Ultrafast all-optical toggle writing of magnetic bits without relying on heat

Ultrafast excitation of matter can violate Curie’s principle that the symmetry of the cause must be found in the symmetry of the effect. For instance, heating alone cannot result in a deterministic reversal of magnetization. However, if the heating is ultrafast, it facilitates toggle switching of magnetization between stable bit-states without any magnetic field. Here we show that the regime of ultrafast toggle switching can be also realized via a mechanism without relying on heat. Ultrafast laser excitation of iron-garnet with linearly polarized light modifies magnetic anisotropy and thus causes toggling magnetization between two stable bit states. This new regime of ‘cold’ toggle switching can be observed in ferrimagnets without a compensation point and over an exceptionally broad temperature range. The control of magnetic anisotropy required for the toggle switching exhibits reduced dissipation compared to laser-induced-heating mechanism, however the dissipation and the switching-time are shown to be competing parameters.

For instance, the discovery of ultrafast all-optical toggle switching magnetization in metallic ferrimagnetic alloy GdFeCo 2 is probably one of the most impactful in the field.It inspired the discovery of current-induced toggle switching in GdFeCo 16,17 and studies of the switching mechanisms in other classes of metallic ferrimagnets [4][5][6] .In all these cases, ultrafast heating of the ferrimagnet on a timescale much faster than the characteristic time scale of interaction between the spins of two magnetic sublattices was one of the key requirements for the realization of the mechanism 18 .The ultrafast heating was shown to turn the ferrimagnets into such a strongly non-equilibrium state that the preferable route for the subsequent relaxation from this state has to be accompanied by magnetization reversal.The laser-induced toggle switching without relying on heat would tremendously decrease dissipations during the writing of magnetic bits, but so far seemed to be unrealistic.
Aiming to find media for the 'cold' toggle switching, we would like to emphasize that such a switching, in principle, contradicts thermodynamic Curie's principle 1 , according to which symmetries of the causes are to be found in the symmetry of the effect 19 .Indeed, while every excitation event is identical and thus the symmetry of the cause does not change, toggling implies that the symmetry of the effect alters from pulse to pulse.Such a toggle switching becomes possible, for instance, in the case of ultrafast precessional switching, when a pulse of a magnetic field is applied perpendicular to the magnetization precisely during the half of the precession period [20][21][22] .Thermodynamic Curie's principle in this case is violated, because the field is applied on a time scale, which is much shorter than the time required for the magnetization to arrive at the thermodynamic equilibrium i.e. become parallel with respect to the applied magnetic field.Hence, to demonstrate 'cold' all-optical toggle switching, one has to find a way to generate an effective magnetic field acting on the magnetization on a time scale of half the period of the magnetization precession.
In order to generate such effective fields and demonstrate 'cold' all-optical toggle switching, we propose to employ photo-induced magnetic anisotropy in cobalt-substituted iron garnets (YIG:Co).In these garnets was shown that resonant excitation of the d-d transition in Co ions can effectively change their orbital state and thus strongly affect the magnetic anisotropy 23,24 .In particular, such an excitation destroys the balance between the intrinsic cubic magneto-crystalline anisotropy and the extrinsic magnetic anisotropy promoted by the Co ions.The effective fields of the photo-induced magnetic anisotropy were found to be strong enough to permanently switch the magnetization to another bit state defined by the polarization of the laser pulse.However, toggle switching in such Co-substituted iron garnets has not been reported.
We would like to note that in the previous papers, it was suggested that reported polarizationdependent switching in iron garnets could only be explained if the point group of the iron garnet films had a rather low symmetry 4. Such a low symmetry could be realized through the growth of the film on a Gd3Ga5O12 (001) substrate with a miscut of 4.It is thus proposed that growing the film on a substrate without a miscut would increase the symmetry of the point group up to 4mm and facilitate the toggle switching.In order to test this hypothesis we grew a new Co-substituted iron garnet film on Gd3Ga5O12 (001) substrate which with precision of 0.1 had no miscut (see Methods).
Figure 1a shows magneto-optical images of the iron-garnet film before and after illumination with subsequent femtosecond laser pulses.In principle, from the images, it is possible to see that each pulse changes the magneto-optical contrast, which evidences each pulse reverses the out-of-plane component of the magnetization.However, the positions of the domain walls seem to be preserved.Due to the regular labyrinth-like domain structure of the garnet, which hinders clear observation of changes, the switching is presented using differential images with respect to the initial state before laser pump excitation (see Fig. 1b).It is seen that in contrast to the earlier studies of the garnet with miscut 23 , every pulse toggles the magnetization state.Hence, the magnetic domains are thus written and erased with the same pump polarization (see Fig. 1c,d).Note that regarding the used laser fluences, optical absorption, and heat capacities of the samples, the heating induced by a single laser pulse is about 1 K 23 and thus way too small to explain such dramatic magnetic changes.To the best of our knowledge, this is the first demonstration of all-optical toggle switching via a mechanism that does not rely on heat.To reveal the dynamics of the switching we performed time-resolved single-shot experiments 25 (see Methods).Figure 2a shows the time-resolved magneto-optical images of the YIG:Co film acquired with picosecond temporal resolution.It is seen that the contrast seen in the final image develops during 10-50 ps.We assign the characteristic time of the contrast developing to the switching time which is defined from the fitting an exponential increase 1 − (−∆ / ) to the data (see Fig. 2b), where ∆ is the pump-probe time delay (see Methods).We performed these measurements in a broad temperature range and for every temperature we deduced the switching time ( ) (see Fig. 2c).Firstly, the switching is observed in a remarkably broad range of temperatures from 200 K to 450 K and not only in the vicinity of specific points such as compensation temperature, as in the case of heatinduced toggle switching.Secondly, the switching time is strongly temperature-dependent.
In order to reveal the origin of this dependence in detail, we performed stroboscopic pump-probe measurements of the magneto-optical Faraday rotation at lower pump fluences than that required for the switching (see Methods).Such an excitation is not sufficient to bring the magnetization over the potential barrier and the excitation results in magnetization precession around the old thermodynamic equilibrium at the frequency of the ferromagnetic resonance 26,27 .It is known that the precession frequency is defined by the strength of the applied magnetic field and the effective field of magnetic anisotropy 28 .Figure 2d illustrates the magnetization dynamics in the broad range of temperatures in the form of a 3D plot, where the amplitude of the detected signal is given by the color code.It is clear that the precession frequency is strongly temperature-dependent.
Using fits with a damped sine function (see Fig. 2b and Methods) we deduced the frequency of the ferromagnetic resonance mode from the measurements in the range from 200 K to 450 K and plotted the frequency as a function of temperature in Fig. 2e.It is seen that both the switching time and the frequency scale similarly with a temperature.As the external field in our measurements is zero and the magnetization precession in domains is coherent, the dependence of the frequency on temperature must originate from the temperature dependence of the effective field of magnetic anisotropy.Using Kittel's formula for the frequency of ferromagnetic resonance mode in cubic (001) crystal, we estimated the effective field of magnetic anisotropy for the frequency of precession (see Fig. 6c in Methods).
The correlations in the temperature dependence of the switching time and the precession frequency show that the switching between the stable bit-states proceeds via magnetization precession.
Obviously, the switching time between two magnetization states must be extracted from the precessional motion of magnetization during roughly /4 which is similar obtained in time-resolved imaging (see Fig. 2b).The characteristic time must be also comparable with the lifetime of the photoinduced magnetic anisotropy in the Co-substitute iron garnet 26,29 .In order to estimate the intensity dissipated during the switching processes we performed measurements as a function of the pump fluence and temperature (see Fig. 3).At each temperature point, the sample was illuminated by a series of single pump pulses, maintaining consistent focusing and fluence in the range of 1 -90 mJ/cm 2 .The switched area was defined as an envelope covering the pattern of both labyrinth-like switched domain states visible on differential images (see Fig. 3a).While reducing the fluence, we see a decrease in the switched area.Extrapolating the experimental data to the x-axis, we obtain an estimate of the threshold fluence required for the switching (see Fig. 3b).
Figure 3c shows a summary of the measurements in the form of a 3D plot, where the color code indicates the normalized switched area.The volume density of heat dissipated during toggle switching of magnetization in YIG:Co is estimated as a fraction of the threshold fluence absorbed by the sample (see Methods).Figure 4 shows that the switching time correlates with the dissipated energy.By choosing the sample temperature or samples with different anisotropy fields, we can either speed up the switching at the cost of larger dissipations or reduce the dissipation at the cost of the switching time.We note that the heat load during the toggle switching is found in the range from 15 J/cm 3 to 3 J/cm 3 which is much smaller compared to the heat load in heat-induced toggle switching (about 1500 J/cm 3 ) 2 .We report on a new mechanism of all-optical 'cold' toggle switching in dielectric ferrimagnets, which does not rely on heat and facilitates writing of magnetic bits with a much lower heat load than in the case of heat-induced toggle switching in metallic ferrimagnets.This new mechanism of toggle switching can be realized in a remarkably broad range of temperatures and not only in the vicinity of special points such as compensation temperature in RE-TM ferrimagnetic alloys.In particular, the ability to adjust the competition between cubic and uniaxial growth-induced anisotropy in photomagnetic materials allows for changing the angle between magnetization states, which can also reduce the switching energy threshold.The switching time in this mechanism can be controlled by tuning the intensity of the laser pulse, but the switching time and the heat load are found to be competing parameters.We anticipate that using a train of identical laser pulses and employing the discovered switching mechanism one can toggle the magnetization of iron garnet at the frequency reaching 50 GHz.Such a high amplitude magnetization changes at so high frequency with the minimum heat load, leading to a remarkably small temperature increase of only about 0.6 K, opens up new opportunities in such fields technologically relevant fields as magneto-photonics 30,31 , magnonics [32][33][34] , superconducting 35 and topological spintronics 36,37 , in a particular.Further design of photo-sensitive ferri-and antiferromagnets opens a plethora of opportunities for ultrafast and least dissipative magnetic writing with the help of light.

Methods
Materials.The investigated thin films of Co-doped monocrystalline yttrium iron garnet (YIG:Co) have the composition of Y2CaFe3.9Co0.1GeO12and the thickness of 8 µm.The garnets were fabricated by liquid phase epitaxy method on the gadolinium gallium garnet (Gd3Ga5O12) on (001)-plane substrate.The substrate is characterized by pure cubic symmetry without miscut angle with a precision of 0.1.
The saturation magnetization at room temperature was 4 = 75 G and the Néel temperature was 445 K.The magnetic anisotropy of the sample is defined at room temperature.The constant of the cubic magnetic anisotropy is = -5.5×10 3 erg/cm 3 , and for the uniaxial anisotropy the constant is = 0.6×10 3 erg/cm 3 .This configuration results in four distinct easy magnetization axes in <111> directions leading to eight possible magnetization states (Fig. 5a).Pure cubic symmetry in relation to sample with a 4 miscut angle 23   azimuthal angles, respectively.The energy was defined as: 9( , ) = (sin = sin ( cos ( + sin ( cos ( cos ( + sin ( cos ( sin ( ) + sin ( − 2 ( sin (

Fig. 1 
Fig. 1  Cold all-optical toggle switching of magnetization.a, (left panel) Magnetic domain pattern, where initially the magnetization can be either in the [11-1] state (black domain) or in the [1-11] state (white domain).Schematic illustration of the magnetic switching between [11-1] and [1-11] in iron garnet.b, Magneto-optical images of Co-substituted yttrium iron garnet (YIG:Co) after illumination with a series of pump pulses.The fluence of a single laser pulse is 50 mJ/cm 2 .The central wavelength of the laser is 1300 nm.The pump is linearly polarized along the [100] crystallographic axis.Dashed circles indicate the area exposed to the laser excitation.Small solid circles indicate the region, where the measurements of the magneto-optical Faraday effect.c, Differential magneto-optical images obtained as the difference between the images after -th and ( − 1)-th pump pulses.The images reveal the toggle switching.d, Changes of the Faraday rotation in the black domain upon excitation by a sequence of laser pulses.Every single pulse changes the magneto-optical effect suggesting that the magnetization is toggled between two stable bit-states.

Fig. 2 
Fig. 2  Dynamics of the toggle switching.a, Time-resolved differential images obtained as the difference between the images after the -th and ( − 1) -th pump pulses at room temperature.The sample was illuminated by the pump pulse linearly polarized || [100] and the fluence of 50 mJ/cm 2 .b (upper panel), Temporal evolution of the magnetic contrast in time-resolved imaging, and determination of the characteristic switching time by fitting 1 − (−∆ / ) function (red solid line) to the data.b (lower panel), Time-resolved Faraday effect resulting from low amplitude precession, which allows for the determination of the precession period and the frequency by fitting a damped sin function (blue solid line) to the data.c, Switching time as a function of temperature deduced from time-resolved imaging (full dots) and magnetization precession (open

Fig. 3 
Fig. 3  Dissipation during all-optical toggle switching.a, The switching pattern measured at various fluences at room temperature.Dashed circle indicates the area exposed to the laser excitation.b, Normalized switched area as function of fluence at different temperatures.Dashed lines are guides to the eye.c, Diagram representing the toggle switching efficiency.The color code represents the normalized switching area.The dark color corresponds to intensities insufficient for switching.The white dots highlight the minimum fluence IC required for detectable switching.

Fig. 4 
Fig. 4  Energy-time relation of the 'cold' toggle photo-magnetic switching.Green dots show the minimum heat load that accompanies the switching as function of temperature and magnetic anisotropy field HA (see Methods).Red dots show the corresponding switching time as function of temperature.Solid lines are guides for the eye.
leads to the regular magnetic domain structure.Temperature changes can influence the orientations of the easy magnetization axes and can induce spin-reorientation phase transitions38 .In the range of temperatures 200-450 K, four easy magnetization axes along the <111> directions are maintained.The domain structures of the YIG:Co samples with non-miscut and miscut (as reference) angles are shown in Fig.5.Notably, the image contrast corresponds to the value of the out-of-plane magnetization component [001], while the direction of the initially applied magnetic field establishes the in-plane [-110] component for both visible domains.

Fig. 5 
Fig. 5  Comparison of the YIG:Co films grown on substrates with and without miscut.The easy magnetization axes and the magnetic domain structure in the YIG:Co at zero magnetic field for the sample without miscut are shown on panel a, with miscut -on panel b.Laser-induced transient Faraday rotation representing laser-induced spin dynamics measured at various orientations of pump polarization (see the color code).c, shows the measurements on the sample without miscut.d, shows the measurements on the sample with miscut.The angle of the pump polarization set as 0 is parallel with respect to the [100] crystalographic axis in YIG:Co films.The pump fluence was set to 10 mJ/cm 2 .

Fig. 6 
Fig. 6  Temperature dependence on magnetization precession in YIG:Co.a, Time-resolved magnetization precession at zero magnetic field.Inset shows the magnetization precession at 300 K with a color code used in the 3D map in Fig. 2d.The precession traces show the out-of-plane magnetization component dynamics stimulated by the pump pulse with polarization E || [100] and fluence of 10 mJ/cm 2 in the pump and probe geometry.b, Temperature dependence of the normalized amplitude of the photoinduced magnetization precession which is extracted from time-resolved Faraday rotation.c, The results of the calculation of effective anisotropy field % & as a function of frequency f using the Kittel formula 28 .