A vortex-like magnetic state with zero net magnetization—called a magnetic toroidal dipole (MTD)—exhibits a variety of fascinating magnetoelectric (ME) cross-coupling functionalities. However, designing and controlling MTDs in conventional crystals remains challenging. Here, we fabricated a model system of mesoscopic MTDs using planar patterned nanomagnets. By exploiting a symmetry-resolved nonlinear optical technique, we directly detected mesoscopic MTDs whose magnitude and direction are well-controlled using external magnetic fields. This approach may provide a guide for the design and control of nanoscopic-to-mesoscopic functional ME materials working at room temperature.
References
1.
M.
Fiebig
, J. Phys. D: Appl. Phys.
38
, R123
(2005
).2.
W.
Eerenstein
, N. D.
Mathur
, and J. F.
Scott
, Nature
442
, 759
(2006
).3.
S. W.
Cheong
and M.
Mostovoy
, Nat. Mater.
6
, 13
(2007
).4.
Y.
Tokura
, S.
Seki
, and N.
Nagaosa
, Rep. Prog. Phys.
77
, 076501
(2014
).5.
L. J.
Heyderman
and R. L.
Stamps
, J. Phys.: Condens. Matter
25
, 363201
(2013
).6.
T.
Shinjo
, T.
Okuno
, R.
Hassdorf
, K.
Shigeto
, and T.
Ono
, Science
289
, 930
(2000
).7.
J.
Sklenar
, Y.
Lao
, A.
Albrecht
, J. D.
Watts
, C.
Nisoli
, G.-W.
Chern
, and P.
Schiffer
, Nat. Phys.
15
, 191
(2019
).8.
J.
Lehmann
, C.
Donnelly
, P. M.
Derlet
, L. J.
Heyderman
, and M.
Fiebig
, Nat. Nanotechnol.
14
, 141
(2019
).9.
E.
Mengotti
, L. J.
Heyderman
, A. F.
Rodríguez
, F.
Nolting
, R. V.
Hügli
, and H.-B.
Braun
, Nat. Phys.
7
, 68
(2011
).10.
A.
Farhan
, M.
Saccone
, C. F.
Petersen
, S.
Dhuey
, R. V.
Chopdekar
, Y.-L.
Huang
, N.
Kent
, Z.
Chen
, M. J.
Alava
, T.
Lippert
, A.
Scholl
, and S.
van Dijken
, Sci. Adv.
5
, eeav6380
(2019
).11.
N.
Kida
, T.
Yamada
, M.
Konoto
, Y.
Okimoto
, T.
Arima
, K.
Koike
, H.
Akoh
, and Y.
Tokura
, Phys. Rev. Lett.
94
, 077205
(2005
).12.
S.
Prosandeev
, I.
Ponomareva
, I.
Kornev
, and L.
Bellaiche
, Phys. Rev. Lett.
100
, 047201
(2008
).13.
O. G.
Udalov
, M. V.
Sapozhnikov
, E. A.
Karashtin
, B. A.
Gribkov
, S. A.
Gusev
, E. V.
Skorohodov
, V. V.
Rogov
, A. Y.
Klimov
, and A. A.
Fraerman
, Phys. Rev. B
86
, 094416
(2012
).14.
V. L.
Krutyanskiy
, I. A.
Kolmychek
, B. A.
Gribkov
, E. A.
Karashtin
, E. V.
Skorohodov
, and T. V.
Murzina
, Phys. Rev. B
88
, 094424
(2013
).15.
B. B.
Van Aken
, J.-P.
Rivera
, H.
Schmid
, and M.
Fiebig
, Nature
449
, 702
(2007
).16.
M.
Matsubara
, Y.
Kaneko
, J.-P.
He
, H.
Okamoto
, and Y.
Tokura
, Phys. Rev. B
79
, 140411(R)
(2009
).17.
A. S.
Zimmermann
, D.
Meier
, and M.
Fiebig
, Nat. Commun.
5
, 4796
(2014
).18.
N. A.
Spaldin
, M.
Fiebig
, and M.
Mostovoy
, J. Phys.: Condens. Matter
20
, 434203
(2008
).19.
Y. F.
Popov
, A. M.
Kadomtseva
, G. P.
Vorob'ev
, V. A.
Timofeeva
, D. M.
Ustinin
, A. K.
Zvezdin
, and M. M.
Tegeranchi
, J. Exp. Theor. Phys.
87
, 146
(1998
).20.
J. H.
Jung
, M.
Matsubara
, T.
Arima
, J. P.
He
, Y.
Kaneko
, and Y.
Tokura
, Phys. Rev. Lett.
93
, 037403
(2004
).21.
T.
Arima
, J.-H.
Jung
, M.
Matsubara
, M.
Kubota
, J.-P.
He
, Y.
Kaneko
, and Y.
Tokura
, J. Phys. Soc. Jpn.
74
, 1419
(2005
).22.
M.
Baum
, K.
Schmalzl
, P.
Steffens
, A.
Hiess
, L. P.
Regnault
, M.
Meven
, P.
Becker
, L.
Bohatý
, and M.
Braden
, Phys. Rev. B
88
, 024414
(2013
).23.
T.
Sato
, N.
Abe
, S.
Kimura
, Y.
Tokunaga
, and T.
Arima
, Phys. Rev. Lett.
124
, 217402
(2020
).24.
J.
Mund
, D. R.
Yakovlev
, A. N.
Poddubny
, R. M.
Dubrovin
, M.
Bayer
, and R. V.
Pisarev
, Phys. Rev. B
103
, L180410
(2021
).25.
H.
Saito
, K.
Uenishi
, N.
Miura
, C.
Tabata
, H.
Hidaka
, T.
Yanagisawa
, and H.
Amitsuka
, J. Phys. Soc. Jpn.
87
, 033702
(2018
).26.
H.
Watanabe
and Y.
Yanase
, Phys. Rev. B
98
, 220412(R
) (2018
).27.
M. J.
Donahue
and D. G.
Porter
, “OOMMF user's guide, version 1.0
,” Interagency Report No. NISTIR 6376
(National Institute of Standards and Technology
, Gaithersburg, MD
, 1999
).28.
S.
Yakata
, M.
Miyata
, S.
Nonoguchi
, H.
Wada
, and T.
Kimura
, Appl. Phys. Lett.
97
, 222503
(2010
).29.
M.
Fiebig
, V. V.
Pavlov
, and R. V.
Pisarev
, J. Opt. Soc. Am. B
22
, 96
(2005
).30.
31.
M.
Matsubara
, A.
Schmehl
, J.
Mannhart
, D. G.
Schlom
, and M.
Fiebig
, Phys. Rev. B
81
, 214447
(2010
).32.
M.
Matsubara
, C.
Becher
, A.
Schmehl
, J.
Mannhart
, D. G.
Schlom
, and M.
Fiebig
, J. Appl. Phys.
109
, 07C309
(2011
).33.
M.
Matsubara
, A.
Schroer
, A.
Schmehl
, A.
Melville
, C.
Becher
, M.
Trujillo-Martinez
, D. G.
Schlom
, J.
Mannhart
, J.
Kroha
, and M.
Fiebig
, Nat. Commun.
6
, 6724
(2015
).34.
K.
Konishi
, T.
Higuchi
, J.
Li
, J.
Larsson
, S.
Ishii
, and M.
Kuwata-Gonokami
, Phys. Rev. Lett.
112
, 135502
(2014
).35.
A.
Kirilyuk
and T.
Rasing
, J. Opt. Soc. Am. B
22
, 148
(2005
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
