Magnon Another Carrier of Thermal Conductivity

1. Magnon Another Carrier of Thermal Conductivity Final Presentation for ME 381R Nov. 30 2004 Park, Keeseong Ha, Eun

2. 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

3. 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.

4. 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.

5. 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)

6. Magnon? • Magnon • Quantized spin wave

7. Qausi-One Dimensional Systems Exchange Coupling (J) a Elastic Coupling (k)

8. 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

9. 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

10. 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)

11. 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

12. 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

13. 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?

14. Questions?