NMR and field-induced magnetic ordered phases in the S =1 spin dimer system Ba 3 Mn 2 O 8

1. NMR and field-induced magnetic ordered phases in the S=1 spin dimer system Ba3Mn2O8 Stanford E. Samulon I. R. Fisher UCLA S. Suh SB FSU/NHMFL L. Lumata J. S. Brooks P. Kuhns A. Reyes LANL C. Batista

2. Ba3Mn2O8 Magnetic properties: spin gap =12.3K single layer coordination M. Uchida, et al. PRB 66 054429 (2002). c powder samples Trigonal structure→S=1 dimers arranged in layers with hexagonal coordination, oriented vertically in layers

3. T=650mK S=1 spin dimer compound with spin gap Electron counting→3d2, S=1 for Mn5+ ions  given by form for S=1 with dominant J0+interdimer interactions B closes spin gap. Two plateaus for T→0 corresp. to Sz=1,2 Uchida, et al., 2002 From M(B) -plateau separation a result of dispersive excitations linked to interdimer coupling

4. Jaime, et al., PRL (2004) BaCuSi2O6 In applying a magnetic field H>Hc1, possibility for various magnetic phases, qu. criticality- e.g., Magnetization plateaus in isolated dimers →spin liquid states=no broken symmetry coupled dimers Interdimer AF exchange→LRMO between the plateaus (order is in component transverse to field), finite T phase transitions and possibility for QCP →phase transition sometimes described as condensation of hard-core (no double occupancy) bosons. → BEC if rotational symmetry spontaneously broken

5. Ba3Mn2O8--this time S=1, with single-ion anisotropy D<>0, intralayer frustration… H/T phase diagram established by specific heat-several phases evident: At least 3 phases for H<Hc2 [Tsujii, et al., PRB 72 214434 (2005)] →S=1 dimers: model Hamiltonians allow for possibility of broken translational symmetry (fractional plateaus), and nearby supersolid phase(s). See, e.g., Sengupta and Batista, PRL (2007).

6. 3 phases identified by Tsujii, et al., PRB 72 214434 (2005) Broken symmetry phases between the plateaus from Cp, magnetocaloric effect [(Samulon, et al., Phys. Rev. B 77, 214441 (2008)]

7. What is to be learned from NMR? • Nature of broken symmetry phases I, II from spectra • Critical behavior in physical properties, such as: Tc(H-Hc1), order parameter Mt(H-Hc1), M(T,Hc1) • Correlations/fluctuations, characteristic of broken symmetries, near quantum phase transitions from relaxation I. A little more about Ba3Mn2O8 II. Basic 135,137Ba NMR observations for B(||,)c III. B||c IV. Bc

8. …frustration…? Phase I, B//c AF J1→intralayer FM order, interlayer AF order AF J2→=120° state (total spin zero in the plane) Compromise result: Spiral w/ <>120 ° (Uchida, et al.) BaCuSi2O6: interlayer frustration→2D Qu. Cr.

9. Cristian Batista’s model of phases I, II

10. Cristian Batista’s model of phases I, II

11. 135,137Ba NMR, I=3/2------2 isotopes • 135=432Hz/G, 135Q=0.18(10-24)cm2 • 137=472Hz/G, 137Q=0.28(10-24)cm2 • uniaxial point group symmetry for Ba(1,2) • 12 transitions total m=1: 2 isotopes • x 2 sites • x 3 transitions (I=3/2)

12. Evidence for incommensurate phase T=1.5K I (-) (+) • Ba(1) consistent with sinusoidal modulation of hyperfine field • Ba(2) symmetry breaking; 2 different field modulations

13. Evidence for incommensurate phase I • Ba(1) consistent with sinusoidal modulation of hyperfine field

14. Relevance of the hyperfine couplings Ba(2) (intra-layer) Acc=1.8T/B Aaa=2.8T/ B Ba(1) (inter-layer) Acc=4.8T/B Aaa=5.8T/ B non-zero anisotropic part Ba H0 Mn Mn …values way too big for direct dipolar

15. Chirality of triangles is relevant to spectrum seen by Ba(2)-situated in the middle of each but offset vertically Mn layer above Mn layer below

16. Ba(2)+ Couple dipole fields of 3 nearest Mn spins to Ba(2) Sinusoidal variation of longitudinal field for 120° state, + chirality Ba(2)- No variation of longitudinal field for 120° state, - chirality

17. With anisotropic coupling, introduces linewidth to the Ba(2-) site

18. Spectra, (B>Bc)  c, entering phase II: (incommensurate) Samulon, et al., PRB (2008) Phase II, Phase I near phase II …and maybe in REALLY High field range phase I? Goal: interpretation of spectra, phases Approach: Use Heff from (Cristian B.) and dipole couplings to Mn-spins to model spectral features from perspective of symmetry

19. Dipolar+contact interaction Dipolar interaction only ml=0.10 ml=0.10 ml=0.075 ml=0.075 ml=0.050 ml=0.050 ml=0.025 ml=0.025 ml=0.0 ml=0.0

20. 2nd feature Samulon, et al. Transverse mag. mT~[mL(1-mL)]1/2 Modulation of longitud. mL~mL full width Order parameter near QCP at edge of phase II:

21. Samulon, et al. Transverse mag. mT~[mL(1-mL)]1/2 Modulation of longitud. mL~mL Order parameter near QCP at edge of phase I: B//c

22. At the critical field, H=Hc1 • M(H~Hc1)~Td/z • B//c: d=3, z=2 • M~T3/2 • 2. Bc: • M~? • …to be determined B//c

23. At the critical field, H=Hc1 • B//c: d=3, z=2 • T1-1~T3/4 ? BEC case Variety of dynamical behavior in neighborhood of BEC QCP Orignac, Citro, Giamarchi, PRB 75, 140403 (2007)

24. Ba3Mn2O8 is an S=1 spin dimer compound where frustration, AF exchange interactions, and single-ion anisotropy each play a role in establishing field-induced quantum phases • By rotating the field, possibility for changing character of QCP from BEC (B//c) to Ising or… XY (?). • NMR is sensitive to transverse components of magnetization. I, II are incommensurate phases. NMR spectroscopy is consistent with phase II as easy-plane phase. • Order parameter follows expected form for QCP for both phases. mT~[H-Hc1]1/2. More complicated structure near boundary of I/II. • M(Hc1,T) for B//c consistent with BEC univerality class. • Dynamics on approach, as probed by T1-1, is not behaving in a simple way-a result of incommensurability?

25. 12T 11.5T 11T 10.5T Spectra going into phase I for Bc “Complicated” spectra moving from II into I