Experimental demonstration of 55-fs spin canting in photoexcited iron nanoarrays Free

About 20 years ago, Beaurepaire and his coworkers¹ reported a surprisingly fast laser-induced demagnetization in ferromagnetic nickel thin films.¹ This phenomenon is commonly called femtosecond magnetism, or femtomagnetism, in the literature.^2,3 The observed 1 ps magnetization reduction was puzzling when explained through traditional spin-phonon interactions, where typical time scales are on the order of 100 ps.⁴ However, the experimental evidence was overwhelming,^5–9 and extensive experimental and theoretical investigations have established this phenomenon to be a true magnetic effect with nonthermal origins.^6,10–12 In 2005, Kimel and his coworkers realized 50 ps inverse-Faraday writing,¹² where magnetization switching occurs nonthermally without spin reorientation or precession.¹³ It is natural to ask what is the ultimate speed limit of such magnetic switching? and how the limit depends on the material?

Differing from many prior experiments where bulk materials or thin films are used, our experiments used quasi-two-dimensional Fe, Fe/Pt, and Fe₃O₄ nanoparticle arrays with their nominal thicknesses ranging from 50 nm to 200 nm. Samples are either metallic or half-metallic and were grown by electron beam evaporation through a porous anodic alumina template and lift-off process. Details of the deposition conditions and structural analysis, such as x-ray diffraction, magnetic hysteresis loops, and typical scanning electron microscopy (SEM) have been reported elsewhere.^14,15 The lower right inset in Fig. 1 shows a typical scanning near-field optical microscopy image of the Fe nanoparticle arrays. For this particular sample, the dot diameter is $∼50$ nm and the center-to-center distance is 100 nm. The dots assume a hemispherical shape and possess quasi-hexagonal closed packing spatial ordering. Magnetic easy axes of the samples are in-plane as determined from magnetic hysteresis loops measured both in-plane and out-of-plane. Before transient measurements, the sample was magnetized in a 0.5 T external magnetic field along the easy axis.

An 800 nm pump pulse, delivered by a mode-locked Ti-Sapphire laser system with a pulse duration of 50 fs, is incident normal to the sample plane. The pump peak energy is 10 nJ per pulse with a repetition rate of 80 MHz. The pump fluence is fixed at 25 μJ/cm². Both linear and circular polarizations were used. After a time delay, a linearly polarized probe beam (5 μJ/cm²) hits the sample at 35° with respect to the sample surface normal. The transmitted probe signal is detected by a balanced photoreceiver and a lock-in amplifier. This constitutes a standard Voigt geometry and Faraday configuration, respectively, while the magnetization is along the applied field direction and cants out-of-plane. Figure 1 schematically shows our experimental setup. The Faraday rotation can have both magnetic and nonmagnetic contributions. We determine the magnetic Faraday rotation by measuring the magnetic field dependence of the transmitted probe signal. In the laser-induced spin canting process, the magnetization is not along the applied field direction, and therefore, collected Faraday signals include mixtures of various Faraday components. We eliminated the transverse component by using a s-polarized probe beam. The collected Faraday signal therefore only contains contributions from the longitudinal and polar Faraday effects.

Figure 2 shows the Faraday rotation angle (unfilled circles) as a function of the time delay between the pump and probe in the zero magnetic field. An unprecedented sharp signal reduction is observed with the maximum reduction at 55 fs. Since the Faraday rotation angle correlates with the magnetization, this result indicates the laser-induced canting of spins. The time scale of the maximum magnetization change being less than 100 fs is rather striking. To show that the reduction is of magnetic origin,^11,16,17 we directly measure four complete hysteresis loops at four delays, T = 0, 15, 55, and 150 fs, by the transmitted probe beam with a chopper frequency and with the magnetic field sweeping from −800 Oe to 800 Oe. Each data point is statistically averaged over 25 shots.

We start with the hysteresis loop at T = 0 fs (Fig. 2(a)) when the pump pulse overlaps with the probe pulse. The magnetic hysteresis loop is quantitatively similar to the magnetization measured by the vibrating sample magnetometer (VSM). The magnetization saturates at high fields and reaches about 90% of the saturation value at the zero field. The coercivity is consistent with the value obtained by VSM measurements. It should be noted that the highest field of 800 Oe used in the time-resolved Faraday rotation measurement is not sufficient to completely saturate the sample. However, the minor hysteresis loop measured by VSM using the highest field of 800 Oe is very close to the major hysteresis loop and should not affect our subsequent discussion. At 15 fs, a significant change in the hysteresis loop's shape is detected (Fig. 2(b)). More strikingly, the in-plane magnetization appears to decrease with the increasing field, leading to a negative slope of the curve. The same phenomenon is also observed for the reverse field. At T = 55 fs, the absolute value of the slope reaches the maximum, and the signal becomes undetectable at 600 Oe (Fig. 2(c)). Further increasing the field has no influence on magnetization. Below 600 Oe, the hysteresis loop resembles a diamond. This is counterintuitive since the external magnetic field works against aligning the spins. It is also important to note that the absolute scale of the maximum signal is not changed in comparison to the loop at 15 fs. At T = 150 fs, the square hysteresis loop recovers (see Fig. 2(d)). In all the hysteresis loops, the saturated field is always at 600 Oe, which shows that our sample remains virtually intact under laser illumination.

Our finding is distinctively different from most previously reported experimental results. The diamond-like hysteresis loop was previously reported in Co films grown on a vicinal substrate and was accompanied by an anomalous increase in the out-of-plane magnetization component.¹⁸ In the time domain, a rotation of the magnetization vector, not diamond hysteresis loop, was reported in a ferromagnetic/antiferromagnetic exchange coupled system,^19,20 but on a much longer time scale (a few hundred picoseconds). Beaurepaire et al.²¹ reported a complete collapse of the hysteresis loop in CoPt₃, so did our prior study in the Fe/GaAs film,²² but no diamond shape was found. We find that in the case of Fe nanoparticle arrays, a complete collapse is possible if we use a stronger pump pulse (such as 85 μJ/cm²). The diamond shape may indicate that it is a precursor to complete demagnetization in these nanoparticle arrays. Kimel et al. noticed a linear demagnetization through the inverse-Faraday effect, without spin rotation.¹² Here, our data suggest a new scenario: ultrafast spin canting. The spin is not destroyed completely; instead, it rotates out of the in-plane orientation. The diamond shape is the hallmark of a polar contribution though the longitudinal contribution is still present but much weaker.

To understand such an ultrafast canting, we first examine the possible role of the magnetic field of the laser pulses in the demagnetization process. We choose the z axis along the static external magnetic field direction (see the bottom inset in Fig. 2). The pump laser propagates along the y-direction, with its electric field polarization along the z axis and its magnetic field direction along the x direction. The spins process along the resultant magnetic field of the applied DC field $B0$ and the laser's magnetic field $Blaser(t)$⁠, through the Zeeman effect, or $−gμBℏS·(B0+Blaser(t))$⁠, where g is the Lande g-factor, μ_B is the Bohr magneton, $ℏ$ is the Plank constant over $2π$⁠, and S is the total spin operator of the system, $S=∑iSi$⁠, where the summation is over all electrons. Since $Blaser(t)$ is along the x-axis, the spin initially does rotate out-of-plane. However, it is important to note the time scale of such a rotation. The Zeeman energy of our laser pulse's magnetic field is in the order of $10−6$ eV, which would correspond to a one nanosecond time scale, or four orders of magnitude slower than our time scale of 55 fs. Therefore, the direct involvement from the laser's magnetic field cannot explain our observation.

Next, we examine other possible interactions which are relevant to our time scale. We realize that 55 fs corresponds to an energy scale of 0.075 eV. This helps us to narrow down the things to a few possible interactions: Exchange interaction anisotropy, spin-orbital coupling (SOC), magnon-magnon interactions, and electron-phonon interactions. Pure magnon-magnon and electron-phonon interactions, without SOC, do not flip spins since their operators commute with the total spin. Exchange interaction anisotropy, if due to SOC, may play a role, but it still relies on SOC. Therefore, we conclude that SOC plays a central role in the observed ultrafast timescale of the magnetization dynamics. This is supported by the experimental values of SOC. Daalderop and his coworkers showed that for a group of 3d ferromagnetic metals, the spin-orbit coupling constant is $λ=0.07$ eV.²³ Another group recently reported the SOC constant of $λ=0.06$ eV.²⁴ These values are consistent with our own investigation in ferromagnetic nickel.²⁵ Therefore, the spin-orbital coupling strength indeed coincides with our time scale very well.

While a complete theoretical calculation is beyond the scope of this paper, here, we develop a qualitative understanding of our findings. We first check whether the spin excitation is possible in our current experimental geometry. Since the spin operator permutes with the laser electric field and exchange interaction, the spin change (along the z direction) is

where λ is the spin-orbital coupling, $Lx(y), Sx(y)$ are orbital and spin angular momenta along the x(y) directions, respectively, and τ_r is the remagnetization time. In order to excite S_z, the term on the right-hand side must be nonzero. One notices that the laser field does not enter the spin equation; its role is hidden in the orbital and angular momenta, whose time evolution is determined by²⁶ $L̇x=−eEyz+eEzy+λ(LzSy−LySz)$⁠, where $Ey(z)$ is the electric field along the y(z) axis. A similar expression can be found for L_y. The equation of motion for the electron dynamics is^28–30 

where $P$ is the momentum of the electron, m_e is the electron mass, and Ω is the resonance frequency. We choose a Gaussian pulse for our laser field, $|E(t)|=A0 exp(−t2/τ2)cos(ωt)$⁠, where the laser field amplitude A₀, pulse duration τ, and carrier frequency ω are all fixed by our experimental ones. Equations (1) and (2) are solved numerically.

The red solid line in Fig. 2 is our theoretical results. We see that there is a general agreement between our theoretical spin moment change and our experimental one. The theoretical spin moment also reaches its minimum of around 55 fs. Our theory reveals some crucial insights into the spin canting time τ_s. The initial momentum has a dominant effect. A larger momentum induces a stronger spin moment change and a shorter τ_s because of a larger orbital momentum, where the spin precession has multiple oscillations. For a smaller momentum, a single minimum is observed, but the precession also depends on whether the photon resonantly excites the system or not. When approaching resonance, τ_s increases. This is similar to the Fermi liquid theory, where the quasiparticle lifetime is inversely proportional to the excitation energy. Different from these charge responses, the initial spin momentum has an effect on the canting time as well. The larger the spin momentum is, the shorter the canting time is, which is fully consistent with our early analytic results.²⁷ 

Experimentally, we probed both the spin projection along the z-axis and the polar spin component along the y-axis. Direct evidence of spin canting comes from our theoretical investigations. Figure 3(a) shows that upon laser excitation, both S_x and $Sy$ oscillate strongly with time, which unambiguously proves that the spin indeed cants out-of-plane. Both S_x and S_y precede earlier than $Sz$⁠. This is fully expected since S_x and S_y feel the effect of the laser field earlier due to our specific geometry. To reveal more insight into this spin canting process, we present the spin excitation path in Fig. 3(b). Since the excitations of S_x and S_y are similar, we take S_x as an example. We find that these excitation paths in general are very much involved and strongly depend on the initial spin configuration. In our configuration, the spin initially aligns along the z axis, which preselects the orbital angular momentum L_y path. This means that in order to excite S_z, the orbital L_y must be excited first. Since L_y is a cross product of the position x(z) and momentum $Pz(x)$⁠, a nonzero L_y requires that at least one pair of the initial position and momentum not be zero. Since our laser is along the z axis, we choose a pair of nonzero position and momentum along the x axis. This is the reason for choosing the initial velocity of 1 nm/fs along the x and y directions. Once the laser pulse is fired, it drives the electron to move along the z axis and generates L_y. Figure 3(b) shows that S_x is excited through $Ly$ and S_z (which is nonzero in the beginning). Only then is S_z excited through the joint effect of L_y and S_x. This is the origin of the delayed $Sz(t)$⁠.

One important prediction of the spin excitation path from Fig. 3(b) is that left and right circularly polarized light can cant spins equally. Since the circular polarization plane is in the xz plane, a few extra spin and orbital components play a role in spin dynamics, but the fundamental conclusion remains the same. Experimentally, we indeed observe similar hysteresis shapes for different polarizations. Figures 4(a)–4(c) show that at 50 fs, irrespective of light helicity, a diamond hysteresis loop is observed. This is fully consistent with our theoretical findings.

Ultrafast spin canting is not limited to the Fe nanoarrays. Moreover, we performed transient optical measurements on different nanostructures, including Fe/Pt and Fe₃O₄. All experimental parameters were kept the same as those in Fe nanoparticle arrays throughout our time-resolved measurements. We found that the ultrafast spin canting also occurs in these nanoparticle arrays under the current longitudinal geometry. We start with the Fe/Pt nanoparticle array, where an additional cap layer of Pt (5 nm) was grown on the top of the 50 nm Fe magnetic nanoparticle arrays. Due to the reduced low crystal symmetry and strong spin-orbit coupling near the interface between the Fe nanoparticles and Pt layer, partial spins are already oriented along the perpendicular axis before the laser excites the sample. This leads to a partially rotated hysteresis loop as shown (see the solid line in Fig. 4(d)). Upon laser excitation, a clear spin canting at 50 fs is observed from the in-plane direction toward the out-of-plane axis (see the dashed line in Fig. 4(d)). Figure 4(e) shows the results for the half-metallic Fe₃O₄ nanoparticle arrays. Differing from the Fe/Pt array, before laser excitation, the hysteresis loop is a square, but after the laser excites the sample a diamond shape is observed. Therefore, our results demonstrate, unambiguously, ultrafast spin canting in the metallic and half-metallic ferromagnetic nanoparticle arrays. These characteristics are ideal for future high density and ultrafast read/write magnetic storages.

The initial nanoparticle array samples were provided by Dr. Hao Zeng from the University at Buffalo of the State University of New York. Research at Hunter was supported by the AFOSR (Grant No. FA9550-14-1-0179), a PSC-CUNY grant (CUNY-RF No. 66501-00 45), and by NYSTAR through the photonics Center for Applied Technology at the City University of New York (CUNY-RF No. 55418-11-07). G.P.Z. was supported by the U.S. Department of Energy under Contract No. DE-FG02-06ER46304. The research used the resources of the National Energy Research Scientific Computing Center, which was supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Our calculations also used the resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which was supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357.