The discovery of new phenomena in layered and nanostructured magnetic devices is driving rapid growth in nanomagnetics research. Resulting applications such as giant magnetoresistive field sensors and spin torque devices are fuelling advances in information and communications technology, magnetoelectronic sensing and biomedicine1, 2. There is an urgent need for high-resolution magnetic-imaging tools capable of characterizing these complex, often buried, nanoscale structures. Conventional ferromagnetic resonance3, 4 (FMR) provides quantitative information about ferromagnetic materials and interacting multicomponent magnetic structures with spectroscopic precision and can distinguish components of complex bulk samples through their distinctive spectroscopic features. However, it lacks the sensitivity to probe nanoscale volumes and has no imaging capabilities. Here we demonstrate FMR imaging through spin-wave localization. Although the strong interactions in a ferromagnet favour the excitation of extended collective modes, we show that the intense, spatially confined magnetic field of the micromagnetic probe tip used in FMR force microscopy can be used to localize the FMR mode immediately beneath the probe. We demonstrate FMR modes localized within volumes having 200 nm lateral dimensions, and improvements of the approach may allow these dimensions to be decreased to tens of nanometres. Our study shows that this approach is capable of providing the microscopic detail required for the characterization of ferromagnets used in fields ranging from spintronics to biomagnetism. This method is applicable to buried and surface magnets, and, being a resonance technique, measures local internal fields and other magnetic properties with spectroscopic precision.
Figures at a glance
Figure 1: Observation and characterization of localized FMR modes. 
a, FMRFM geometry: the ferromagnetic film is magnetized perpendicular to its plane by an external magnetic field, H0. The moment, mp, of the micromagnetic probe is antiparallel to H0 and is separated from the film by a distance z (the distance from the surface to the centre of the probe magnet). b, The micromagnetic probe creates a well of magnetic field, shown by the solid light-blue line, that localizes spin-wave excitations mloc,n(r), indicated by the solid red and blue lines for the first two modes. The probe field (Hp), the dynamic field (Hdyn) and the modes are calculated for z = 1,270 nm. c, FMRFM spectra of a continuous permalloy film for the indicated values of z. The vertical dotted line shows the resonance field for the uniform FMR mode (ZFR). The first and second confined modes are indicated by the arrows. d, Dependence on z of the resonance fields for the first and second FMR modes. The solid lines are calculations obtained from the variational method described in the text. e, Calculated local-mode radius, Rloc,n, versus z for the first two magnetostatic modes obtained using the variational method.
Figure 2: Field-position FMRFM imaging of a permalloy dot using localized modes. 
FMRFM images of the FMR resonance shift (such as shown in Fig. 1c) at different lateral positions over the dot (indicated by the thick blue bar), measured for a series of probe–sample separations. These separations describe the distance from the centre of the probe tip to the sample surface, so the bottom of the probe is approximately 350 nm from the surface at the smallest separation shown. The rightmost four panels compare theoretical expectations (dotted lines) assuming no modification of FMR modes by the probe field (equation (1)). Although it is adequate at large separation (weak probe field), this approach fails upon closer probe approach. The leftmost three images show comparison with confined-mode predictions (coloured solid lines) using variationally calculated values, Rloc,n (equation (3)), for the probe-localized magnetostatic mode. The black solid line shows the inhomogeneous demagnetizing field of the dot (shifted by appropriate dynamic and probe fields) corresponding to the first local mode (equation (5)), demonstrating that the first-order localized mode accurately images the internal magnetic field of the dot.
Figure 3: Field-position FMRFM image of a continuous permalloy film. 
Variation in the resonance fields of the n = 1 and n = 2 localized modes with lateral position, for z = 1.32 μm, reflecting variation in the internal field in a permalloy film (see text). The inset shows a section through the n = 1 mode for a fixed lateral position. By setting the external field to Hfix, such that the variation in the FMRFM signal with internal field is a maximum, we realize a high-sensitivity detector of the internal field as a function of x–y position. Variations in the detected force, δF(x, y), reflect internal field variations through shifts in the resonance field: δH(x, y) ≈ δF(x, y)(ΔH/F0), where ΔH is the FMR linewidth and F0 is the FMRFM force at resonance. Images obtained by this method are shown in Fig. 4a and in Supplementary Fig. 5a.
Figure 4: Two-dimensional x–y FMRFM images of a continuous permalloy film. 
a, FMRFM images of δH(x, y) measured at the indicated tip–sample separations. The image size is 6 μm × 6 μm. b, Dependence of the FMRFM signal on wavevector, obtained from Fourier transform (FT) of the images in a; the panel dimensions are 60 μm−1 × 60 μm−1. Seventy-five per cent of the signal energy is enclosed within the dotted circles. c, Dependence of resolution on probe–sample separation, obtained from experimental FMRFM images.
