Neutron scattering as a tool to understand quantum magnetism: Magnetism and the European Spallation Source Pascale Deen. ESS: Senior Scien,st Adjunct associate professor: Niels Bohr Inst., Copenhagen University 1

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron scaBering and magne,sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 2

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne-sm : a very basic overview • Neutron scaBering and magne,sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 3

Magnetism: Ferromagnetism hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 6th Century BC Lodestone Magnet: lodestones found in Magnesia, Turkey Natural magnets Used early for navigation (Fe3O4 + Fe2O3 ) Ferromagnet electromagnets, electric motors, generators, transformers, magnetic storage, credit cards ….. 4

Magnetism: Ferromagnetism hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Signatures Ferromagnet electromagnets, electric motors, generators, transformers, magnetic storage, credit cards ….. 5

Magnetism: Antiferromagnetism, a hidden order hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Signatures MnO ∑μ (T

hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Antiferromagnetism, theoretical debate. Louis Néel Lev Landau •mean field theory •quantum paramagnet, fluctuating •AF is described as magnetic spins in opposition order on two sublattices. •no time averaged moment. •Macroscopic picture. •Associated with quantum order 7

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 8

Neutrons for magne,c and electronic phenomena hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 9

hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Calculate scaBering probabili,es Calculate the interaction potential (Nuclear, magnetic, incoherent contributions) No equivalent interaction for x-rays (or any other probe) 10

Neutron Scattering hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Intensity α S(Q, ∆ω) = Theory Intensity = Experiment Separate from Probe Absolute units 11

Neutron Scattering hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Intensity α S(Q, ∆ω) = Theory Intensity = Experiment Differential neutron cross section : Separate from Probe Sum of all processes in which Absolute units (1) State of the scatterer changes from λ to λ’ (2) Wavevector of the neutron changes from k to k’ (3) Spin state of the neutron changes from s to s’ (4) within a solid angle Ω 12

Magnetic Neutron Scattering hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Dy 3+ International Tables of crystallography C. J.P.Brown. F(Q) V = μ.B = μ(BS+BL) V ∝ 1/2 g F(Q): Only scattering at low Q V ∝ δ𝛼β - Q𝛼Qβ: moments normal to Q contribute 13 Q = 4πsinθ/λ

Neutrons Interac,ng with maBer hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 1994 Nobel prize: for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter Development of neutron diffraction Development of neutron spectroscopy Where atoms/spin are What atoms/spins do 14

NeutronshBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Interac,ng with maBer Inelastic neutron scattering 80 K 300 K Where atoms are How they move 15

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac-on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 16

Neutrons Interac,ng with maBer hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 1994 Nobel prize: for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter Development of neutron diffraction Where atoms/spin are 17

NeutronshBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Interac,ng with maBer 80 K 300 K Where atoms are 18

Elastic scattering/Diffraction Braggs law: nλ = 2 dhkl sin(θ) hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Q = 2π/dhkl Q = 4π √[(h2+k2+l2)/a2] (cubic) (powder!) (0 0 2) Ki (1 1 0) (1 0 2) Q Kf Static behaviour Only interested in atomic positions (Qx, Qy, Qz) Static correlations 19

Elastic scattering/Diffraction Braggs law: nλ = 2 dhkl sin(θ) hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Q = 2π/dhkl Q = 4π √[(h2+k2+l2)/a2] (cubic) (powder!) (0 0 2) Ki (1 1 0) (1 0 2) Q Kf Sta,c behaviour Only interested in atomic posi,ons (Qx, Qy, Qz) Sta,c correla,ons 20

Form factors Neutrons interact with hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 1. Atomic nuclei (strong nuclear force — short-range) 2. Magnetic fields from unpaired electrons (dipole-dipole interaction) X-rays Neutrons f(electrons) b Nuclear Magnetic & also paramagnetic scattering sin(θ)/λ sin(θ)/λ 21

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac,on – Inelas-c neutron sca:ering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 22

Neutrons Interac,ng with maBer hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 1994 Nobel prize: for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter Development of neutron spectroscopy What atoms/spins do 23

NeutronshBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Interac,ng with maBer Inelastic neutron scattering How they move 24

Inelastic scattering hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Collective excitations: phonons (sound) Energy: dynamic information Interaction Strength k = 2π/2d k = 2π/4d λ = 2d λ = 4d k=0 -π/d 0 -π/d λ=d k = 2π/λ: spatial information 25

Inelastic scattering Collective excitations: phonons hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Phonons in diamond J.L. Warren et al. Phys.Rev. 158 805 (1967) 26

Inelastic scattering hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Collective excitations: magnons Ferromagnetism FM Spin wave Antiferromagnetism AFM Spin wave https://www.ill.eu/fileadmin/user_upload/ILL/1_About_ILL/Films_and_animations/Animations/Scientific-animations/Magnons/activity/Magnetic_phases_and_Magnons.html 27

Collective excitations: magnons hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Ferromagne,c spin waves 𝒽ω(q) = 4SJ(1-cos(qa)) Energy: dynamic information k = π/d 8JS λ = 2d k = 2π/4d λ = 4d kk ==00 -π/d 0 -π/d k = 2π/λ: spatial information λ=d 28

Collective excitations: magnons hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg An,ferromagne,c spin waves 𝒽ω(q) = 4SIJIIsin(qa)I Energy: dynamic information 4JS k = π/d λ = 4d k = 3π/4d λ = 4d/3 k = π/d π/2d π/d π/3d λ = 2d k = 2π/λ: spatial information 29

Collective excitations: FM vrs AFM hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Sm0.55Sr0.45MnO3 Y. Endoh, H. Hiraka, Y. Tomioka, Y. Tokura, N. Nagaosa and T. Fujiwara: Phys. Rev. Lett. 94 (2005) 17206. 30

hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg S(Q,ω) on a single crystal = 4 D space (Qx,Qy,Qz, E) Strength of the exchange interactions / anisotropy Information on the spin structure 31

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa-on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 32

hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg History of neutron polarisation analysis Phys. Rev. 181, 920 (1969) neutron spin is either spin up or spin down 1st comprehensive experimental work (Bragg scattering, Incoherent scattering, spin wave scattering) Illustration of Polarisation Analysis 33

History of neutron polarisation analysis hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg neutron spin is either spin up or spin down 34

History of neutron polarisation analysis Moon, Riste Koehler, Phys. Rev. 181 (1969) 920. hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg MnF = simple antiferromagnet 2 Measurement of formfactor above Tn Unpolarised off Flipper off Flipper on 35

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 36

2 examples: hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Elucidate typical neutron scaBering signals today YMnO3 Multiferroicity 3D quantum spin liquid in PbCuTe2O6 Ferrromagnetic & Ferroelectricity Interplay between magnon & phonons Phys. Rev. B 97, 134304 (2018) NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-15594-1

YMnO3 Multiferroicity hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg ∆E = 0 - 30 meV J1, J2 Anisotropy M/P Hybridisation Phys. Rev. B 97, 134304 (2018) 38

YMnO3 Multiferroicity hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg ∆E = 0 - 30 meV J1, J2 Anisotropy M/P Hybridisation Need to study broad region of S(Q, omega) High energy resolution Signal to noise > 104 Phys. Rev. B 97, 134304 (2018) 39 Interplay between phonons and magnon

Quantum Spin liquids hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Understand, drive and manipulate quantum effects https://scitechdaily.com • Coherence, entanglement, superposi,on, quantum transport. • Quantum compu,ng x ZnCu3(OH)6Cl2 Signatures: •A lack of broken symmetry •No magne,c order (S = 1/2) •Frac,onalised excita,ons 40

Volborthite (Cu3V2O7(OH)2·2H2O) (powder) hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg S = 1/2 Kagome Heisenberg antiferromagnet 25 Total Scattering Intensity (arb.units) 20 Nuclear Scattering Spin incoherent Magnetic Scattering 15 10 5 0 0.5 1 1.5 2 2.5 3 Wavevector transfer (Å-1) Phys. Rev. B 84, 172401 XYZ neutron polarisa,on analysis, D7 @ ILL, T = 50 mK 41

Spin liquid? A lack of broken symmetry hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg No magne,c order (S = 1/2) Magne,c ScaBering only, T = 50 mK Intensity (arb.units) 1 0.8 0.6 0.4 0.2 SRO - RVB or VBS or neither ? 0 0.5 1 1.5 2 2.5 3 Wavevector Transfer (Å-1) Determina,on not possible without Polarisa,on Analysis 42

A 2D spin liquid state in hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Herbertsmithite ZnCu3(OD)6Cl2 Nature 492, 406 ,Nature Phys.12, 942 Inelastic neutron scattering measured along symmetry directions and at high symmetry locations. T = 1.6 K. NB: No well defined excitations & correlations. Fractionalised excitations. 43

A 3D spin liquid state in hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg PbCuTe2O6 44

Overview hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg • Magne,sm : a very basic overview • Neutron sca:ering and magne-sm – Diffrac,on – Inelas,c neutron scaBering – Polarisa,on analysis • Recent examples of magne,c states of maBer (Quantum behaviour) • Overview of some instruments at ESS relevant to magne,sm 45

Neutron scaBering at ESS hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Current: Fe-arsenide single crystals Small single crystals: high quality, few imperfections. High pressure synthesis:global behaviour. Study many stochiometries 2.0 mm Study high absorption isotopes. Magnetic multilayers. AJ Drew et al., Nature Materials 8 (2009) 310 ZTA:%W.G.%Marshall%(ISIS),%unpublished% R.%Iizuka%et%al.,%High%Press.%Res.%(2013)% α ∼ ± 15°# Strongly correlated physics: High pressure, high magnetic field and low temperature 7 GPa : W.G. Marshall (ISIS) S. Klotz, unpublished R. Iizuka et al.46 simultaneously. Out of equilibrium physics High Press. Res. (2013)

Long pulse versus short pulse of ESS hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 15 x1013 ESS 5 MW! 2015 design! Brightness (n/cm2/s/sr/Å) λ = 5 Å! 10 5 JPARC! 0.3-1 MW SNS! 1-2 MW ISIS TS1! ISIS TS2! 128 kW 32 kW! ILL 57 MW 0 1 2 3 4 time (ms) 47

ESS Instrument suite (Phase 1) 2023-2025 hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg 48

ESS Instrument suite (Phase 1) hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg Novel magnetic states Protons 49

MAGIC: Diffraction 17 hBp://www.sciencevillage.com/assets/ess-web-1024x735.jpg % 59 24 % % •High flux: up to 4x109 n/s/cm2 • Polarised over 0.62 Å • Flexible longitudinal and transverse resolutions • Focusing capabilities: study of sub-mm3 samples 50

CSPEC The Cold Chopper spectrometer of the ESS Increased flux with reduced noise Ei = 2 - 20 Å Instrument length = 160 m Bandwidth = 1.72 Å Energy resolution = 1 - 5 % of Ei Sample size 1x 1 cm2 & 4 x 2 cm2 Polarisation analysis 51

CSPEC The Cold Chopper spectrometer of the ESS (1) 160 m = more flux. In-situ/kinetic phenomena. 1 min resolution. Photon 1.72 Å (CSPEC) Sample 1.6 M-chopper frequency = 336 Hz Energy Resolution, (%) 1.5 1.4 1.3 8 Å (LET, AMATERAS, CNCS ) 1.2 ESS pulse 1.1 2 4 6 8 10 3 Å = E min = 5.67, E max = 16.9 meV 6 Å = E min = 1.76, E max = 3.02 meV 8 Å = E min = 1.06, E max = 1.58 meV - Add pulses when possible - gain in flux 52

CSPEC The Cold Chopper spectrometer of the ESS (2) 160 m & cold neutrons & spallation source = less noise. S/N 105. Cold neutrons: S-Bender Sample Sample No ambient background Reactor Spallation 53

CSPEC The Cold Chopper spectrometer of the ESS Guide shielding Guide shielding Detector tank: 2.49 Steradian - see all of S(Q, omega) Guide production : TUM Ready December 2022. 54

CSPEC The Cold Chopper spectrometer of the ESS E01 experimental Hall https://europeanspallationsource.se/instruments/cspec 55

ESS December 2020 We welcome you all soon. 56