Magnetization statics and dynamics in (Ir/Co/Pt)₆ multilayers with Dzyaloshinskii–Moriya interaction

A large amount of magnetism research in today’s time is concentrated on inhomogeneous magnetic textures, e.g., periodic magnetic textures as stripe domain patterns,¹ chiral textures as spin spirals,² particle-like textures as magnetic skyrmions^3–6 and various other textures.⁷ In addition, in magnonics, particular attention is focused on nonreciprocal media,^8,9 i.e., systems with broken time-reversal symmetry of spin wave (SW) propagation. Particularly interesting in this context are multilayered magnetic systems with perpendicular magnetocrystalline anisotropy and Dzyaloshinskii-Moriya interaction (DMI).

DMI is an anti-symmetric exchange interaction^10,11 that occurs for materials possessing spatial inversion asymmetry. Initially “bulk DMI” was discovered in B20 weak magnetics due to their structural properties, i.e., broken inversion symmetry.^4,12 Subsequently, it was found that broken inversion symmetry can be generated artificially for ultrathin ferromagnetic films adjacent to heavy metal materials.^13,14 Interfaces of ferromagnetic/heavy metal materials produce a symmetry breaking termed as interfacial Dzyaloshinskii-Moriya interaction (IDMI).^15,16 It is known that IDMI affects many fundamental static and dynamical magnetic properties - from SW reciprocity to magnetic domain structures.^17,18 Due to the IDMI, SWs propagating in Damon-Eshbach geometry manifest an asymmetric dispersion relation, and it can be studied using Brillouin Light Scattering (BLS) spectroscopy.¹⁷ Quantification of the value of IDMI strength D_eff (effective IDMI constant) and its sign in magnetic multilayers such as Ir/Co/Pt (due to large IDMI)¹⁹ is crucial to understand the behavior of magnetization statics (determination of all the possible magnetic configurations and ways to achieve them) and spin wave dynamics.

In this work, we investigate magnetic multilayers [Ir/Co/Pt]₆ where one can expect: (i) strong IDMI and (ii) quality factor (ratio of uniaxial anisotropy to demagnetization energy) Q<1. Domain structures were deduced from complementary experimental techniques and supported by micromagnetic simulations. BLS spectroscopy was performed as a function of the magnitude of the in-plane applied magnetic field.

Magnetic multilayer of Ir/Co/Pt (nominal structure: Ti(4)/Au(30)/Ir(2)[Ir(1)/Co(1.8)/Pt(1)]₆/Pt(2), where thickness in brackets are in nm) was deposited at room temperature using magnetron sputtering on oxidized Si substrate. Magnetization hysteresis loops measurements were performed using vibrating sample magnetometer (VSM) for both in-plane and out-of-plane applied magnetic field. Measurements based on X-band (9.5 GHz) ferromagnetic resonance (FMR) spectroscopy were performed to characterize magnetic anisotropy. The magnetic domain structures were studied at: (i) micrometer resolution using longitudinal magneto optical Kerr effect (LMOKE) microscopy and (ii) tens of nanometers resolution by magnetic force microscopy (MFM) microscopy using low moment CoCr magnetic tips.

BLS spectroscopic measurements were performed in backscattering geometry using green light laser (wavelength λ =532 nm). Due to the formation and annihilation of magnons, the frequency positions of Stokes f_S and anti-Stokes f_aS peaks were obtained in this inelastic scattering process.

Fig. 1a shows the magnetization hysteresis loops acquired for the out-of-plane (black line) and the in-plane (red line) directions of the magnetic field. Comparing the shapes of these curves one can deduce the in-plane (negative) magnetic anisotropy.

It is confirmed after determination of negative uniaxial effective magnetic anisotropy field μ₀H_ueff =-0.45 T, from the X-band FMR spectra measured for magnetic field applied in-plane. Weak stripe domain structure^20,21 with magnetization distribution modified by IDMI could be expected. Labyrinth pattern of magnetic domains (characterized by out-of-plane magnetization and a period of about 100 nm) is clearly visible in MFM image obtained in the remanent state (Fig. 1(b)).

In-plane field-driven magnetization reversal was studied by LMOKE microscopy, sensitive to in-plane magnetization, see Fig. 2. Initially, the sample was saturated by the field aligned along the +y-axis. Therefore, at the remanence, the in-plane magnetization is aligned along the +y-axis (see the uniformly dark monodomain state in Fig. 2(a)). The following domain evolution was observed while decreasing the value of the magnetic field. Firstly, the nucleation of the domains with the magnetization aligned along the −y-axis and an increase of its area occurs (see the brighter domains emerging and increasing in Fig. 2(b) and (c)). Finally, the domains aligned along the +y-axis (the darker domains) vanish, leading to the saturation of the sample along the -y-axis, brighter monodomain state creation. Noteworthy, the magnetic domains (with tens micrometer size) of irregular shape are elongated along the applied magnetic field. The in-plane magnetization loop derived from the series of LMOKE images in applied field is shown in Fig. 2(d).

Dynamical studies were performed using BLS spectroscopy in Damon-Eshbach geometry, i.e., for SWs propagating perpendicularly to the applied in-plane magnetic field. Exemplary BLS spectra (black lines) measured at magnetic field μ₀H_y =-12.6 mT (slightly smaller than coercivity field) is shown in Fig. 3(a). Stokes (negative frequency shift) and anti-Stokes (positive frequency shift) lines have been fitted by the Lorentz function to define their peak frequencies f_S and f_aS. IDMI in system breaks the time-reversal symmetry of SW propagation, i.e., SWs propagating at the same frequency in the opposite directions have different wavelength and, therefore, wave number k.^22,23 This effect can be observed as a difference between f_s and f_aS peak frequencies Δf= f_S − f_aS and it determines the strength of IDMI by using the equation:

where γ is gyromagnetic ratio and M_S is the saturation magnetization.

In Fig. 3(a) mirror curve of Lorentz fitting (red curve) was done to calculate the Δf= −1.9 GHz. Performing the similar measurement at in-plane saturated state (μ₀H_y=300 mT) for fixed k=11.8 μm⁻¹ and using equation (1) give us D_eff = +1.74 ± 0.12 mJ/m² (γ=176 GHz/T and M_S =1210 kA/m²⁴).

To discuss the experimental results, micromagnetic simulations of static magnetization distribution were performed using MuMax software.^25,26 The system consisted of 100×1×6 cells of sizes of 1×10×3.8 nm³. Such an y-elongated shape, with periodic boundary conditions along the x- and y-axis, allow to consider the sample as infinite xy-plane. The sample length (100 nm) was selected to impose the experimental value of domain size period. Each magnetic film together with adjacent nonmagnetic spacers was treated as single film with total thickness of (1.8+1+1=3.8) nm, with effective magnetic parameters, as proposed by Woo et al.,²⁶ scaled by a factor e=1.8/3.8 (fraction of magnetic film within the effective film). Thus the scaled experimental values of M_S = e×1.2 MA/m, D_eff = e×1.74 mJ/m² were used. The value of interlayer exchange scaling factor S²⁴ was tested as a free parameter, and the value of S=0.015 was found, yielding the best agreement of 〈m_y〉 with the experimental remanence.

The cross-section view of the calculated magnetization distribution at remanence (H=0) is shown Fig. 3(b). The directions of magnetization are represented by the arrows and color bar defining the m_x, m_z and m_y magnetization components, respectively. In the remanent state m_y component has positive value (visible as red color) resulting in high value of in-plane magnetization observed in the experiment. Analyzing the m_x and m_z components, one can find the domain walls resembling vortices with alternating clockwise and anticlockwise magnetization rotation around the region saturated along the y-direction for subsequent domain walls. These vortices separate domains with magnetization tilted towards up (+z) and down (−z) directions. The positive sign of IDMI is responsible for the shift of the magnetization core towards the upper multilayer boundary.²⁷ The neighbor regions with opposite out-of-plane magnetization m_z>0 and m_z<0 make the domain structure visible in MFM. On the other hand, the in-plane driven magnetization switching observed in LMOKE and VSM loops correspond to the “cores” switching between the +y and −y directions. With all the cores oriented along the +y direction, the shown distribution obviously represents the remanence state after the saturation by a high enough magnetic field applied along the +y direction. The simulated values of in-plane magnetization as function of applied field starting from remanence are shown in Fig. 2(d). Selected set of parameters in simulation provide good agreement with experimental data obtained from LMOKE measurements.

BLS spectra were also studied as a function of the value of the in-plane magnetic field H_y. Fig. 4(a) and (b) show the Stokes f_S (red squares) as well as anti-Stokes f_aS (black circles) frequencies measured for the fixed wave number k = 11.8 μm⁻¹, when H_y was sweeping from positive to negative and negative to positive field directions, respectively. As the magnetic field decreases from μ₀H_y = 15 mT (see Fig. 4(a)) one can distinguish three field ranges: (i) H_y > –H_C, when f_S > f_aS; (ii) Hy ≈ –H_C with strong increase of f_aS (see the green shades); (iii) Hy < –H_C, where f_S < f_aS. Notably, in the first region (i), the frequency shifts f_S and f_aS decrease to achieve the minimum of f_aS and f_S for the field of value μ₀H_y ≈ −6.5 mT. This value corresponds well to the coercivity field -H_C observed from the LMOKE magnetization curve (see Fig. 2).

As the magnetic field is swept in the opposite direction, i.e., μ₀H_y from −15 mT up to 15 mT (see Fig. 4(b)), similar three field ranges can also be distinguished. However, in this case, the switching of f_S and f_aS frequency shifts occur at the field of value H_y ≈ +H_C. Therefore, f_aS > f_S for fields smaller than +H_C, and f_aS < f_S for fields H_y> +H_C.

The dependence Δf (H_y) is shown in Fig. 5 reveals hysteretic behavior with switching at H_C (similarly as switching of 〈m_y〉 in Fig. 2(d)). This means that for -H_C<H_y< H_C fields, depending on the history of magnetization changes, the frequency f_aS is greater or smaller than the frequency f_aS. It is closely correlated with how the static configuration behaves with the magnetic field changes. Namely, when the sign of the overall space-averaged m_y component of the magnetization (〈m_y〉) changes (in the +H_C field), the sign of Δf changes, as well. It takes negative sign (Δf <0) for 〈m_y〉 greater than 0 and positive (Δf >0) for 〈m_y〉<0. Therefore, this switching property (i.e., different frequency of counterpropagating SWs at the same wavelengths depending on magnetization history) is a clear consequence of the IDMI presence combined together with the coercivity of the in-plane magnetization.

In summary, the hybridization of the in-plane and out-of-plane magnetization state was studied using LMOKE microscopy and MFM for (Ir/Co/Pt)₆ multilayer structure, respectively. The micromagnetic simulation well supports the proposed model of these two coexisting orthogonal magnetization distributions. Exploiting BLS spectroscopy the SW propagation and their asymmetry corresponding to the wave vector orientation was investigated. Subsequently, the strength and sign of IDMI (D_eff = +1.74 ± 0.12 mJ/m²) was calculated, confirming a noticeably larger value than in the case of single Ir/Co/Pt and Pt/Co/Ir trilayers. Due to the switching of the in-plane magnetic domains switching of BLS frequencies (f_S and f_aS) occurs at non-zero magnetic field (switching field) value, and it leads to a hysteresis-like behavior of frequency shift difference Δf (=f_S − f_aS) as a function of the applied magnetic field.

This kind of system can be applicable as binary operator where at switching field two peaks Stokes and anti-Stokes interchanges it’s frequencies (f_S and f_aS) and intensities, and it is well guided by the magnetic history i.e., changes of the direction of in-plane applied magnetic field.

This work is supported by Polish National Science Center projects: DEC-2016/23/G/ST3/04196 Beethoven and UMO-2018/28/C/ST5/00308 SONATINA. And also partly supported by IEEE Magnetics Society student project 2020. PG acknowledges support by the National Science Centre of Poland, project no. 2019/35/D/ST3/03729. Micromagnetic simulations were performed in the Computational Centre of University of Bialystok.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.