Spin dynamics of S=1/2 Hesienberg AFM chains in magnetic fields. Sergei Zvyagin

Transcription

1 Spin dynamics of S=1/2 Hesienberg AFM chains in magnetic fields Sergei Zvyagin Dresden High Magnetic Field Laboratory (HLD) Helmholtz-Zentrum Dresden-Rossendorf Dresden, Germany

2 In collaboration with Experiment: M. Ozerov, J. Wosnitza Dresden HMF Lab/HZDR, Dresden, Germany E. Čižmár Safarik University, Koisice, Slovakia J. Krzystek - NHMFL, Tallahassee, USA Samples: R. Feyerherm, HZB-ME, Berlin, Germany Theory: O. Kolezhuk Institute of Magnetism, Kiev, Ukraine S.R. Manmana UC, Boulder, USA F. Mila EPFL, Lausanne, Switzerland 1. S.A. Zvyagin, A.K. Kolezhuk, J. Krzystek, and R. Feyerherm, Excitation hierarchy of the quantum sine-gordon spin chain in strong magnetic field, Phys. Rev. Lett. 93, , S.A. Zvyagin, A.K. Kolezhuk, J. Krzystek, and R. Feyerherm, Electron Spin Resonance in sine-gordon spin chains in the perturbative spinon regime, Phys. Rev. Lett. 95, , S.A. Zvyagin, E. Čižmár, M. Ozerov, J. Wosnitza, R. Feyerherm, S.R. Manmana, and F. Mila, Field-induced gap in a quantum spin-1/2 chain in a strong magnetic field, Phys. Rev. B 83, (R), 2011

3 ESR = Electron Spin Resonance EPR = Electron Paramagnetic Resonance EMR = Electron Magnetic Resonance III. Magnet II. Detector IV. Probe I. Radiation source, cm, mm, sub-mm range

4 1944: discovery of EPR by Evgeny Zavoisky (Kazan University, USSR) 1946: further development of EPR by Brebis Bleaney (Oxford University, UK)

5 First EPR spectrometer

6 10 MHz, 7.5 Oe MAGNET SAMPLE HEATER RF HEAD

7 1950s: rapid development of microwave technology (radar techniques) 50-60s: Major contributions toward the ESR spectrum interpretation (laser technologies) Late 50s: pioneering high-field ESR works of M. Date in Japan 60-70s: ESR in USSR, France and Germany 90s: ESR in UK, USA, Hungary, Italy, etc. ESR = Electron Spin Resonance = EPR = Electron Paramagnetic Resonance = EMR = Electron Magnetic Resonance

8 Commercially available spectrometers: 1-2 GHz (L-band) 2-4 GHz (S-band) 8-10 GHZ (X-Band) 35 GHz (Q-band) 95 GHz (W-band) 263 GHz (mm-wave) Major producers: Bruker Corporation (Germany) JEOL (Japan) Fixed parameters: frequency Variable parameters: field, temperature, angle Lack of commercially-available tunable-frequency (multiple-frequency) ESR spectrometers

9 THz Gap X-band Bruker 9 GHz Microwave Network Analyzer GHz Free Electron Laser FZD THz Gunn/Schottky Diodes/VDIs GHz Backward Wave Oscillators GHz Available at HLD: frequency range: 9 GHz 75 THz (quasicontinuously covered)

10 High-field ESR lab at the Dresden High Magnetic Field Laboratory Mike Ozerov BWO FT-FIR spectrometer 16 T SC magnet

11 Diversity of low-d magnets J J N J J 1 J 2 J l J r J l J r J 1 J 2 Ideal playground for testing various theoretical concepts

12 Uniform S=1/2 Heisenberg chain the simplest model system The excitation spectrum is formed by spinons J J H ( z ) n n+ 1 B = S S J gµ HS n

13 Inelastic neutron scattering in S=1/2 Heisenberg chain Cu-Pyz π + 2π m Stone et al. (2003)

14 S=1/2 Heisenberg chain with alternating g-factor or DM interaction B J Field-induced staggered moment

15 Staggered-field effect in Copper Pyrimidine Dinitrate Chem. formula: [PM Cu(NO 3 ) 2 x(h 2 0) 2 ] n Spin-spin interaction: J = 36 K B R. Feyerherm et al. (2000)

16 Oshikawa and Affleck (2002) Cu-PM: linewidth vs temperature Cu-PM: g-factor vs temperature

17 Influence of the field-induced staggered moment on ESR line-width and g-factor shift Experiment: Blue symbols Theory: Oshikawa and Affleck (2002) Linewidth [mt] Linewidth [mt] Linewidth [mt] a) b) c) Temperature [K] 184 GHz 93.1 GHz 9.4 GHz g-factor Linewidth [T] GHz Temperature [K] Field [T] c = 0.08 h~ch B

18 Effective spin Hamiltonian: uniform + staggered field H ( % % % % ( ) ) z % x n n+ n s n J S S HS h S n eff = 1 1 n xt, ( ) Spin operators can be represented through a phase field relative to incommensurate quasi-long-range order with Lagrangian density L 2 cos = % % + % ( ) ( ) ( ( ) ) tφ xφ Chs πr H φ φ % This is sine-gordon model with interaction term proportional to h s Spectrum consists of 1 Solitons, anti-solitons Bound states (breathers) H% h 2 RH ( ) M J 2 s π % = A J J M = 2M sin nπξ H /2 n ( ) ( ) Oshikawa and Affleck (1997)

19 The Sine-Gordon equation can be solved exactly: soliton, antisoliton and soliton-antisoliton bound states (breathers).

20 Effective spin Hamiltonian: uniform + staggered field H ( % % % % ( ) ) z % x n n+ n s n J S S HS h S n eff = 1 1 n xt, ( ) Spin operators can be represented through a phase field relative to incommensurate quasi-long-range order with Lagrangian density L 2 cos = % % + % ( ) ( ) ( ( ) ) tφ xφ Chs πr H φ φ % This is sine-gordon model with interaction term proportional to h s Spectrum consists of 1 Solitons, anti-solitons Bound states (breathers) H% h 2 RH ( ) M J 2 s π % = A J J M = 2M sin nπξ H /2 n ( ) ( ) Oshikawa and Affleck (1997)

21 Effect of the staggered field Broken translation symmetry due to alternating g-tensor and DM interaction Staggered magnetization Field-induced gap!

22 Field-induced gap in Copper Pyrimidine Dinitrate Should we try to probe the gap DIRECTLY?

23

24 429.3 GHz, 1.4 K Transmittance [arb. units] C3 C1 C2 U1 B3 S DPPH B Magnetic Field [T]

25 750 Frequency (GHz) Magnetic Field (T) c = 0.08 h~ch Oshikawa and Affleck, PRL 79, 2883 (1997) Essler, PRB 59, (1999) Affleck and Oshikawa, PRB 60, 1038 (1999); ibid. 62, 9200 (2000)

26 S.Z. et al C3 C2 C1 U1 Soliton Breather Frequency (GHz) Breather 2 Breather Magnetic Field (T) A complete set of solutions of the sine-gordon equation for a quantum spin chain - soliton and three breathers - has been observed. Excellent agreement with the theory. What happens in higher magnetic fields?

27 Transition into fully spin-polarized phase. Magnetization and the gap behavior. Sine-Gordon phase SOLITONS & BREATHERS Fully spin-polarized phase MAGNONS J J No further development of the transverse staggered magnetization. Growing of the longitudinal magnetization - a dip H sat = 48.5 T (for Cu-PM) Fouet et al., (2007) H sat

28 Pulsed-field facility at the Dresden High Magnetic Field Laboratory in Dresden-Rossendorf Available for users: Magnetization El. Transport Ultrasound ESR Magnetostriction T B (T) t (ms)

29 Transition into fully spin-polarized phase. Magnetization and the gap behavior. Sine-Gordon phase SOLITONS & BREATHERS Fully spin-polarized phase MAGNONS J J No further development of the transverse staggered magnetization. Growing of the longitudinal magnetization - a dip H sat = 48.5 T (for Cu-PM) Fouet et al., (2007) H sat

30 Frequency (GHz) Transition into fully spin-polarized phase. Field-induced gap behavior (calculations) Cu-PM DMRG calculations c = 0.08 Magnon H sat = 48.5 T Breather Magnetic Field (T)

31 Blue line: theoretical predictions Frequency (GHz) C1 Soliton C2 U1 C3 Breather 3 Magnon Breather 2 H sat Breather Magnetic Field (T)

32 ESR in Cu-PM in pulsed magnetic fields

33 Blue line: theoretical predictions Frequency (GHz) C1 Soliton C2 U1 C3 Breather 3 Magnon Breather 2 H sat Breather Magnetic Field (T)

34 Open symbols: pulsed-field results Frequency (GHz) C1 Soliton C2 U1 C3 Breather 3 Magnon Breather 2 H sat Breather Magnetic Field (T)

35 CONCLUSIONS 750 C3 C2 C1 U1 Soliton Breather 3 The universality of the sine-gordon formalism has been demonstrated, this time for quantum spin chains. A complete set of solutions of the sine-gordon equation for a quantum spin chain - soliton and three breathers - has been observed A characteristic ESR parameter behavior (linewidth, resonance field shift) at the spinon-soliton crossover has been observed. The soliton-magnon crossover has been observed in Cu-PM for the first time. All the obtained data were described using the same set of spin-hamiltonian parameters. Excellent agreement with theory was obtained. g-factor Frequency (GHz) Frequency (GHz) Magnetic Field (T) C2 C3 C1 Soliton U1 Breather 3 Breather GHz Temperature [K] Magnon Breather 2 Breather Breather 1 H sat Magnetic Field (T)

36 Thank you and organizers!