Quantum Magnetism. P. Mendels Lab. Physique des solides, UPSud From basics to recent developments: a flavor

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1 Quantum Magnetism P. Mendels Lab. Physique des solides, UPSud From basics to recent developments: a flavor Quantum phase transitions Model physics for fermions, bosons, problems Playground for new concepts, exotic states Frustration spin liquids

2 1/ Néel state: a well-known (Q) case H J ij S i. S, J j ij 0 Néel Landau T N ~q q T J sets the energy scale of the problem T

3 Néel state: a conventional (Q) case Neutrons: Fourier tranform of spin-spin correlation function S i. S j e r i r j / ; Magnons = bosons (S=1)

4 Playground: localized moments Quantum materials: u 2+, V 4+ S=1/2

5 The u 2+, S=1/2 world b

6 uo 2 F plane e - hole nderson uprates Strange metal F Pseudogap Superconducting doping F order at T=0, reduced moment % S=1/2 (fluctuations)

7 From superconducting cuprates to novel Fe pnictides e - hole uprates Organic superconductors Fe-Pnictides Strange metal F Pseudogap F Superconducting SUPR doping pressure 0.05 doping 0.15

8 Intermediate cases: from 1D to 2D Spin ½ chain Sr 2 uo 3 2D planes YBa 2 u 3 O 6 La 2 uo 4

9 Intermediate cases: from 1D to 2D Spin ½ chain Sr 2 uo 3 Spinons : S=1/2 excitations!

10 Intermediate cases: from 1D to 2D Spin ½ chain Sr 2 uo 3 J Isolated Spin Ladders Sru 2 O 3 J oupled Spin Ladders Biu 2 PO 6 2D planes YBa 2 u 3 O 6 La 2 uo 4

11 Strong coupling ladders: dimer physics Excitations = triplons: gapped in zero field (J) DE=J

12 pplying a field: quantum critical point The gap vanishes for a critical field:q transition mapping to bosons or fermions physics S=1 DE S=0 H H c

13 Triplons = bosons; above Hc oupled ladders: BE: Tlul 3 BauSi 2 O 6 T. Giamarchi et al, Nature Physics (2008)

14 Triplons Saut de hopping triplons Inter-dimer interactions

15 BE in coupled ladders Triplons = bosons

16 BE in BauSi 2 O 6 Low T, High Field: quite challenging

17 Perturb to reveal!

18 Spin textures: spinless defects Spin 1 hain Y 2 BaNiO 5 Spin ½ hain Sr 2 uo 3 Gap 6 Gapless ~1/T J Spin-Peierls hain ugeo 3 Gap J Isolated ladders Sru2O3 Doped high Tc cuprates Dimerisation Gap 7 Pseudo Gap Zn S=1/2 S=0

19 Model systems, new grounds states, new materials, extreme expts How to destabilize a Néel state? Hamiltonien Heisenberg: H J d=1: no gap for S=1/2, gap for integer S Fractional excitations Field induced quantum phases. S, J d>1: frustration of interactions geometry of the network Exotic ground states: spin liquids, spin ice fractional excitations ij S i j ij 0

20 FRUSTRTION: pair interactions non satisfied! Disorder : Spin glasses (e.g. umn) No disorder : Geometric Frustration? NETWORK GEOMETRY : Triangular based lattice F coupling? J 2 J 1? INTERTIONS GEOMETRY: 2nd n.n. interactions J 2 / J 1 =0.5, J 1 (F)

21 1973 lassical % Quantum B S Néel S S B 0 RVB nderson (Mat. Res. Bull., 8, 153, 1973) Fazekas et nderson (Philos. Mag., 30, 423,1974)

22 KGOME: a popular japanese basket! KGOME: a lattice of corner sharing triangles

23 Quantum: on-going research: Exact diagonalizations Energie Triangular Edge sharing geometry Kagome orner sharing geometry <J/20 Fundamental Néel S=0 1 2 S=0 1 2 Fundamental spin liquid Néel ontinuum of singlet excitations 1998

24 B B B B B B B B B B B B S S S Soft modes Macroscopic degeneracy lassical kagome lattice

25 From dimers to spin liquids RVB

26 2005 Herbertsmithite: Znu 3 (OH) 6 l 2 u 2+, S=1/2

27 The first example of a quantum kagome antiferromagnet perfect kagomé lattice no freezing at least down to J/4000 -> renewal ofthe search for scenarios for the kagome ground state Sciences, perspectives sept 2008

28 Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high Tc problem where significant progress has been made recently. (P.. Lee) Short range RVB Long range RVB

29 What is a quantum spin liquid? What are the different types of QSL? What are the simplest models with a QSL ground state? Do QSL exist in nature? Which other frustrated exotic states?

30 Highly Frustrated Magnetism orner sharing geometry: Kagomé (2D), hyperkagome or pyrochlore (3D) lattice «perturbations» (anisotropy, dipolar interaction, n.n. interactions, dilution) -

31 Superconductivity: (Everywhere!) hains, Ladders: (Th) Roux, Jolicoeur (LPTMS, Orsay) (Exp) Bobroff (LPS, Orsay) Horvatic (LNMI, Grenoble) Quantum frustration: (Th) Misguich, Messio (IPhT, Saclay) LeHur (PhT X) Lhuillier (LPTM, PVI) epas, Ralko (Néel, Grenoble) (Exp) Mendels, Bert (LPS, Orsay) (Néel, Grenoble) lassical frustration: (Th) Lacroix, anals (Néel Grenoble) Holdsworth (ENS Lyon) (Exp) Mirebeau, Petit (LLB, Saclay) (Néel, Grenoble) Extreme T, H, p conditions. Local techniques: NMR, µsr. Macroscopic Techniques Large scale facilities: neutrons, muons, high fields New concepts, challenging models, challenging techniques

32 Some introductory papers J J T.Giamarchi, h. Ruegg, O. Tchernyshyov, Nature Physics 4, 198 (2008) H. lloul, J. Bobroff, M. Gabay and P. Hirschfeld, Rev. Mod. Phys. 81, 45 (2009) J. Bobroff, nnales de Physique, 30, 1 (2005): Impuretés et systèmes corrélés S. Sachdev, Nature Physics 4, 173 (2008): Quantum magnetism and criticality B. Levy, Physics Today, p16, Feb 2007 L. Balents, Nature 464, 199 (2010) F. Bert, P. Mendels, O. épas and. Lhuillier: à paraître dans les Images de la Physique, voir