Electron Spins Resonance and Anitferromagnetic Resonance in Correlated Electron Systems:
LaMnO₃, La₂CuO₄ and NaNiO₂

• Absorption by electron spins when ħw₀=  2m_BH or w₀=  g(m_B/ħ)H   ; g  ~ 2 or w₀=  gH
• Dissipation described by complex susceptibility c"=Imc= c₀w₀T₂ / 2[1+(w-w₀)²T₂²]
• Needs unpaired electron (paramagnet, metal, spin label)
• Resonance line width, integral, splitting, position measures interaction of electrons, local environment, internal magnetic and exchange fields etc.
  • "Traditional" ESR
    • Typical: f=9GHz, H=0.35Tesla
    • Resonant cavity
    • Conventional microwave source
  • High field ESR:
    • Superconducting magnet (9Tesla - 18Tesla)
    • IR laser, Gunn diode etc. source
  • Pulsed ESR:
    • Holczer/Bruker
  All of the above are restricted to a single frequency, or a limited number of fixed frequencies

• Magnet: Oxford Instruments, 16Tesla, max 37 mm sample size
• Temperature: 1.3K-300K
• Spectrometer: Sciencetech, Martin-Puplett, 2cm^-1 to 2000cm^-1 , 0.01cm^-1 resolution, works with internal and external sources

• Coupling to light source
• Coupling between magnet and spectrometer
• Sample holder, support structure, safety devices

• Parent compound of CMR materials
• Distorted perovskite structure
• Mn sites have localized spins, undregoes antiferromagnetic ordering at 145K
• Spins are ferromagnetic in ab plane, AF in c direction
• k=0 magnon  - collective precession of spins
• Same as AF resonance 

ESR at fixed frequencies

• The resonance line in "pure" LaMnO₃ is too broad for Q-band
• In doped samples spin diffusion leads to motional narrowing, yields narrower line. Paramagnetic state studied in great detail by Oseroff, Muller and others.
• High field ESR: Mitsudo, Pimenov's group
• Budapest results: measured 3 frequencies: 75GHz, 150GHz, 225GHz
  • Paramagnetic state: g = 2 (& new lines, strongly temperature dependent)
  • AF state: More complex behavior

• Large body of work in '50s, theory by Keffer, Kittel and others
• Experiments: Richards, Tinkham, Foner
• Fields in effective Hamiltonian (uniaxial anisotropy):
  Exchange (H_e), anisotropy (H_a), external (H₀), excitation (H_rf)
• Zero external field: 
• resonance at w₀= gÖ2H_aH_e
• precession around local field
• two degenerate modes
• Finite external field lifts degeneracy.
  Parallel to easy axis: two branches (circular polarization)

Perp to easy axis: one mode is independent of the external field (linear polariztion)

• Sample: Oriented single crystal, ~0.5 mm thick, 4.0mm diameter disk
• Easy axis is perpendicular to surface (Susceptibility)
• Incident EM waves perpendicular to surface
• Measured absorption as a function of frequency at many fields; convert to map
• Paramagnetic state: linear relationship, as for quasi-free spins
• AF state
  • Advantage of method: full mapping
  • Low temperature full agreement with theory
  • Clear evidence for Dzyalushinskii-Moriya field, H_d
• Temperature dependence

• Parent compound of high T_c materials
• CuO₂ layered structure
• Copper ions have localized spins, antiferromagnetic below ~120K
• AF resonance has not been detected
• Preliminary results on "powder" samples

• Frustrated antiferromagnet
• High temperature structure: rhombohedral, with triangular Ni lattice
• Ni³⁺ ions in t⁶_2ge¹_g configuration
• Cooperative JT distortion at 475K; becomes monoclinic
• Magnetic order at 20K
• H - w mapping was done on a powder sample
• Next: LaNiO₂, with no known JT distortion