Magnon Another Carrier of Thermal Conductivity Final Presentation for ME 381R Nov. 30 2004 Park, Keeseong Ha, Eun
Contents • Review of Thermal Conductivity -Insulator -Metal • Unusual Data for Thermal Conductivity • Magnon - Definition - Thermal Conductivity from Magnon • More Data for Magnon’s Thermal Conductivity • Summary
General Behavior of Thermal Conductivity (Insulator) v is const. assumed from Debye model. At high T (D) .. Interactions among phonons are dominant - l T-1 ; C = const. => T-1 At intermediate T .. - l exp(T*/T); C decreases as T goes down and T3 where T*= a fraction of the Debye Temp. D => exp(T*/T) At low T ( << D) .. - l = const. (depending on the shape and size of the specimen) C T3 => T3 R. Berman, Thermal Conduction in Solids, 1976. Chap 3.
General Behavior of Thermal Conductivity (Metal) • Wiedemann-Franz-Lorenz law At high T ( TF ) .. Interactions among phonons are dominant - l T-1 ; C T. => = const At intermediate T .. - l increases ; C decreases as T goes down => T-2 At low T (~1 to ~100 K << TF) .. - l = const. (depending on the imperfections) C T => T R. Berman Thermal Conduction in Solids, 1976. Chap 3.
Unusual Thermal ConductivityT.Lorenz, Nature 418,614 (2002) Bachgaard Salt ..Magnetic insulator No electron’s contribution Phonon contribution acoustic ..Tmax << D = 60K optical .. 0.1~0.2W/Km Magnetic Excitation (Magnon)? Large magnetic exchange interaction (J ~ 500 K) Dominating contribution at high T (J >> D)
Magnon? • Magnon • Quantized spin wave
Qausi-One Dimensional Systems Exchange Coupling (J) a Elastic Coupling (k)
Comparison with phonon Magnon Phonon • Density of state • Energy of crystal vibration • Thermal equilibrium occupancy • Energy of each phonon hω • Total energy • Density of modes • Energy of a mode • Number of magnons excited in the mode k • Energy of each magnon excited • Total energy
Explanation for the TC in 1-D systems Debye model for magnon scattering where x=/kBT, and Each ls,i represents an independent channel including spinon phonon scattering, spinon defect scattering .. Debye model for phonon scattering where Each p,i represents an independent channel such as Boundary, Point defects, Phonon-phonon, dislocation, resonance scattering
Sr14-xCaxCu24O41 A.V Sologubenko PRB. 64, 054412 (2001) A.V Sologubenko PRL. 84, 2714 (2000) 1-D Anti-Ferromagnetic System Strong 180O Cu-O-Cu Coupling SrCuO2 & Sr2CuO3 .. J~ 2100-3000K (=J’/J~10-5) Sr14-xCaxCu24O41 .. J~ 1500 K (~0.55) Two peaks in chain direction Low T peak .. Phonon fitting Second peak .. Spin excitations (Spinon)
Y. Ando, PRB 58, R2913 (1998) 1-D Anti-Ferromagnetic System(Spin-Peierls system) Low T peak .. Strong suppression with high magnetic fields Phonon scattering by defects and by spin excitation High T peak.. Almost unchanged with increasing magnetic fields. Interaction between Magnons *1% increase if spin energy gap > Zeeman Energy Here, 25K > 18.6K for 14T *C. Hess PRB 64 184305 Jnn ~ 120 K , energy gap = 25K Tsp = 14.08K, Peaks at T=5.5K, 22K
TC of 1-D chain system Heisenberg Hamiltonian Antiferromagntic system (J>0) Ferromagntic system (J<0) Heisenberg chain .. Sr2CuO3 (J~2500 K) No Data !!! Spin ladder system.. : Sr14Cu24O41(J~1500 K) ..Anisotropy, Double peaks in the chain direction
Summary • Magnon .. Magnetic Excitation • Magnon’s contribution to Thermal conductivity of 1-D Anti-ferromagnetic Systems • Properties - Maximum Peak at High Temperature - Big Anisotropy - Big magnetic Exchange interaction • Ferromagnetic Systems?