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I got this diagram from wikipedia, but my physics book and Jim Hawkins WA2WHV give the same diagram. The complete derivation from Maxwell's equations fills entire college-level textbooks, and is too involved to get into here. But when considering radiation from an antenna (a current flowing in a linear conductor), it boils down to the fact that there are several distinct components to both the E (electric) and H (magnetic) fields around the antenna. The electric and magnetic parts of the field stand in a fixed ratio of strengths in order to satisfy the two Maxwell equations that specify how one is produced from the other. The confusion stems from the fact that they (the instantaneous electric and magnetic vector fields) are 90 degrees apart in space, not in time.
Aren't you confusing the induced voltage in an antenna with the E field of the electromagnetic wave? Not the answer you're looking for?Browse other questions tagged rf radio electromagnetism theory or ask your own question. Why does EM radiation travel much further than the magnetic field of an equivalent power electromagnet? Crustal fluids exist near fault zones, but their relation to the processes that generate earthquakes, including slow-slip events, is unclear.
Estimates of the amplitude ratio of the horizontal magnetic field (H) at sites 118 and 122 relative to the reference site 001 are shown together with the associated phase difference at a frequency of 0.2?Hz. Estimates of the apparent resistivity are shown with impedance phase at sites 118 and 122 at a frequency of 0.2?Hz. Estimates before the earthquake (black), immediately after the earthquake (solid red) and 1 month after the earthquake (solid blue) are shown for comparison. Crustal structure in the fault zones is often characterized by low resistivity1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 that indicates crustal fluid and suggests a possible relation to earthquake generation. In this study, we focus on the time variations of MT parameters, such as the apparent resistivity and impedance phase.
Figure 3 shows examples of the apparent resistivity and impedance phase derived from the off-diagonal elements of the impedance tensor relating two components of the electrical field to two components of the horizontal magnetic field at sites 118 and 122.
We question whether the observed changes in resistivity occurred in association with the foreshock cluster. Figure 5a shows the co-seismic and post-seismic changes in the average apparent resistivity and impedance phase for each frequency at each site, together with the minimum changes in the confidence level, corresponding to ~99%.
As the co-seismic changes are largest at frequencies near 0.2?Hz, we presume a probable area of resistivity change as follows. Considering some ambiguities in the 2D approximation and errors in the observations, we conclude that these models can be used only to infer the possible location of an area of a resistivity anomaly and the magnitude of change. Thin films of a germanium-antimony-tellurium alloy are typically used in conventional phase-change random access memories (PCRAMs). This research was supported by a grant from the Cabinet Office's Funding Program for World-Leading Innovative R&D on Science and Technology.
Figure 1: Switching operation of the PCRAM device employing the superlattice phase-change film. In the area of next-generation non-volatile memory, attention is being focused on PCRAM, which exploits the difference in electrical resistance between the crystalline and amorphous states of chalcogenide alloys, MRAM, which exploits the difference in electrical resistance generated by a magnetoresistance effect of magnetic alloys, and a resistive random access memory (RRAM), which exploits the difference in electrical resistance generated by the crystalline states of oxides through the application of a strong electric field. With the ongoing evolution of mobile IT devices such as smart phones, the radical reduction of the power consumption of solid-state memories and the realization of increased component density and speed are urgent issues, necessitating the development of next-generation non-volatile memories.
The memory layer of the low power consumption PCRAM was a crystalline laminated film formed by multilayering germanium-tellurium and antimony-tellurium crystal sub-layers. The cause of the fact that PCRAM using the superlattice phase-change film has an electrical resistance one order of the magnitude higher than that of PCRAM using the alloy with the same composition, in spite of its high crystallinity, was analyzed. Measurement of the change in electrical resistance in a PCRAM employing the superlattice phase-change film in response to a magnetic field at room temperature revealed a giant magnetoresistance effect, with a change in resistance of more than 2000% in response to a 0.1 tesla magnetic field (Fig. A superlattice phase-change film was fabricated on a silicon substrate and differences in the spin-polarized current at the surface of the film due to the Rashba effect were measured.
Figure 2: Optical reflectance of the superlattice phase-change film fabricated on a silicon substrate. This research fabricated the world's first topological insulator functioning at room temperature and higher, in addition to providing the world's first demonstration of the feasibility of spintronics exploiting the Rashba effect, using an artificial superlattice phase-change film. The replacement of conventional PCRAM recording films with the developed artificial superlattice film will not only reduce power consumption, but will also make it possible to change phase by independently controlling external electrical and magnetic fields, thus enabling control of electrical resistance.
Single-phase induction motors are widely used as small output motors for the drives in household electrical appliances and office machinery, like fans and washing machines, because they can use single-phase AC, the typical power source for home electronics. The current density distributions for maximum torques at rotation speeds of 2,100 rpm are shown in fig.
The B and E fields are actually 90 degrees out of phase with each other, not in phase as the diagram shows. I always understood them to be in quadrature, but I don't have time to look that up right now.
These E and B fields are also in phase, with both reaching maxima and minima at the same points in space (see illustrations). If you interchanged the axes of the E and B fields, some types of antenna would fail to pick up the signal until you rotated the antenna by 90 degrees.
Therefore induced voltage is highest when magnetic field is zero, when its derivative is highest. Here the estimates over 6?h, including the mainshock, which is indicated by the dotted vertical line (purple), are only shown. However, the amount of data is not sufficient for this purpose; MT data sampled at 24?Hz are only available for 15?h, from 1700 to 0800 hours in local time, and for 7 days at site 118, 6 days at site 120, and 3 days at sites 121 and 122. 5b shows the co-seismic and post-seismic changes in the average amplitude ratios and phase.
A conductive zone with a resistivity of ~10??m extends to a depth of 3?km, as shown in Fig. At 3–6?km depth, the resistivity is decreased by 50% in its shallow part (3–4?km) and by 80% in its deep part (4–6?km). Conventionally, crustal resistivity is thought to change gradually, reflecting the diffusion of fluid as in a classical dilatancy diffusion model33. This giant magnetoresistance effect originates in a physical phenomenon known as a topological insulator. The research group has engaged in the development of an interfacial phase-change memory multilayered using the germanium-tellurium alloy sub-layers and the antimony-tellurium alloy sub-layers while aligning their orientation axes. Details of the results will be published in a scientific journal, "Applied Physics Letters," Vol. PCRAM and MRAM have already been in practical use, but PCRAM has the disadvantage of joule heating to at least the melting point of the memory layer in order to form an amorphous state, significantly increasing power consumption. Competition in the development of solid-state memories, which has been advanced separately, makes management decisions of companies difficult, for example with regard to the development of multiple products and increased manufacturing costs. In 2004, analysis of the switching mechanism of phase change in germanium-antimony-tellurium alloys used in conventional PCRAM at the atomic level revealed that the valence numbers of germanium atoms are the cause of changes in electrical resistance (AIST press release on September 29, 2004). The thickness of each crystal sub-layer was determined by quantum mechanics-based simulations known as the first principle simulation.
The results showed that the cause was the fact that the antimony-tellurium crystal layers (in a composition ratio of 2:3) possess a special property, topological insulating. The reflectance of light in the visible wavelength region, from 400 nm to 800 nm, which are far shorter than the band gap energy was measured at room temperature. A magnetoresistance effect exceeding 2000 % has never been obtained at room temperature, even when using ferromagnetic materials.
PCRAM and MRAM have been considered to be entirely different memory types so far, but the present discovery makes it possible to combine both electrical and magnetic operations in a single memory film, and to produce multiple-valued devices through independent control of parameters, enabling us to expect the future development of ultra-high-density solid-state memories fusing PCRAM and MRAM. Unlike three-phase AC, however, single-phase AC cannot create a rotating magnetic field by itself, meaning that it cannot start a motor. The two fields should have a fixed ratio, I believe, which cannot happen when out of phase. This represents the "self inductance" of the antenna conductor, in which the magnetic field produced by the current induces a "back EMF" on the conductor itself. A common misconception is that the E and B fields in electromagnetic radiation are out of phase because a change in one produces the other, and this would produce a phase difference between them as sinusoidal functions (as indeed happens in electromagnetic induction, and in the near-field close to antennas).
Here we investigate the time-dependent crustal resistivity in the rupture area of the 1999 Mw 7.6 Izmit earthquake using electromagnetic data acquired at four sites before and after the earthquake. Open circles indicate other sites where MT observations were made before and after the Izmit earthquake10, whose epicentre is shown by the red star31.
The left three arrows correspond to the first, second and third pairs of foreshocks, and the right-most arrow indicates the largest foreshock. A local pre-seismic model beneath site 122 corresponds to the co-seismic model without the shallow (1–2?km) zone denoted by the dashed rectangle.
However, continuous data are available for 10?h before the Izmit earthquake and 5?h after it. Nearly all co-seismic changes are characterized by decreasing apparent resistivity, suggesting a temporary decrease in crustal resistivity.
Nearly all co-seismic changes are characterized by increasing amplitude ratio, again suggesting a temporary decrease in crustal resistivity. We propose an alternative model: a transition from the state of isolated fluids to the state of interconnected fluids. It was also discovered that this superlattice phase-change film has a magneto-optical effect in which its optical reflectivity in relation to circularly polarized light in the visible wavelength region (from 400 nm to 800 nm) changes in response to the direction of an external magnetic field.

The group recently discovered that the memory has a magnetoresistance effect of more than 2000% at room temperature and higher without including any magnetic elements such as cobalt and platinum. While, in MRAM, the structural complexity prevents the memory cells from being downsized, and the difference in electrical resistance is significantly smaller than that obtained from PCRAM. Since then, the research has been conducted in order to exploit this principle by synthesizing compounds in which change in the valence numbers of germanium atoms is controlled by the atomic displacement with one-dimensionally aligned orientations rather than relying on random three-dimensional transfers, and electrical resistance could be changed without melting. Germanium-tellurium crystals are distorted cubic crystals, while antimony-tellurium crystals have a hexagonal crystal structure. Topological insulators have a special pair of cross bands (Draic cones) as part of their electron band structure, enabling electrons to migrate from the valence band to the conduction band without scattering, generating spin current on the surface or the interface. In addition, it was confirmed that the voltage required for phase change can be controlled to between 1 and 2 V. When a magnetic field was applied, the reflectance of circularly polarized light changed, irrespective of wavelength (Fig. The developed superlattice phase-change films are expected to be employed in new devices going beyond memory devices, for example in readout-heads for next-generation hard disk drives. Based on the present results, the project will now proceed with research and development of entirely new memory technologies that integrate PCRAM and MRAM.
Romalis, "Limits on CP Violation from Searches for Electric Dipole Moments." Presented at DAMOP 2002.
Romalis, "Constraints on CP Violation from Searches for Nuclear Electric Dipole Moments." Presented at the University of Illinois at Urbana-Champaign. For this reason, it needs to use an alternate method to generate a rotating magnetic field to start the motor.The induced current flowing in the secondary conductor largely affect the performance of the motor because the motor rotates by using the interaction between this current and the magnetic field of the stator coils. The difference in speed between the rotor and rotating magnetic field becomes smaller as the rotor reaches high speed. The torque of the induction motor is zero when the motor is driven slower than synchronous speed, and it becomes braking torque at synchronous speed. The red magnetic field creates a blue electric field, which creates the next magnetic field, and so on.
One field is horizontal and the other vertical, there's a 90 degrees angle - the diagram is an attempt to show three dimensions.
Estimates with partial coherencies lower than the threshold value shown in the figure are excluded. The short horizontal bars (orange and purple) denote the mean values for 20?min before the mainshock. Although these MT sites were aimed at investigating the resistivity structure of the NAFZ4, 9, 10, they provide an extremely rare opportunity for studying pre- and co-seismic electromagnetic phenomena. Similar data are also available at sites 121, 122 and 001 (the reference site) on 17 and 18 September, 1 month after the earthquake.
Large fluctuations are due mostly to the inherently indeterminate nature of the two-input system with an imperfect independency between two inputs.
The post-seismic changes are characterized by increasing values, indicating recovery to the level before the earthquake. Below this conductive layer is a resistive zone on the order of 100??m, with a skin depth of 10–20?km for 0.2?Hz.
This depth range is shallower than the hypocentre of the mainshock, which is estimated to be 10–15?km (refs 26, 31), but it is consistent with the distribution of major fault slip during the Izmit earthquake32. The crustal resistivity is primarily controlled by conductive crustal fluid and its interconnectivity at the microscopic level, such as on grain boundaries or along micro-cracks34, 35, 36, 37, 38, 39. Here we combine two surface sensitive effects: magnetic second-harmonic generation (MSHG) and SP to enhance the detection sensitivity of the surface magnetization in a single-crystal iron film. The discovery of a room-temperature giant magnetoresistance effect in a PCRAM is expected to lead to an entirely new ultra-high density memory, namely a multiple-functional memory by the fusion or integration of PCRAM and magnetic resistance memory (MRAM) technologies that are being advanced as one of next-generation non-volatile memory technologies.
In addition, despite the fact that power consumption is relatively lower for RRAM, the principle of its functioning is poorly understood, and it has the fatal disadvantage of limited write-erase cycles. This research has been positioned as one of the core themes of the Funding Program for World-Leading Innovative R&D on Science and Technology since 2010, and the discovery of the giant magnetoresistance effect was made during the course of this research.
When these two crystal phases are alternately layered, they naturally layer so as to align the c axes (the longitudinal axes) of the hexagonal crystals and the axes connecting the diagonals of the apices of the cubic crystals with an identical direction, which is normal to a substrate surface. The interesting characteristics of topological insulators are induced by spin-orbit coupling of internal electrons of which velocity is close to light speed, and this effect occurs in materials including heavy elements. The current-voltage characteristic does not obey Ohm's law and stepped changes were confirmed. Strong magnetic saturation distribution is also generated near the gap, so the nonlinear characteristics of the magnetic properties have a big influence on performance, as well.
This makes the variations in the magnetic field acting on the cage grow smaller, which in turn reduces the eddy currents flowing in the bars accordingly. In quadrature, the sum of the squares of each field's amplitude is a constant, which gives a good explanation of how the energy can persist.
Data acquired at two sites 1 month after the Izmit earthquake indicate that the resistivity had already returned to pre-seismic levels. In the first and second figures, the changes seem to have started ~20?min before the mainshock, whereas no pre-seismic change is seen in the third figure. Our preliminary analyses4, however, have not provided clear examples of anomalous changes, except for those associated with seismic waves24 that could be interpreted in terms of the seismic dynamo effect25. In this article, we average all estimates before and after the Izmit earthquake to examine co-seismic changes.
If the attenuation in the shallow conductive zone is considered, the penetration depth is likely to be shallower than 10?km.
Our conceptual model is as follows: before the earthquake, some fluids were partially in an isolated state, and the pore pressure changed immediately before and during the earthquake, connecting the fluids through a new fluid-path network. We show that the MSHG signal can be significantly enhanced by SP in an attenuated total reflection (ATR) condition, and that the magnetic contrast can be varied over a wide range by the angle-of-incidence. In addition, it is thought that the film has the potential for high-speed switching by an electric field, and it is therefore expected to find application in non-volatile logic technologies. Precise control of the thickness of the sub-layers of each alloy based on the simulations enabled a superlattice phase-change film to be formed from different alloys. In other words, superlattice phase-change films are able to internally generate spin-orbit coupling and an intrinsic magnetic field without including any ferromagnetic element such as cobalt and iron. In addition, the reflectance changed even when the magnetic field of different polarization was applied. Romalis, "Nonlinear Effects from Dipolar Interactions in Hyperpolarized Liquid 129Xe", Phys. Ledbetter, "Transverse Spin Relaxation in Liquid 129Xe in the presence of Large Dipolar Fields," Phys. At the step before the design phase, it is helpful to run an analysis and evaluation using the finite element method (FEM) to understand a single-phase induction motor's characteristics by accounting for induced current and magnetic saturation characteristics.This Application Note explains how to obtain the current density distribution and Speed-Torque curve created by auxiliary winding that uses a capacitor.
The rotation region that provides maximum or high torque varies depending on the electric resistance, so changing the cage materials or geometry makes it possible to study the motor characteristics that most closely meet the goals of the design.
We interpret such changes as the pressure-induced transition between isolated and interconnected fluids. Estimates with partial coherencies lower than the threshold coherency shown in each figure are excluded. Co-seismic changes are characterized by abrupt decrease in crustal resistivity, while post-seismic changes suggest increase within 1 month. A similar precursory change is also seen in the magnetic field amplitude ratio at site 118. The horizontal extent is estimated as 6?km due to the large co-seismic changes observed at sites 120 and 122.
In this respect, the role of crustal fluids in the triggering of earthquakes has been discussed previously40, 41, 42, and we propose that this transition may be triggered by the release of stress due to slow slip at the rupture initiation zone and during the earthquake rupture. Furthermore, the magnetic contrast of transverse and longitudinal MSHG display opposite trends, which originates from the change of relative phase between MSHG components.
PCRAM using the superlattice phase-change film was employed in devices, and it was demonstrated that it could be operated using one-tenth or less the power of conventional PCRAM. However, up to the present, physical properties as a topological insulator has only been demonstrated at ultra-low temperatures, and there have been no reported examples emerged at room temperature. Some data show pre-seismic changes and this suggests that the transition is associated with foreshocks and slow-slip events before large earthquakes.
Based on these considerations, we searched for a plausible model using the 2D forward-modelling code29.The models of the initial and co-seismic stages are shown in Fig.
This new effect enhances the sensing of magnetic switching, which has potential usage in quaternary magnetic storage systems and bio-chemical sensors due to its very high surface sensitivity and simple structure.IntroductionMagneto-plasmonics (MP) describes hybrid systems where plasmonics and magnetic properties coexist, and has great potential for magneto-optical (MO) devices1. However, through first principle simulations, the group found that some of the electron bands in the germanium atoms in germanium-tellurium layers (not a topological insulator) would sprit into the bands with an energy difference of a maximum of 200 meV (the Rashba effect).
The waveforms of these events were similar to the mainshock, suggesting that they occurred where the mainshock began.
Two-dimensional (2D) models imply that the resistivity is decreased by 50–80% at 3–6?km depth. Romalis, "Numerical and experimental studies of long-range magnetic dipolar interactions", J. Inspired by this report, we examined our MT data and found that two foreshocks and the mainshock caused electromagnetic field disturbances at site 120, from which we determined arrival times for these earthquakes. We interpret the abrupt changes in crustal resistivity found in association with the Izmit earthquake in terms of a transition from the state of isolated fluids to the state of interconnected fluids. The pre-seismic model is uncertain due to a very limited data set, and it is supposed to be the same as the co-seismic stage except for a shallow layer between 1 and 2?km depth below site 122.

In fact, earthquakes tend to occur at boundaries between high- and low-resistivity areas4, 6, 7, 9, 22. Before the earthquake, some fluids are partially in an isolated state, and pore pressure change immediately before and during the earthquake connects the fluids through a new fluid-path network. In this approximation, the components (xx) of the horizontal magnetic field ratio and phase and (yx) of the apparent resistivity and impedance phase correspond to the TE (transverse electric) mode. In this article, we demonstrate a large variation of magnetic contrast with nonlinear magneto-plasmonics (NMP).
Pre-seismic change suggests that the transition is associated with foreshocks and slow-slip events before the earthquake. The components (xy) of apparent resistivity and impedance phase correspond to the TM (transverse magnetic) mode.
Here NMP refers to the nonlinear optical response from a MP system.As a surface sensitive magneto-optical effect, magnetic second-harmonic generation (MSHG) is sensitive to the interface or surface magnetization where the inversion symmetry is broken. Recent detailed analysis of seismic data27 has shown that foreshocks and numerous smaller events can be interpreted as indicating a slow rupture leading to the mainshock, as may have occurred before the 2011 Mw 9.0 Tohoku-Oki earthquake28. MSHG contains nonzero magnetic components of the second-order nonlinear susceptibility tensor which makes MSHG extremely sensitive to subtle modifications of the spin-polarized electronic structure of transition metal surfaces7,8,9,10,11, the same region where surface plasmons (SP) are present. Addition of the second layer (2–3?km depth) better explains the observed results at site 122. The surface sensitivity of MSHG is different from the bulk effect of magneto-optical Kerr effect (MOKE)12,13, which is often used in MP systems. The computed and observed changes in the apparent resistivity and impedance phase are shown in Fig.
Historically, one dilemma for MP systems is that the noble metal layer supports high quality SP, but a very large magnetic field (several Tesla) is needed to achieve MO activity.
7a and changes in the horizontal magnetic field amplitude ratio and phase are shown in Fig. On the other hand, the ferromagnetic (FM) layer exhibits large MO activity, which makes it possible to make real MO devices, but the high losses in the FM layer causes an over-damping of plasmon resonance, and thus impairs the strength of SP14,15. The authors attributed this enhancement to a change in phase difference between magnetic and non-magnetic responses. In this article, we find that the contrast ratios of transverse and longitudinal MSHG exhibit different trends when changing the angle-of-incidence. Moreover, we clearly separate the L- and T- component by studying the anisotropy and the two-jump hysteresis loops from a single-crystal Fe film, while others did not. We developed formulas for the two-jump switching loop to extract the ratios of magnitude and the phase differences between magnetic and non-magnetic components for both L- and T-MSHG, while only the longitudinal one has been studied previously11. This new effect enhances the sensing of magnetic switching, which has potential usage in quaternary magnetic storage systems because it enables the read-out of all four magnetization states from crystalline iron with high contrast ratio, and it is also of interest for bio-chemical sensor applications due to its very high surface sensitivity and simple structure.Here, all experiments are carried out on single-crystalline iron films grown on MgO (001) substrates17 (see Supplementary Information – sample growth and characterization), which show unique magnetic switching behavior due to cubic magneto-crystalline anisotropy.
The two-step switching characteristic of the Fe film generated by its cubic magnetic anisotropy18,19,20 (Fig. 1) allows us to simultaneously study both longitudinal (L) and transverse (T) component for MSHG and MOKE.
The L-component corresponds to the magnetization (M) component parallel to the plane-of-incidence, i.e. The magnetization of a thin Fe film is always in the sample plane if the external magnetic field (H) is applied parallel to the surface. The cubic magnetic anisotropy of single-crystal iron leads to two easy axes ([100] and [010]) and two hard axes ([110] and [?110]), and the magnetization tends to align along the easy axes (Fig.
Beginning from an initial state MI along [100], with increasing magnetic field along [?110], the magnetization overcomes the hard axis [110], which causes a change in the longitudinal magnetic component (MI to MII). As H increases further, the magnetization overcomes another hard axis [?110], which causes a change in the transverse magnetic component (MII to MIII).
We note that the jumps from MII to MIII and MIV to MI are possible because the external magnetic field can never be perfectly parallel to the hard axis [?110], and a slight mis-orientation can cause such jumps. In the MSHG and MOKE hysteresis loops, each magnetization state corresponds to different signal intensity, I(M). The L-jump occurs at low coercivity while the T-jump happens at higher coercivity, because H is applied along the longitudinal direction and only a small field is needed to switch the L-component. Each magnetization state corresponds to different signal intensity, I(M), in the hysteresis loop.Full size imageResultsWe use the Kretschmann-Raether configuration21 to excite the SP in our experiments (Fig.
For a P-polarized incident beam, the reflection is maximized when the total reflection angle (? = 40°) is reached.
The reflection decreases sharply when the incident angle increases further, which is called attenuated total reflection (ATR). The ATR curve can be explained by the coupling of light energy into the SP on the metal surface. The intensity of the electro-magnetic field on the metal surface at the metal-air interface becomes enhanced under the ATR condition, and reaches its maximum at the bottom of the ATR curve for noble metals22,23. The T-component increases with incident angle until it dominates the switching process, while the L-component decreases. The T-component remains small even for very large incident angles, while the L-component remains mostly unchanged.Full size imageFigure 2b shows an enhancement of MSHG intensity by SP of more than one order of magnitude. For iron, the width of ATR is very large and the difference of incident angle for highest field strength and minimum of ATR curve is also large. For ? = 41° ATR just begins, the hysteresis loop shows clear contrast with only the L-component switching at H = 5?Oe. The switching of T-component at H = 40?Oe begins to appear at ? = 41.5°, but the L-component still dominates the switching. This important observation demonstrates the large variation of L- and T-component in MSHG, which is absent in MOKE. There is no such huge effect for MSHG under normal reflection geometry or MSHG under Kretschmann-Raether configuration with S-polarized fundamental field.
The magnetic contrast can be understood as the height of the jump in the hysteresis loop divided by the average intensity of both magnetizations.
We note that CL and CT are directly related to the direction of the magnetization, rather than the external magnetic field. This means that the same contrast ratios are obtained when the external magnetic field H is applied along the longitudinal or transverse direction, i.e.
The most important finding is that for MSHG, CL () and CT () can be varied by the SP resonance with opposite trend. CL initially increases sharply when ATR begins and reaches its maximum at around 42.5°, but then decreases as ? increases further, until it totally disappears at around 55°. In contrast, for MOKE the L-component does not change much over the total reflection, and the enhancement of the T-component is also limited. For longitudinal MOKE, CL () shows only a small change as a function of the angle-of-incidence. The small minimum which occurs where CL (MSHG) reaches a maximum indicates a small SP field enhancement in the longitudinal MOKE which interferes destructively with the bulk MOKE signal.DiscussionTo elucidate the origin of the large variation in the MSHG contrast ratios, we studied CT and CL as a function of the angular position ? of the analyzer11,25 (? = 0 corresponds to p-polarization). The magnetic contrasts can be expressed as [see Supplementary Information for details]: where kT and kL are the ratios of magnitude between the magnetic and non-magnetic MSHG response for T- and L-magnetization components, both of which are composed of fundamental fields and corresponding effective susceptibility tensors. We note that when kT = 0, the expression for CL becomes identical to the one for the one-jump MSHG hysteresis loop measured in the L-geometry.
Furthermore, kT and ?T can only be obtained from the two-jump MSHG hysteresis loop, because Eq. The ratios kT and kL hardly change within experimental errors and hence cannot account for the large variation. In contrast, ?L exhibits a large monotonic increase from 72° to 90° over the ATR range, while ?T decreases from 88° to 77°.
This trend is consistent with the large decrease of CL and the steady increase of CT with increasing incident angle under ATR. Therefore, the large variation of magnetic contrast originates from the change of relative phases caused by SP. The phase difference between magnetic and non-magnetic components of MSHG signal is known to be related to the relative orientation of magnetization and the wave vector of fundamental fields16,26. The phase differences exhibit opposite trends for L- and T- magnetic components, while the ratios of magnitude remain unchanged within experimental errors. Such a system opens the way for simultaneously investigating both longitudinal and transverse magnetization components regardless of the external magnetic field. By studying MSHG hysteresis loops as a function of incident angle and polarization angle, and by fitting the magnetic contrasts to theoretical formulas, we find that the observed effect originates from the change of relative phase between magnetic and non-magnetic MSHG components caused by surface plasmons.
Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor. Second harmonic generation and magnetic-dipole electric-dipole interference in antiferromagnetic Cr2O3. Influence of the magnetic field on the plasmonic properties of transparent Ni anti-dot arrays. Anisotropy and orientational dependence of magnetization reversal processes in epitaxial ferromagnetic thin films. Optical electric-field enhancement at a metal surface arising from surface-plasmon excitation.
Observation of large Kerr angles in the nonlinear optical response from magnetic multilayers.

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