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 Magnons 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.
gt ? ? 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
gt ? ? exp(T/T) At low T ( ltlt ?D) ..
- l const. (depending on the shape and size of
the specimen) C ? T3 gt ? ?
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.
• gt ? const
• At intermediate T ..
• - l increases C decreases as T goes down
• gt ? ? T-2
• At low T (1 to 100 K ltlt TF) ..
• - l const. (depending on the
  imperfections)
• C ? T
• gt ? ? T

R. Berman Thermal Conduction in Solids, 1976.
Chap 3.
5
Unusual Thermal ConductivityT.Lorenz, Nature
418,614 (2002)
Bachgaard Salt ..Magnetic insulator No
electrons contribution Phonon contribution
acoustic ..Tmax ltlt ?D 60K optical ..
0.10.2W/Km Magnetic Excitation (Magnon)?
Large magnetic exchange interaction (J
500 K) Dominating contribution at high T
(J gtgt ?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
• h?
• 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
1-D Anti-Ferromagnetic System
Strong 180O Cu-O-Cu Coupling SrCuO2 Sr2CuO3 ..
J 2100-3000K (?J/J10-5) Sr14-xCaxCu24O41 ..
J 1500 K (?0.55) Two peaks in chain direction
Low T peak ..
Phonon fitting
Second peak .. Spin excitations (Spinon)
11
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 gt Zeeman Energy Here, 25K gt
18.6K for 14T C. Hess PRB 64 184305
Jnn 120 K , energy gap 25K Tsp 14.08K,
Peaks at T5.5K, 22K
12
TC of 1-D chain system
Heisenberg Hamiltonian
Antiferromagntic system (Jgt0)
Ferromagntic system (Jlt0)
Heisenberg chain .. Sr2CuO3 (J2500 K)
No Data !!!
Spin ladder system.. Sr14Cu24O41(J1500 K)
?..Anisotropy, Double peaks in the chain direction
13
Summary

• Magnon .. Magnetic Excitation
• Magnons 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?