Separation of atomic-scale spin contrast on NiO(0 0 1) by magnetic resonance force microscopy

The further downsizing of magnetic recording devices is very important for future developments in our information-based society. For this purpose, it is essential to improve the technology for analyzing the magnetic properties of surfaces. The ordering of atomic spins provides important phenomena such as ferromagnetism and antiferromagnetism. To understand the magnetism on the nanometer scale, information on the arrangement of spins at the atomic scale is necessary.

Magnetic exchange force microscopy (MExFM) is a very powerful method for measuring the arrangement of spins [1]. This method employs atomic force microscopy (AFM), which is used to detect the interaction between a nonmagnetic tip and a sample. In MExFM, the interaction between the spins of an apex atom at a magnetic tip and a spin in a magnetic sample is detected. The atomic-resolution imaging of a spin on surfaces has been demonstrated on surfaces such as NiO(0 0 1) [2–4] and Fe monolayer on W(0 0 1) [5]. However, in MExFM, images contain the topographic contrast mixed with the spin contrast. In addition, measurement of the interaction requires a very specific environment such as a strong external magnetic field [2, 3] or a complicated tip such as a magnetic pasted tip [4].

Recently, we have proposed a new magnetic resonance force microscopy (MRFM) using ferromagnetic resonance (FMR) that can separate a magnetic interaction from a tip-sample interaction [6]. In this MRFM, by modulating the magnetization of the magnetic tip using FMR, only the magnetic interaction between the tip and the sample can be detected (figure 1). In a previous study [6], we succeeded in detecting the stray magnetic field of a thin film with perpendicular magnetization by MRFM using FMR.

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In this paper, we report on the detection of spin contrast on a NiO(0 0 1) surface by MRFM using FMR with atomic resolution. We detected the spin direction at individual magnetic atoms on the surface by measuring the resonance frequency of FMR. We succeeded in detecting the superexchange interaction between the tip apex atom and the second layer of Ni atoms of the NiO (0 0 1) surface.

Here we explain the measurement principle of MRFM. FMR occurs when a magnetic cantilever coated with a thin ferromagnetic film is irradiated with a microwave with resonance frequency f_res. The magnetization of the magnetic cantilever is modulated by irradiation with a frequency-modulated microwave. The frequency-modulated microwave is expressed as

$$\begin{align} \displaystyle f(t)={\rm cos}\left\{2\pi {{f}_{{\rm rf}}}t+\frac{{{f}_{{\rm d}}}}{{{f}_{{\rm m}}}}{\rm sin}(2\pi {{f}_{{\rm m}}}t) \right\},\nonumber \end{align} \tag{ 1 }$$

where f_rf, f_m, and f_d are the microwave frequency, modulation frequency, and maximum frequency shift of the microwave, respectively. The reason why the frequency of the microwave is modulated, and not the amplitude, is to prevent the thermal modulation of the cantilever caused by the modulated power of the microwave. When f_rf coincides with f_res, the magnetic moment of the tip m_z is given by

$$\begin{align} \displaystyle {{m}_{z}}={{m}_{z({\rm dc})}}+{{m}_{z({\rm ac})}}{\rm cos}(2\pi {{f}_{{\rm m}}}t),\nonumber \end{align} \tag{ 2 }$$

where m_z(dc) and m_z(ac) are the amplitudes of the dc and ac components of the magnetic moment, respectively [6].

The tip apex of the magnetic cantilever coated with a thin ferromagnetic film is composed of oblate ellipsoidal magnetic grains [6]. f_res for a ferromagnetic sample in an external magnetic field B is given by [7–9]

$$\begin{align} \displaystyle {{f}_{{\rm res}}}=\frac{\gamma }{2\pi }\left[ B+\left( {{N}_{l}}-{{N}_{a}} \right){{\mu }_{0}}{{M}_{0}} \right].\nonumber \end{align} \tag{ 3 }$$

Here, γ is the electron gyromagnetic ratio, M₀ is the saturation magnetization of the magnetic sample, and µ₀ is the magnetic permeability. N_l and N_a are the demagnetization factors along the long axis l and short axis a of an oblate ellipsoidal magnetic grain, respectively.

In frequency-modulation dynamic force microscopy (FM-DFM), the relationship between the frequency shift of the oscillating cantilever Δf_mag and the tip-sample magnetic interaction force F_mag is given by

$$\begin{align} \displaystyle \Delta {{f}_{{\rm mag}}}=-\frac{{{f}_{0}}}{2k}\frac{\partial {{F}_{{\rm mag}}}}{\partial z}.\nonumber \end{align} \tag{ 4 }$$

Here, f₀, k, and z are the resonance frequency, the stiffness of the cantilever, and the tip-sample distance, respectively. This equation is valid when the oscillation amplitude is much smaller than the decay length of the magnetic interaction force. If the magnetic tip is subjected to a perpendicular magnetic field H_z on a sample surface, Δf_mag is given by

$$\begin{align} \displaystyle \Delta {{f}_{{\rm mag}}}=-\frac{{{f}_{0}}}{2k}{{\mu }_{0}}{{m}_{z}}\frac{{{\partial }^{2}}{{H}_{z}}}{\partial {{z}^{2}}}.\nonumber \end{align} \tag{ 5 }$$

The modulated magnetic force is also a conservative force. Therefore, the magnetization of the magnetic cantilever is modulated at a frequency of f_m with the FMR. From equations (2) and (5), the modulation component of the frequency shift of the magnetic cantilever Δf_m is given by

$$\begin{align} \displaystyle \Delta {{f}_{{\rm m}}}=-\frac{{{f}_{0}}}{2k}{{\mu }_{0}}m{\hspace{0pt}}_{z({\rm ac})}{\rm cos}(2\pi {{f}_{{\rm m}}}t)\frac{{{\partial }^{2}}{{H}_{z}}}{\partial {{z}^{2}}}.\nonumber \end{align} \tag{ 6 }$$

From equation (6), the magnetic field gradient ∂²H_z/∂z² on the surface can be obtained by measuring the modulation component Δf_m of Δf.

Figure 2 presents a block diagram of MRFM. The tip-sample interaction was measured using the frequency modulation (FM) detection method [10]. The cantilever was self-oscillated at its resonance frequency f₀ with a constant amplitude A using an oscillator controller. The frequency shift Δf of the oscillating cantilever caused by the tip-sample interaction was detected by a phase-locked-loop (PLL) circuit. The frequency-modulated microwave from the microwave generator irradiates the magnetic cantilever, and the magnetization of the magnetic cantilever was modulated with frequency f_m. As a result, the magnetic interaction between the tip and the sample was modulated. The modulated magnetic interaction was detected as the magnitude (LIR) and phase (LIPhi) of the f_m component contained in the frequency shift Δf using a lock-in amplifier. The surface topography was obtained from the change in Δf in constant-height mode.

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Microwave was introduced into the observation chamber with a coaxial cable. The core part of the coaxial cable was bared up to a distance of about 1 mm from the tip. The simulation result shows that the microwave is leaked at a distance of about 0.5 mm from the end of the coaxial cable. Therefore, by bringing the tip to a distance of less than 0.5 mm from the end of the coaxial cable in the magnetic probe, the tip apex can be irradiated with a near-field microwave [11]. The end of the coaxial cable and the tip were fixed and the sample was scanned so that the tip apex was irradiated by a near-field microwave with a constant power during scanning. The microwave power was 250 mW and the modulation frequency was f_m  =  50 Hz.

As a magnetic tip, an FePt-coated Si cantilever with a spring constant of 1600 N m⁻¹ and a resonant frequency of 850 kHz was used. The FePt film is a perpendicular magnetic film and has a high coercivity of 1.53  ×  10⁶ A m⁻¹. Before the measurement, the FePt-coated tip was magnetized along the perpendicular direction to the sample surface under a pulsed magnetic field. The radius of curvature of the tip apex is approximately 30 nm.

As a sample surface, antiferromagnetic NiO(0 0 1) was used. NiO has a NaCl-type structure with a lattice spacing of 0.417 nm. Ni atoms in {1 1 1} planes are coupled ferromagnetically and neighboring Ni planes are coupled antiferromagnetically via a superexchange interaction mediated by O atoms. Ni atom spins with opposite orientations alternate along the 〈1 1 0〉 directions on the (0 0 1) surface and are oriented in the 〈2 1 1〉 directions (figure 3(a)) [12]. The magnetic structure is a 2  ×  1 structure (figure 3(b)).

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The experiments were all carried out using an optical beam deflection DFM system [13] at a very low temperature of 5 K and under ultrahigh vacuum (5  ×  10⁻¹¹ Torr).

In our previous experiment [6], we determined the FMR frequency f_res of a magnetic cantilever by measuring the f_rf dependence of Δf while the distance between the tip and the magnet surface was kept constant by interrupting the feedback loop to control the distance. The f_rf dependence of Δf has a broad negative peak, which indicates that the magnetization was changed by the FMR. The broad peak suggests the difficulty of determining f_res accurately. To determine f_res more accurately, we measured the magnitude LIR and phase LIPhi of the modulation frequency component of the frequency shift Δf_m as a function of f_rf while the magnetic cantilever was irradiated with a frequency-modulated microwave in the f_rf range of 2.0–2.3 GHz. Figures 4(a) and (b) show the magnitude LIR and phase LIPhi of Δf_m as functions of f_rf measured at a Ni atom site on the NiO(1 1 0) surface, respectively. In this measurement, using the atom-tracking technique, the distance between the tip and the Ni atom site on the NiO(1 1 0) surface was kept constant by interrupting the feedback loop to control the distance. In figure 4(a), there is a sharp dip of the magnitude at f_rf  =  2.06 GHz as well as large two peaks at f_rf  =  2.045 GHz and f_rf  =  2.09 GHz. In figure 4(b), there is a change in the phase (about 180º) at f_rf  ≈  2.06 GHz. The dip of the magnitude and the change in the phase indicate that the magnetization of the FePt tip was changed by FMR. The sharp changes in the magnitude and phase suggest that f_res can be measured accurately and it was estimated to be f_res  ≈  2.06 GHz. In the range of f_rf  ≈  2.13–2.30 GHz, there are many small peaks in the magnitude and phase. These peaks appear to originate from the noise in the modulation frequency component of the frequency shift.

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According to equation (3), the microwave frequency at the FMR f_res should depend on the external magnetic field B. Next, we investigated the B dependence of f_res at the atomic scale. Figure 4(c) shows the magnitude of the modulation component of the frequency shift Δf_m as a function of f_rf measured at Ni atom sites on the NiO(1 1 0) surface for the FePt-coated cantilever. To change the external magnetic field B, two Ni atoms whose spins were opposite were chosen. Using the atom-tracking technique, the distance between the tip and the Ni atom was kept constant by interrupting the feedback loop to control the distance at Δf  =  −275 Hz for both Ni atoms. In figure 5, each result was low-pass-filtered. It can be seen that each f_rf dependence of Δf_m has a minimum value at approximately f_res. The values of f_res measured on the two Ni atoms were different. The difference in f_res was found to be approximately 1.03 MHz. This difference is caused by the difference in the magnetic field B on the Ni atom with the opposite spin direction. Using equation (3), the change in B is calculated to be about 36 µT. This experimental result indicates that the magnetization of the magnetic tip was changed by the spin direction at the Ni atom. This is the first reported detection of the spin direction at individual magnetic atoms on a surface using FMR.

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We imaged the NiO(0 0 1) surface to demonstrate the usefulness of MRFM using FMR. In figures 5(a) and (b), we present AFM and magnitude (LIR) images of the modulation component of the frequency shift Δf_m, respectively. In the irradiation of the frequency-modulated microwave on the FePt-coated cantilever, f_rf was set to f_res at the Ni atom, where LIR for the modulation frequency component of the frequency shift Δf_m become a minimum. The images were acquired in constant-height mode. The AFM image was obtained from the absolute value of the frequency shift. The images are averaged over a unit cell. In the AFM image in figure 5(a), we can clearly observe periodic bright and dark spots with an interval of approximately 0.4 nm, which correspond to O and Ni atoms on the NiO(1 1 0) surface, respectively [14]. In the magnitude image in figure 5(b), we can also observe periodic bright and dark spots. The positions of the bright spots in the magnitude image are coincident with those in the AFM image. This indicates that the bright and dark spots in the magnitude image correspond to the O and Ni atoms, respectively. Thus, we succeeded in atomic-resolution imaging of the magnitude of the modulated magnetic force on the NiO(0 0 1) surface by MRFM.

Figures 5(c) and (d) present line profiles of the AFM and magnitude images, respectively. In figure 5(c), we can observe an almost sinusoidal variation of the frequency shift; the variation shows no difference among the local maxima at the Ni atoms and among the local minima at the O atoms. In contrast, in figure 5(d), we can observe the additional modulation of the magnitude. First, the magnitudes at the O atoms are larger than those at the Ni atom. Second, a difference in the magnitude between the Ni atoms appears, which is estimated to be 0.35. Third, a difference in the magnitude between the O atoms also appears, which is estimated to be 0.1. The difference in the magnitude for the O atoms is over three times smaller than that for the Ni atoms.

The reason why the AFM image did not show additional modulation depending on the sample spin was that the nonmagnetic interaction was too strong to detect the magnetic interaction stably. The difference in the magnitude between the Ni and O atoms is because f_rf was set to f_res at the Ni atom, and hence the magnitude at the O atoms is increased by the shift of f_res (figure 5(f)). The difference in the magnitude between the Ni atoms is due to the spin direction at the Ni atoms [2–4] (figure 5(e)), as described in section 4. The small difference in the magnitude at the O atoms is due to the superexchange interaction between the tip apex atom and the second layer of Ni atoms of the NiO (0 0 1) surface [2–4]. Thus, we succeeded in observing the spin contrast on the NiO(0 0 1) surface by MRFM using FMR.

We investigated the atomic-resolution imaging of spins on a NiO(0 0 1) surface. In this method, the magnetization of the magnetic tip was modulated using FMR. As a result, we achieved atomic-resolution imaging of the spins on a NiO(0 0 1) surface for the first time. We detected the superexchange interaction at the O atom sites. This success is a promising development in the exploration of atomic-scale physical interactions between magnetic atoms/molecules and is expected to lead to deeper insight into the various magnetic processes and functions on surfaces [15].

This work was supported by JSPS KAKENHI Grant Numbers JP16H06327, JP17H01061, and JP16H06504 for Scientific Research on Innovative Areas 'Nano-Material Optical-Manipulation'.