spin densitiesFlipping ratio method


Flipping ratio method

only non-spin-flip scatteringx and y within scattering plane

z vertical

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Spin densities


Flipping ratio method

only non-spin-flip scatteringx and y within scattering plane

z vertical

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Spin densities


Spin densitiesMagnetic Compton scattering

J(pz) =

Z Z⇢(px, py, pz)dpxdpy

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‣ Incoherent scattering technique using circularly polarised X-rays

‣ based on well-known Compton effect

‣ one can measure the projection of all electron momenta on the

scattering vector (defined as Compton profile)

Compton shift projection of p on q

@2�

@⌦@!2/ |A|2J(pz) + 2i ·A⇤B · Jmag(pz)

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‣ Total cross section:

‣ Magnetic Compton Profile:


Spin densitiesMagnetic Compton scattering

J(pz) =

Z Z⇢(px, py, pz)dpxdpy

<latexit sha1_base64="UF/HoxnHkyCIWwvd8pw57egVHxw=">AAACEnicbVDLSsNAFJ3UV62vqEs3wSK0UEqigm6EghtxVcE+oAlhMpm0QyeTMDMRY+g3uPFX3LhQxK0rd/6NkzYLbT1w4cw59zL3Hi+mREjT/NZKS8srq2vl9crG5tb2jr671xVRwhHuoIhGvO9BgSlhuCOJpLgfcwxDj+KeN77M/d4d5oJE7FamMXZCOGQkIAhKJbl6/boWuw/1C5swmZdh81GkpPtG7KaN3PLVQ1Xq6lWzaU5hLBKrIFVQoO3qX7YfoSTETCIKhRhYZiydDHJJEMWTip0IHEM0hkM8UJTBEAsnm540MY6U4htBxFWprabq74kMhkKkoac6QyhHYt7Lxf+8QSKDcycjLE4kZmj2UZBQQ0ZGno/hE46RpKkiEHGidjXQCHKIpEqxokKw5k9eJN3jpnXStG5Oq61GEUcZHIBDUAMWOAMtcAXaoAMQeATP4BW8aU/ai/aufcxaS1oxsw/+QPv8AWG8nT4=</latexit>

‣ Incoherent scattering technique using circularly polarised X-rays

‣ based on well-known Compton effect

‣ one can measure the projection of all electron momenta on the

scattering vector (defined as Compton profile)

momentum density in Co3V2O8

@2�

@⌦@!2/ |A|2J(pz) + 2i ·A⇤B · Jmag(pz)

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‣ Total cross section:

‣ Magnetic Compton Profile:


Spin densitiesCorrelation of real and momentum space

Spin polarized orbital occupation

Ab initio MO wave functions

Real space Momentum space


Spin densitiesCorrelation of real and momentum space

Spin polarized orbital occupation

Real space Momentum space

observed calculated observed calculated

orbital occupations, super-exchange pathways, hybridization, etc.


Polarized analysisNeutrons

More information can be extracted by analysing the final polarization of the neutrons.

Longitudinal Polarization Analysis (LPA): set along x, y or z and analyse the component

of along the same direction

6 possibilities: 3 directions x 2 cross sections

Spherical Neutron Polarimetry (SNP): set along x, y or z and analyse the component of along x, y or z 36 possibilities: 3 directions x 3 directions x 4 cross sections

x,y,z I++(I��), I+�(I�+)

x,y,z x,y,z I++, I��, I+�, I�+

Pi<latexit sha1_base64="9Isfhiz3xMBgMzcLI3xBVFBnPcs=">AAAB83icbVDLSsNAFL2pr1pfVZduBovgQkqigi4LblxWsA9oQplMJ+3QySTM3Agl9DfcuFDErT/jzr9x2mahrQcGDufcyz1zwlQKg6777ZTW1jc2t8rblZ3dvf2D6uFR2ySZZrzFEpnobkgNl0LxFgqUvJtqTuNQ8k44vpv5nSeujUjUI05SHsR0qEQkGEUr+X5McRRGeXPaF/1qza27c5BV4hWkBgWa/eqXP0hYFnOFTFJjep6bYpBTjYJJPq34meEpZWM65D1LFY25CfJ55ik5s8qARIm2TyGZq783chobM4lDOznLaJa9mfif18swug1yodIMuWKLQ1EmCSZkVgAZCM0ZyokllGlhsxI2opoytDVVbAne8pdXSfuy7l3VvYfrWuOiqKMMJ3AK5+DBDTTgHprQAgYpPMMrvDmZ8+K8Ox+L0ZJT7BzDHzifPzyGkb0=</latexit>

Pf<latexit sha1_base64="0MZ3FfpRBeOBFD+xbI85cGxenFo=">AAAB83icbVDLSsNAFL2pr1pfVZduBovgQkqigi4LblxWsA9oQplMJ+3QySTM3Agl9DfcuFDErT/jzr9x2mahrQcGDufcyz1zwlQKg6777ZTW1jc2t8rblZ3dvf2D6uFR2ySZZrzFEpnobkgNl0LxFgqUvJtqTuNQ8k44vpv5nSeujUjUI05SHsR0qEQkGEUr+X5McRRGeXPaj/rVmlt35yCrxCtIDQo0+9Uvf5CwLOYKmaTG9Dw3xSCnGgWTfFrxM8NTysZ0yHuWKhpzE+TzzFNyZpUBiRJtn0IyV39v5DQ2ZhKHdnKW0Sx7M/E/r5dhdBvkQqUZcsUWh6JMEkzIrAAyEJozlBNLKNPCZiVsRDVlaGuq2BK85S+vkvZl3buqew/XtcZFUUcZTuAUzsGDG2jAPTShBQxSeIZXeHMy58V5dz4WoyWn2DmGP3A+fwA3+pG6</latexit>

Pi<latexit sha1_base64="9Isfhiz3xMBgMzcLI3xBVFBnPcs=">AAAB83icbVDLSsNAFL2pr1pfVZduBovgQkqigi4LblxWsA9oQplMJ+3QySTM3Agl9DfcuFDErT/jzr9x2mahrQcGDufcyz1zwlQKg6777ZTW1jc2t8rblZ3dvf2D6uFR2ySZZrzFEpnobkgNl0LxFgqUvJtqTuNQ8k44vpv5nSeujUjUI05SHsR0qEQkGEUr+X5McRRGeXPaF/1qza27c5BV4hWkBgWa/eqXP0hYFnOFTFJjep6bYpBTjYJJPq34meEpZWM65D1LFY25CfJ55ik5s8qARIm2TyGZq783chobM4lDOznLaJa9mfif18swug1yodIMuWKLQ1EmCSZkVgAZCM0ZyokllGlhsxI2opoytDVVbAne8pdXSfuy7l3VvYfrWuOiqKMMJ3AK5+DBDTTgHprQAgYpPMMrvDmZ8+K8Ox+L0ZJT7BzDHzifPzyGkb0=</latexit>

Pf<latexit sha1_base64="0MZ3FfpRBeOBFD+xbI85cGxenFo=">AAAB83icbVDLSsNAFL2pr1pfVZduBovgQkqigi4LblxWsA9oQplMJ+3QySTM3Agl9DfcuFDErT/jzr9x2mahrQcGDufcyz1zwlQKg6777ZTW1jc2t8rblZ3dvf2D6uFR2ySZZrzFEpnobkgNl0LxFgqUvJtqTuNQ8k44vpv5nSeujUjUI05SHsR0qEQkGEUr+X5McRRGeXPaj/rVmlt35yCrxCtIDQo0+9Uvf5CwLOYKmaTG9Dw3xSCnGgWTfFrxM8NTysZ0yHuWKhpzE+TzzFNyZpUBiRJtn0IyV39v5DQ2ZhKHdnKW0Sx7M/E/r5dhdBvkQqUZcsUWh6JMEkzIrAAyEJozlBNLKNPCZiVsRDVlaGuq2BK85S+vkvZl3buqew/XtcZFUUcZTuAUzsGDG2jAPTShBQxSeIZXeHMy58V5dz4WoyWn2DmGP3A+fwA3+pG6</latexit>


Polarized neutronsLPA experiment








Polarized neutronsHelmholtz coils

Pi k x<latexit sha1_base64="oDT750b1HVG+wFchc4W3B6vLsZQ=">AAACAHicbVBNS8NAEJ3Ur1q/qh48eFksggcpiQp6LHjxWMHWQhPCZrtpl242YXcjlpCLf8WLB0W8+jO8+W/ctDlo64OBx3szzMwLEs6Utu1vq7K0vLK6Vl2vbWxube/Ud/e6Kk4loR0S81j2AqwoZ4J2NNOc9hJJcRRweh+Mrwv//oFKxWJxpycJ9SI8FCxkBGsj+fUDN8J6FIRZO/eZm2CJOaccPfr1ht20p0CLxClJA0q0/fqXO4hJGlGhCcdK9R070V6GpWaE07zmpoommIzxkPYNFTiiysumD+To2CgDFMbSlNBoqv6eyHCk1CQKTGdxrpr3CvE/r5/q8MrLmEhSTQWZLQpTjnSMijTQgElKNJ8Ygolk5lZERiYEok1mNROCM//yIumeNZ3zpnN70WidlnFU4RCO4AQcuIQW3EAbOkAgh2d4hTfryXqx3q2PWWvFKmf24Q+szx8K25ad</latexit>

Pf k x<latexit sha1_base64="x9x1lC58Fn/NOveGL/qPYLEGaVA=">AAACAHicbVBNS8NAEJ3Ur1q/qh48eFksggcpiQp6LHjxWMHWQhPCZrtpl242YXcjlpCLf8WLB0W8+jO8+W/ctDlo64OBx3szzMwLEs6Utu1vq7K0vLK6Vl2vbWxube/Ud/e6Kk4loR0S81j2AqwoZ4J2NNOc9hJJcRRweh+Mrwv//oFKxWJxpycJ9SI8FCxkBGsj+fUDN8J6FIRZO/dDN8ESc045evTrDbtpT4EWiVOSBpRo+/UvdxCTNKJCE46V6jt2or0MS80Ip3nNTRVNMBnjIe0bKnBElZdNH8jRsVEGKIylKaHRVP09keFIqUkUmM7iXDXvFeJ/Xj/V4ZWXMZGkmgoyWxSmHOkYFWmgAZOUaD4xBBPJzK2IjEwIRJvMaiYEZ/7lRdI9azrnTef2otE6LeOowiEcwQk4cAktuIE2dIBADs/wCm/Wk/VivVsfs9aKVc7swx9Ynz8GLpaa</latexit>


Spherical neutron polarimetry

Powerful technique used to determine …

‣ complex magnetic structures

‣ chiral domain populations

by selectively measuring generalized cross sections of a polarised

neutron beam with a single-crystal sample.

Possible to reconstruct the 3D rotation [and (de)polarisation] of

the neutron spin.

Polarized neutrons



Powerful technique used to determine …

‣ complex magnetic structures

‣ chiral domain populations

by selectively measuring generalized cross sections of a polarised

neutron beam with a single-crystal sample.

Possible to reconstruct the 3D rotation [and (de)polarisation] of

the neutron spin.

Polarized neutronsCircularly polarised X-rays

Sag

ayam

a et

al.,

J.

Phys

. Soc

. Jp

n. 7

9 0

4371

1 (2

010)



CRYOgenic Polarization Analysis Device

Cryocradle setup allowing for

out-of-plane access

Polarized neutrons



Polarisation tensor

Local coordination system:

x || Q z vertical

y completes right-handed set

Pf = PPi +P0<latexit sha1_base64="pjHZuH8uZ6qbtwAm00+lydx5zLA=">AAACG3icbVDLSsNAFL2pr1pfUZduBosoKCWpgm6EghuXFewD2hAm00k7dPJgZiKU0P9w46+4caGIK8GFf+OkDVhbDwyce869zL3HizmTyrK+jcLS8srqWnG9tLG5tb1j7u41ZZQIQhsk4pFoe1hSzkLaUExx2o4FxYHHacsb3mR+64EKyaLwXo1i6gS4HzKfEay05JrVboDVwPPT+tj10TWalARzXc847PS3OHbNslWxJkCLxM5JGXLUXfOz24tIEtBQEY6l7NhWrJwUC8UIp+NSN5E0xmSI+7SjaYgDKp10ctsYHWmlh/xI6BcqNFFnJ1IcSDkKPN2ZrSjnvUz8z+skyr9yUhbGiaIhmX7kJxypCGVBoR4TlCg+0gQTwfSuiAywwETpOEs6BHv+5EXSrFbs84p9d1GuneVxFOEADuEEbLiEGtxCHRpA4BGe4RXejCfjxXg3PqatBSOf2Yc/ML5+AIupoag=</latexit>

Pf,i =

0

BBBBBBBBB@

�N��Myy��Mzz��x

�x

�IIz��x

�x

�IIy��x

�x

��IIz+�IRy

�y

�N+�Myy��Mzz+�IRy

�y

�Myz+�IRy

�y

��IIy+�IRz�z

�Mzy+�IRz�z

�N��Myy+�Mzz+�IRz�z

1

CCCCCCCCCA

<latexit sha1_base64="R5rKpOj3oUsgX2mg/pK+q2k57FI=">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</latexit>

Final neutron polarization is related to initial one by rotational part

created/annihilated polarisation

Easily distinguish nuclear, magnetic, chiral and interference terms.

Polarized neutrons


Polarized neutronsSpherical neutron polarimetry

CRYOgenic Polarization Analysis Device

Pi k x Pf k y

Pf,i = Pyx =n+ � n�

n+ + n�


Comparison: Neutron vs. X-ray single crystal diffraction

Magnetic structures

‣ Born approximation valid ‣ Magnetic scattering amplitude comparable to nuclear

one

‣ Large penetration depth -> bulky sample environments

‣ Manipulation of polarisation and analysis (but costly)

‣ Large divergence, relatively poor Q-resolution

‣ Lack of spatial resolution

‣ No direct L/S separation (only by fitting magnetic form factor)

‣ No powder

‣ Off resonance gives quantitative results, but scaling to charge scattering not always easy

‣ Small magnetic cross section compensated by flux

‣ Beam heating can be a problem (no dilution)

‣ Not easy to do k=0 work

‣ Manipulate polarization and analysis ‣ Highly collimated, excellent Q-resolution

‣ Spatial resolution down to 20 nm

‣ Direct L/S separation

‣ Element specific information from resonance


Diffuse scattering

Short-range order

‣ Some magnetic systems do not order even down to

very low temperatures

‣ often bear very interesting physics

‣ short-range order revealed in diffuse scattering


Diffuse scattering

Short-range order





‣ most prominent example: spin ice

‣ highly frustrated although ferromagnetic

Bramwell and Gingras, Science 294 1495 (2001)

water ice spin ice local anisotropy <111>


Diffuse scattering

Short-range order







‣ pinch points in diffuse scattering pattern perfectly

reproduced by Monte Carlo analysis

Fennell et al., Science 326 415 (2009)

SF NSF total

ob

sca

l


Diffuse scattering

Short-range order







‣ pinch points in diffuse scattering pattern perfectly

reproduced by Monte Carlo analysis

‣ excitations interpreted as magnetic monopoles

Fennell et al., Science 326 415 (2009)


‣ SrGd2O4 containing natural Gd

‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1

‣ 50 K background subtracted

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 30 K

Short-range orderDiffuse scattering, RMC and mPDF


Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 30 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 30 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1


Diffuse scattering, RMC and mPDF


Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 20 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 20 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 14 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 14 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 10 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 10 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 6 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 6 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 4.1 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 4.1 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 3.2 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 3.2 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 2.4 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.4 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 2.2 K

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K

FT


‣ TN = 2.73 K

‣ 𝜆 = 0.5 Å, Qmax = 7 Å-1




Short-range order

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K



Short-range order

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K

3.45 Å



Short-range order

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K

3.54 Å3.45 Å

3.59

Å



Short-range orderF AF

Frandsen et al., Acta Cryst. A70 3 (2013)

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K

3.45 Å

3.54 Å

3.59

Å

3.88 Å

4.03

ÅDiffuse scattering, RMC and mPDF


Short-range orderF AF

Frandsen et al., Acta Cryst. A70 3 (2013)

3.45 Å

3.54 Å

3.59

Å

3.88 Å

4.03

Å

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K



I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�

<latexit sha1_base64="kawdHQwmyJilRGesczu/bZJ81oQ=">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</latexit>

17496 spins

Aij = Sxi S

xj

<latexit sha1_base64="2FmZKBHVKSPesPt0dbNO+2GT37Y=">AAAB+nicbVBNT8JAEJ3iF+JX0aOXRmLiibRqohcT1ItHDPKRYGm2ywIL222zu1VI5ad48aAxXv0l3vw3LtCDgi+Z5OW9mczM8yNGpbLtbyOztLyyupZdz21sbm3vmPndmgxjgUkVhywUDR9JwignVUUVI41IEBT4jNT9wfXErz8QIWnI79QoIm6Aupx2KEZKS56Zv/QS2h9fVDzaGla8fmvomQW7aE9hLRInJQVIUfbMr/t2iOOAcIUZkrLp2JFyEyQUxYyMc/exJBHCA9QlTU05Coh0k+npY+tQK22rEwpdXFlT9fdEggIpR4GvOwOkenLem4j/ec1Ydc7dhPIoVoTj2aJOzCwVWpMcrDYVBCs20gRhQfWtFu4hgbDSaeV0CM78y4ukdlx0TorO7WmhdJXGkYV9OIAjcOAMSnADZagChkd4hld4M56MF+Pd+Ji1Zox0Zg/+wPj8ARc5k+M=</latexit>

Bij = 2Szi S

zj � Sx

i Sxj

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‣ Ising anisotropy

‣

‣ 9x27x9 super cell, adapted to coherence volume on D4

gjpJ(J + 1)µB = 7.94µB

<latexit sha1_base64="Gj/agneM+vPYShmQaZ5sFEflDYY=">AAACCnicbZDLSsNAFIYn9VbrLerSzWgRKkJJtFBdCKVupKsK9gJNCJPppB07uTgzEUro2o2v4saFIm59Ane+jdM0C63+MPDxn3M4c343YlRIw/jScguLS8sr+dXC2vrG5pa+vdMWYcwxaeGQhbzrIkEYDUhLUslIN+IE+S4jHXd0Oa137gkXNAxu5Dgito8GAfUoRlJZjr4/cG4tccdl0ig1js2jieXHTv0CVsvnFZiyoxeNspEK/gUzgyLI1HT0T6sf4tgngcQMCdEzjUjaCeKSYkYmBSsWJEJ4hAakpzBAPhF2kp4ygYfK6UMv5OoFEqbuz4kE+UKMfVd1+kgOxXxtav5X68XSO7MTGkSxJAGeLfJiBmUIp7nAPuUESzZWgDCn6q8QDxFHWKr0CioEc/7kv9A+KZunZfO6UqzVszjyYA8cgBIwQRXUwBVoghbA4AE8gRfwqj1qz9qb9j5rzWnZzC74Je3jGxbpmJQ=</latexit>

Short-range orderDiffuse scattering, RMC and mPDF

SpinvertPaddison et al., J. Phys.: Condens. Matter 25, 454220 (2013)


Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 30 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 30 K

Spinvert fit

FT

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 20 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 20 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 14 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 14 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 10 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 10 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 6 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 6 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 4.1 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 4.1 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 3.2 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 3.2 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 2.4 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.4 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




FT0 1 2 3 4 5 6 7

-1

0

1

2

3

4

5

SrGd2O

4 2.2 K

Spinvert fit

0 2 4 6 8 10 12 14 16 18

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

SrGd2O4 2.2 K

Spinvert fit

Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj





Short-range order

I(Q) = C[µf(Q)]2 · 1

N

X

i,j

Aij

sinQrijQrij

+Bij

✓sinQrij(Qrij)2

� cosQrij(Qrij)2

◆�



‣




Aij = Sxi S

xj


Bij = 2Szi S

zj � Sx

i Sxj


0 5 10 15 20 25 30

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

spin-spin correlation functionDiffuse scattering, RMC and mPDF



Large-scale structuresSmall angle neutron scattering (SANS)

‣ Large-scale structures up to 5000 Å —> low q —> SANS

‣ Skyrmions (particle-like objects described as magnetic

hedgehogs)

‣ Flux line lattices in superconductors

Mühlbauer et al., Science 323 915 (2011)

taken from riken.jp

Dewhurst et al., Physica B 385 176 (2006)


Phonons and magnonsInelastic neutron scattering

‣ Lattice dynamics, atomic forces

‣ Spin waves, magnetic exchange parameters

Lynn et al., Phys. Rev. B 8 3493 (1973)

Senff et al., J. Phys.: Condens. Matt. 20 434212 (2008)

T H E E U R O P E A N N E U T R O N S O U R C ET H E E U R O P E A N N E U T R O N S O U R C E

I N S T I T U T L A U E L A N G E V I N

Documents

OSNS - Neutrons and X-rays in magnetism · 16th Oxford School on Neutron Scattering | Navid Qureshi THE EUROPEAN NEUTRON SOURCE Result: Diffraction pattern 0 20 40 60 80 100 120 140