magnon transport in condensation: josephson effects and `persistent’ quantized currents
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Magnon Transport in Condensation:
Kouki Nakata University of Basel
All the responsibilities of this slide rest with Kouki Nakata (Dec. 2016)
Josephson Effects and `Persistent’ Quantized Currents
KN, K. A. van Hoogdalem, P. Simon, D. Loss, Phys. Rev. B 90, 144419 (2014) KN, P. Simon, D. Loss, Phys. Rev. B 92, 014422 (2015) See also review article [KN, P. Simon & D. Loss, arXiv:1610.08901]
Magnon Carries 𝜇B & 𝑘B
≤ ≪
Magnon 𝜇B 𝑘B
Low-energy collective mode in insulating magnet
Yes !
QUESTION
Can magnon 𝜇B (boson) transport be similar to electron 𝑒 (fermion) transport ?
Electron 𝑒 = Fermion
Magnon 𝜇B = Boson
Wiedemann-Franz (WF) law Franz and Wiedemann, Annalen der Physik (1853)
Magnonic Wiedemann-Franz law KN, P. Simon & D. Loss, PRB (2015)
Superconductors
Onnes (1911)
Quasi-equilibrium magnon condensate Demokritov et al., Nature (2006)
Condensed magnon current Hillebrands-group, Nat. Phys. (2016)
Josephson effect Josephson, Phys. Lett. (1962)
Magnonic Josephson effect KN, K. A. van Hoogdalem, P. Simon & D. Loss, PRB (2014)
KN, P. Simon & D. Loss, PRB (2015)
Quantum Hall effetc (QHE) Klitzing et al., PRL (1980)
Magnonic QHE KN, J. Klinovaja & D. Loss (2016), arXiv:1611.09752
QUESTION
Can magnon 𝜇B (boson) transport be similar to electron 𝑒 (fermion) transport ?
See review article [KN, P. Simon & D. Loss, arXiv:1610.08901]
QUESTION
Q. What is transport properties of such a macroscopic coherent state ?
Magnon: Bosonic quasi-particle quasi-equilibrium condensation
QUESTION
Condensate
Q. What is transport properties of such a macroscopic coherent state ?
Magnon: Bosonic quasi-particle quasi-equilibrium condensation
Demokritov et al., Nature 443, 430 (2006): Microwave pumping at room temperature
Quasi-equilibrium Bose-Einstein Condensation of Magnon
Clausen et al., PRB (2015): Hillebrands-group
A magnon current in condensation: Hillebrands-group, Nat. Phys. (2016)
Incoherent spin precession Macroscopic coherent
spin precession
Sum of several modes Single mode: Macroscopic coherent state
Noncondensed magnon Quasi-equilibrium magnon BEC
Approximate conservation of magnons
𝑎(𝑡) ~ 𝑆+(𝑡) = 𝑆𝑥(𝑡) + 𝑖 𝑆𝑦(𝑡)
With the same frequency 𝜔B = 𝜗
Bunkov & Volovik (Review: arXiv:1003.4889)
𝑇B = 2𝜋/𝜔B~1ns ≪ 𝑇Decay ~400ns
BEC = Metastable state:
Noncondensed vs BEC
𝜗 ≠ 0
(Electrically) charged particle:
Magnetic vector potential
Magnon = Magnetic dipole:
Aharonov-Bohm phase Aharonov-Casher (AC) phase
Electric vector potential ~
Meier & Loss, PRL (2003). Loss & Goldbart, Phys. Lett. A (1996)
Aharonov and Bohm, Phys. Rev. 115, 485 (1959) Aharonov and Casher, PRL, 53, 319 (1984)
𝑩 = 𝜵× 𝑨
= A pair of oppositely charged magnetic monopoles
NOTE) Katsura et al., PRL (2005): Dzyaloshinskii-Moriya int. Aharonov-Casher effect Hoogdalem et al., PRB (2013) Mook et al., PRB (2014, `15, `16). Zhang et al., PRB (2013)
To electrically control magnon transport in condensation:
GOAL
Geometric Phases
BEC
Aharonov-Casher phase
Tunneling: 𝐽ex
Magnon condensate order parameter:
𝐿
𝑅
BEC
Δ𝑥: Distance between boundary spins
Tunneling in Aharonov-Casher effect:
Josephson Junction for Magnon BEC
Condensate order parameter
Number of condensed magnons:
FI:
Tunneling:
Gross-Pitaevski ℋGP with junction:
Josephson Junction for Magnon BEC
∈ ℂ
Two-state model
ℰR
ℰL
Condensation
KN, Hoogdalem, Simon, and Loss, Phys. Rev. B 90, 144419 (2014)
BEC
BEC
𝑇 = 0
Population imbalance:
Relative phase:
Rescaled time:
Josephson magnon current:
Time-evolution of relative phase:
Magnon Josephson Eq.
Josephson Junction for Magnon BEC KN, Hoogdalem, Simon, and Loss, Phys. Rev. B 90, 144419 (2014)
MQST
Josephson current Period 𝑡ac of ac effect:
𝑡ac = 10ns
𝐽ex = 0.03𝜇eV S = 10 Λ = 0 𝑧(0) ≠ 0
Macroscopic quantum self-trapping:
ac & dc Josephson Effects: Quantum Self-Trapping KN, Hoogdalem, Simon, and Loss, Phys. Rev. B 90, 144419 (2014)
See also [KN, Simon, and Loss, Phys. Rev. B 92, 014422 (2015)]
MQST
Josephson current Period 𝑡ac of ac effect:
𝑡ac = 10ns
𝐽ex = 0.03𝜇eV S = 10 Λ = 0 𝑧(0) ≠ 0
Macroscopic quantum self-trapping:
ac & dc Josephson Effects: Quantum Self-Trapping
dc
𝜃A−C ≠ 0
KN, Hoogdalem, Simon, and Loss, Phys. Rev. B 90, 144419 (2014)
See also [KN, Simon, and Loss, Phys. Rev. B 92, 014422 (2015)]
dc ac
BEC
BEC
Magnetic field difference:
Noncondensed vs BEC
I) Noncondensed II) BEC
Current: 𝒪(𝐽ex2) Current: 𝒪(𝐽ex)
𝑎 = 0 𝑎 ≠ 0
with 𝑧 0 = 0
See also [KN, Simon, and Loss, Phys. Rev. B 92, 014422 (2015)]
: Phase winding number
Quantization
dc `persistent’ condensed magnon current (𝑇 = 0)
: Quantized
Single-valuedness of the wave function
BEC Persistent Current
Aharonov-Casher phase in the ring
BEC
BEC
𝐸
KN, Hoogdalem, Simon, and Loss, Phys. Rev. B 90, 144419 (2014)
See also [KN, Simon, and Loss, Phys. Rev. B 92, 014422 (2015)]
Magnon Transport in Condensation: Josephson Effects and ̀ Persistent’ Quantized Currents
KN, K. A. van Hoogdalem, P. Simon, D. Loss, Phys. Rev. B 90, 144419 (2014) KN, P. Simon, D. Loss, Phys. Rev. B 92, 014422 (2015) See also review article [KN, P. Simon & D. Loss, arXiv:1610.08901]
SUMMARY
ac/dc properties
A good platform to experimentally establish magnon transport in condensation: Macroscopic coherence of magnon condensates
Aharonov-Casher phase
A handle to electromagnetically control magnon transport in condensation: -Josephson effects -Persistent quantized current
See also
Thermomagnetic condensation in equilibrium:
Nikuni et al., PRL (2000). Radu et al., PRL (2005). Giamarchi et al., Nat. Phys. (2008).
Kinetic condensation in quasi-equilibrium:
Demokritov et al., Nature (2006). Serga et al., Nat. Commun. (2014). Clausen et al., PRB (2015).
REMARK: Snoke, Nature (2006).
REMARK: Bunkov & Volovik, arXiv:1003.4889. Yukalov, Laser Phys. (2012). Zapf et al., RMP (2014). Mills, PRL (2007).
See also [A. Ruckriegel and P. Kopietz, Phys. Rev. Lett. 115, 157203 (2015)]