Probing non-integral spin magnons via spin current noise · Probing non-integral spin magnons via spin current noise Akashdeep Kamra and Wolfgang Belzig Department of Physics, University

Probing non-integral spin magnons via spin current noise

Akashdeep Kamra and Wolfgang BelzigDepartment of Physics, University of Konstanz,

78457 Konstanz, Germany

Reference: Phys. Rev. Lett. 116, 146601 (2016).

Akashdeep Kamra Uni Konstanz 18th August 2016

Akashdeep Kamra Uni Konstanz

What's that noise!DC current through a resistor vs. time

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Shot NoiseDC current through a resistor vs. time

Discrete/Quantized nature of transport!

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Quantifying Noise

Current fluctuation

δ I=I−⟨ I ⟩

δ I

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Quantifying Noise

One-sided Noise Power Spectral Density

Current fluctuation

δ I=I−⟨ I ⟩

Sδ I (Ω)

δ I

⟨(δ I )2⟩=∫0

∞

Sδ I (Ω)d Ω

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Quantifying Noise

One-sided Noise Power Spectral Density

Current fluctuation

δ I=I−⟨ I ⟩

Sδ I (Ω)

δ I

Sδ I (Ω)=∫−∞

∞

{δ I (t )δ I (0 )}e iΩ t d t

⟨(δ I )2⟩=∫0

∞

Sδ I (Ω)d Ω

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Poissonian Transport

Y. V. Nazarov and Y. M. Blanter, Quantum Transport Introduction to Nanoscience (Cambridge University Press, 2009).

Probability rate of a charge transfer event is constant.

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Probability rate of a charge transfer event is constant.

⟨N 2⟩=⟨N ⟩

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S (0)=2 q ⟨ I ⟩Probability rate of a charge transfer event is constant.

⟨N 2⟩=⟨N ⟩

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Interacting Systems

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Interacting SystemsNormal metal/superconductor junction

X. Jehl, M. Sanquer, R. Calemczuk, and D. Mailly, Detection of doubled shot noisein short normal-metal/ superconductor junctions, Nature 405, 50 (2000).

2 e

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Interacting SystemsFractional Quantum Hall Effect

L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Observation of the e/3 Fractionally Charged Laughlin Quasiparticle, Phys. Rev. Lett. 79, 2526 (1997).

e /3

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Shot Noise

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Spin Currents

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Spin CurrentsNon-magnetic metal (N)/Ferromagnetic insulator (FI)

e

e

e

e

ee

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

e

ee

e

eee e

e

e

e

e

e

e

e

e

e

e

e

e

V. V. Kruglyak, S. O. Demokritov, and D. Grundler, Magnonics, Journal of Physics D: Applied Physics 43, 264001 (2010).

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Thermal Spin Current Noise

A. Kamra, F. P. Witek, S. Meyer, H. Huebl, S. Geprägs, R. Gross, G. E. W. Bauer, and S. T. B. Goennenwein, Spin Hall Noise, Phys. Rev. B 90, 214419 (2014).

y y

4268

4270

4272

4274

4276YIG(60nm)|Pt(2.2nm) 291.5K

Rlo

ng

()

0 90 180 270 360

6.870

6.873

6.876

6.879

6.882

SV

,lon

g(V

2/H

z)

(°)

x10-17

Pt YIG GGG

Non-magnetic metal (N)/Ferromagnetic insulator (FI)

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Magnon

Considering only exchange interaction and Zeeman energy!

C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, New York, 1953)

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Magnon



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Magnon

+

ℏ



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Classical Hamiltonian

C. Kittel, Quantum Theory of Solids (John Wiley & Sons, London 1963).

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Linearization about equilibrium orientation: Magnetization saturated along z direction


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Linearization about equilibrium orientation: Magnetization saturated along z direction


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Mean-field description of dipolar interaction:Demagnetization field


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Mean-field description of dipolar interaction:Demagnetization field


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Quantization: HP transformations


T. Holstein and H. Primakoff, Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet, Phys. Rev. 58, 1098 (1940).

With the magnon ladder operators in real space

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Quantization: HP transformations



With the magnon ladder operators in real space

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Quantum Hamiltonian

With the magnon annihilation operators in Fourier space

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Quantum Hamiltonian

With the magnon annihilation operators in Fourier space

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Ferromagnet Eigenmodes

With magnon annihilation operators

Effect of dipolar interactions!

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Squeezed-magnons

Bogoliubov transformation to new quasi-particles

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Spin Current Injection

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Hamiltonian

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Ferromagnetic Resonance

Under coherent excitation

⟨M x⟩∝ℜ(β) ⟨M y ⟩∝ℑ(β)

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Ferromagnetic Resonance

Under coherent excitation

Resonant excitation of the uniform mode and spin current injection!

⟨M x⟩∝ℜ(β) ⟨M y ⟩∝ℑ(β)

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Spin Current Shot Noise

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Squeezed-magnon


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Squeezed-magnon

Specimen in the shape of a film

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Squeezed-magnon

0 0.1 0.2 0.3 0.4 0.50

1

2

3

4

5

6

7

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

0

5

10

15

20

Specimen in the shape of a film

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A Primer on Squeezing

C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, 2005).

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Uncertainty Relations

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M x M y

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Squeezed Vacuum

Define (single mode) Squeeze operator:

Squeezed vacuum

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Squeezed Vacuum

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Squeezed Number States

Alternate (equivalent) approach to squeezing:

Squeezed zero number state

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Squeezed-magnon

What's in the name – relation to squeezed light


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Squeezed-magnon



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Squeezed-magnon


Two mode squeezing


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Finite Temperature Noise

A. Kamra and W. Belzig, Magnon-mediated spin current noise in ferromagnet|nonmagnetic conductor hybrids, Phys. Rev. B 94, 014419 (2016).

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0.1 1 10 10010 17

10 18

10 19

10 20

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0.1 1 10 10010 17

10 18

10 19

10 20

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0.1 1 10 10010 17

10 18

10 19

10 20

0.1 1 10

10 12

10 14

10 16

10 18

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Summary● Dipolar interaction mediated squeezing of

magnons● Non-integer spin quasiparticles● Dominance of shot over thermal noise● Quantum effects of squeezing

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Probing non-integral spin magnons via spin current noise · Probing non-integral spin magnons via spin current noise Akashdeep Kamra and Wolfgang Belzig Department of Physics, University

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