Near-field magneto-caloritronic nanoscopy on ferromagnetic nanostructures

Near-field optical microscopy by means of infrared photocurrent mapping has rapidly developed in recent years. In this letter we introduce a near-field induced contrast mechanism arising when a conducting surface, exhibiting a magnetic moment, is exposed to a nanoscale heat source. The magneto-caloritronic response of the sample to near-field excitation of a localized thermal gradient leads to a contrast determined by the local state of magnetization. By comparing the measured electric response of a magnetic reference sample with numerical simulations we derive an estimate of the field enhancement and the corresponding temperature profile induced on the sample surface.

(IR) radiation. We analyze the magneto-caloritronic contributions [25] which depend on the local magnetization distribution.
The nanostructure we investigate is magnetized perpendicularly to the surface allowing us to image the local magnetization distribution by exploiting the anomalous Nernst effect (ANE) [26] and the anisotropic magneto-Seebeck effect [27]. In contrast to high-resolution scanning magnetic force microscopy where the sample magnetization can be affected by the strayfield of the scanning magnetic tip [28,29], our non-invasive magnetic photocurrent nanoscopy does not rely on the magnetic dipole interaction.
For tip-enhanced magneto-caloritronic nanoscopy an AFM (NanoWizard II, JPK Instruments, Germany) operated in tapping mode was used as shown schematically in Figure 1 (A). An Au coated Si cantilever (4XC-GG, NanoAndMore GmbH, Germany) with typical tip diameter below 30 nm oscillates at an amplitude z = 50 nm just above the sample surface at its mechanical resonance frequency  ~ 150 kHz. The emission of a quantum cascade laser (QCL, ~ 50 mW at 1661 cm -1 , DRS Daylight Solutions Inc., CA, USA) was focused to the tip apex by a 90° off-axis parabolic mirror (diameter: 12.7 mm, focal length: 15 mm, angle-of-incidence: 75°). The IR induced temperature gradient, T, is indicated by the false color profile below the AFM tip in Figure 1 (A). The tip-mediated electric response of the sample to IR excitation was analyzed using a lock-in scheme. In short, the thermo-current generated in the magnetic wire was first amplified by a transimpedance amplifier (10 6 V/A, DHPCA-100, FEMTO Messtechnik GmbH, Germany) and further analyzed by a lock-in amplifier (HF2LI, Zurich Instruments, Switzerland) at the tip modulation frequency . Both the in-phase and out-of-phase components were registered while scanning the magnetic wire relative to the tip. The in-phase component typically exhibited a stronger contrast. The resulting thermal electromotive force (EMF), V T , induced by the tip-enhanced IR radiation will be analyzed in the following as a function of the magnetization state of a ferromagnetic microbar.
In our experiment, we investigate the magnetization distribution in a 1μm wide and 60 μm long magnetic bar containing a central 500 nm wide triangular shaped notch (Figure 2 (A)). The microbar was defined by electron beam lithography on a poly(methyl methacrylate) (PMMA) resist layer. Subsequently, a Ta(3 nm)/Pt (3 nm)/Co(0.6 nm)/AlO x (2 nm) magnetic multilayer was deposited on a thermally oxidized silicon wafer by DC magnetron sputtering followed by a lift-off procedure.
The magnetic parameters in our Pt/Co/AlO x multilayers are as follows: exchange stiffness A ≅ 16 pJ/m, saturation magnetization M s ≅ 1.1 MA/m, perpendicular anisotropy K ≅ 1.3 MJ/m 3 and Dzyaloshinskii-Moriya interaction (DMI) parameter D ≅ 2.6 mJ/m 2 [30,31]. The constriction is designed to act as a magnetic domain wall pinning center [32]. The bar is characterized by a perpendicular magnetic anisotropy and large interfacial DMI forcing magnetic domain walls to follow a Néel-like geometry with the magnetization direction at the domain wall center oriented along the bar direction [33].
The thermal EMF, V T , was mapped over the microbar, as shown in Figure 2 Figure 2 (B) shows a gradient of V T along the x-direction near the constriction in the center of the wire. Moreover, the gradient of V T along the y-direction changes sign between the left and right hand side of the constriction.
In order to understand the origin of the different contributions we first consider the local electric field E generated by the temperature gradient, ∇ . In a coordinate system as shown in Figure 1 (B),  = 0 is considered since the magnetization lies in the x-z-plane in the Néel-like domain wall. In this case, the local electric field E is given by where the anisotropic magneto-Seebeck coefficient ∥ is measured when the temperature gradient is parallel to the magnetization while ⊥ is measured when it is perpendicular to the magnetization direction. The elements represent the anomalous Nernst effect which can be estimated [28] Our experimental setup is designed to detect the thermal EMF, V T , between the two terminals along x. We estimate the thermal EMF, dV T = E x dx, by integration along the microbar of width w assuming two independent magnetic domains A (l/2<x < 0 and B (l/2 > x > 0), which are magnetized along the z-direction, i.e. orand separated by a domain wall located a x = 0.For our sample with a high perpendicular anisotropy, the width of the Néel-like domain wall is less than 10 nm and hence too small to be resolved by our measurements. Therefore, in the domain wall region where  is different from 0 or  the contribution to V T generated by the anisotropic magneto-Seebeck effect could be neglected. We approximate the thermal EMF by the following formula:  The position of the AFM tip is denoted by (x 0 , y 0 ). In our uniaxial thin film samples, the measured thermal EMF depends predominantly on the local perp.-to-plane saturation magnetization via  for the two domains.
The contributions to the thermal EMF compensate as long as the temperature variation due to the thermal point source falls off completely within the microbar and within one domain. If the thermal point source approaches the constriction, the For a semi-quantitative analysis, the following considers a V Ttrace along the y-direction sufficiently far away from the constriction for the two magnetization directions, as shown in Figure 3 (A). The trace has been averaged over 12 neighboring lines with x = 15 nm spacing and subsequently smoothed by a Savitzky-Golay filter. The inversion of V T upon magnetization reversal is verified. A line scan without illumination by the QCL, but otherwise identical experimental conditions, didn't yield the characteristic asymmetric shape (see supplementary information). We also simulated the temperature distribution caused by the illuminated tip using a circularly shaped heat source. A Gaussian power density distribution of 50 nm in diameter (FWHM) was assumed, where the peak value serves as fitting parameter. With dedicated heater structures (not shown) on this particular sample we were able to determine [27] the ANE coefficient for our microbar experimentally as |N ANE | = 0.054 V/KT, from which we obtain the trace V T (y) in Figure 3 (B) by employing Eqn. (2). It reproduces the anti-symmetric shape and absolute range of variation of the measured V T when a peak power density loss at the surface of 4 GW/m 2 (4 mW/m 2 ) was assumed, with an estimated input power density close to the tip of 0.01 GW/m 2 .
This is consistent with a field enhancement factor of about 20 -30 as expected for metallized AFM tips [35]. The inset of Figure 3 (B) also shows the corresponding temperature distribution, indicating a temperature rise of 20 -30K of the surface underneath the tip, which is still well below the Curie temperature of our thin Co layer. The ability to estimate the local temperature is an important byproduct of our measurement.
In summary, the magneto-caloritronic response of a conducting sample to near-field excitation leads to a novel contrast mechanism at magnetic domain boundaries as well as near the edges of the magnetic nanostructure due to the anomalous Nernst effect. The contrast was demonstrated by reversing the magnetization of the nanostructure resulting in a corresponding reversal of the ANE generated thermal EMF. The interpretation was supported by a 2D numerical simulation. Magnetocaloritronic nanoscopy can provide information on magnetic surface properties without relying on the magnetic dipole interaction.