Abstract

We employ an extended finite-element model as a design tool capable of incorporating the interaction between plasmonic antennas and magneto-optical effects, specifically the magneto-optical Kerr effect (MOKE). We first test our model in the absence of an antenna and show that for a semi-infinite thin-film, good agreement is obtained between our finite-element model and analytical calculations. The addition of a plasmonic antenna is shown to yield a wavelength dependent enhancement of the MOKE. The antenna geometry and its separation from the magnetic material are found to impact the strength of the observed MOKE signal, as well as the antenna’s resonance wavelength. Through optimization of these parameters we achieved a MOKE enhancement of more than 100 when compared to a magnetic film alone. These initial results show that our modeling methodology offers a tool to guide the future fabrication of hybrid plasmonic magneto-optical devices and plasmonic antennas for magneto-optical sensing.

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    [Crossref] [PubMed]
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    [PubMed]
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    [PubMed]
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    [Crossref]
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2017 (1)

P. Keatley, T. H. J. Loughran, E. Hendry, W. L. Barnes, R. J. Hicken, J. R. Childress, and J. A. Katine, “A platform for time-resolved scanning kerr microscopy in the near-field,” Rev. Sci. Instrum. 88, 123708 (2017).
[Crossref]

2016 (1)

P. S. Keatley, S. R. Sani, G. Hrkac, S. M. Mohseni, P. Dürrenfeld, T. H. J. Loughran, J. Åkerman, and R. J. Hicken, “Direct observation of magnetization dynamics generated by nanocontact spin-torque vortex oscillators,” Phys. Rev. B 94, 060402 (2016).
[Crossref]

2015 (4)

R. A. J. Valkass, W. Yu, L. R. Shelford, P. S. Keatley, T. H. J. Loughran, R. J. Hicken, S. A. Cavill, G. van der Laan, S. S. Dhesi, M. A. Bashir, M. A. Gubbins, P. J. Czoschke, and R. Lopusnik, “Imaging the equilibrium state and magnetization dynamics of partially built hard disk write heads,” Appl. Phys. Lett. 106, 232404 (2015).
[Crossref]

W. Yu, P. S. Keatley, P. Gangmei, M. K. Marcham, T. H. J. Loughran, R. J. Hicken, S. A. Cavill, G. van der Laan, J. R. Childress, and J. A. Katine, “Observation of vortex dynamics in arrays of nanomagnets,” Phys. Rev. B. 91, 174425 (2015).
[Crossref]

N. Maccaferri, K. E. Gregorczyk, T. V. A. G. de Oliveira, M. Kataja, S. van Dijken, Z. Pirzadeh, A. Dmitriev, J. Åkerman, M. Knez, and P. Vavassori, “Ultrasensitive and label-free molecular-level detection enabled by light phase control in magnetoplasmonic nanoantennas,” Nat. Commun. 6, 6150 (2015).
[Crossref] [PubMed]

A. Berger, R. A. de la Osa, A. Suszka, M. Pancaldi, J. Saiz, F. Moreno, H. Oepen, and P. Vavassori, “Enhanced magneto-optical edge excitation in nanoscale magnetic disks,” Phys. Rev. Lett. 115, 187403 (2015).
[Crossref] [PubMed]

2014 (1)

D. Kumar, P. Gupta, and A. Gupta, “In situ surface magneto-optical Kerr effect (s-MOKE) study of ultrathin soft magnetic FeCuNbSiB alloy films,” Mater. Res. Express,  1, 046405 (2014)
[Crossref]

2013 (3)

W. Yu, P. Gangmei, P. S. Keatley, R. J. Hicken, M. A. Gubbins, P. J. Czoschke, and R. Lopusnik, “Time resolved scanning Kerr microscopy of hard disk writer structures with a multilayered yoke,” Appl. Phys. Lett. 102, 162407 (2013).
[Crossref]

N. Maccaferri, A. Berger, S. Bonetti, V. Bonanni, M. Kataja, Q. H. Qin, S. van Dijken, Z. Pirzadeh, A. Dmitriev, J. Nogués, J. Åkerman, and P. Vavassori, “Tuning the magneto-optical response of nanosize ferromagnetic Ni disks using the phase of localized plasmons,” Phys. Rev. Lett. 111, 167401 (2013).
[Crossref] [PubMed]

N. Maccaferri, J. B. González-Díaz, S. Bonetti, A. Berger, M. Kataja, S. van Dijken, J. Nogués, V. Bonanni, Z. Pirzadeh, A. Dmitriev, J. Åkerman, and P. Vavassori, “Polarizability and magnetoplasmonic properties of magnetic general ellipsoids,”, Opt. Express 21, 9875–9889 (2013).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (3)

P. S. Keatley, V. V. Kruglyak, A. Neudert, M. Delchini, R. J. Hicken, J. R. Childress, and J. A. Katine, “Time and vector-resolved magneto-optical kerr effect measurements of large angle precessional reorientation in a 2×2um ferromagnet,” J. Appl. Phys. 105, 07D308 (2009).
[Crossref]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1, 438–483 (2009).
[Crossref]

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).
[Crossref] [PubMed]

2008 (2)

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and Mikael Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-optical Activity,” Small 4202–205 (2008).
[PubMed]

G. Armelles, J. B. González-Díaz, A. García-Martín, J. Miguel García-Martín, A. Cebollada, M. Ujué González, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 1616104–16112 (2008).
[PubMed]

2007 (1)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref] [PubMed]

2006 (1)

P. S. Keatley, V. V. Kruglyak, R. J. Hicken, J. R. Childress, and J. Katine, “Acquisition of vector hysteresis loops from micro-arrays of nano-magnets,” J. Magn. Magn. Mater. 306, 298–301 (2006).
[Crossref]

2005 (1)

S. B. Chaney, S. Shanmukh, R. A. Dluhy, and Y.-P. Zhao, “Aligned silver nanorod arrays produce high sensitivity surface-enhanced raman spectroscopy substrates,” Appl. Phys. Lett. 87, 031908 (2005).
[Crossref]

2004 (1)

F. Festy, A. Demming, and D. Richards, “Resonant excitation of tip plasmons for tip-enhanced raman snom,” Ultramicroscopy 100, 437–441 (2004).
[Crossref] [PubMed]

2003 (1)

G. Neuber, R. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Bäckström, and M. Rübhausen, “Temperature-dependent spectral generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 83, 4509–4511 (2003).
[Crossref]

2002 (1)

Th. Gerrits, H. A. M. van den Berg, J. Hohlfeld, L. Bär, and Th. Rasing., “Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping,” Nature 418, 509–512 (2002)
[Crossref] [PubMed]

2001 (1)

R. G. Milner and D. Richards, “The role of tip plasmons in near-field raman microscopy,” J. Microsc. 202, 66–71 (2001).
[Crossref] [PubMed]

2000 (3)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112, 7761–7774 (2000).
[Crossref]

J. Wu, J. R. Moore, and R. Hicken, “Optical pump-probe studies of the rise and damping of ferromagnetic resonance oscillations in a thin fe film,” J. Magn. Magn. Mater. 222, 189–198 (2000).
[Crossref]

Q. Qiu and S. D. Bader, “Surface magneto-optic Kerr effect,” Rev. Sci. Instrum. 71, 1243–1255 (2000)
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, T. Ghaemi, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

1997 (2)

P. Ma and P. R. Norton, “Growth of ultrathin Fe films on Ge(100): Structure and magnetic properties,” Phys. Rev. B. 56, 9881–9886 (1997)
[Crossref]

W. K. Hiebert, A. Stankiewicz, and M. R. Freeman, “Direct Observation of Magnetic Relaxation in a Small Permalloy Disk by Time-Resolved Scanning Kerr Microscopy,” Phys. Rev. Lett. 79, 1134–1137 (1997)
[Crossref]

1996 (1)

M. R. Freeman and J. F. Smyth, “Picosecond time-resolved magnetization dynamics of thin-film heads,” J. Appl. Phys. 79, 5895–5900 (1996)
[Crossref]

1992 (1)

1990 (1)

J. Zak, E. Moog, C. Liu, and S. Bader, “Fundamental magneto-optics,” J. Appl. Phys. 68, 4203–4207 (1990).
[Crossref]

1974 (1)

M. Fleischmann, P. Hendra, and A. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26, 163–166 (1974).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1878 (1)

J. Kerr, “On reflection of polarized light from the equatorial surface of a magnet,” London, Edinburgh, Dublin Philosophical Mag. J. Sci. 5, 161–177 (1878).
[Crossref]

1877 (1)

J. Kerr, “On rotation of the plane of polarization by reflection from the pole of a magnet,” London, Edinburgh, Dublin Philosophical Mag. J. Sci. 3, 321–343 (1877).
[Crossref]

Acimovic, S.

Åkerman, J.

P. S. Keatley, S. R. Sani, G. Hrkac, S. M. Mohseni, P. Dürrenfeld, T. H. J. Loughran, J. Åkerman, and R. J. Hicken, “Direct observation of magnetization dynamics generated by nanocontact spin-torque vortex oscillators,” Phys. Rev. B 94, 060402 (2016).
[Crossref]

N. Maccaferri, K. E. Gregorczyk, T. V. A. G. de Oliveira, M. Kataja, S. van Dijken, Z. Pirzadeh, A. Dmitriev, J. Åkerman, M. Knez, and P. Vavassori, “Ultrasensitive and label-free molecular-level detection enabled by light phase control in magnetoplasmonic nanoantennas,” Nat. Commun. 6, 6150 (2015).
[Crossref] [PubMed]

N. Maccaferri, A. Berger, S. Bonetti, V. Bonanni, M. Kataja, Q. H. Qin, S. van Dijken, Z. Pirzadeh, A. Dmitriev, J. Nogués, J. Åkerman, and P. Vavassori, “Tuning the magneto-optical response of nanosize ferromagnetic Ni disks using the phase of localized plasmons,” Phys. Rev. Lett. 111, 167401 (2013).
[Crossref] [PubMed]

N. Maccaferri, J. B. González-Díaz, S. Bonetti, A. Berger, M. Kataja, S. van Dijken, J. Nogués, V. Bonanni, Z. Pirzadeh, A. Dmitriev, J. Åkerman, and P. Vavassori, “Polarizability and magnetoplasmonic properties of magnetic general ellipsoids,”, Opt. Express 21, 9875–9889 (2013).
[Crossref] [PubMed]

Alaverdyan, Y.

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and Mikael Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-optical Activity,” Small 4202–205 (2008).
[PubMed]

Armelles, G.

G. Armelles, J. B. González-Díaz, A. García-Martín, J. Miguel García-Martín, A. Cebollada, M. Ujué González, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 1616104–16112 (2008).
[PubMed]

J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and Mikael Käll, “Plasmonic Au/Co/Au Nanosandwiches with Enhanced Magneto-optical Activity,” Small 4202–205 (2008).
[PubMed]

Atkinson, R.

Bäckström, J.

G. Neuber, R. Rauer, J. Kunze, T. Korn, C. Pels, G. Meier, U. Merkt, J. Bäckström, and M. Rübhausen, “Temperature-dependent spectral generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 83, 4509–4511 (2003).
[Crossref]

Badenes, G.

Bader, S.

J. Zak, E. Moog, C. Liu, and S. Bader, “Fundamental magneto-optics,” J. Appl. Phys. 68, 4203–4207 (1990).
[Crossref]

Bader, S. D.

Q. Qiu and S. D. Bader, “Surface magneto-optic Kerr effect,” Rev. Sci. Instrum. 71, 1243–1255 (2000)
[Crossref]

S. D. Bader and J. L. Erskine, “Magneto-Optical Effects,” in Ultrathin Magnetic Structures II, B. Heinrich and J. A. C. Bland, eds. (Springer, 1994), pp. 287–303.

Bär, L.

Th. Gerrits, H. A. M. van den Berg, J. Hohlfeld, L. Bär, and Th. Rasing., “Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping,” Nature 418, 509–512 (2002)
[Crossref] [PubMed]

Barnes, W. L.

P. Keatley, T. H. J. Loughran, E. Hendry, W. L. Barnes, R. J. Hicken, J. R. Childress, and J. A. Katine, “A platform for time-resolved scanning kerr microscopy in the near-field,” Rev. Sci. Instrum. 88, 123708 (2017).
[Crossref]

Bashir, M. A.

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Figures (9)

Fig. 1
Fig. 1 Schematic of the various MOKE geometries. The single ended arrow indicates the direction of the magnetization in each case. The incident optical beam is assumed to be p-polarized. The transverse MOKE configuration produces no change in polarization state, but instead modifies the amplitude of the reflected electric field.
Fig. 2
Fig. 2 Schematic of the periodic model geometry for calculation of the polar MOKE. (a) General schematic showing the magnetic region, air region, and slices through the model used in the recovery of the MOKE signal. (b) Model with the incident electric field polarization parallel to the direction. (c) The ŷ component of the electric field, which is the result of the magneto-optical rotation induced by the MOKE.
Fig. 3
Fig. 3 Schematic of the non-periodic cylindrical model used for calculation of the MOKE signal for an arbitrary angle of incidence. The incident beam (not shown) propagates in the direction, which is fixed. The detector plane and magnetic material rotate relative to the incident beam so as to maintain a standard θ 2θ geometry. As such the angle of incidence changes, while the geometry of the incident beam remains unaltered in COMSOL’s coordinate system.
Fig. 4
Fig. 4 Comparison of Kerr rotation/ellipticity values obtained from finite element modelling (data points) and analytical formulae (curves) for different angles of incidence. The finite element calculations were performed with the cylindrical model shown in Fig. 3. No data are shown for angles greater than 60° because at this point the detector plane enters the magnetic layer.
Fig. 5
Fig. 5 Schematic of the periodic, model with addition of a gold nano-disc. A series of disc diameters were used, from 80 nm to 160 nm with the 100 nm diameter disc shown. The gold disc is separated from the magnetic material by a variable air gap (10 nm in this figure). The disc diameter was fixed at 50 nm for all modeling presented in this manuscript.
Fig. 6
Fig. 6 Wavelength-dependent MOKE response for gold discs of different diameter (diameters are indicated in the legend). The discs were located 20 nm from the magnetic layer, and centered within the unit cell of the periodic model. (a) Kerr rotation, and (b) ellipticity. (c) The absolute Kerr signal (the sum of the rotation and ellipticity in quadrature) serves as a useful figure of merit, since the interplay between rotation and ellipticity is complicated. (d) Shows the reflected y component of the electric field normalized to the incident field amplitude (linearly polarized along the x axis with an amplitude of 1 V/m). This serves as a figure of merit when considering the practical implications of measuring the MOKE signal, and is comparable to the figure of merit derived in [4]. The dashed line in (d) shows the response of the model in the absence of a gold disc. The magnetic material modeled is the same as in the planar models without gold discs, and as such even the smallest resonance shown represents an enhancement of the MOKE signal on resonance.
Fig. 7
Fig. 7 Wavelength dependence of magneto-optical response for a gold disc of 120 nm diameter diameter placed at different distances from the magnetic layer (the separation between the gold disc and magnetic layer is indicated in the legend). (a) Shows the absolute Kerr rotation, and (b) shows the absolute y component of the normalized electric field. For clarity, data for the small smallest wavelengths has been omitted, since these showed behavior most likely associated with the periodicity of the model rather than the particle/under-layer separation.
Fig. 8
Fig. 8 Wavelength dependence of magneto optical response for a gold disc of 120 nm diameter diameter placed at different distances from the magnetic layer (again separation between the gold disc and magnetic layer is indicated in the legend). The spacing has been changed in finer steps around the value that showed the largest MOKE response in Fig. 7. As in the previous figure, (a) shows the absolute Kerr signal and (b) the normalized amplitude of the back reflected y component of the electric field. Here we see the maximum Kerr signal for a 9 nm gap, with a fall off in signal for gaps larger or smaller than this value. In addition, around 9 nm separation the resonant wavelength depends upon spacing, which was not observed for models with separations larger than 15 nm.
Fig. 9
Fig. 9 Electric field distribution of a 120 nm diameter gold disc placed at distances of 40 nm, 30 nm, 20 nm, and 9 nm from the magnetic material. The cross-sections show the x component of local field, normalized by the incident field amplitude, plotted at one instance in phase. a) The field distribution for a cross section through the center of the , plane. For clarity the color scale is limited to a maximum of 10 in the positive direction, the peak values are 16.0 for the 40 nm separation, and 29.3 for the 9 nm separation. b) The field distribution for a cross section through the center of the , ŷ plane. The field appears to penetrate further into the magnetic layer for the case of 9 nm separation, which can be most clearly seen in the comparison of the , ŷ plane field distribution.

Equations (9)

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MO = 0 r [ 1 i B z Q i B y Q i B z Q 1 i B x Q i B y Q i B x Q 1 ] ,
r s s = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1
r p p = n 1 cos θ 0 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 + 2 i Q n 1 n 0 cos θ 0 sin θ 1 B y ( n 1 cos θ 0 + n 0 cos θ 1 ) 2
r p s = i Q n 0 n 1 cos θ 0 ( sin θ 1 B x cos θ 1 B z ) cos θ 1 ( n 0 cos θ 0 + n 1 cos θ 1 ) ( n 1 cos θ 0 + n 0 cos θ 1 )
r s p = i Q n 0 n 1 cos θ 0 ( sin θ 1 B x + cos θ 1 B z ) cos θ 1 ( n 0 cos θ 0 + n 1 cos θ 1 ) ( n 1 cos θ 0 + n 0 cos θ 1 )
ϕ p = Re { r s p r p p }
ξ p = Im { r s p r p p }
ϕ = ( Re E x ) ( Re E y ) + ( Im E x ) ( Im E y ) ( Re E x ) 2 + ( Im E y ) 2
ξ = ( Re E x ) ( Im E y ) ( Im E x ) ( Re E y ) ( Re E x ) 2 + ( Im E y ) 2 ,

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