band structure of helimagnons in mnsi resolved by ... · band structure of helimagnons in mnsi...

Band Structure of Helimagnons in MnSiResolved by Inelastic Neutron Scattering

M. Kugler1, 2, G. Brandl1, 2, J. Waizner3, M. Janoschek4,R. Georgii1, 2, A. Bauer1, K. Seemann1, 2, A. Rosch3,

C. Pfleiderer1, P. Böni1 and M. Garst3

1 Physik-Department E21, Technische Universität München, 85748 Garching, Germany2 Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universität München, 85748 Garching, Germany

3 Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany4 Condensed Matter and Magnet Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

3. DMI Workshop: 26-30 May 2015 Pskov, Russia

Outline

I summary of the helimagnon model

I introduction to the instrument MIRA

I specific setups and example scans

I result: helimagnon dispersion relation

Basics on MnSi

S. Mühlbauer et al., Science 323 915 (2009).

a =4.56 Å P 21 3

I B20, no inversion symmetry⇒ DMI

I model system for chiral magnetism:

I exchange interaction⇒ parallel spinsI DM interaction⇒ perpendicular spinsI together⇒ long spin spiral: ∼180 ÅI cubic anisotropy⇒ pinning: <111>

I increasing magnetic field:

1. helices align⇒ single-domain: ∼0.1 T

2. spins cant ⇒ field-polarized: ∼0.6 T

I skyrmion phase: three phase-coherenthelices in an equilateral triangle:∼0.2 T

Basics on MnSi

S. Mühlbauer et al., Science 323 915 (2009).

λh ≈175Akh

q‖

q⊥

I B20, no inversion symmetry⇒ DMI

I model system for chiral magnetism:I exchange interaction⇒ parallel spinsI DM interaction⇒ perpendicular spinsI together⇒ long spin spiral: ∼180 Å

I cubic anisotropy⇒ pinning: <111>





Basics on MnSi

S. Mühlbauer et al., Science 323 915 (2009). I B20, no inversion symmetry⇒ DMI

I model system for chiral magnetism:I exchange interaction⇒ parallel spinsI DM interaction⇒ perpendicular spinsI together⇒ long spin spiral: ∼180 ÅI cubic anisotropy⇒ pinning: <111>





Basics on MnSi

S. Mühlbauer et al., Science 323 915 (2009). I B20, no inversion symmetry⇒ DMI

I model system for chiral magnetism:I exchange interaction⇒ parallel spinsI DM interaction⇒ perpendicular spinsI together⇒ long spin spiral: ∼180 ÅI cubic anisotropy⇒ pinning: <111>

I increasing magnetic field:1. helices align⇒ single-domain: ∼0.1 T



Helimagnons in Single-Domain State

model parameters (MnSi, 20 K):

1. momentum scale:kh = 2π/λh = 0.036 Å−1

2. energy scale:gµBµ0H int

c2 = Dk2h = 0.062 meV

3. dipolar strength: χintcon = 0.34





c2 = Dk2h = 0.062 meV


here: (H/Hc2)2 � 1⇒ neglect field dependence

parameters are well known⇒ absolute prediction !





c2 = Dk2h = 0.062 meV


here: (H/Hc2)2 � 1⇒ neglect field dependence

parameters are well known⇒ absolute prediction !

q⊥ = 0: ~ω(q‖) = D|q‖|√

q2‖ + (1 + χint

con)k2h centered at ±kh and 0


q⊥ = 0: ~ω(q‖) = D|q‖|√

q2‖ + (1 + χint

con)k2h centered at ±kh and 0

q⊥ > 0: number, energies and ’flatness’ of bands increase with q⊥

Multi-Domain vs. Single-Domain

I momentum notation: with respect to the red domain || [111]I zero field: contributions from four domains⇒ intensity plateausI small field: single-domain state⇒ well defined peaks

multi-domain measurements: Janoschek et al., PRB 81 214436 (2010).

Triple-Axis Spectrometer (TAS)

I neutron guide⇒ white beam

I three rotation axes:

1. monochromator angle:selects initial energy Ei

2. scattering angle at sample:selects Q = G + q

3. analyzer angle:selects final energy Ef

I energy transfer ~ω = Ei − Ef :

I magnon creation: ~ω > 0I mag. annihilation: ~ω < 0

I find dispersion relation ~ω(q)

Mon

o

ColdSource

Neu

tron

Gui

de

C1

Ana

C2

M1

M2

Detector

Cryostat & Magnets

Legend:

C: CollimatorsM: Masks

S

S: Sample

Available angle:100°



I three rotation axes:1. monochromator angle:

selects initial energy Ei



I energy transfer ~ω = Ei − Ef :

I magnon creation: ~ω > 0I mag. annihilation: ~ω < 0


Mon

o

ColdSource

Neu

tron

Gui

de

C1

Ana

C2

M1

M2

Detector

Cryostat & Magnets

Legend:


S

S: Sample




I three rotation axes:1. monochromator angle:

selects initial energy Ei



I energy transfer ~ω = Ei − Ef :I magnon creation: ~ω > 0I mag. annihilation: ~ω < 0


Mon

o

ColdSource

Neu

tron

Gui

de

C1

Ana

C2

M1

M2

Detector

Cryostat & Magnets

Legend:


S

S: Sample


The Cold TAS MIRA@FRM-II

I location: guide hall of FRM-II

I cold neutrons: Ei = 3...5 meVI multi-purpose instrument:

I SANS⇒ structureI TAS ⇒ dynamics

I two samples ∼8 cm3, η ≈ 10’

I mostly at 20 K (∼ 2/3TC)

I Ei and q constant⇒ scan ~ω

I generic example scan −−−−→

The Cold TAS MIRA@FRM-II

I location: guide hall of FRM-II

I cold neutrons: Ei = 3...5 meVI multi-purpose instrument:

I SANS⇒ structureI TAS ⇒ dynamics

I two samples ∼8 cm3, η ≈ 10’

I mostly at 20 K (∼ 2/3TC)

I Ei and q constant⇒ scan ~ωI generic example scan −−−−→

Setup 1: Dispersive Branches

I horizontal B⇒ kh in plane

I can select both: q‖ & q⊥

I suboptimal for the bands,but can show: they’re flat

I ideal for the 3 dispersivebranches at q⊥ = 0 −−−−→

(example scans at 20 K)

Setup 2: Helimagnon Bands

I vertical field⇒ kh ⊥ plane

I tune band energies with q⊥

I course vertical resolution (q‖)⇒ collect large band intensity

I resolve the first two bands −→

(T = 20 K, Ei = 4.06 meV)

Setup 3: Even More Bands

I another orientation: q⊥ || [111]→ q⊥ || [001]⇒ same result, decoupled from nuc. lattice

I ~ω < 0: increases efficiency⇒ more bandsE-dependent analyzer efficiency overcomes Bose statistics.

Results for the Helimagnon Bands

I band energies vs. q⊥at 20 K, setups 2 & 3

I dotted lines:-universal spectrum-agrees at low ~ω X-deviates at large ~ω

I full lines:-higher order correction-agreement for all ~ω X-A ∼ (akh)

2 ≈ 0.01 X-at 3kh → 32(akh)

2 ∼ 10%

Results for the Helimagnon Bands

I band energies vs. q⊥at 20 K, setups 2 & 3

I dotted lines:-universal spectrum-agrees at low ~ω X-deviates at large ~ω

I full lines:-higher order correction-agreement for all ~ω X-A ∼ (akh)

2 ≈ 0.01 X-at 3kh → 32(akh)

2 ∼ 10%F ∼ (∇i nj)

2 + 2khn(∇× n) + Ak2

h(∇2n)2 + dipolar + Zeeman

Results for the Dispersive Branches

I dispersive modes vs. q‖at 20 K, setup 1

I higher order correction:-important for blue branch-not for the red/green one

I black dashed lines:-vertical resolution ± 1/2 kh

-along q⊥ ⇒ band split-off-10% effect for red branch-small effect for the others

I resolve all three modes X

Renormalization of the Helimagnons

I until now: ~ω(q,T = 20 K)

I next: ~ω(q= constant,T ):-setup 1: q‖ = 2.1 kh

-setup 2: q⊥= 2.5 kh

I two modes for each setup

I full lines include:-mainly H int

c2(T )← χac [1]-kh(T )← SANS [2] & TAS-resolution convolution

Renormalization of the Helimagnons

I until now: ~ω(q,T = 20 K)

I next: ~ω(q= constant,T ):-setup 1: q‖ = 2.1 kh

-setup 2: q⊥= 2.5 kh

I two modes for each setup

I full lines include:-mainly H int

c2(T )← χac [1]-kh(T )← SANS [2] & TAS-resolution convolution

[1] Bauer et al., PRB 82, 064404 (2010).[2] Grigoriev et al., PRB 74, 214414 (2006).

Conclusion

I summary:I clear identification due to the single-domain stateI all three dispersive branches and at least five bandsI softening of the helimagnons like Hc2(T ) along q‖ & q⊥I parameter-free prediction confirmed for low energiesI single parameter A = −0.0073± 0.0004 for all energies

I outlook:I helimagnons in the conical phase, up to Hc2

I spin-waves within the skyrmion crystalI helimagnons under pressure→ NFL phaseI polarized TAS⇒ polarization of spin-wavesI other DM-helimagnets: Cu2OSeO3, Fe1−xCoxSi, ...I damping of helimagnons

for details, see arXiv:1502.06977 and thanks for your attention!

band structure of helimagnons in mnsi resolved by ... · band structure of helimagnons in mnsi...

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