Recent developments in microelectronic devices and spintronics lead researchers to the task of local characterization of the dynamical response in small magnetic structures and devices [Chappert 2007]. Local measurement of ferromagnetic resonance (FMR) that can have quantized or localized modes due to sample boundaries is one of the fascinating topics among them [Demokritov2009]. Recently, various techniques probing local magnetic resonances associated with spin and magnetostatic waves, such as microfocus Brillouin light-scattering spectroscopy [Perzlmaier 2005] and time-resolved scanning Kerr microscopy[Neudecker 2006], have been developed. Using these techniques, real-space images showing spatial distribution of FMR intensities have been demonstrated[Perzlmaier 2005, Neudecker 2006].
While spatial resolutions of the aforementioned optical methods are fundamentally limited by the diffraction limit, which is around 0.5 μm, the methods using a local probe proved to have a potential of nanometer-scale spatial resolutions. Various techniques based on scanning probe microscopy(SPM) for imaging spatial distributions of magnetic response in a range of radio frequency (RF), such as electron paramagnetic resonance and FMR, have been developed [Smith 2008, Rugar 2004, Meckenstock 2008, Obukhov 2008]. Scanning near-field microwave microscopy developed by Lee  detects spatial variation of magnetic permeability using a coaxial transmission line, whose end is short-circuited. The looped transmission line forms a resonator, and variations in its resonance frequency and quality factor reveal the magnetic properties of samples located near the line [Lee 2000, Imitaz 2006]. Mircea and Clinton  reported an alternative FMR detection method using a loop probe without a resonant circuit, which enables the broadband detection.They detected absorption signals in the reflection spectra of RF transmitted to magnetic samples. For sensing local ferroelectric properties, an open-ended coaxial probe has been used [Imitaz 2006], which can be easily implemented into SPM setups. While the open-ended geometry promises highly resolved imaging, as demonstrated by the local ferroelectric detection, it has yet not been utilized for the magnetic detection and imaging.
In this study, we report on a broadband detection of magnetic RF signals using an open-ended coaxial electric probe. With this approach, we have successfully detected localized FMR signals on a polycrystalline yttrium iron garnet (YIG)disk and observed strong spatial dependences in detected signal intensities over the sample. While the sample studied in this experiment is relatively large with millimeter-size dimensions and the demonstrated spatial distribution is in submillimeter scale, limited by the wavelength of the excited magnetostatic waves, the introduced method is promising as a tool for localized FMR imaging, since its fundamental spatial resolution is limited mainly by the radius of the tip apex, which can be scaled down to nanometer dimensions.
Fig. 1(a) shows a schematic of our experimental setup. The open-ended probe used in this experiment is composed of a semirigid coaxial cable (SC-219/50-C/Tu, Coax Corporation) that transmits RF over 10 GHz and a sharp metal tip on its end [Imitaz 2006].As shown in Fig. 1(b), the diameter d1 (d2) of the outer(inner) conductor of the coaxial cable is 2.2 (0.5) mm. An electrochemically etched tungsten tip is inserted inside the inner conducting tube [Imitaz 2006]. For the signal detection, the probe was located close to a sample (The tip–sample distance is typically 0.1 mm). The RF current IRF of the probe generates circular RF magnetic field hRF in the sample, as shown in Fig. 1(a). Static magnetic field H was applied in the in-plane direction to the sample surface, and the orthogonal component of the circular RF magnetic field to the applied field excites the magnetization. When the RF coincides with the FMR frequency, the resonance response appears in the resulting absorption signal in the reflection (S11) spectrum, which can be measured with a vector network analyzer (ZVB 8, Rhode & Schwarz GmbH) [Mircea 2007].The output RF power of the network analyzer was set at 0 dBm (1 mW). At each probe position, the S11 parameter was measured with and without the static magnetic field, and the differential spectrum Δ S11 was analyzed for evaluating the resonance frequencies and their intensities.
Fig. 1. (a) Schematic and (b) photograph of the RF probe. (c) FMR signals detected from a YIG disk sample in the reflection spectra( Δ S11) with the RF probe and a CPW located under the disk. In-plane static magnetic field of 44 kA/m (550 Oe) was applied in the x direction defined in the inset. The RF probe was located on three different positions on the YIG disk: in millimeters,(x, y) = (0, 0), (3, 0), and (0, 3).
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A polycrystalline Al-doped YIG disk with 10 mm/(1 mm) diameter/(thickness)was used as the sample. The saturation magnetization Ms, the coercivity Hc, and the FMR line width ΔH of the sample are 145.3 kA/m (4πMs = 1826 G), 36 A/m (0.45 Oe), and 1.65 kA/m (20.7 Oe), respectively.YIG is known to be a low-loss dielectric magnetic material with a large exchange-dipole correlation length, allowing one to study the dynamical magnetization phenomena recently observed in microscopic magnetic metals, for instance, permalloy, using millimeter-size samples [Demokritov 2009]. For this reason, YIG is an ideal sample to demonstrate the capability of our RF probe to detect FMR signals locally and visualize its spatial distribution.
RESULTS AND DISCUSSION
Fig. 1(c) shows the Δ S11 absorption spectra taken by our RF probe under the static magnetic field of 44 kA/m (550Oe) at the three different positions on the YIG disk; one at the center of the disk, in millimeters ( x, y) = (0,0), and the other two at the coordinates of (3, 0) and (0, 3), as indicated in the figure. Here, the x-axis is defined as the direction of the applied static magnetic field, as shown in the inset of Fig. 1(c). One can clearly recognize a resonance signal as an absorption dip at frequency of 2.79 GHz in the spectrum taken at the center (0, 0). This frequency is denoted as f1 hereafter. At the off-center positions, additional resonance signals at 3.03 (f2)and 3.13 GHz (f3) are also observed.
Fig. 2. Δ S11 absorption spectra measured with the RF probe on the YIG disk along the (a) parallel (x) and (b) orthogonal ( y) lines crossing the center to the static magnetic field [ H = 44 kA/m (550Oe)]. The three FMR modes f1,f2, and f3 are marked with dashed lines at the frequencies of 2.79, 3.03, and 3.13 GHz, respectively.
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As a reference, we also measured the RF reflection spectrum using a coplanar waveguide (CPW) located under the YIG sample, which generates uniform and linearly polarized RF fields in the entire area of the sample [Takeda 2009]. The absorption spectrum taken with the CPW, shown in Fig. 1(c), shows all the three resonance signals (f1, f2, and f3). These measurements clearly demonstrate the capability of the RF probe to locally detect the FMR signals that are found in the integrated CPW spectrum. It should be noted here that the RF probe and the CPW have different excitation mechanisms; the RF probe excites FMR locally with circular magnetic field, whereas the CPW excites the sample uniformly [Imitaz 2006, Mircea 2007, Takeda 2009].
By utilizing the scanning capability of the RF probe, we then investigated the spatial dependence of the detected FMR signals. The Δ S11 spectrum was measured at each position while scanning the probe in the parallel (x) and orthogonal (y) directions to the applied static field H.The measured spectra are shown in Fig. 2. During the measurements, H was fixed at 44 kA/m (550 Oe), in the in-plane of the disk. From the spectra in Fig. 2(a), we found that the intensity of f1 decreases in the parallel direction to the applied field (x), and disappears at around 3 mm from the center. During the scanning in this direction, a new signal f2 emerges. The intensity of the emerging resonance signal grows with the distance and reaches a maximum around 3 mm from the center. In the orthogonal(y) direction, as shown in Fig. 2(b), the f1 signal decreases gradually toward the edge, whereas a new signal f3 appears around 1.5 mm from the center. The intensity of the f3 signal is rather weak compared to f1, but reaches a maximum around3 mm from the center.
In order to clarify the spatial distribution, we performed 2-D mapping of the absorption intensity for each FMR signals f1, f2, and f3 [see Fig. 3(a)–(c)], in the area covering the whole sample (−5 < x, y < 5), as shown schematically in an inset of Fig. 3. Here, the intensity was defined as the difference between the highest and lowest Δ S11 values around the absorption dip. The intensity of the f1 ( f2 and f3) mode was obtained by subtracting Δ S11 measured at 2.86 (3.08 and 3.26) GHz by Δ S11 at 2.78 (3.03 and 3.15) GHz. Figs. 3(d) and(e) show the cross-sectional intensity profiles of the detected FMR signals along the x-and y-axis, which were normalized by the intensity of f1 at the center. If assuming that the intensity of the detected FMR signals corresponds to that of the dynamic magnetization component of the spin precessional motion at the position below the probe, we can conclude that the f1 mode has no node in both x and y directions and its precessional motion is pinned at the edges in the y direction.In the x direction, which is parallel to H, internal magnetic field in the disk is steeply reduced near the edges because of the demagnetization, and the f1 mode is thus pinned around 3.5mm from the edges [see Fig. 3(d)][Neudecker 2006, Zivieri 2006, von Geisau 1995].
Fig. 3. 2-D mapping of the FMR signal intensities of the (a) f1,(b) f2, and (c) f3 modes.The FMR measurements were performed on the square area covering the whole YIG sample shown in the inset. The intensity profiles along the (d) x and (e) y axes were normalized with that of f1 mode at the center.
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Contrary to the f1 mode, the intensity of the f2 mode has a minimum at the center and becomes significant near the edges in the x direction [see Fig. 3(d)].We thus speculate that the wave vector of the f2 mode is parallel to H having one node at the center without pinning at the edges in the x direction. This mode represents one of the eigenmodes of the circular disk [Zivieri 2006, Giesen 2007]. Because of the parallel wave vector, the mode can be treated as a magnetostatic backward volume wave (MSBVW) like mode [Zivieri 2006, Giesen 2007, Damon 1961, Stancil 1993, Stancil 2009].The f2 mode could be an edgemode, which is localized at the edge outside the region of the effective internal magnetic field [Neudecker 2006, Zivieri 2006]. This possibility is, however, ruled out since the frequency of the edge mode should be lower than any other eigenmodes, which is inconsistent with our experimental results (f2 < f1). In addition, the spatial extent of the edge mode should shrink with higher H [Neudecker2006]. We examined the intensity profile of f2 in the x direction under various magnetic fields up to 112 kA/m (1400 Oe), but no apparent change in its spatial distribution was observed, unlike the case of the edge mode.
The f3 mode shows a minimum at the center and finite intensities in the y direction [see Fig. 3(e)]. The observed spatial distribution indicates that the wave vector of the f3 mode is orthogonal to H with one node at the center. A wave vector perpendicular to H suggests that the mode is magnetostatic surface wave (MSSW) like mode of the circular disk, also called the Damon–Eshbach (DE) mode[Damon 1961, Stancil 1993, Stancil 2009]. The spatial profile of the f3 mode is qualitatively consistent with that of the MSSW mode denoted as 1-DE in the calculation performed by Zivieri .
Let us now discuss the f1 mode. Due to its spatial distribution, this mode represents the fundamental eigenmode pinned at the edges of the internal magnetic field. Because the frequency of the f1 mode is lower than that of the f2 mode, which was identified as an MSBVW-like mode, we conclude that f1 is also an MSBVW-like mode. One could argue from its spatial distribution that f1 could be a uniform mode (UM) in which the magnetization precesses in-phase throughout the entire sample. Since the frequency of UM for an in-plane magnetized disk should be higher than that of MSBVW (e.g., f2), it is unlikely that f1 is a true uniform precession mode. In fact, we measured the resonance frequency of the three FMR signals as a function of the magnetic field, and we have found that the three modes keep the same frequency relation up to 112 kA/m (1400Oe), the maximum field applied in the experiment.
As a backward-like wave, the frequency of the MSBVW mode decreases with increasing the wave number. Since the wave number of the f2 mode is larger than that of the fundamental f1 mode, f2 should have lower frequency than f1, which is not the case in our measurements. The discrepancy can be explained by considering distribution of the dynamic magnetic field in the thickness direction of the disk. According to the theory of MSBVW [Damon 1961, Stancil 1993, Stancil 2009], dispersion relation of the MSBVW modes have several branches depending on the number of nodes in the thickness direction of a sample, and the modes having nodes in the thickness direction have higher frequencies than the zero-node modes.If we assume that the f2 mode has one node in the thickness direction, whereas the f1 mode does not have nodes in the same direction, the frequency relation is consistent with our measurements, although we cannot directly detect the number of the nodes in the direction. The spatial distribution and the frequency relation of the three modes can thus be explained with the MSBVW-like (f1 and f2) and the MSSW-like ( f3) modes.
In this study, we have developed an RF probe with an open-ended sharp tip, which can be implemented into SPM, aiming for spatially resolved imaging of magnetic resonance. We were able to detect FMR signals electrically using this RF probe and have demonstrated its capability of the spatially resolved detection. From the observed spatial distribution of their intensities, we could identify the observed modes.
The spatial variation of the FMR-mode intensities is in millimeter range because of the size of the sample and the nature of the excited waves. The spatial resolution of the RF probe itself should be better than the observed variation. The spatial resolution for detecting ferroelectric properties using an open-ended probe has been estimated by Imitaz  based on a calculation of electrical and magnetic fields localized on the tip. The calculation showed that both electrical and magnetic fields are confined on the tip within the distance of the tip curvature from the tip apex, indicating that the spatial resolution is comparable to the tip curvature. Since the probe tip can be sharpened down to nanometer dimensions [Akiyama 2005], we believe that it is possible to detect and image the FMR signals in nanometer spatial resolution.This method will open up possibilities of nanometer-scale imaging of FMR, which is not accessible by the other techniques.