Magnets without Direction Collin Broholm Johns Hopkins University and NIST Center for Neutron Research  Introduction  Moment Free Magnetism in one dimension  Higher dimensional MFM  Frustrated origins of MFM  Interesting aspects of MFM  Conclusions

G. Aeppli P. Bischer Y. Chen J. F. DiTusa D. V. Ferraris C. D. Frost T. Ito T. Lectka K. Oka Acknowledgements R. Paul D. H. Reich J. Rittner M. B. Stone H. Takagi M. Treacy G. Xu H. Yardimci I. Zaliznyak NIST Center for Neutron Research ISIS Facility, Rutherford Appleton Laboratory National Science Foundation DMR Civilian Research and Development Foundation

Rutgers 10/17/01 Many electrons, few magnetic materials Filled shell in solid: Ti V Cr Mn Fe Co Ni Cu Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm U Np Pu Am Cm Partially filled shell in solid:

Rutgers 10/17/01 Magnetization of Solid with unfilled Shells Susceptibility data for paramagnetic salt Spin susceptibility diverges as T 0 FeBr(C 44 H 28 N 4 ) Dilute Fe in organic matrix FeBr(C 44 H 28 N 4 ) Dilute Fe in organic matrix

Rutgers 10/17/01 S=1/2 Coulomb + Pauli = Heisenberg Coulomb interactions plus Pauli principle split 4-fold spin degeneracy The level scheme is reproduced by Heisenberg Exchange Hamiltonian |J| S=1/2 |J| Singlet gnd. State: J > 0 Triplet gnd. State: J < 0

Rutgers 10/17/01 Interactions orient moments Ferromagnetic EuO Antiferromagnetic KNiF 3

Rutgers 10/17/01 Unconventional magnetism in NENP  Negative Curie Weiss temperature indicates AFM interactions  No phase transition and  Negative Curie Weiss temperature indicates AFM interactions  No phase transition and

Rutgers 10/17/01 A can of magnetic worms Magnetic interactions link spins in chains Magnetic interactions link spins in chains Ensemble of Quasi-one-dimensional Antiferromagnets chains Ensemble of Quasi-one-dimensional Antiferromagnets chains NENP=Ni(C 2 H 8 N 2 ) 2 NO 2 ClO 4

Rutgers 10/17/01 1. Assume Neel order, derive spin wave dispersion relation 2. Calculate the reduction in staggered magnetization due to quantum fluctuations 3. If then Neel order is an inconsistent assumption diverges if on planes in Q-space When is the Neel state unstable? A putative D=1 Neel state has soft planes and so is unstable

Moment Free Magnetism averts infrared catastrophe Y 2 BaNiO 5 Ajiro et al. (1989) 

Rutgers 10/17/01 Unconventional magnetism in PHCC  Negative Curie Weiss temperature indicates AFM interactions  No phase transition and  Negative Curie Weiss temperature indicates AFM interactions  No phase transition and

Rutgers 10/17/01 b c Structure is “consistent” with spin chains PHCC = C 4 H 12 N 2 Cu 2 Cl 6 a c Cu Cl C N

Rutgers 10/17/01 Magnetic Neutron Scattering The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

Rutgers 10/17/01 SPINS cold neutron triple axis spectrometer at NCNR

Rutgers 10/17/01 PHCC is magnetically two dimensional Dispersion to “chains” Not chains but planes

Rutgers 10/17/01 Unconventional magnetism in CuHpCl  Negative  CW indicates AFM interactions  No phase transition and  Spin ladder model consistent with  (T)  Negative  CW indicates AFM interactions  No phase transition and  Spin ladder model consistent with  (T) Putative Spin ladder model for CuHpCl

Rutgers 10/17/01 CuHpCl hydrogenous single crystals

Rutgers 10/17/01 ….But there is dispersion to “ladder” Q // to chainQ to chain  ….and there are two modes when ladder gives only one

Rutgers 10/17/01 A frustrated route to Moment Free Magnetism? Magnetic Frustration: All spin pairs cannot simultaneously be in their lowest energy configuration Weak connectivity: Order in one part of lattice does not constrain surrounding spins Frustrated Weakly connected

Rutgers 10/17/01 1. Assume Neel order, derive spin wave dispersion relation 2. Calculate the reduction in staggered magnetization due to quantum fluctuations 3. If then Neel order is an inconsistent assumption diverges if on planes in Q-space When is the Neel state unstable? Frustration can produce local soft modes that destabilize Neel order Frustration can produce local soft modes that destabilize Neel order

Rutgers 10/17/01 Neutrons can reveal frustration The first  -moment of scattering cross section equals “Fourier transform of bond energies” For a powder sample we know only Q=|Q|  high Qd plateau measures ground state energy  negative terms are “frustrated bonds”  bond energies are small if small   drrd SSand/or J

Rutgers 10/17/01 Neutrons reveal frustration in CuHpCl Peak to plateau ratio Mixed signs for bond energies Frustration

Rutgers 10/17/01 Structure of CuHpCl CuHpCl is hydrogen bonded crystal of Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 Molecules possess approximate centro symmetry Exchange interaction within molecule |J|<1 meV

Two lattices from H-bond exchange b

Rutgers 10/17/01 Building an enigma Dispersion throughout a-c plane Spin liquid on 3-dimensional lattice

Rutgers 10/17/01 Detailed bond energy distribution a* c* (101) (100) (001) Point size First moment

Rutgers 10/17/01 Frustrated three dimensional spin liquid

Significance of findings so far  Neutron scattering required to classify quantum spin liquids  Systems thought to be one dimensional may represent a richer class of materials  Experimental realizations of spin liquids were sought, not found, in symmetric frustrated magnets  Spin liquids may be more abundant in complex geometrically frustrated lattices

Rutgers 10/17/01 Field induced T=0 phase transition PHCC

Rutgers 10/17/01 Reentrant behavior close to critical point 3 D long range order Moment free

Rutgers 10/17/01 Impurities in a quantum spin liquid Ca 2+ Y 3+ Mg 2+ on Ni 2+ sites finite length chains Ca 2+ on Y 3+ sites mobile bond defects Mg Ni Kojima et al. (1995) Mg Ca 2+ Pure

Rutgers 10/17/01 Holes dressed by spin polarons Y3+Y3+ Ni O FM Ca 2+

Rutgers 10/17/01 Transport in Ca doped Y 2 BaNiO 5 T. Ito et al. Submitted to PRL (2001) Charge Transfer excitation Charge polaron 1D conductivity, no Charge ordering

Rutgers 10/17/01 Holes in a quantum spin liquid  Experiments in one dimensional spin liquids show holes dressed by spin polaron  However, impurities localize charge in one dimension  Some organic materials can be doped and conduct in Field Effect Transistors [Schon et al. Science (2000)]  Moment free organo-metallic systems should have interesting transport properties if they can conduct. PHCC

Conclusions  Spin systems with a gap can be mistaken for being quasi-one-dimensional  Two and three dimensional moment free magnetism found in PHCC and CuHpCl  Neutron scattering reveals frustrated bonds in the corner-sharing triangular clusters of these materials  Hypothesis: Moment free magnetism may be a common state of interacting spin systems with triangular motif and weak connectivity  Idea: Interesting transport properties may exist if the materials can be doped