Jeanne Colbois PRO
Physicist @ CNRS. Here you find slides for *some* of my presentations, as well as visual abstracts for recent publications.
Artificial out-of-plane Ising antiferromagnet
on the kagome lattice
with very small farther-neighbor couplings
Jeanne Colbois¹, Kevin Hofhuis² ³, Zhaochu Luo² ³, Xueqiao Wang² ³, Aleš Hrabec ² ³ , Laura J. Heyderman² ³, and Frédéric Mila¹
(1) EPF Lausanne Institute of Physics, (2) ETH Zürich Department of Materials, (3) Paul Scherrer Institute Laboratory for Multiscale Materials experiments
Switzerland
OASIS session 7 - 23.08.2021 - Jeanne Colbois
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Motivation
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Chioar et al., Phys. Rev. B 90, (2014)
1
Motivation
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Chioar et al., Phys. Rev. B 90, (2014)
1
Motivation
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Chioar et al., Phys. Rev. B 90, (2014)
H=∑(i,j)Ji,jσiσjJi,j∝1/∣ri−rj∣3
H = \sum_{(i,j)} J_{i,j} \sigma_i \sigma_j \\
J_{i,j} \propto 1/|r_i -r_j|^3
1
Motivation
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
- The resulting models are of intrinsic interest
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Chioar et al., Phys. Rev. B 90, (2014)
H=∑(i,j)Ji,jσiσjJi,j∝1/∣ri−rj∣3
H = \sum_{(i,j)} J_{i,j} \sigma_i \sigma_j \\
J_{i,j} \propto 1/|r_i -r_j|^3
Hamp et al., Phys. Rev. B 98, (2018)
1
Motivation
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
- The resulting models are of intrinsic interest
- There has been increased interest in the possibility of tuning couplings
OASIS session 7 - 23.08.2021 - Jeanne Colbois
2
Motivation
with a magnetic underlayer (Kempinger et al., arXiv:2104.00126)
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
- The resulting models are of intrinsic interest
- There has been increased interest in the possibility of tuning couplings
OASIS session 7 - 23.08.2021 - Jeanne Colbois
with a magnetic underlayer (Kempinger et al., arXiv:2104.00126)
With chirally coupled nanomagnets
Luo et al., Science 363, 1435-1439 (2019)
2
Motivation
- Artificial spin systems can be (surprisingly) well modeled by Ising Hamiltonians
- The resulting models are of intrinsic interest
- There has been increased interest in the possibility of tuning couplings
OASIS session 7 - 23.08.2021 - Jeanne Colbois
with a magnetic underlayer (Kempinger et al., arXiv:2104.00126)
With chirally coupled nanomagnets
Luo et al., Science 363, 1435-1439 (2019)
Motivation
2
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Chirally coupled nanomagnets
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Luo et al., Science 363, 1435-1439 (2019)
Chirally coupled nanomagnets...
3
Pt(6 nm)/Co(1.6 nm)/Al(2 nm)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Dzyaloshinskii-Moryia interaction
- Here : interfacial DMI
3
Chirally coupled nanomagnets...
Luo et al., Science 363, 1435-1439 (2019)
Pt(6 nm)/Co(1.6 nm)/Al(2 nm)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
3
Chirally coupled nanomagnets...
Luo et al., Science 363, 1435-1439 (2019)
Pt(6 nm)/Co(1.6 nm)/Al(2 nm)
The magnetic anisotropy is controlled by the oxidization of the Co/Al interface
(the in-plane regions are protected and the out-of-plane regions are oxidized)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
The magnetic anisotropy is controlled by the oxidization of the Co/Al interface
(the in-plane regions are protected and the out-of-plane regions are oxidized)
3
Chirally coupled nanomagnets...
Luo et al., Science 363, 1435-1439 (2019)
Pt(6 nm)/Co(1.6 nm)/Al(2 nm)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
3
Chirally coupled nanomagnets...
Luo et al., Science 363, 1435-1439 (2019)
Pt(6 nm)/Co(1.6 nm)/Al(2 nm)
Result : an effective antiferromagnetic nearest neighbour coupling for the out-of-plane (OOP) regions
(MFM image)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... on the kagome lattice...
Chirally coupled nanomagnets...
4
Luo et al., Science 363, 1435-1439 (2019)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Effective model
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
5
Chirally coupled nanomagnets...
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
SEM
5
Chirally coupled nanomagnets...
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
SEM
5
Chirally coupled nanomagnets...
OOP
IP
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
SEM
5
Chirally coupled nanomagnets...
It is far from obvious what the long-range effective model should be!
OOP
IP
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
SEM
6
Chirally coupled nanomagnets...
- Effective model for the OOP spins on a 5-sites island
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
SEM
- Effective model for the OOP spins on a 5-sites island
- Systematic micromagnetic simulations assuming that the IP region takes the configuration of minimal energy
Chirally coupled nanomagnets...
6
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
- Effective model for the OOP spins on a 5-sites island
- Systematic micromagnetic simulations assuming that the IP region takes the configuration of minimal energy
Chirally coupled nanomagnets...
6
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
- Effective model for the OOP spins on a 5-sites island
- Systematic micromagnetic simulations assuming that the IP region takes the configuration of minimal energy
Chirally coupled nanomagnets...
J1dipJ1≅8.7±0.1
\frac{J_1}{J_1^{\text{dip}}} \cong 8.7 \pm 0.1
6
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
- Effective model for the OOP spins on a 5-sites island
- Systematic micromagnetic simulations assuming that the IP region takes the configuration of minimal energy
Chirally coupled nanomagnets...
J1dipJ1≅8.7±0.1
\frac{J_1}{J_1^{\text{dip}}} \cong 8.7 \pm 0.1
J2dipJ2≅1.67±0.01
\frac{J_2}{J_2^{\text{dip}}} \cong 1.67 \pm 0.01
6
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
- Effective model for the OOP spins on a 5-sites island
- Systematic micromagnetic simulations assuming that the IP region takes the configuration of minimal energy
J1dipJ1≅8.7±0.1
\frac{J_1}{J_1^{\text{dip}}} \cong 8.7 \pm 0.1
J2dipJ2≅1.67±0.01
\frac{J_2}{J_2^{\text{dip}}} \cong 1.67 \pm 0.01
J3∣∣dipJ3∣∣≅1.12±0.01
\frac{J_{3||}}{J_{3||}^{\text{dip}}} \cong 1.12 \pm 0.01
6
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
7
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
7
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
7
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... interaction strengths
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
Farther-neighbor to nearest-neighbor couplings ratios are much smaller than in the dipolar case!
7
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... Results.
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
8
MFM
AFM
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... Results.
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Chirally coupled nanomagnets...
MFM
x 20
8
OASIS session 7 - 23.08.2021 - Jeanne Colbois
- An overall up magnetization : criterion 1
- 10% to 15% of ferromagnetic triangles (not respecting the 2-up 1-down, 2-down 1-up rule) : criterion 2
... Results.
Chirally coupled nanomagnets...
9
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
m=0.19±0.05
m = 0.19 \pm 0.05
OASIS session 7 - 23.08.2021 - Jeanne Colbois
... Results.
Chirally coupled nanomagnets...
9
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
- An overall up magnetization : criterion 1
- 10% to 15% of ferromagnetic triangles (not respecting the 2-up 1-down, 2-down 1-up rule) : criterion 2
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Short-range spin-spin correlations
... Results.
Chirally coupled nanomagnets...
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
9
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Short-range spin-spin correlations
... Results.
Chirally coupled nanomagnets...
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
ck=⟨σiσj⟩k−⟨σi⟩⟨σj⟩
c_k = \langle \sigma_i \sigma_j \rangle_k - \langle \sigma_i \rangle \langle \sigma_j \rangle
9
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Short-range spin-spin correlations
... Results.
Chirally coupled nanomagnets...
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
9
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Short-range spin-spin correlations
∣c1∣>c3∣∣≳2c2
|c_1| > c_{3||} \gtrsim 2c_2
... Results.
Chirally coupled nanomagnets...
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
9
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Short-range spin-spin correlations
∣c1∣>c3∣∣≳2c2
|c_1| > c_{3||} \gtrsim 2c_2
... Results.
Chirally coupled nanomagnets...
9
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
criterion 3
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Can our effective model describe these results?
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Can our effective model describe these results?
Not really...
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Can our effective model describe these results?
Not really...
... but we can learn a lot about the impact of the couplings on the correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Towards the J1-J2-J3||-h model
Monte Carlo : Rakala, Damle, PRE 96 (2017)
Tensor Networks : Vanhecke, JC, et al. PRR 3 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
NN
2-up 1-down, 2-down 1-up rule
m=0
m = 0
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
S=0.501833...
S = 0.501833...
Kano, Naya, Prog. Theor. Phys. 10, 158 (1953)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
NN
2-up 1-down rule
Moessner, Sondhi
PRB 63, 224401 (2001)
m=1/3,S=STLIAF
m = 1/3, S = S_{\text{TLIAF}}
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
1. The nearest-neighbor model in a field
m=1/3,S=STLIAF
m = 1/3, S = S_{\text{TLIAF}}
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
m=0.59966(2)
m = 0.59966(2)
First-order PT
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
m=1
m = 1
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
1. The nearest-neighbor model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Sejman, Zukovic, Acta Phys. Pol. A 137, 622 (2020)
Loh, Yao, Carlson, Phys. Rev. B 77, 134402 (2008)
Li et al., Phys. Rev. B 82, 134434 (2010)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
11
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Takagi, Mekata, J.Phys. Soc. Jpn. 62, 3943 (1993)
Wills, Ballou, Lacroix, PRB 66, 144407 (2002)
Chern, Tchernyshyov, P. Trans. R. Soc. A 370, 5718 (2012)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Takagi, Mekata, J.Phys. Soc. Jpn. 62, 3943 (1993)
Wills, Ballou, Lacroix, PRB 66, 144407 (2002)
Chern, Tchernyshyov, P. Trans. R. Soc. A 370, 5718 (2012)
11
OASIS session 7 - 23.08.2021 - Jeanne Colbois
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Takagi, Mekata, J.Phys. Soc. Jpn. 62, 3943 (1993)
Wills, Ballou, Lacroix, PRB 66, 144407 (2002)
Chern, Tchernyshyov, P. Trans. R. Soc. A 370, 5718 (2012)
11
OASIS session 7 - 23.08.2021 - Jeanne Colbois
NN g.s. physics?
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
See also: Takagi, Mekata, J.Phys. Soc. Jpn. 62, 3943 (1993)
Wills, Ballou, Lacroix, PRB 66, 144407 (2002)
Chern, Tchernyshyov, P. Trans. R. Soc. A 370, 5718 (2012)
11
OASIS session 7 - 23.08.2021 - Jeanne Colbois
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
12
OASIS session 7 - 23.08.2021 - Jeanne Colbois
In the g.s. the selected correlations are very different from the nearest neighbor model (J2 ice rule)
12
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
But if J2 is small enough the temperature can restore the correlations from the NN ground state
12
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
12
However, not for J2 > 1%J1
2. The next-nearest neighbor model
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
13
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
2. The next-nearest neighbor model
OASIS session 7 - 23.08.2021 - Jeanne Colbois
13
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
2. The next-nearest neighbor model
OASIS session 7 - 23.08.2021 - Jeanne Colbois
13
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
2. The next-nearest neighbor model
OASIS session 7 - 23.08.2021 - Jeanne Colbois
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
14
OASIS session 7 - 23.08.2021 - Jeanne Colbois
14
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
OASIS session 7 - 23.08.2021 - Jeanne Colbois
14
J1,J2 model
J_1, J_2 \text{ model }
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
OASIS session 7 - 23.08.2021 - Jeanne Colbois
14
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
Stripe long-range order
m=1
m = 1
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
15
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
The ground state still has a macroscopic degeneracy!
OASIS session 7 - 23.08.2021 - Jeanne Colbois
18
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
Magnetization plateaus at J3∣∣<J2
\text{Magnetization plateaus at } J_{3||} < J_2
3. Magnetization plateaus in the ground state
of the J1-J2-J3|| model in a field
Tokushuku, Mizoguchi, Udagawa, J. Phys. Soc. Jpn. 89, 053708, (2020)
m=1/3,S=STLIAF/3
m = 1/3, S = S_{\text{TLIAF}}/3
m=17/27,S≥271ln(3)
m = 17/27, S \geq \frac{1}{27} \ln (3)
m=1/9,S≅0.12
m = 1/9, S \cong 0.12
m=5/9,S≥271ln(2)
m = 5/9, S \geq \frac{1}{27} \ln (2)
m=1
m = 1
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Can our effective model describe the experimental results?
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Can our effective model describe the experimental results?
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
+ a magnetic field to account for the magnetization
Results
19
OASIS session 7 - 23.08.2021 - Jeanne Colbois
OASIS session 7 - 23.08.2021 - Jeanne Colbois
We recover our magnetization plateaus in the ground state
Results
19
OASIS session 7 - 23.08.2021 - Jeanne Colbois
We recover a similar behaviour as in the J1 model w.r.t. the plateau
Results
19
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Results
19
Region of fields and temperatures where the experimental magnetization matches the numerical results
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Comparison in field and temperature
20
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
Comparison in field and temperature
20
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
Comparison in field and temperature
20
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbour correlations
Comparison in field and temperature
21
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbour correlations
Comparison in field and temperature
21
We recover our magnetization plateaus in the ground state
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbour correlations
Comparison in field and temperature
21
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbour correlations
Comparison in field and temperature
21
J1−J2−J3∣∣
J_1 - J_2 -J_{3||}
from micromagnetics
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Comparison in field and temperature
22
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Comparison in field and temperature
22
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Comparison in field and temperature
23
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Comparison in field and temperature
24
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Conclusions
25
- Chirally coupled nanomagnets create very strong nearest-neighbor antiferromagnetic couplings
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Conclusions
25
- Chirally coupled nanomagnets create very strong nearest-neighbor antiferromagnetic couplings
- Yet farther-neighbor couplings cannot be neglected even at finite temperature and even when they are as small as 2% of the nearest-neighbor couplings
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Conclusions
25
- Chirally coupled nanomagnets create very strong nearest-neighbor antiferromagnetic couplings
- Yet farther-neighbor couplings cannot be neglected even at finite temperature and even when they are as small as 2% of the nearest-neighbor couplings
- We present numerical results for the J1-J2-J3||-h model in a field based on MC and TN simulations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Conclusions
25
- Chirally coupled nanomagnets create very strong nearest-neighbor antiferromagnetic couplings
- Yet farther-neighbor couplings cannot be neglected even at finite temperature and even when they are as small as 2% of the nearest-neighbor couplings
- We present numerical results for the J1-J2-J3||-h model in a field based on MC and TN simulations
- It is a first step (no full quantitative picture of the experiments)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Outlook
26
- Long-range effective model?
- Role of disorder in the couplings?
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Outlook
26
- Long-range effective model?
- Role of disorder in the couplings?
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Outlook
26
- Long-range effective model?
- Role of disorder in the couplings?
- Experimental observation of the IP configurations to validate the effective model?
- Design with a triangular hole to reduce the farther-neighbor couplings?
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Acknowledgments
Kevin Hofhuis
Zhaochu Luo, Ales Hrabec, Xueqiao Wang, Laura Heyderman, Frédéric Mila
Thank you for your attention!
Bram Vanhecke, Laurens Vanderstraeten, Andrew Smerald, Frank Verstraete, Patrick Emonts, Mithilesh Nayak, Natalia Chepiga
And the Centro de ciencias de Benasque Pedro Pascual
Discussions:
Collaborators:
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Results : order of the correlations
There is the region where the correlations are again in the order corresponding to the NN model (thanks to the field!)
20
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Results : order of the correlations
There is the region where the correlations are again in the order corresponding to the NN model (thanks to the field!)
Nearest-neighbor model in a field
20
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Numerical techniques
Monte Carlo simulations
8
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Numerical techniques
Monte Carlo simulations
Monte Carlo simulations
In zero field
- "myopic worm" loop update
- single spin flip
- parallel tempering
8
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Numerical techniques
Monte Carlo simulations
Monte Carlo simulations
In zero field
- "myopic worm" loop update
- single spin flip
- parallel tempering
Rakala, Damle, PRE 96,023304 (2017)
In a field
- single spin flip
- parallel tempering
8
OASIS session 7 - 23.08.2021 - Jeanne Colbois
A few words about tensor networks
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
Nearest-neighbor model in zero field
... and a benchmark ...
OASIS session 7 - 23.08.2021 - Jeanne Colbois
10
Nearest-neighbor model in zero field
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Barry and Khatun, Int. J. Mod. Phys. B 11, 93 (1997)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor model in zero field
10
... and a benchmark ...
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
JC, Hofhuis, Luo et al., PRB 104, 024418 (2021)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
11
Lifting the ground state degeneracy (partially!)
h/J1
h/J_1
0
4
Nearest neighbour model : S=0.501833...ξ=1.250559...
\text{Nearest neighbour model : }\\
S = 0.501833...\\
\xi = 1.250559...
Verified with TN
NN
2-up 1-down, 2-down 1-up rule
Kano, Naya,
Prog. Theor. Phys 10, 158 (1953)
Apel, Everts,
J. Stat. Mech. 2011, 09002, (2011)
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
11
Lifting the ground state degeneracy (partially!)
h/J1
h/J_1
0
4
NN
2-up 1-down rule
Charge order
NN
2-up 1-down, 2-down 1-up rule
m=31S=STLIAF/3
m = \frac{1}{3}\\
S = S_{\text{TLIAF}}/3
Moessner, Sondhi
PRB 63, 224401 (2001)
Verified with TN
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
For a relatively large field and temperature, we explain the vertex populations ...
11
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
For a relatively large field and temperature, we explain the vertex populations ...
11
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
11
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
... but not the descending order of the correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
Nearest-neighbor in a field
11
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
... but not the descending order of the correlations
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Comparison in field and temperature
Disorder in coupling strengths pinning ice-rule breaking triangles?
22
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Demagnetization protocol switching domains of a certain size (e.g. five OOP sites), preserving the ratio of ferromagnetic triangles while reducing the magnetization and the correlations?
Comparison in field and temperature
23
OASIS session 7 - 23.08.2021 - Jeanne Colbois
1. Overall magnetization
2. Ratio of ferromagnetic triangles
3. Order of the farther-neighbor correlations
Farther-neighbor couplings underestimated from the micromagnetic simulations?
An impact from even farther neighbor couplings?
Comparison in field and temperature
24
Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings Jeanne Colbois¹, Kevin Hofhuis² ³, Zhaochu Luo² ³, Xueqiao Wang² ³, Aleš Hrabec ² ³ , Laura J. Heyderman² ³, and Frédéric Mila¹ PRB 104 , 024418 (2021) (1) EPF Lausanne Institute of Physics, (2) ETH Zürich Department of Materials, (3) Paul Scherrer Institute Laboratory for Multiscale Materials experiments Switzerland OASIS session 7 - 23.08.2021 - Jeanne Colbois
Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings
By Jeanne Colbois
Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings
Invited talk at the Online Artificial Spin Ice Sessions (OASIS) session 7, organized by Gavin Macauley, Kevin Hofhuis and Laura Heyderman
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