Magnetoplasmonic Crystals for Highly Sensitive Magnetometry

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Article Cite This: ACS Photonics 2018, 5, 4951−4959

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Magnetoplasmonic Crystals for Highly Sensitive Magnetometry Grigory A. Knyazev,†,‡ Pavel O. Kapralov,†,§ Nikolay A. Gusev,*,†,§ Andrey N. Kalish,†,‡ Petr M. Vetoshko,†,# Sarkis A. Dagesyan,‡ Alexander N. Shaposhnikov,⊥ Anatoly R. Prokopov,⊥ Vladimir N. Berzhansky,⊥ Anatoly K. Zvezdin,§,∥ and Vladimir I. Belotelov†,‡ †

Russian Quantum Center, 45, Skolkovskoye shosse, Moscow 121353, Russia Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia § Prokhorov General Physics Institute RAS, 38 Vavilov Street, Moscow 119991, Russia # Kotelnikov Institute of Radioengineering and Electronics, Mokhovaya 11-7, Moscow 125009, Russia ⊥ Vernadsky Crimean Federal University, Vernadsky Avenue 4, Simferopol 295007, Russia ∥ Faculty of Physics, National Research University - Higher School of Economics, Moscow 105066, Russia

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‡

ABSTRACT: Magnetometry and visualization of very small magnetic fields are vital for a large variety of the areas ranging from magnetocardiography and encephalography to nondistractive defectoscopy and ultra-low-frequency communications. It is very advantageous to measure magnetic fields using exchange-coupled spins in magnetically ordered media (flux-gate magnetometry). Here we introduce and demonstrate a novel concept of a roomtemperature magnetoplasmonic magnetic field sensor with high sensitivity and spatial resolution. It is based on the advanced fluxgate technique in which magnetization of the fully saturated magnetic film is rotated in the film plane and the monitored magnetic field is measured by detecting variation of transmittance through the sensing element: a magnetoplasmonic crystal. The experimental study revealed that such an approach allows one to reach the nT sensitivity level, which was limited by the noise of the laser. Moreover, we propose an approach to improve the sensitivity up to fT/Hz1/2 and reach micrometer spatial resolution. Therefore, the demonstrated magnetoplasmonic magnetometry method is promising for mapping and visualization of ultrasmall magnetic fields. KEYWORDS: magneto-optics, magnetometry, plasmonics agnetic fields of different animate and inanimate objects carry vital information about the nature, structure, composition, and state of objects. Thus, registration of small magnetic fields in space is essential for better understanding of cosmic charged particle dynamics.1 On the other hand, precise measurement of tiny magnetic fields in biomedicine establishes magnetocardiography suitable for early diagnostics of coronary artery disease2 and cardiomyopathy.3 In many cases, magnetometry requires not only high sensitivity but also micrometer and even sub-micrometer spatial resolution in combination with large-frequency band up to 1 GHz and even further. For example, the magnetoencephalography that is necessary, for example, for mindcontrolled cars and exoskeletons deals with magnetic fields less than 1 pT at hundreds of kHz frequencies at micrometer scales.4 The necessity to detect small magnetic fields at kHz frequencies also appears in magnetic nondestructive testing methods and ultra-low-field magnetic resonance imaging.5,6 Apart from that, it is very important to measure different components of the magnetic field vector. Vector magnetometry and magnetic field mapping are essential for reconstruction of the corresponding current density distribution in magnetocardiography as well as for geomagnetic

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© 2018 American Chemical Society

measurements, marine survey, magnetic GPS space research, etc.7,8 Among different types of sensitive magnetometers including superconducting quantum interference devices (SQUIDs),9 optically pumped magnetometers,10 cantilever magnetometers,11 and magnetometers with nitrogen vacancies (NVs) in diamond, the latter attract much research interest nowadays.12−14 The magnetometers based on the NV centers are similar to the magnetometers with optical pumping but have much higher spatial resolution and do not require heating of the sensing element. Such magnetometers allow measuring magnetic fields of several tens of nT at 50 nm scale.15 However, there is a trade-off between spatial resolution and sensitivity of the NV-center magnetometers. The spin−spin interactions within the ensemble drastically degrade the coherence of the system, leading to inhomogeneous broadening. In view of this fact, a large number of NV centers, which is necessary for the high sensitivity, demands the increase of the sensing element size, thus reducing the spatial resolution. Received: August 14, 2018 Published: November 21, 2018 4951

DOI: 10.1021/acsphotonics.8b01135 ACS Photonics 2018, 5, 4951−4959

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variation of the transmitted or reflected light intensity caused by magnetizing the film perpendicular to the grating slits.37 Similarly to the Voigt effect, the LMPIE is quadratic in the magneto-optical parameter, but nevertheless, it can be of the order of several percent and even larger. Importantly, the LMPIE takes place for normal light incidence, which perfectly fits requirements of the magnetometry with the in-plane magnetized films. Furthermore, in contrast to the Faraday effect and other bulk magneto-optical effects, to get high values of the LMPIE one does not need to use thicker magnetic films. In fact, the LMPIE almost saturates for the one micrometer thick magnetic films, which provides room for miniaturization. In the present work we propose and demonstrate a novel type of magneto-optical magnetic field sensor based on the LMPIE in the magnetoplasmonic crystal: a structure of an iron garnet film and a thin gold layer pierced with a periodic slit array. We show that such a structure provides enhancement of magneto-optical magnetometry and allows using the planar component of magnetization for reading low magnetic fields. The proof-of-concept sample of the magnetoplasmonic sensor demonstrates in the experimental study a sensitivity level of 2 nT/Hz1/2. Potentially the sensitivity of the proposed magnetoplasmonic sensor can be significantly improved up to fT/Hz1/2, while the lateral spatial resolution of such a sensor will reach several micrometers.

Apart from that, the NV magnetometry provides high sensitivity at a rather narrow frequency band. On the other hand, it is very advantageous to measure the magnetic field using coupled spins in magnetically ordered media. A strong exchange interaction between spins allows dealing with spin densities several orders of magnitude higher than for NV centers but without broadening of the magnetic resonances line width. This approach gave birth to flux-gate magnetometers,16−18 and its further development allowed reaching a 100 fT/Hz1/2 sensitivity.19 Most importantly, such level of sensitivity remains up to GHz frequencies. The magnetic field is measured by its influence on the medium magnetization detectable either by electromagnetic induction in the operating coils or by the magneto-optical effects. The magneto-optical reading in the flux-gate magnetometry provides additional functionality including vector character20,21 and imaging and micrometer spatial resolution.22 In the absence of the reading coils in such magnetometers the Schottky noise can be avoided. Moreover, magneto-optical measurements are contactless, allowing one to use the magnetic sensors in conjunction with optical fibers, which opens new horizons for invasive and probing magnetometry.23,24 The magneto-optical sensors are usually based on ferromagnetic metals (iron, nickel, cobalt, and their alloys) and ferrimagnetic dielectrics represented by bismuth irongarnet films.25−32 The latter are very efficient since they have quite high specific Faraday rotation and optical transparency in the visible and near-infrared spectral ranges.33,34 Moreover, the monocrystalline iron-garnet films with in-plane magnetic anisotropy demonstrate very high magnetic susceptibility that makes them valuable for sensing.19,20,35,36 However, the in-plane magnetization of the transparent magnetic films is not straightforwardly detectable by light. For technical reasons it is preferable to observe magnetic films at normal or slightly oblique incidence, otherwise special correcting optics or prisms are required that make the sensing element bulky and introduce excess noise. Therefore, one should exploit magneto-optical effects that are sensitive to the magnetization component orthogonal to the light wavevector. Among such effects, the widely used transverse and longitudinal magneto-optical Kerr effects require oblique incidence at large angles, and in addition the transverse effect is negligibly small for transparent media. Apart from the Kerr effects, there is the Voigt effect, but it is usually quite small for transparent media and may be insufficient for employment in magnetometry. Recently, it was demonstrated that a plasmonic cover of the transparent films significantly modifies their magneto-optical response, and the Faraday and transverse Kerr effects are resonantly enhanced by several orders of magnitude.37−48 The concept of the magnetic field measurement based on the transverse Kerr effect in a magnetoplasmonic nanostructure with graphene layer was proposed theoretically.49 However, magnetoplasmonic magnetometry has not been demonstrated yet. Moreover, in this respect, the transverse Kerr effect might not be an optimal option compared to other magneto-optical effects arising in the magnetoplasmonic crystals. Thus, such structures give birth to novel magneto-optical effects that do not appear for the smooth magnetic films. In particular, in the case of a magnetic film covered with a one-dimensional gold grating of subwavelength slits the longitudinal magnetophotonic intensity effect (LMPIE) arises. The LMPIE is a

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LMPIE-BASED MAGNETOMETRY Let us consider a magnetic dielectric film of a cubic crystal lattice and crystallographic axis orientation (111) placed into a saturating magnetic field H applied in-plane. As a result, the magnetic film is magnetized almost uniformly in-plane except some relatively small regions near its edges, where some magnetic domains might remain to minimize the demagnetizing magnetic field energy. If the control magnetic field H is rotated in the film plane at a frequency ω, so that its azimuthal angle varies as φH = ωt, then the film magnetization M follows with some delay in azimuthal angle, Δφ = φ − φH, where φ is the azimuthal angle of M (Figure 1). The magnetocrystalline anisotropy of the film deviates the magnetization from the film plane by an angle θ and provides its out-of-plane component. In the presence of the monitored magnetic field h the time dependences of both angles Δφ(t) and θ(t) are modified, and by analyzing their spectra it is possible to find the external magnetic field value and direction. The behavior of Δφ(t) and θ(t) depends on the relation between the control magnetic field and the field of the cubic magnetic anisotropy, HC ≈ K1/Ms, where K1 is the cubic anisotropy constant and Ms is the saturation magnetization. We restrict our consideration to the case of a relatively weak field of the cubic magnetic anisotropy HC ≪ H. At this the angle, θ is negligibly small and it is more preferable to detect Δφ(t). Therefore, it is necessary to use a magneto-optical effect that is sensitive to the in-plane magnetization. However, in the case of the transparent magnetic films the Voigt and transverse Kerr effects governed by the in-plane magnetization are quite small and are not suitable. For that reason, we deposited on the magnetic film a plasmonic one-dimensional grating to make optical transmittance and reflectance strongly sensitive to the in-plane magnetization (Figure 1). It becomes possible due to the longitudinal magneto-photonic intensity effect.37 The origin of the LMPIE is the following. Let us consider a dielectric magnetic film on a substrate covered by a one4952

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resonances at the wavelengths corresponding to the TE mode excitation when longitudinal magnetization is present. Therefore, at these wavelengths the intensity of the reflected or transmitted light pronouncedly depends on Mx. This is the essence of the LMPIE.37 Due to symmetry reasons, for normal incidence this dependence is even in Mx. The LMPIE is measured by the relative change of the detected light intensity δ for the remagnetization of the structure from the state with Mx = Ms to Mx = 0. For the sake of mechanical stability, it is more advantageous to detect the transmitted signal. In this case the LMPIE magnitude is given by37 δ=

T (Ms) − T0 T0

(2)

where T(Ms) and T0 are transmittance for Mx = Ms and Mx = 0, respectively. Due to the LMPIE, the rotating magnetization causes variations in transmittance that are quadratic in Mx:37 ÄÅ É 2 Ñ ÅÅ ij Mx(t ) yz ÑÑÑÑ ÅÅ zz δ Ñ T (t ) = T0ÅÅÅ1 + jjj j Ms zz ÑÑÑÑ ÅÅ k { ÑÖ ÅÇ (3) where δ is the LMPIE value measured for the fully saturated magnetic film. Consequently, measuring and analyzing light transmittance through the magnetoplasmonic crystal allows finding Mx(t) from eq 3. To establish a magnetometer scheme on this basis, one needs to relate Mx(t) and the monitored magnetic field h. To derive main expressions characterizing the proposed magnetic sensor, we assume that the monitored magnetic field h varies much slower than H(t), and consequently, it can be considered constant. In this case, the total magnetic field influencing the magnetization is

Figure 1. Schematics of the sample and the light incidence (a) and the schematics of the applied magnetic fields and magnetization direction (b). The one-dimensional metallic grating is placed on top of a magnetic film with the thickness d. Light with an intensity I0 hits the sample normally. The signal is measured in transmitted light; the transmittance of the sample is T. The rotating magnetic field H, the monitored field h, the total field Htot = H + h, and the magnetization M are shown schematically for visibility (in reality h ≪ H and M is close to parallel to Htot).

dimensional metallic grating, the z-axis is normal to the film plane, and the metal strips are aligned along the y-axis. When the structure is illuminated from the grating side, due to the diffraction, modes propagating along the x-axis are excited. At zero magnetization there are two series of waveguide modes, namely, the TE and TM ones. If the slits are rather narrow compared to the grating period, the modes’ dispersion law can be estimated by the approximation of smooth interfaces. For the latter case the dispersion law can be obtained from Maxwell’s equations and the boundary conditions:

H tot(t ) = H(t ) + h = [H cos(ωt ) + hx ]ex + [H sin(ωt ) + hy]ey + hzez

(4)

where ei are unitary vectors along the coordinate axes (Figure 1). As the sensor is aimed at the measurement of weak magnetic fields (h ≪ H), we use the linear in h approximation. Neglecting the influence of anisotropy, we assume that magnetization is directed along Htot. Then, taking into the account that the magnetization is fully saturated, for the component of magnetization perpendicular to the slits Mx, from eq 4 one can find

ij α yz ij α yz γ2d = tan−1jjj 1 zzz + tan−1jjj 3 zzz + πm jα z jα z (1) k 2{ k 2{ where αi = γi for TE modes and αi = γi/εi for TM modes, γ2 = (ε2k02 − β2)1/2, γ1,3 = (β2 − ε1,3k02)1/2, d is the magnetic film thickness, m is an integer, β is the mode propagation constant, k0 is the vacuum wavenumber, ε2 is the dielectric constant of the film, and ε1 and ε3 are dielectric constants of the adjacent media. The TE modes have Hx, Ey, and Hz field components, while the TM modes have Ex, Hy, and Ez components. However, when the film is magnetized along the x-axis, the modes’ polarization is modified, so that all six field components are nonzero, with magnetization-induced components being linear in magnetization. This leads to the fact that, for example, TM-polarized incident illumination causes excitation of not only TM modes but also TE modes as well. It implies that the reflectance and transmittance spectra acquire additional

l hy o o h | h sin(2ωt ) + x o = M so mcos(ωt ) − x cos(2ωt ) − } o o o o 2 2 H 2 H H n ~

M x (t )

(5)

Substitution of eq 5 with eq 3 provides the dependence of the optical transmittance on h, which can be presented as the decomposition into the temporal harmonics: T (t ) = T0̃ + T1̃ (t ) + T2̃ (t ) + ...

(6)

where Tk(t) is the combination of terms with cos(kωt) and sin(kωt). In particular, 4953

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ACS Photonics ÄÅ ÉÑ ÅÅ h ÑÑ hy x Å ̃ Å cos(3ωt ) + sin(3ωt )ÑÑÑÑ T3(t ) = −δT0ÅÅ ÅÅÇ 2H ÑÑÖ 2H

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K12 4Ms(2πMs2 − KU)

(7)

, where KU and K1 are the uniaxial and

cubic anisotropy constants, respectively. These constants are material parameters that characterize the energy of the magnetic anisotropy.50 The origin of the uniaxial anisotropy is the growth of the magnetic film in a certain direction, which leads to the fact that the magnetization properties are different in this very direction and the perpendicular one. Then, the frequency of the rotation should be low to ensure that the quasistatic consideration is relevant. It leads to the following restrictions: ω ≪ γK1/Ms, αω ≪ γH, where γ is the gyromagnetic ratio, and α is the Gilbert damping constant. Therefore, for the measurement of h∥ one can analyze the first or the third harmonics of the modulated transmittance. In the experiment it is preferable to measure the third harmonic to neglect some additional noise from the controlling field H, so further reasoning is carried out for the third harmonic. Since the photodetector current J is equal to the number of electrons knocked out by photons received by the photodetector per unit time, i.e., J=

ηeλ I0T 2πcℏ

Table 1. Parameters of the Magnetoplasmonic Samples name magnetic layer thickness, μm specific Faraday rotation, degree/μm (at 632 nm) grating period, nm grating slit width, nm

h e RηλI0T0δ 4πcℏ H

sample 1

sample 2 sample 3

1.9 1.4

1.9 1.4

1.6 1.3

340 120

335 200

350 170

Optical properties of the magnetoplasmonic samples were measured by the optical setup using a broadband illumination by a halogen lamp polarized either parallel (s-polarization) or perpendicular (p-polarization) to the grating slits. Light was focused on the sample and analyzed by a spectrometer. To measure the magnitude of the LMPIE δ, the sample was initially magnetized across the grating slits, which corresponds to Mx = M, and then remagnetized by rotating the magnetization in-plane by 90°, which corresponds to Mx = 0. A scheme of the experimental setup for demonstration of the proposed magnetic field sensing method, based on the optical balanced method, is shown in Figure 2. In the experiment two Thorlabs tunable semiconductor lasers were used: LD808-SE500 with a power of 500 mW

(8)

for the amplitude of the third harmonic of the photodetector voltage U3, using eq 8, one can obtain U3 =

EXPERIMENTAL SECTION

For the magnetoplasmonic crystals we used two rare-earth iron-garnet films of Bi 0 . 9 Gd 2 . 1 Fe 4 . 4 1 Sc 0 . 5 9 O 1 2 and Bi0.9Y1.2Lu0.9Fe4.2Sc0.8O12 composition. They were grown by the liquid phase epitaxy on the gadolinium gallium-garnet substrate with an orientation of (111). The composition of the magnetic films was measured using an electron probe microanalyzer. The first film is 1.9 μm thick and has a saturation magnetization of 4πMs = 1330 G, uniaxial anisotropy constant of KU = −6000 erg/cm3, and coercive field of 0.2 Oe. The second film is 1.6 μm thick and has a higher 4πMs = 1800 G, KU = −32600 erg/cm3, and coercive field of 0.3 Oe. As the uniaxial anisotropy constant for both films is negative, KU < 0, they both possess in-plane growth anisotropy, which leads to rather small in-plane saturating magnetic fields of 1 and 1.6 Oe, respectively. To fabricate the magnetoplasmonic structure, 80 nm thick gold films were thermally deposited on both magnetic films and then were perforated with periodic arrays of subwavelength slits. Two gratings were fabricated on the thicker magnetic film. They differ in the period and slit width. The third grating was fabricated on the thinner film. Parameters of the magnetoplasmonic samples are given in Table 1.

This means that the third harmonic of T(t) is proportional to the in-plane component h∥ = (hx, hy, 0) of the monitored magnetic field. The same is valid also for the first harmonic of T(t). The proposed concept implies restrictions on H and ω. The rotating field H should be strong enough so that its contribution to the free energy of the magnetic field is much stronger than that of anisotropy, which implies H≫

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(9)

where I0 and λ are the intensity and wavelength of the incident radiation, R is the photodetector transimpedance amplifier photocurrent-to-voltage conversion ratio, η is the quantum yield of the photodetector, e is electron charge, c is the speed of light in a vacuum, and ℏ is Planck’s constant. One can conclude that the detected signal is proportional to the laser intensity, optical transmittance through the magnetoplasmonic crystal, and the LMPIE magnitude. In conclusion of this section it should be noted that both δ and T0 depend on the parameters of the metallic grating. The grating period defines the resonant wavelengths, since the modes are excited due to higher diffraction orders. The influence of the grating thickness and dimension of the slits is not straightforward. The increase of the thickness, as well as the decrease of the slit width, leads to a decrease of the transmittance and interaction of light with the magnetic layer. The presence of the slits affects the efficiency of the mode excitation and their quality factor due to radiation losses. A more detailed analysis on the influence of the grating parameters on the LMPIE is presented in ref 51.

Figure 2. Scheme of the experimental setup for demonstration of the magnetoplasmonic magnetometer. 1, diode laser; 2, collecting lens; 3, polarizer; 4, sample with coils; 5, diffuser lens; 6, Wollaston prism; 7, balanced photodetector. 4954

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Figure 3. Transmittance and LMPIE spectra of sample 1 (a), sample 2 (b), and sample 3 (c) for the p-polarized (blue line) and s-polarized (red line) light. Light incidence is normal. For the LMPIE measurements the external magnetic field was 10 Oe.

the first U1 at 126 kHz and third U3 at 378 kHz harmonics in the spectrum of the photodetector signal. Thus, the output photodetector signal consists of three harmonics: U = U1 + U2 + U3, where U1 and U3 are proportional to the measured field h. In the experiment the field h was formed by the reference system of Helmholtz coils with a diameter of 100 mm. The inductance of this coil allowed generating a magnetic field at frequencies below 1 kHz. As a result of the magneto-optical modulation, this spectral range was transferred to frequencies near the first (126 kHz) and third (378 kHz) harmonics of the photodetector signal.

(laser A) and wavelength near 805 nm and L785P090 with a power of 90 mW and wavelength near 780 nm (laser B). The laser wavelength was tuned by changing the temperature of its box. The box temperature was thermostatically controlled with an accuracy of 0.02 °C. The optical setup was based on a balanced measurement method. The radiation generated by the laser diode 1 was collected by aspherical close-focus lens 2 into a converging beam. The polarization of this beam was set linear by the Glan-Taylor polarizer 3 so that, on the sample 4, which is an iron-garnet film with a gold grating layer, it was oriented at an angle of 45° to the grating lines. Due to the small focal length of lens 2 equal to 6 mm, the optical waist length reached 1.2 mm, which allowed the sample to be set in the center of the waist and to provide a narrow angular spectrum of optical radiation incident on the plasmon crystal and high intensity of light at the same time. The transmitted light was modulated by a magnetic field in accordance with the laws described above. Next, the radiation was divided into two beams with TE and TM polarization using a Wollaston 6 prism and was focused by lens 5 on photosensors of a balanced photodetector 7, as shown in Figure 2. The photodetector contained two FDS100 Si photodiodes (Thorlabs) and a specially made transimpedance amplifier with its own output noise of about 0.6 μV/Hz1/2 and a current-to-voltage conversion ratio R = 2500 ohm. The photodetector signal was digitized by the National Instruments USB-6351 data acquisition board and transferred to a PC for further processing. The signal processing consisted in obtaining its spectrum by a fast Fourier transform and extracting first three harmonics from this spectrum: the second one to estimate the LMPIE value and the first and third ones to measure the external field h. To minimize the influence of magnetic noise from the irongarnet film and eliminate the influence of 1/f noise, the following technique was used. The sample was placed in a magnetic field H rapidly rotating in the film plane. The field was formed in a small volume, about 10−3 cm3, by a system of coils without a core to eliminate the influence of its magnetic noise. The frequency of rotation of the magnetic field in the experiment was 126 kHz. The field amplitude did not exceed 4 Oe, which is significantly larger than the coercive field of each sample and sufficient to saturate it, providing a single domain state. Optical radiation passing through the sample was modulated by a magnetic field at a doubled frequency of rotation of the magnetic field due to the LMPIE. The inhomogeneity of the rate of rotation of the magnetization of the sample caused by the presence of a constant or oscillating external field h with a low frequency led to the appearance of

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MODULATION OF THE TRANSMITTED LIGHT VIA THE LMPIE The transmittance and LMPIE spectra of the three samples demonstrate multiple Fano-like resonances in the wavelength range from 720 to 820 nm (Figure 3). They are due to the excitation of the hybrid plasmonic-guided TM modes and the guided TE modes in the structures. The LMPIE has pronounced resonances for the illumination with both p- and s-polarizations, but the largest LMPIE values are observed in the p-polarized light. In particular, sample 1 has highest magnitude of the LMPIE in the negative peak (δ = −28%) at λ = 804 nm for illumination with p-polarized light (blue line in Figure 3a, Table 2). For that reason we performed magnetoTable 2. Magnetometer Performance of the Studied Magnetoplasmonic Structure operating wavelength λ, nm U3 at 10 nT, mV δ I0T0δ, mW best observed sensitivity, nT sensor noise hn at ν = 0, pT/Hz1/2

sample 1

sample 2

sample 3

804.1 0.26 0.28 16.1 8.5 10

781 0.04 0.093 2.7 2.4 41

776.4 0.05 0.074 3.2 2.9 42

metry measurements with sample 1 using diode laser A, having an emission central wavelength of λ = 805 nm, which was tuned to the optimal wavelength of the LMPIE by changing the laser enclosure-box temperature. Sample 2 was fabricated on the basis of the same magnetic film as sample 1, but the gold grating period is 5 nm smaller and, most importantly, the slit width is as large as 200 nm. For this reason, the maximum magnitude of the LMPIE is smaller (δ = 13%), and it is shifted to λ = 793 nm. It should be noted that in this case the positive peak of the LMPIE is larger than the absolute value of the negative one: δ = 13% and δ = −7%. 4955

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of the incident light intensity, transmittance through the grating, and the LMPIE magnitude: U3 ≈ I0T0δ. The relative values of this product are in nice agreement with the observations: the product for sample 1 is approximately 6 times larger than for sample 2 and 5 times larger than for sample 3. The sensitivity of the magnetometer scheme is also related by the noise level, which is U3c = 0.225 mV for laser A (at λ = 802.9 nm), U3c = 0.011 mV for laser B (at λ = 781.0 nm), and U3c = 0.015 mV for laser B (at λ = 776.6 nm). Therefore, laser B is much more suitable for the magnetometer measurements. As a result, the lowest monitored field was detected with sample 2: hmin = 2.4 nT (red asterisk in Figure 4). For sample 3, it is a bit larger: hmin = 2.9 nT. Potentially, sample 1 would give much better results if laser B could be tuned to its main resonance at λ = 804.1 nm; in this case the minimum detectable field would be less than 1 nT: hmin = 0.9 nT. As can be seen from Figure 4, the magnetometer has a large dynamic range. It could be considered that the maximal measured field is about 11 μT for sample 1 and 75 μT for samples 2 and 3: above the given values of the monitored fields, the scheme passes in a nonlinear mode, due to the fact that such values are close to the magnitude of the control field.

For the magnetometry measurements we used the available laser B with a central wavelength of λ = 783 nm to detect near the second LMPIE resonance at λ = 781 nm, where the LMPIE is still rather pronounced and reaches δ = 9% (Figure 3b, Table 2). The magnetic film of sample 3 has a bit different composition and is 300 nm thinner than for the two previous samples. It leads to the spectral shift of the resonances with respect to the two previous gratings (Figure 3c). The LMPIE reaches |δ| = 14% at λ = 741 nm. This time, similarly to sample 1, the positive LMPIE peak becomes smaller than the absolute value of the negative peak: δ = −14% and δ = 9%. For the magnetometry measurement of sample 3 we used the same laser as for sample 2 and investigated the LMPIE peak for the s-polarized illumination at 776 nm (δ = 7.4%, Figure 3c, Table 2). The s-polarization was chosen since near the central wavelength of laser B the LMPIE resonances in s-polarization are stronger than in p-polarization.

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EXPERIMENTAL DEMONSTRATION OF THE MAGNETOPLASMONIC MAGNETOMETRY Let us now consider the performance of these three samples for detection of small magnetic fields. For this purpose we applied a monitored magnetic field h parallel to the slits of the magnetoplasmonic crystal, varied its value from 1 nT to 10 μT, and measured time dependence of the transmitted light intensity at the operating wavelengths corresponding to the maxima of the LMPIE. The noise characteristic of the setup measured for sample 2 at frequencies less than 1 kHz is shown in the inset of Figure 4. In this range the noise level almost does not change with frequency, which is essential for the magnetometry of low-frequency magnetic fields.

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ESTIMATION OF THE SENSITIVITY LIMITS Let us now estimate the limit values of the magnetic noise and sensitivity of the proposed magnetometry scheme. The noise value of the third harmonic of the photodetector current Jn3 in the frequency band Δf is composed of the shot noise arising from the photodetector and the laser intensity fluctuations that are related to the physical processes of photon generation and are caused by fluctuations in the laser pump current, in particular, its flicker noise, i.e., Jn3 =

2e⟨J ⟩Δf + ν⟨J ⟩Δf

(10)

Here the first term describes the photodetector noise, while the second term stands for the flicker noise, ν is the relative amplitude of the noise modulation of the laser intensity, and ⟨J⟩ is the average photodetector current. Taking into account eqs 8 and 9 and the mean value of transmittance ⟨T⟩ = T̃ 0 = T0(1 + δ/2), one can obtain the magnetometer noise hn in the Δf band, determining the sensitivity level: hn =

yz 2H ijj 4πcℏ zz Δf jj + ν zz δ jk ηλI0T0 {

(11)

which determines the sensitivity. The noise level of the system is thus inversely proportional to the LMPIE value and nonlinearly depends on the transmitted light intensity. In the case where the photodetector noise prevails over the noise level of the laser (i.e., if ν ≪ 4πcℏ/(ηλI0T0)), then the sensitivity increases proportionally to the product of δ I0T0 . However, if the laser noise is larger than the photodetector noise (i.e., ν ≫ 4πcℏ/(ηλI0T0)), then the sensitivity increases proportionally to δ. In the experimental setup the noise was mainly due to the laser noise. However, assuming use of an ideal laser, i.e., ν = 0, so that the only noise source of the measuring scheme is the shot noise, one could find the detection limit of this magnetometer scheme for three samples (see last row in Table 2). The highest sensitivity is expected for sample 1 and might reach 10 pT/Hz1/2.

Figure 4. Dependence of the third-harmonic amplitude, U3, on the monitored magnetic field hy oscillating at 515 Hz (indicated by a red arrow on the noise characteristic in the inset). Inset: Noise characteristic of the magnetometer setup measured for sample 2.

The photodetector signal third-harmonic amplitude U3 is proportional to hy for all three samples (see linear fits for the experimental data for samples 1, 2, and 3 shown with circles, triangles, and squares, respectively in Figure 4). This completely agrees with eq 9. The largest signal is observed for sample 1 (circles, blue line in Figure 4). It exceeds U3 for the other two samples by 6 and 5 times, respectively. Actually, in accordance with eq 9, for a given monitored magnetic field the signal of the photodetector is proportional to the product 4956

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It should be noted that the noise related to the fluctuations of the magnetization, estimated for these samples for the square garnet film of 1 × 1 × 0.0001 cm3 with 4πMs = 1750 G and α = 0.0001 at room temperature according to ref 52, is at the level of 1 fT/Hz1/2. To reach this level of sensitivity, one should overcome the shot noise and other types of noise coming from the optical detection system. This problem can be solved using the phenomenon of the frequency shift of the photons inelastically scattered on the rotating spins at the frequency ω. Due to the magneto-optical interaction via the LMPIE, the spectrum of the scattered photons acquires multiple harmonics: ω0 + mω, where m is an integer. As we discussed above, the third harmonic (m = 3) carries information about the monitored magnetic field and should be measured with reduced noise. Schottky noise is determined by the average signal intensity including both the central component (ω0) and the modulation peaks (ω0 ± 3ω). At the same time, the measured signal is determined only by the modulation components. Therefore, one needs to minimize the intensity of the central component and keep the modulation component at the same level. For this purpose, a scheme with two Fabry−Perot interferometers of a high quality factor can be used. To diminish the noise of the laser, optical radiation can be passed through the first interferometer tuned to transmit the central frequency of the laser, ω0. Moreover, the transmittance minima of the interferometer should be spectrally located at a distance of 3ω from the laser frequency. The light passing through the first interferometer is incident on the sample, and due to the LMPIE the photons at ω0 ± 3ω appear. Modulated optical radiation is passed through the second interferometer tuned to suppress the main spectral component ω0 and to almost fully transmit ω0 ± 3ω. As a result, the use of a second interferometer should improve the signal-to-noise ratio by a multiple of the interferometer’s Qfactor. Consequently, detection of the in-plane magnetization rotation via the LMPIE in plasmonic crystals can potentially allow the detection of weak magnetic fields with sensitivity limited by magnetic noise. One of the main advantages of this approach with respect to the induction method is related to the high spatial resolution that can be obtained. In the lateral direction it is limited by the diameter of the focused laser beam. To achieve necessary functionality of the plasmonic grating at least several periods of the grating must be illuminated by the laser beam, which gives a size of the illuminating beam of a few micrometers. On the other hand, spatial resolution orthogonal to the magnetic film direction is determined by the thickness of the magnetic film. The LMPIE magnitude remains at a rather high level even for magnetic films of a hundred nanometers thickness that provides submicrometer resolution in this direction. One should note that the in-plane magnetization can also be detected without any plasmonic cover by the Faraday effect but in obliquely incident light. The ratio of the noise level for the detection via LMPIE and Faraday effects, taking into account Schottky noise (at ν = 0), is given by hn = hnF

of 45 deg. In accordance with eq 12, the LMPIE detection scheme advances the Faraday one by an order of magnitude for the investigated sample.

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CONCLUSION To conclude, here we propose and demonstrate a novel approach for the magneto-optical magnetometry based on the longitudinal magnetophotonic intensity effect in magnetoplasmonic crystals. The periodically nanostructured plasmonic cover of the magnetic dielectric film provides pronounced resonances of the LMPIE, where the light intensity modulation reaches tens of percent. Most importantly, this detection scheme is applicable to the observation of in-plane magnetization, which allows operating with small controlling magnetic fields of a few Oe and potentially provides sensitivity at the fT level. A simple implementation scheme with a diode laser and a balanced detector is demonstrated. A theoretical model of the sensor is provided, which is in good agreement with the conducted experiment. It was found that the effectiveness of the method depends on the optical properties of the magnetoplasmonic crystal: the transmittance and the LMPIE magnitude. In particular, the signal of the photodetector, which corresponds to the monitored field, is proportional to the product of the transmittance and LMPIE, and the sensitivity of the method increases in proportion to the product of the transmittance and the square LMPIE in the case when the shot noise is predominant. The best level of sensitivity obtained in the experimental setup was about 2 nT/Hz1/2. However, potentially if the shot noise is overcome, it can be made up to fT/Hz1/2, i.e., at the level of magnetic noise. The method is characterized by a dynamic range of up to 0.1 mT and a bandwidth from a few Hz to half of the frequency of the rotating control field. The other feature of this method is high spatial resolution of a few micrometers.

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*E-mail (N. Gusev): [email protected]. ORCID

Nikolay A. Gusev: 0000-0001-8333-7773 Andrey N. Kalish: 0000-0001-9984-9028 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Russian Foundation for Basic Research (grant no. 18-29-02120) and Russian Presidential Grant MD-1615.2017.2. V.I.B. also acknowledges financial support by the Foundation for the Advancement of Theoretical Physics BASIS. A.N.S. acknowledges the financial support by Ministry of Science in the framework of the state task (project no. 3.7126.2017/8.9).

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REFERENCES

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2T0FΦ2 T0δ 2

AUTHOR INFORMATION

Corresponding Author

(12)

where T0F is the transmittance of the magnetic film in the scheme with the Faraday effect and Φ is the Faraday angle of rotation of the polarization plane for light incidence at an angle 4957

DOI: 10.1021/acsphotonics.8b01135 ACS Photonics 2018, 5, 4951−4959

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DOI: 10.1021/acsphotonics.8b01135 ACS Photonics 2018, 5, 4951−4959