SUPPLEMENTARY INFORMATION

Transcription

1 In the format provided by the authors and unedited. Room temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures: Supplementary Information Olivier Boulle, Jan Vogel, Hongxin Yang, Stefania Pizzini, Dayane de Souza Chaves, Andrea Locatelli, Tevfik Onur Menteş, Alessandro Sala, Liliana D. Buda-Prejbeanu, Olivier Klein, Mohamed Belmeguenai, Yves Roussigné, Andrey Stashkevich, Salim Mourad Chérif, Lucia Aballe, Michael Foerster, Mairbek Chshiev, Stéphane Auffret, Ioan Mihai Miron, Gilles Gaudin 1 Sample preparation and magnetic characterization The Ta(3)/Pt(3)/Co(0.5-1)/MgO x /Ta(2) (thickness in nm) film was deposited by magnetron sputtering on a 100 mm high resistivity Si wafer and was then annealed for 1.5h at 250 C under vacuum and under an in-plane magnetic field of µ 0 H = 240 mt. The Co layer was deposited using a wedge deposition, so that its thickness varies between approximately 0.5 and 1.1 nm across the sample. The nominal thickness of the studied film is t =0.98 nm (except in the XCMD-PEEM experiments presented in Fig. 5 of the main text where t=1.08 nm). The magnetic moment per unit area µ S = (1.529 ± 0.03) 10 3 A was measured by SQUID magnetometry. The effective anisotropy field µ 0 H k = 200 mt was measured by Kerr effect microscopy experiments in the presence of an external in-plane magnetic field. To evaluate the value of D from the BLS experiments, due to the uncertainty in the magnetic thickness resulting from the wedge deposition of the Co and the magnetic polarisation of the Pt 1, the value of the saturation magnetisation M s was chosen equal to the bulk value M s = A/m. Previous measurements we carried out on Pt(3 nm)/co (x nm)/x/pt where X =Cu, Pt, Au, have indeed shown that M s is close to the bulk value for a thickness x larger than 1 nm, when taking into account the presence of a dead layer 2. With this value of M s, an effective thickness of Co of t =1.06 nm is obtained from the magnetic moment per unit area and D =2.05 ± 0.3 mj/m 2 (see below). 1 NATURE NANOTECHNOLOGY 1

2 These values of M s, D and t were used for the micromagnetic simulations. Note that the relevant parameters in the micromagnetic simulations are the magnetic moment per unit area µ S = M s t as well as the interfacial DMI parameter D s = Dt =2.17 ± 0.14 pj/m, which have been measured experimentally using SQUID magnetometry and Brillouin Light Scattering experiments. 2 Brillouin Light Scattering experiments To quantify the amplitude of the DMI in our films, we measured the frequency shift of oppositely propagating spin waves using spin wave spectroscopy experiments?, 3 7. The idea of the measurement is the following: When the magnetisation is pulled in the plane by an external magnetic field H y, the D vector is oriented along y for spin waves propagating along the x axis (see Fig. S3(a)). Thus, at a given time t, when moving along the x axis, the magnetisation rotates anticlockwise around the D vector for spin waves with k x < 0 and clockwise for k x > 0. This leads to an energy shift for spin waves with opposite k x vector due to the DMI and the corresponding frequency shift writes f(k x )=f(k x ) f( k x )=2γk x D/(πM s ). To measure f, we have carried out spin wave spectroscopy experiments using the Brillouin Light Scattering technique in a backscattering geometry 7. A spin wave spectrum is shown on Fig. S3(b) (red dots) for an in-plane magnetic field of 0.7 T and k x =4.1µm 1. The Stokes (S) and Anti - Stokes (AS) peaks are observed, corresponding to ±k x. The blue line is a Lorentzian fit of the experimental data inverted with respect to f =0, which shows that the Stokes peak has a frequency different to the Anti-Stokes peak, as is expected in the presence of DMI. The shift in frequency f = f S f AS scales linearly with k x (Fig. S3(c)), which allows to extract a DM parameter D =2.05 ± 0.3 mj/m 2. Note that the sign of f is consistent with the sign of D and the left handedness of the Néel DW we observe experimentally. As D is expected to be inversely proportional to the film thickness t 7, one can also evaluate a related interfacial DM parameter D s = Dt =2.17 ± 0.14 pj/m. 2 NATURE NANOTECHNOLOGY 2

3 b Intensity (a.u) f c f (GHz) Frequency (GHz) f AS k x (µm -1 ) f S Frequency (GHz) k x (µm -1 ) Figure S1: Brillouin Light Scattering experiments (a) Principle of the measurement. At a given time t, when moving along x, the magnetisation rotates clockwise (/counterclockwise) around the D vector for spin waves propagating along x (-x), which leads to a different DM energy. (b) BLS spectra for an in-plane magnetic field H=0.7 T and k x = 4.1µm 1. The red squares are experimental data whereas the red lines are Lorentzian fits. The blue line is a Lorentzian fit of the experimental data inverted with respect to f =0. (c) f = f S f AS as a function k x for H =0.7T, where f S and f AS are respectively the Stokes and Anti-Stokes resonance frequency. Inset: f S and f AS as a function k x. 3 Fitting procedure We discuss in this section the fitting procedure of the linescan of the dichroic contrast of Fig. 1(a) (white dotted line) of the article. This linescan crosses two consecutive up/down - down/up domain walls normally to their surface. We considered the following standard Néel domain wall profile for the magnetisation angle θ : θ = ±2 arctan[exp(x/ )], where is the DW width parameter. The dichroic contrast C is proportional to the projection of the magnetisation along the X-ray beam direction, which impinges at an angle α = 16 on the sample surface plane. The in-plane direction 3 NATURE NANOTECHNOLOGY 3

4 a Magnetic contrast (a.u) Experiments =12 nm =14 nm =16 nm =18 nm =20 nm = 22 nm Distance (nm) b (nm) (nm) Figure S2: (a) Dark blue line : Linescan of the dichroic contrast of Fig. 1(b) of the main article. The other colored lines are fits using a Gaussian convoluted Néel chiral DW profile assuming a fixed value for the standard deviation σ. (b) Dependence of the domain wall width π deduced from the fits on σ. The error bars show the 95% confidence interval. of the X-ray beam being here perpendicular to the DW surface C m z sin α + m x cos α, where m z = cos θ(x) and m x = ± sin θ(x) for a chiral Néel domain wall (the axis x is normal to the DW surface). To take into account the finite lateral spatial resolution of the technique, C was convoluted with a Gaussian function with standard deviation σ. The fitting curve shown in Fig.1(b) of the article was obtained with and σ chosen as free parameters. This leads to a DW width π = 29.5 ± 4 nm and 2σ = 40 nm. The error in the DW width is estimated from the 95% confidence interval of the fit as well as the error in the angle α of 1. We show on Fig. S2(a) the fitting curves assuming σ is a fixed parameter with values ranging between 12 and 22 nm. One can see that the effect of the fit is a modulation of the height of the dip/peak due to the DW signal, as well as a slight change in the slope of the signal at the DW position. This leads to a weak change in the DW width when σ varies, as can be seen on Fig. S2(b). For the fitting of the linescan of the skyrmion shown in Fig.3 of the article, a value 2σ = 4 NATURE NANOTECHNOLOGY 4

5 a Contrast (a.u) Experiments =12 nm =14 nm = 16 nm = 18 nm = 20 nm = 22 nm = 24 nm Diameter (nm) b Distance (nm) (nm) Figure S3: (a) Dark blue line : Linescan of the dichroic contrast across the skyrmion of Fig. 3 of the main article. The other colored lines are fits using a Gaussian convoluted Néel chiral DW profile assuming a fixed values for the standard deviation σ. (b) Dependence of the skyrmion diameter deduced from the fits as a function of σ. The error bars show the 95% confidence interval. 28 nm was used. This value was deduced from a linescan of the topographic image of the dot, which was fitted with an error function. Note that the spatial resolution may vary from one image to another due to differences in the focus and astigmatism correction settings as well as the drift compensation. To estimate the influence of the resolution on the fit, we fitted this linescan assuming different values of σ. We show on Fig. S3(a) the fitting curves when σ varies and on Fig. S3(b), the deduced diameter. The quality of the fit is still good for higher values of σ and the value of the diameter changes little when σ varies. 4 Larger dots Square dots with lateral sides of 1 µm were also observed using XMCD-PEEM (see Fig. S4(ab)). We did not observe single isolated skyrmions in these dots but larger distorted bubbles (see Fig. S4(a)) or worm like magnetisation patterns (see Fig. S4(b)). Micromagnetic simulations predict that the skyrmion becomes unstable above lateral dimensions of about 1.2 µm, leading to worm like pattern (see Fig. S4(c)). These results underline the important role of the confinement 5 NATURE NANOTECHNOLOGY 5

6 a b c hν hν mz Figure S4: (a-b) XMCD-PEEM image of magnetisation patterns observed in 1 µm long squared dots at zero applied magnetic field. The white arrow indicates the in-plane direction of the X-ray beam. (c) magnetisation pattern in a 1.2 µm square dot obtained by micromagnetic simulation. This state was obtained after relaxation from an initial magnetic state composed of a 350 nm diameter skyrmion. to stabilize single isolated skyrmions at zero external magnetic field in this material. 5 Ab-initio calculations The Vienna ab initio simulation package (VASP) was used in our calculations with electron-core interactions described by the projector augmented wave method for the pseudopotentials, and the exchange correlation energy calculated within the generalized gradient approximation of the Perdew- Burke-Ernzerhof (PBE) form 8, 9. The cutoff energies for the plane wave basis set used to expand the Kohn-Sham orbitals were chosen to be 320 ev for all the calculations. The Monckhorst-Pack scheme was used for the Γ-centred k-point sampling. In order to extract the DMI vector, calculations were performed in three steps. First, structural relaxations were performed until the forces become smaller than ev/å for determining the most stable interfacial geometries. For DMI calculations, one to five monolayers of Co were stacked between several layers of Pt and MgO films in a 4 1 surface unit cell with π/2 spin rotations along (111) direction (Fig. S5). The 6 NATURE NANOTECHNOLOGY 6

7 oxygen bonds on the top layer have been passivated. Next, the Kohn-Sham equations were solved, with no spin-orbit coupling, to find out the charge distribution of the systems ground state. Finally, the spin-orbit coupling was included and the self-consistent total energy of the system was determined as a function of the orientation of the magnetic moments which were controlled by using the constrained method implemented in VASP. This method has been used for DMI calculations in bulk frustrated systems and insulating chiral-lattice magnets 10, 11 and was adapted here to the case of interfaces 12. Figure S5: Crystalline structure of the Pt[3]/Co[3]/MgO multilayer. 6 References 1. Grange, W. et al. Magnetocrystalline anisotropy in (111) CoPt 3 thin films probed by x-ray magnetic circular dichroism. Physical Review B 58, 6298 (1998). 2. Bandiera, S., Sousa, R., Rodmacq, B. & Dieny, B. Asymmetric Interfacial Perpendicular Magnetic Anisotropy in Pt/Co/Pt Trilayers. IEEE Magnetics Letters 2, (2011). 7 NATURE NANOTECHNOLOGY 7

8 3. Moon, J.-H. et al. Spin-wave propagation in the presence of interfacial Dzyaloshinskii-Moriya interaction. Phys. Rev. B 88, (2013). 4. Di, K. et al. Asymmetric spin-wave dispersion due to Dzyaloshinskii-Moriya interaction in an ultrathinpt/cofeb film. Appl. Phys. Lett. 106, (2015). 5. Nembach, H. T., Shaw, J. M., Weiler, M., Jué, E. & Silva, T. J. Spectroscopic confirmation of linear relation between Heisenberg- and interfacial Dzyaloshinskii-Moriya-exchange in polycrystalline metal films. ArXiv Cond-Mat (2014). 6. Stashkevich, A. A. et al. Experimental study of spin-wave dispersion in Py/Pt film structures in the presence of an interface Dzyaloshinskii-Moriya interaction. Physical Review B 91, (2015). 7. Belmeguenai, M. et al. Interfacial Dzyaloshinskii-Moriya interaction in perpendicularly magnetized Pt/Co/AlO x ultrathin films measured by Brillouin light spectroscopy. Phys. Rev. B 91, (2015). 8. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, (1993). 9. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, (1996). 10. Xiang, H. J., Kan, E. J., Wei, S.-H., Whangbo, M.-H. & Gong, X. G. Predicting the spin-lattice order of frustrated systems from first principles. Phys. Rev. B 84, (2011). 11. Yang, J. H. et al. Strong Dzyaloshinskii-Moriya interaction and origin of ferroelectricity in Cu 2 OSeO 3. Phys. Rev. Lett. 109, (2012). 12. Yang, H., Thiaville, A., Rohart, S., Fert, A. & Chshiev, M. Anatomy of Dzyaloshinskii-Moriya interaction at Co/Pt interfaces. Phys. Rev. Lett. 115, (2015). 8 NATURE NANOTECHNOLOGY 8