Long-range magnetic ordering can be stabilized in arrays of single-domain nanomagnets through dipolar interactions. In these metamaterials, the magnetic properties are determined by geometric parameters such as the nanomagnet shape and lattice symmetry. Here, we demonstrate engineering of the anisotropy in a dipolar magnetic metamaterial by tuning of the lattice parameters. Furthermore, we show how a modified Kittel's law explains the resulting domain configurations of the dipolar ferromagnetic arrays.
References
1.
R. P.
Cowburn
, D. K.
Koltsov
, A. O.
Adeyeye
, M. E.
Welland
, and D. M.
Tricker
, “ Single-domain circular nanomagnets
,” Phys. Rev. Lett.
83
, 1042
–1045
(1999
).2.
S.
Bedanta
and W.
Kleemann
, “ Supermagnetism
,” J. Phys. D: Appl. Phys.
42
, 013001
(2009
).3.
M.
Varón
, M.
Beleggia
, T.
Kasama
, R. J.
Harrison
, R. E.
Dunin-Borkowski
, V. F.
Puntes
, and C.
Frandsen
, “ Dipolar magnetism in ordered and disordered low-dimensional nanoparticle assemblies
,” Sci. Rep.
3
, 1234
(2013
).4.
M.
Ewerlin
, D.
Demirbas
, F.
Brüssing
, O.
Petracic
, A. A.
Ünal
, S.
Valencia
, F.
Kronast
, and H.
Zabel
, “ Magnetic dipole and higher pole interaction on a square lattice
,” Phys. Rev. Lett.
110
, 177209
(2013
).5.
N.
Leo
, S.
Holenstein
, D.
Schildknecht
, O.
Sendetskyi
, H.
Luetkens
, P. M.
Derlet
, V.
Scagnoli
, D.
Lançon
, J. R. L.
Mardegan
, T.
Prokscha
, A.
Suter
, Z.
Salman
, S.
Lee
, and L. J.
Heyderman
, “ Collective magnetism in an artificial 2D XY spin system
,” Nat. Commun.
9
, 2850
(2018
).6.
R.
Streubel
, N.
Kent
, S.
Dhuey
, A.
Scholl
, S.
Kevan
, and P.
Fischer
, “ Spatial and temporal correlations of XY macro spins
,” Nano Lett.
18
, 7428
–7434
(2018
).7.
E.
Digernes
, S. D.
Slöetjes
, A.
Strømberg
, A. D.
Bang
, F. K.
Olsen
, E.
Arenholz
, R. V.
Chopdekar
, J. K.
Grepstad
, and E.
Folven
, “ Direct imaging of long-range ferromagnetic and antiferromagnetic order in a dipolar metamaterial
,” Phys. Rev. Res.
2
, 013222
(2020
).8.
P.
Politi
, M. G.
Pini
, and R.
Stamps
, “ Dipolar ground state of planar spins on triangular lattices
,” Phys. Rev. B
73
, 020405
(2006
).9.
H.
Benson
and D. L.
Mills
, “ Spin waves in thin films; Dipolar effects
,” Phys. Rev.
178
, 839
–847
(1969
).10.
K.
De'Bell
, A. B.
Maclsaac
, and J. P.
Whitehead
, “ Dipolar effects in magnetic thin films and quasi-two-dimensional systems
,” Rev. Mod. Phys.
72
, 225
–257
(2000
).11.
J. M.
Luttinger
and L.
Tisza
, “ Theory of dipole interaction in crystals
,” Phys. Rev.
70
, 954
–964
(1946
).12.
J. M.
Luttinger
and L.
Tisza
, “ Erratum: ‘Theory of dipole interaction in crystals’ [Phys. Rev. 70, 954 (1946)]
,” Phys. Rev.
72
, 257
(1947
).13.
V. M.
Rozenbaum
, “ Vibrational and orientational states of surface atomic groups
,” Sov. Phys. Usp.
34
, 883
–902
(1991
).14.
P.
Politi
and M. G.
Pini
, “ Dipolar interaction between two-dimensional magnetic particles
,” Phys. Rev. B
66
, 214414
(2002
).15.
R. F.
Wang
, C.
Nisoli
, R. S.
Freitas
, J.
Li
, W.
McConville
, B. J.
Cooley
, M. S.
Lund
, N.
Samarth
, C.
Leighton
, V. H.
Crespi
, and P.
Schiffer
, “ Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands
,” Nature
439
, 303
–306
(2006
).16.
L. L.
Guyader
, A.
Kleibert
, A.
Fraile Rodríguez
, S. E.
Moussaoui
, A.
Balan
, M.
Buzzi
, J.
Raabe
, and F.
Nolting
, “ Studying nanomagnets and magnetic heterostructures with X-ray PEEM at the Swiss Light Source
,” J. Electron Spectrosc. Related Phenom.
185
, 371
–380
(2012
).17.
C.
Kittel
, “ Theory of the structure of ferromagnetic domains in films and small particles
,” Phys. Rev.
70
, 965
–971
(1946
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
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