Introduction

A route simultaneously achieving competing goals for good thermal stability of magnetization (high coercive field Hc) and low switching field Hsw is indispensable for the further development of spintronic and magnetic storage nanodevices1. Energy-assisted switching2,3,4,5,6,7,8,9,10,11,12, spin-transfer switching13,14 and voltage-induced Hc modulation15 are examined to overcome this predicament. One of the energy-assisted switching methods is microwave-assisted magnetization reversal (MAMR), which is considered to be a promising recording method for future ultrahigh density magnetic storage2,3,4,5,6,7,8,9. It applies a radio-frequency (rf) magnetic field Hrf to a highly coercive magnet to obtain induction of uniform magnetization precession to reduce Hsw. However, MAMR has an inherent undesirable characteristic. The frequency of Hrf is around the ferromagnetic resonance (FMR) frequency fFMR, which is of the order of 100 GHz for a highly coercive magnet. This is a serious obstacle for practical applications. Indeed, although several papers3,4,5 reported Hsw reduction at single-digit gigahertz frequencies using soft magnetic materials such as a Ni–Fe alloy with fFMR<10 GHz, a high excitation frequency >10 GHz was required in the case of a highly coercive magnet with fFMR>10 GHz7,8. There are no reports of clear Hsw reduction for a highly coercive magnet at single-digit gigahertz frequencies. Thus, another way of reducing Hsw while maintaining high Hc is desired. The concept of magnetization switching presented here is based on the utilization of spin wave modes in a soft magnet to switch the magnetization in a hard magnet. A similar method has been theoretically proposed by Li et al.16 and Fal et al.17 However, there has been no experimental demonstration to date as far as we are aware. Here we show the significant reduction in Hsw of highly coercive FePt due to the spin wave excitation.

Results

Magnetic structure and FMR

We combined a hard magnetic FePt layer with a soft magnetic permalloy (Fe19Ni81; Py) layer, as schematically illustrated in Fig. 1a. In this FePt/Py bilayer, FePt has an uniaxial easy magnetization axis along the in-plane [001] direction. The magnetic moments in Py are spatially twisted after the magnetic field H has been applied in the opposite direction to the magnetic moments in FePt18. The Py layer thickness tPy was varied in the range from 40 to 120 nm, whereas the FePt layer thickness was fixed at 10 nm. The full magnetization loop of an FePt/Py bilayer with tPy=100 nm (Fig. 1b) shows two steep decreases in magnetization. The first steep decrease at around H=−100 Oe corresponds to the twist of magnetic moments in Py. The second steep decrease at around H=−1,600 Oe means that the bilayer’s magnetization has switched. The minor loop is superimposed on the full loop. After all the magnetizations has been saturated in the positive direction at H=50 kOe, H was swept to −1,400 Oe (magenta circles). Then, H was returned to zero (cyan circles). The minor loop is completely reversible without any hysteresis. This behaviour is well known as spring-back19, indicating that FePt and Py are exchange-coupled through the interface and that the magnetic moments in Py are spatially twisted by applying H.

Figure 1: Magnetization loops and FMR for an FePt/Py bilayer.
figure 1

(a) Illustrations of magnetic structures in an FePt/Py bilayer. The left (right) panel depicts the direction of magnetic moments in the saturated (twisted) state together with the coordinate axes. Magnetic field H was applied along the in-plane [001] direction of the MgO (110) substrate, which corresponds to the easy magnetization direction of FePt. (b) Magnetization full loop (dashed line) and minor loop for the bilayer with the Py layer thickness tPy of 100 nm. For the minor loop measurements, H=50 kOe was first applied to saturate all the magnetizations in the positive direction. Then, H was swept to −1,400 Oe (magenta circles) and back to zero (cyan circles). (c) FMR spectra of tPy=100 nm for experiment (upper panel) and simulation (lower panel) at H=−700 Oe. The triangles indicate the resonant frequencies. (d) Snapshots of the deviation of magnetic moments from the equilibrium position in the y direction my–my0. The red, blue and green curves correspond to the first, second and third FMR peaks, respectively. These excitation modes are the PSSW modes with n=0 (red), n=1 (blue) and n=2 (green), where n is the number of nodes. The interface between FePt and Py is located at z=10 nm. (e) Experimentally obtained resonant frequencies of n=0 (red), n=1 (blue) and n=2 (green) plotted as a function of H for tPy=100 nm (open circles). The simulated resonant frequencies are also shown by solid lines.

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We measured the FMR spectra of the FePt/Py bilayers using a coplanar waveguide (CPW) and a vector network analyser20,21 (see Methods). Figure 1c shows the FMR spectrum for tPy=100 nm at H=−700 Oe under the application of Hrf=6 Oe. We observed three resonant peaks at the frequencies f=8.0, 9.5 and 13.5 GHz, as indicated by red, blue and green triangles, respectively. The shape of the experimental FMR spectrum is well reproduced by the simulation (for more details of experimental FMR spectra, see Supplementary Fig. S1). To classify the excited magnetization dynamics at each resonance, we plotted snapshots of the deviation of magnetic moments from the equilibrium position in Fig. 1d. The red, blue and green curves correspond to the first, second and third FMR peaks, respectively. These excitation modes are known as the perpendicular standing spin wave (PSSW) modes 22 with n nodes. Figure 1e shows the experimental results for the H dependence of resonant frequencies (open circles) together with the simulated results (solid lines). The simulated results were obtained using the calculation method reported by Livesey et al.23 (for more details, see Methods). We successfully observed the higher-order PSSW modes, which have never been reported for previous experimental studies24,25,26, and the frequencies of all modes agree well with the simulation. The present results are also in good agreement with the simulation reported by Fal et al.17 Looking at Fig. 1d carefully, one can see that the dynamics of magnetic moments in FePt are also induced by PSSW. In other words, depinning occurs in FePt due to the excitation of PSSW in Py. This leads us to the idea that high Hrf enhances the amplitude of PSSW and should reduce Hsw of the FePt/Py bilayer.

Spin wave-assisted magnetization switching

We microfabricated rectangular FePt/Py bilayer elements on the signal line of a CPW (Fig. 2a) to study the Hsw reduction by PSSW. The device resistance R depends on the direction of magnetic moments in the FePt/Py bilayer owing to the anisotropic magnetoresistance effect27,28. Figure 2b shows the R–H curve for tPy=100 nm without Hrf being applied. When H was swept from positive to negative (denoted by red circles), R showed an abrupt decrease at H=−175 Oe, reflecting the twist of magnetic moments in Py. R returned to the baseline resistance RB at H=Hsw=−2,050 Oe (green arrows), where the magnetic moments of the bilayer were switched. Figure 2c displays ΔR–H curves for tPy=100 nm with Hrf=145 Oe, where ΔR is defined as R–RB. No remarkable changes in Hsw were observed for f=6.0 GHz. However, the application of Hrf with f=8.0 GHz reduced Hsw to 325 Oe. As f was increased from 8.0 to 12.5 GHz, Hsw monotonically increased. Small dips in ΔR appeared in the saturated state, which are indicated by orange triangles. A two-dimensional map of normalized ΔR as functions of H and f is shown in Fig. 2d. H was swept from positive to negative. The Hsw reduction was obtained in the wide range of f from 8 to 14 GHz. The small dip in ΔR has the same dispersion as that of PSSW in the saturated state. To understand what determined the value of Hsw at each f, we overlapped the resonant frequency of PSSW with n=0 in the twisted state of the microfabricated sample (white dotted line). Note that the frequency dependence of Hsw qualitatively followed that of the resonant magnetic field of PSSW HPSSW, indicating that magnetization switching was induced by PSSW as we expected.

Figure 2: Spin wave-assisted magnetization switching.
figure 2

(a) Schematic illustration of the device structure and measurement setup. The rf power was applied from a signal generator through the rf port of a bias-Tee. The device resistance R as a function of H was measured using a lock-in amplifier. Rs is a reference resistance of 1 kΩ. The FePt/Py was designed to be rectangular, 2 × 50 μm2. (b) R–H curve for tPy=100 nm without the rf magnetic field Hrf. The green arrows denote the switching fields Hsw. (c) ΔR–H curves for tPy=100 nm under the application of Hrf=145 Oe, where ΔR is the resistance change from the baseline resistance. The frequencies f of Hrf were 12.5, 11.0, 8.0 and 6.0 GHz. The small dips in ΔR due to the excitation of PSSW are indicated by orange triangles. (d) Two-dimensional map of normalized ΔR as functions of H and f for tPy=100 nm. H was swept from positive to negative. The white dotted line denotes the resonant frequency of PSSW with n=0 in the twisted state of the microfabricated sample.

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Figure 3a shows the f dependence of Hsw for tPy=100 nm obtained experimentally (circles) and numerically (squares). The experimental results qualitatively coincide with the simulation. The largest reduction in Hsw was achieved at f=10 GHz in the experiment, whereas the simulation showed the largest Hsw reduction at around f=9 GHz. The simulated result has two local minima of Hsw. Analysing the PSSW mode contributing to the magnetization switching, we found that these two local minima originated from the PSSW modes with different n. Because the experiments were performed at room temperature, these two local minima of Hsw were smeared out. For both experiment and simulation, Hrf with low f is ineffective for Hsw reduction because the resonant magnetic field at such low f is so low that it cannot twist the magnetic moments enough to reduce Hsw at Hrf=91 Oe. Spin wave-assisted magnetization switching was also attempted for the FePt/Py bilayer with tPy=40 nm. We did not observe any Hsw reduction even when Hrf=113 Oe was applied (see Supplementary Fig. S2). This result provides two important facts: the excitation of the FMR mode in FePt does not contribute to the Hsw reduction (see Supplementary Fig. S3), and a thin Py layer is not effective for Hsw reduction.

Figure 3: Optimum conditions of Hrf and f for Hsw reduction.
figure 3

(a) Hsw as a function of f for tPy=100 nm (circles), where the value of Hrf was set to 91 Oe. Simulated Hsw as a function of f is also shown by closed squares. (b) Two-dimensional map of Hsw as functions of Hrf and f for tPy=120 nm. (c) ΔR–H curves for tPy=120 nm with Hrf=0 Oe (top panel) and 134 Oe (bottom panel). The frequency of Hrf was 7 GHz.

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Figure 3b shows Hsw as functions of f and Hrf for the FePt/Py bilayer with tPy=120 nm. The frequency giving the lowest Hsw decreased as Hrf was increased. We successfully achieved the largest reduction in Hsw from 2,000 to 250 Oe at f=7 GHz and Hrf=134 Oe (Fig. 3c). Let us introduce the rate of Hsw reduction defined as , where Hsw0 is Hsw without Hrf. According to the MAMR calculation reported by Zhu et al.6, Hsw0=5.3 Hrf and Hsw=1.5 Hrf. Consequently, δHsw for MAMR is about 0.27, which is twice as high as that of spin wave-assisted magnetization switching, δHsw=0.13.

Discussion

We examined the nonlinear magnetization dynamics in the FePt/Py bilayer because large Hrf was applied for spin wave-assisted switching. FMR spectra for the microfabricated device were also measured under the application of large Hrf (see Supplementary Fig. S4), and clear resonant peaks were observed as in the case of small Hrf. The linewidth of resonant peaks became broadened and the asymmetric peak shape was observed for large Hrf, which may be related to the nonlinear magnetization dynamics. However, more pronounced nonlinear effects, such as remarkable nonlinear frequency shift, were not observed. This is different from nonlinear magnetization dynamics observed in spin torque oscillators29, where spatially uniform magnetization precession is induced by spin-polarized electric current. The precession frequency of a spin torque oscillator depends on the precession angle because the change in the precession angle leads to the large change in the effective field. On the other hand, the PSSW mode observed in this study is spatially non-uniform magnetization dynamics, and its precession frequency is mainly determined by the exchange field. The exchange field does not depend on the precession angle. Thus, the absence of the remarkable nonlinear frequency shift for the present devices is attributable to the less dependence of effective field on the precession angle.

An important point is that the PSSW modes were well defined even under the large Hrf application. To understand the magnetization dynamics during switching, the time evolution of magnetization switching behaviour was simulated numerically. Figure 4 shows the snapshots of simulated magnetic structures during magnetization switching under the application of Hrf=90 Oe with f=10 GHz (for more details, see Supplementary Movie 1 and Supplementary Table 1), where H was swept from 0 to −1,500 Oe, and the magnetization switching occurs in the H range from −1,250.5 (Fig. 4a) to −1,260 Oe (Fig. 4f). The amplitude of the PSSW mode in Py is resonantly enhanced, which increases the precessional amplitude of FePt at the interface, and all the magnetic moments are finally switched. The PSSW mode with n=0 largely contributes to the Hsw reduction compared with the other modes (n=1 and 2). According to the simulated result (Fig. 3a), n=1 could also reduce Hsw at the resonant frequency, although the Hsw reduction is not so significant and is smeared out in the experiment. A reason for the large Hsw reduction by n=0 is the larger precession amplitude for n=0 than those for n=1 and 2 (see Fig. 1d and Supplementary Fig. S5). As shown in Fig. 4, the large amplitude magnetization precession in Py induces the large amplitude magnetization precession in FePt, which effectively switches the magnetization of FePt.

Figure 4: Time evolution of magnetization switching behaviour.
figure 4

Simulated magnetic structures in the x–z plane (left panels) and the x–y plane (right panels), where Hrf=90 Oe with f=10 GHz was applied. H was swept from 0 to −1,500 Oe, and the magnetization switching occurs in the range from H=−1,250.5 Oe (a) to H=−1,260 Oe (f). (a–f) The time-evolved snapshots of magnetic structures during the magnetization switching.

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The numerical simulation indicates that the spin wave excitation leads to the magnetization switching in FePt. However, one might think that in the experiment, Hsw is not the real switching field of FePt, but the depinning field in FePt layer because depinning occurs in FePt under the large Hrf application. We confirmed that Hsw corresponded to the real switching field of FePt from the anisotropic magnetoresistance curves measured using different sequences of magnetic field sweep (see Supplementary Fig. S6). One might also suspect that the origin of Hsw reduction is the temperature rise due to the application of Hrf, that is, Joule heating by alternating current. However, this idea can be eliminated because RB, which is a function of the device temperature, did not show any dependence on f (see Supplementary Fig. S7). The large Hsw reduction by spin wave excitation was also confirmed for the other devices (see Supplementary Table S2), indicating that the error in the rate of Hsw reduction is small. Because our results simultaneously achieved the competing goals of both high Hc and low Hsw, spin wave-assisted magnetization switching provides a new nanotechnology for information writing in a wide range of spintronic and magnetic storage applications.

Methods

Thin film preparation

Thin films were prepared on a MgO (110) single-crystal substrate. The stacking of the thin films was MgO (110) substrate/Fe (1 nm)/Au (40 nm)/FePt (10 nm)/Py (tPy)/Au (3 nm). The layers from Fe to FePt were deposited by using an ultrahigh vacuum (UHV) magnetron sputtering system (ULVAC, Inc.) equipped with high-purity targets of Fe (99.99%), Pt (99.99%) and Au (99.9%). The base pressure of the UHV magnetron sputtering system was below 2 × 10−7 Pa. A 1-nm thick Fe seed layer and a 40-nm thick Au buffer layer were deposited at ambient temperature. Subsequently, a 10-nm thick FePt layer was deposited on the Au buffer layer after the substrate temperature was set at 450 °C. Then, the film was transferred from the UHV magnetron sputtering chamber to an ion beam sputtering (IBS) system. In the IBS chamber, a Py layer followed by a 3-nm thick Au capping layer was deposited on the FePt layer at ambient temperature. The compositions of FePt and Py were determined to be Fe48Pt52 and Ni81Fe19, respectively, by electron probe X-ray microanalysis. The epitaxial growth of Au, FePt and Py layers with the (110) preferential crystallographic orientation was confirmed by X-ray diffraction. The X-ray diffraction patterns also indicated the formation of the L10 ordered structure in the FePt layer. The magnetization loops of the thin films were measured at 295 K using a superconducting quantum interference device magnetometer.

FMR measurement

The FMR measurement was carried out at room temperature using a CPW and a vector network analyser. A thin film with a FePt/Py bilayer was put onto the CPW consisting of Cr/Au layers, and the CPW was connected to the rf circuit employing a two-terminal rf probe. The rf power Prf of 0 dBm was applied to the signal line, which induced a transverse rf magnetic field of Hrf ~6 Oe, and the change in the reflected signal was detected with the vector network analyser. The value of S11 is defined as the ratio of the reflected voltage to the input voltage. The frequency dependence of S11 was measured under the application of H, which was applied along the in-plane easy magnetization direction.

Device fabrication and electrical measurement

Rectangular-shaped FePt/Py elements were prepared by using a conventional microfabrication process. First, a negative-type electron beam (EB) resist was spin-coated onto the thin film and patterned into the shape of the CPW by EB lithography (ELS-7500; Elionix Inc.). The width and length of the signal line of CPW were 4 and 50 μm, respectively. After exposure of the EB resist followed by development, the thin film was milled by argon ions through the resist mask. The EB resist was then spin-coated onto the CPW-shaped film and patterned into a rectangular shape with the size of 2 × 50 μm2, which was located on top of the signal line of the CPW-shaped film. The CPW-shaped film was again milled by argon ions. The ion milling was stopped at the top of the Au buffer layer, which was monitored by secondary ion mass spectroscopy. Finally, the Au buffer layer remained as the signal and ground lines of the CPW, and the rectangular FePt/Py element was prepared on the signal line. This rectangular shape induces the shape anisotropy of Py. Because the long axis of rectangle is the same as the in-plane [001] direction of the FePt layer, both uniaxial easy magnetization axes of FePt and Py are in the same direction. The microfabricated device was connected to the rf-compatible circuit via a two-terminal rf probe, and Prf was applied from a signal generator through the rf port of a bias-Tee after −6 dB attenuation. The application of Prf induced Hrf in the y–z plane of the FePt/Py element. The device resistance was simultaneously measured using a lock-in amplifier.

Numerical simulation

Numerical simulation was carried out by solving the Landau–Lifshitz–Gilbert (LLG) equation by using the conventional fourth-order Runge–Kutta algorithm. The effective magnetic field in the LLG equation is the vector sum of the anisotropy field, magnetostatic field, exchange field, H, and Hrf. In the present numerical study, we considered an exchange-coupled FePt/Py bilayer of infinite size in the film plane. The thicknesses of FePt and Py were fixed at 10 and 98 nm, respectively. The film was discretized into 1-nm thick infinite plates, and each plate was assumed to have a uniform magnetization vector. The saturation magnetizations of FePt and Py were determined to be 1000 and 800 emu cm−3, respectively, from the magnetization measurement. The inter- and intra-layer exchange constants of FePt/Py, Aint, AFePt and APy, were chosen to be 1.0 × 10−7, 1.0 × 10−6 and 1.3 × 10−6 erg cm−1, respectively, so as to reproduce the experimental magnetization loop. The small value of Aint results from the slight oxidation and/or the contamination on the FePt surface during the sample transfer from the UHV magnetron sputtering system to the IBS system with breaking the vacuum. The uniaxial anisotropy constant of FePt KFePt was assumed to be 3.3 × 106 erg cm−3, which was determined from the magnetic field required to switch FePt in the lithographically patterned device (see Fig. 2b), whereas KPy was set to 1.0 × 103 erg cm−3. One may consider that KFePt=3.3 × 106 erg cm−3 is small. The one-dimensional model often leads to the underestimation of KFePt to reproduce Hsw because in experiment Hsw is generally much smaller than the anisotropy field. The experimental value of KFePt was about 2.5 × 107 erg cm−3. The Gilbert damping constants for Py and FePt were 0.008 and 0.02, respectively. To evaluate the Hsw reduction under the Hrf application, we set Hrf to 90 Oe. When Hsw as a function of f was evaluated, the magnetization was initially magnetized along +x direction. The magnetization was relaxed for 10 ns under Hrf applied along the y axis. The magnetization curve under the Hrf application was then calculated sweeping the dc magnetic field along the x direction. The field sweep velocity was 50 Oe ns−1. Hsw was defined as the magnetic field at which the magnetization of the FePt layer became zero. To obtain the f dependence of Hsw, f was varied in the range from 1 to 20 GHz.

Using the same parameters as those for the magnetization switching simulation, we calculated the stable magnetic structure at each H by solving the LLG equation. For these stable magnetic structures, we solved the eigenvalue equations corresponding to the linear response to the small Hrf and obtained the resonant frequencies. To construct the eigenvalue equations, we employed the local rotated frame where the coordinates are rotated about the z axis such that the new x axis points in the same direction as the local magnetization vectors.

Additional information

How to cite this article: Seki, T. et al. Spin wave-assisted reduction in switching field of highly coercive FePt magnets. Nat. Commun. 4:1726 doi: 10.1038/ncomms2737 (2013).