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)]