Current‐Driven Switching of Néel Vector of an Antiferromagnetic Insulator Thin Film

Manipulation of antiferromagnetic (AFM) materials as active elements provides a crucial combination of electrical, thermal, and magnetic properties for spintronics. This study shows how the spin current generated in heavy metal is induced by spin‐orbit torque into an adjacent AFM insulator. The bulk unpinned spins of the AFM layer drive a spin current that is transmitted to the top ferromagnet. This mechanism allows the electrical control of the exchange bias, coercive field, and blocking temperature of the system. Further support is provided by a model calculation that quantitatively describes the effect of the spin current injection into the AFM.


Introduction
Materials with antiferromagnetic (AFM) order possess numerous advantages over ferromagnetic (FM) materials, including the absence of a stray field, ultrafast dynamics, and insensitivity to external disturbances. [1]These features have the potential to reduce device size and energy consumption.However, the compensation of net magnetization commonly seen in AFM materials implies that new manipulation and detection techniques are necessary in order to develop advanced all-AFM heterostructures [2,3] and AFM-based spintronics technologies. [1,4]Being the electrical current densities compared to FM systems, broadening the potential of insulating AFM spintronics.

Experimental Section
The experimental trilayer consists of Al 2 O 3 (0001)||NM|AFM|FM, where Al 2 O 3 (0001) is the substrate, NM represents Pt, W (HM), or Au, AFM represents FeF 2 , and FM represents Ni (Figure 1a).The selection of these materials are based on their spin-orbit coupling strength, with Pt and W having a strong coupling and Au having a weaker coupling, and the sign of the spin hall angle between Pt and W. [32] We used a collinear FeF 2 as a proof of concept due to its well established AFM and insulating properties. [33]The trilayer was grown in two steps.First, the HM layer Pt or W (10)  was deposited by sputtering at a base pressure of 3 × 10 −8 Torr and a temperature of 800 K. To obtain a continuous and conductive Au layer, the film was grown at room temperature (RT) by electron beam evaporation at a base pressure of 2 × 10 −7 Torr.Prior to the evaporation of the rest of the layers, a thermal treatment (≈800K) was applied to clean and remove oxidation of the surface.The FeF 2 (50)|Ni(10)|SiO 2 (3) layers were sequentially deposited by e-beam evaporation at temperatures of 600 K, 450 K, and RT, respectively.The numbers in parenthesis represent the layer thicknesses in nanometers.SiO 2 was used as a capping layer to prevent oxidation.A two-contact micro stripe with a width of 80 μm and a length of 1.5 mm was synthesized using a shadow mask during the growth (Figure 1b).The maximum charge-current density in the 10 nm thick NM layer is J c ≈ 2.5 × 1010 A m − 2 (I max ≈ 20 mA), and the corresponding Oersted field generated is calculated to be  0 × I max 2r ≈ 0.1 Oe, where μ 0 is the vacuum permeability, I max is the maximum applied current, and r is the distance to the Ni film.Further details regarding film characterization and experimental methods can be found in the Supplementary Materials.
Magneto-Optical Kerr Effect (MOKE) on the FM layer is used (Figure 1b) to indirectly monitor the AFM spin modification as a function of T and charge-current (I).The I, applied only through the HM layer, generates a (J s ) in the z direction (note the axes in Figure 1a).We have tested experimentally the electrical conductivity between the FM layer and the bottom HM layer at different temperatures.In this fashion, we can ensure that there is no electrical leakage across the AFM.Thus, the AFM insulator acts as a barrier to prevent electrical currents flowing through either the AFM nor the FM, thus eliminating any potential spurious contributions from charge current.During the experiment, the external magnetic field (H FC ) is parallel to I in the x direction (Figure 1b).As a consequence, the FM magnetization (M FM bulk ) and the AFM spins producing the H EB (m AFM ) are aligned along x, while the J s generated by SHE is polarized in the y direction.H c and H EB were extracted from the Ni hysteresis loops, showing that the FM films have similar properties at RT (Figure 1c), regardless of the bottom HM layer.However, after field cooling, the H c and H EB of the hysteresis loops at 20 K are slightly different depending on the bottom HM layer (Figure 1d), indicating non-identical AFM domain size and distributions due to different growth on the HM layers depending on the metal orientation.X-ray diffraction measurements are shown in Figure S1a (Supporting Information).Nevertheless, the effective anisotropies at 10 K are equivalent for the three HM layers (Figure S2a and Table S1, Supporting Information).

Results
We first investigate the behavior of H c and H EB as a function of T above and below (20-120 K) the blocking temperature (T B ) of FeF 2 .T B is the temperature at which the AFM film orders and is reflected in a maximum H c and the beginning of H EB effect [arrows in Figure 2a,b).The T B in these devices occurs at a slightly lower temperature (see Table S1, Supporting Information) than the bulk AFM FeF 2 Néel temperature of 79 K. [33] The T evolution of H c and H EB for the Pt device is shown in Figure 2a,b, respectively, while extended data for Pt, W, and Au devices for various applied currents are shown in Figure S3 (Supporting Information).The charge-current produces two effects: i) The T B shifts to lower temperatures with increasing applied I, for the Pt and W devices but not for the Au device.Above 15 mA applied I, the T B is suppressed, thereby also suppressing the H EB and H cenhancement. ii) At a fixed temperature, both H c (T = T B ) and H EB (T = 20 K) decrease in amplitude with increasing applied I (Figure 2e,f) for the Pt (black) and W (red) devices.No effects are observed in the Au device (blue).There is also a small T B asymmetry (ΔT B ; Figure 2a) depending on the charge-current polarity (±I) (Figure 2d) that can be related to the sign and magnitude of the Pt and W spin Hall angle. [32]o fully explore the underlying mechanisms behind these observations, we conducted systematic measurements as a function of current while maintaining T < T B (typically T = 20 K) fixed.Initially, I was incrementally increased in steps of 0.5 mA until reaching the critical charge-current (I c ) I = I c at which point H EB ≈ 0 and therefore, effectively suppressed T B (Figure 3).Reaching I c , an abrupt increase in H c was observed and, H EB simultaneously vanishes.Increases current above I c leads to a decrease in H c , with H EB remaining at zero.Upon decreasing the current amplitude to 0 mA, the H EB polarity switches for I < I c .While reducing the current, no abrupt peak in H c was observed when I = I c , suggesting that only overcoming I c resulted in the switching of AFM unpinned spins, indicated by the maximum observed H c peak.Similarly, when the polarity of the current was inverted, the same effect was observed resulting in H EB switching back to negative values.Although when I was reduced to 0 only 60% of the H c amplitude recovered.This suggests permanent changes in the dimension and configuration of the interfacial AFM domains, which determine the magnitude of H c .Similar observations were made in both Pt and W devices, while no effects were observed in the Au device.Implying the need for materials with a large spin-orbit coupling (Figure S4, Supporting Information).
To investigate the time dependence of the effect before and after current application, single-step minor current loops were performed.No variation of H c and H EB was observed when the applied I < I c (Figure S4, Supporting Information), indicating that the current effect is volatile at low currents.However, at I = I c , there was a slightly permanent variation in H c and H EB amplitude, which can be connected to a permanent effect the unpinned m AFM spin configuration.Once I > I c , H EB was switchable on demand depending on the current polarity with a single-step current pulse.Furthermore, H EB could be induced by the current in zero-field-cooled devices starting from the centered hysteresis loop (Figure S5, Supporting Information).We emphasize that an identical protocol was performed, i.e., demagnetization of the sample at 150 K, and field cooling to 20 K with H FC = 1.5 kOe.If the sample was not "reset" after the first current (±I) cycle, H EB switching occurred stochastically, not following the polarity of the current.This suggests a permanent variation of the dimensions and spin configurations in the AFM domains, assisted by the SOT, which leads to random H EB switching.
To confirm the presence of the spin-current effect, it is necessary to rule out potential spurious contributions such as Joule heating or Oersted field effects.Calculations show that the maximum Oersted field (≈0.1 Oe) acting on the Ni layer is too weak to switch the magnetization by the applied current polarity.To investigate temperature effects, the variation of the R of the HM can be used as an internal thermometer.The T associated with a change in resistance (ΔR) can be directly determined from independent ΔR versus T measurements (Figure S6c and Table S1, Supporting Information).In this fashion, ΔR provides a direct independent measurement of T during the experiments (Figure S6a,b, Supporting Information).The increment of T (ΔT) at the bottom layer is determined as 40 ± 5 K.For all three systems T (I c ) < T B confirming that T B is not exceeded, in contrast to a previous report where the compensation temperature of the ferrimagnetic compound was fully overcome. [34]However, we cannot discard the possibility that this ΔT may thermally assist Néel vector switching.Nevertheless, clearly large SOC is needed to obtain switching since the effect is present for Pt and W but not for Au devices in good agreement with Ref. [35].Further discussion excluding Joule heating effects is given in the Supporting Information.

Discussion
We showed that the H EB and H c of the FM can be significantly altered by passing a charge-current through the HM layer adjacent to the collinear AFM insulator.Qualitatively, this effect is associated with the spin-current generated at the HM|AFM bottom interface, which is induced by SOT in the AFM bulk spin configuration.This spin current then reaches the AFM|FM top interface and modifies the magnetization reversal, i.e., H c of the FM layer.When I = I c the SOT rotates the unpinned spins m AFM from their original parallel to antiparallel orientation to M FM and H FC .This causes the abrupt peak in the FM coercive field H c and a sign reversal of the H EB , analogous to T B effects under the cooling field.Moreover, reversing the H EB sign can be linked to the switching of the Néel vector, [24,25] which requires overcoming I c through the thermal-assisted process and the previously unpinned spins switching.
A study conducted by Morales et al. on a FM|AFM|FM trilayer showed that the configuration of the FM layers (parallel or antiparallel) produces a long-range interaction across the AFM. [36]eading to a suppression of the magnitude of H EB but has no effect on the temperature dependence of H c around T B , as it does not modify the interfacial AFM spin structure.On the other hand, our experiment shows a reduction of H EB amplitude and a shift of T B to lower temperatures.Moreover, the coercive field changes implying that the spin current leads to modifications on the AFM|FM interface.Leighton et al. suggest that the increase of H c at the Néel temperature is related to AFM spin fluctuations at the surface of the AFM layer inducing a uniaxial anisotropy in the FM layer. [29]In our case the modification of H c can arise from two effects: i) similar to the previous study the spin current modifies the AFM domains without affecting the FM spin structure or ii) the net momentum transmitted from the AFM insulator to the FM (through the AFM|FM interface within the spin diffusion length of the Ni [37] may be responsible.Note that the coercive field at 30 K, when I > I c , is smaller than the 350 K H c , in the absence of current.Since the Joule heating is at most 40 ± 5 K the decrease in H c cannot be a purely thermal effect.Therefore, we conclude that this H c decrease arises from a modification of the effective Ni intrinsic anisotropy.Considering that H c ∝ K ∥ , the 30% coercivity reduction indicates that some spins must be oriented in a perpendicular direction (K ⊥ in Figure 1b) due to the SOT.
[31] The model assumes that the AFM domains only contribute to H EB below T B , whereas AFM spin fluctuations lead to an effective anisotropy on the FM material above T B ∼ J AFM ∕k B (where J AFM is the AFM exchange coupling, and k B is the Boltzmann constant).The temperature dependence of H EB is determined by the AFM surface orderparameter ⟨M AFM ⟩ ∼ (T∕T B )  , with  representing the critical exponent. [31]While calculation based on the Ising model predicts  ≈ 1, [38][39][40][41][42][43] the quantum Heisenberg model predicts  ≈ 2, [44,45] which is applied in the present model.The AFM surface magnetization is expected to break down into domains each with a local quasi-critical temperature. [46]The global H EB and H c are obtained by averaging T B distribution as follows whereas, H c is given by With  the effective anisotropy induced by spin fluctuations above T B .The experimental H c and H EB versus T are fitted using Equations (1) and (2), by assuming that SOT, induced by the AFM spin currents, reduces the AFM exchange coupling up to J AFM − Iℏ/e, where  is the damping of spin-orbitinduced torque, ℏ reduced Planck constant, and e the electron charge.Therefore, as I is applied, T B decreases by a factor ΔT B = Iℏ/ek B , excluding the heating related to the T B shift.The resulting fits are shown in Figure 4a,b for H c and H EB , respectively, as a function of T (black open symbols) and I (orange open symbols).The current-dependent curves have been scaled to match I c and T B .The semi-quantitative agreement with the experiments further confirms that the effect is related to the HM generated spin current, which propagates across the AFM and applies a signifi-cant torque on the FM layer, rather than solely by Joule heating.Furthermore, we note that AFM ordering along the easy axis is reduced independently of the current polarity.The exerted torque is for both polarities oriented along the perpendicular direction.Further details are provided in the Supporting Information.

Conclusion
In conclusion, we have used a HM|AFM|FM trilayer to produce an efficient, non-volatile control of the AFM spin configuration switching the Néel vector on demand.This produces large reproducible and controllable effects on the H c and H EB of the FM.The experimental results show that the spin current transmitted to the AFM by spin-orbit-torque at the HM|AFM plays a significant role in the observed changes in magnetic properties.Large spinorbit coupling is necessary to switch the Néel vector and H EB .A model assuming a distribution of AFM domains provides a semiquantitative agreement with the experimental results.

Figure 1 .
Figure 1.a) Schematic of the experimental sample structure.Blue layer is HM.Black arrow represents the spin current direction.Blue and green circles represent spin polarization due to the spin Hall effect generated by a charge current density J c .The green layer is the AFM FeF 2 with red arrow and circles representing AF moments m AF .Yellow layer represents the FM Ni layer.Purple arrow and circles represent M FM aligned with the external field H FC direction.b) Experimental L-MOKE set-up.Kerr signal versus H x of the samples with Pt (black), W (red), and Au (blue) HM layers at 300 K (c) and 20 K (d).

Figure 2 .
Figure 2. a,b) H c and H EB as function of T and the applied current I, 0 mA (black), 8 mA (orange), and 15 mA (gold).Filled circles are for +I and open circles −I.Vertical arrows represent T B as a function of applied current I. Horizontal arrow represents ΔT B .c,d) T B and ΔT B as functions of the current I. e) H c as a function of applied current I at T = T B .f) H EB as a function of applied current at T = 20K for Pt (black), W (red), and Au (blue) open circles.The data are extracted from panels (a) and (b), and Figure S2 (Supporting Information).

Figure 3 .
Figure 3. Pt|FeF 2 |Ni.a) H c and b) H EB as a function of the applied current I at 20 K.The arrows represent the direction of the I cycle.The blue area represents the region where the current effects are volatile.The dashed lines represent the critical current I c, where the magnetization is switched.The red area represents the region where the current effects are permanent.The sketches represent the exchange bias sign and the coercive field amplitude.

Figure 4 .
Figure 4. a) Pt|FeF 2 |Ni H c and b) H EB as function of the Temperature (black open data) and applied current I (orange open data) at 20K.Continuous lines represent the model.