Nonlocal properties of a multidomain magnetic configuration

We study the nonlocal properties of the magnetic multidomain configuration of a soft ferrimagnetic iron garnet using an original combination of two local probe techniques. The domain pattern of the garnet, which has a strong perpendicular anisotropy, consists of a maze of alternating up and down domains that are several micrometers wide. The magnetic tip of a scanning force microscope is used to locally excite this configuration. The resulting long-range perturbation is measured by a static nickel Hall cross deposited on top of the garnet, which is used as another local (magnetoresistive) sensor. It is found that punctually perturbing a domain-wall affects the magnetic configuration several domains away on distances well over the $5\mu \text{m}$ range.

Figure 1

(Color online) Local influence of the MFM tip stray field on the magnetization at the center of a submicrometer-size nickel cross. The tip is magnetized toward the sample by a large (200 mT) perpendicular field which also saturates the garnet underneath. (a) Atomic force microscopy (AFM) topography image. The nickel cross where the Hall signal is measured is indicated by a white arrow. (b) Hall effect variation with tip position. The position of the Hall cross is indicated with dashed lines. (c) Schematics of the amplitude of the planar Hall effect as a function of the angle between the current $\mathbf{J}$ and the magnetization $\mathbf{M}$. (d) Effect of the planar component of tip stray field (black arrows) on the cross magnetization (blue arrow); the continuous (respectively, dashed) blue arrow shows the perturbed (respectively, unperturbed) magnetization direction in the nickel Hall cross for two different tip positions.

Figure 2

(Color online) Double magnetic imaging with one minority domain of the garnet close to the nickel Hall cross. (a) MFM image. The minority domain can be seen as a black narrow stripe. The contrast associated to the nickel structure is an artifact due to the topography. (b) Hall effect in the cross (represented by dashed lines). The local effect of the tip stray field and the interaction with the minority domain are both visible. (c) Planar Hall effect resulting from the subtraction of the image (b) and the equivalent image after rotating current injection and voltage measurement by $90°$. (d) Profile on (c) (green line) showing the change in planar Hall effect and the corresponding angle $\theta$. Fast scan of the tip is from right to left.

Figure 3

(Color online) Micromagnetic simulations showing the domains backlash effect induced by the magnetic tip in the strong-interaction regime. A homogeneous magnetic field ${\mu }_{0}H=25\text{mT}$ is applied; only the perpendicular magnetization value in the top surface of the garnet is shown. The magnetic monopole $\left(q=-1.0\times {10}^{-9}\text{A}\text{m}\right)$ is scanned 50 nm above the surface of the 96-nm-thick garnet. (a) As the monopole is above a majority domain (red), the domains are close to equilibrium.(b) Getting close to a minority domain (blue), the monopole drags forth the domain walls: the majority domain below the monopole gets larger. (c) After crossing, the monopole pushes backward the minority domain and the next majority domain gets larger.

Figure 4

(Color online) Magnetic force microscopy profiles above the garnet minority domain in the high interaction regime for both scan directions. A perpendicular field of ${\mu }_{0}H=-120\text{mT}$ is applied. A larger (respectively, smaller) value of the MFM signal corresponds to a more (respectively, less) attractive interaction between the tip and the sample.

Figure 5

(Color online) Double imaging of the system including several minority domains. Fast scan of the tip is from left to right. (a) MFM image with the Hall cross position indicated by black dashed lines. The dark contrast lines correspond to the two minority domains artificially narrowed by the tip dragging the domain wall and inducing the backlash effect. (b) Hall voltage sensed in the nanostructured cross as a function of the tip position. The backlash positions given by the dark domains of (a) are reported in dashed lines. A brighter area at the left of the left dashed line is visible, even though the sensing cross is over one period of minority or majority domains away. This is due to the backlash of the left minority domain which induces a rotation of the magnetization in the cross of about $5°$.