Electrically induced and detected Néel vector reversal in a collinear antiferromagnet

Antiferromagnets are enriching spintronics research by many favorable properties that include insensitivity to magnetic fields, neuromorphic memory characteristics, and ultra-fast spin dynamics. Designing memory devices with electrical writing and reading is one of the central topics of antiferromagnetic spintronics. So far, such a combined functionality has been demonstrated via 90° reorientations of the Néel vector generated by the current-induced spin orbit torque and sensed by the linear-response anisotropic magnetoresistance. Here we show that in the same antiferromagnetic CuMnAs films as used in these earlier experiments we can also control 180° Néel vector reversals by switching the polarity of the writing current. Moreover, the two stable states with opposite Néel vector orientations in this collinear antiferromagnet can be electrically distinguished by measuring a second-order magnetoresistance effect. We discuss the general magnetic point group symmetries allowing for this electrical readout effect and its specific microscopic origin in CuMnAs.

SO . Our detection method is based on the fact that the spin-orbit-torques and the resulting exchange torques flip their signs when the sublattice magnetisations reverse and therefore deflect the reversed Néel vector in the opposite direction (see Supplementary figs. 2b,c). This combined with AMR makes the second order magneto-resistance, in general, unequal for the reversed states and allows for the electrical detection of the Néel vector reversal.
At high-amplitude setting current pulses the antiferromagnetic moments are aligned with the direction of the current-induced spin-orbit fields 1,2 . At low probing currents (weak spinorbit fields relative to anisotropy fields), the antiferromagnetic moments are only deflected by a small angle δϕ proportional to the magnitude of the current induced spin-orbit fields.
This combined with the AMR results in a second-order magneto-transport effect and a corresponding resistance variation, δR ij , that depends linearly on the probing current. To de-scribe the ϕ-dependence of δR ij we first recall the angular dependence of the linear-response AMR. Assuming that AMR in CuMnAs is dominated by the non-crystalline component, the longitudinal AMR is given by R xx = R 0 + ∆ AMR · cos(2ϕ) and the transverse AMR by fig. 2b shows a scenario where in one panel the equilibrium Néel vector is set at an angle ϕ = 45 • from the x-axis of the reading current while in the other panel the equilibrium Néel vector is reversed. When the current j is applied, the antiferromagnetic moments are deflected clockwise by −δϕ or counter-clockwise by +δϕ depending on the equilibrium Néel vector direction. The longitudinal resistance of CuMnAs then decreases or increases by δR xx due to the longitudinal AMR. In Supplementary fig. 2c, we sketch the scenario where the Néel vector is aligned with the x-axis of the reading current. In this configuration, the current induced Néel vector deflection results in the transversal resistance variation ±δR xy , depending on the direction of the Néel vector. Since δR xx and δR xy are current depend, we call them nonlinear AMR contributions in contrast to the current independent R xx and R xy which we call linear AMR contributions.
The easy plane magnetic anisotropy of our CuMnAs crossbar devices enabled us to set the Néel vector along a series of different in-plane directions (we measured 8 directions).
With this we could perform extensive consistency checks between the signs of the linear and nonlinear AMR contributions measured in both longitudinal and transverse geometries.
The results are in full agreement with the scenario of the second-order magnetoresistance that combines the current-induced Néel vector deflection with the AMR. We note that these consistency checks did not require the knowledge of the sign of the staggered current induced spin-orbit field on a given spin-subblatice for a given current direction. This is because in our measurements of δR xx and δR xy , the sign enters twice: first, when set the Néel vector direction by the staggered spin-orbit field and, second, when we detect the Néel vector direction via the staggered spin-orbit field deflection of the Néel vector.

B. Detection of the nonlinear AMR
In order to separate the linear and nonlinear AMR contributions, we apply an alternating probing current J 0 sin(ωt) along the x-axis (corresponding to a low current density ∼ 1 × At such a quasi-static condition, assuming that the spin-orbit field is rotated clockwise (anti-clockwise) with respect to the current direction, the deflection angle δϕ ∼ −(+)J 0 cos(ϕ) sin(ωt) and the corresponding longitudinal and transversal resistance variations δR xx (ϕ, t) = ∂Rxx ∂ϕ · δϕ and δR xy (ϕ, t) = ∂Rxy ∂ϕ · δϕ follow directly the alternating current without phase-shift, so that Since both ac-current and device resistance oscillate at the same frequency ω, Ohm's law the nonlinear AMR appears only as a time-independent constant voltage and as a second harmonic voltage signal oscillating at twice of the alternating reading current frequency.
In our experiments we use lock-in amplifiers to measure simultaneously longitudinal and transversal voltage signals at the current frequency ω (first harmonic signals V 1ω xx and V 1ω xy ) and at twice of the current frequency 2ω (second harmonic signals V 2ω xx and V 2ω xy ). The first harmonic signals contain only the linear AMR responses since the contributions from the nonlinear AMR average out to zero. From the second harmonics signal we can exclude contributions from the Joule heating since they do not depend on the Néel vector orientation and a possible contribution from the magneto-thermopower is an even function under Néel vector reversal and also small in our symmetric devices. Contributions from the anomalous Nernst effect do not appear in antiferromagnetic CuMnAs for the same symmetry reason (P T -symmetry) as discussed in the main text in the context of the absence of the anomalous Hall effect. We therefore can assign linear and non-linear AMR to the measured signals as where Re(V ) is the part of the measured signal detected by the lock-in amplifiers which oscillates delayed by the phase-shift ∆φ with respect to the reading current.

SUPPLEMENTARY NOTE 3. EFFECT OF CAPPING LAYERS ON SWITCH-ING PROPERTIES OF THE DEVICES
To evaluate the effect of the 3 nm Pt layer on top of the 10 nm CuMnAs layer, a reference film was grown simultaneously by masking part of the wafer during Pt evaporation.
Supplementary figure 3 shows the bipolar switching characteristics of a 4-contact cross-bar device with 10 µm wide bars patterned from the reference CuMnAs/AlOx film without the Pt-layer. Here we measured the transverse second-harmonic resistance R 2ω xy as a response to the probing ac-current of effective value J ac = J 0 / √ 2 = 1 mA (j ac ∼ 1×10 6 A cm −2 ) applied along the x-axis after 20 ms long, 9 mA writing pulses (j ac ∼ 9 × 10 6 A cm −2 ) applied along the y-axis. The measured R 2ω xy shows again the expected dependence of the second harmonics signal on the polarity of the setting current pulses corresponding to reversed Néel vector states. Note that in this reference sample, setting current pulses of a ∼ 30% higher current density were required. We assign the difference in required switching current densities to the difference in Joule heating between the devices patterned from the CuMnAs/Pt/AlOx film and the devices patterned from the CuMnAs/AlOx film without Pt.
The total sheet resistance R T of the CuMnAs(10nm)/Pt(3nm)/AlOx stack is ∼ 100 Ω, which is approximately 4× lower than the sheet resistance of the refernce CuMnAs(10nm)/AlOx film. Therefore, in the stack containing the Pt layer, only 1/4-th of the total applied current flows through the CuMnAs layer and 3/4-th of the current flow through the highly conductive Pt layer, which increases the sample temperature during the setting current pulse and facilitates the current induced switching. Note that the Joule heating in the film containing Pt at the same current density in the CuMnAs layer is about 4× larger than in the reference CuMnAs/AlOx film, since R Pt · I 2 Pt + R CuMnAs · I 2 CuMnAs = 1/3R CuMnAs · (3 · I CuMnAs ) 2 + R CuMnAs · I 2 CuMnAs = 4R CuMnAs · I 2 CuMnAs .
Apart from Joule heating, an additional spin-orbit torque generated by the current flowing through the CuMnAs/Pt interface could be considered to affect magnetisation dynamics 1,4 .
This torque can originate from the spin Hall effect in Pt or from the inverse spin galvanic (Edelstein) effect at the CuMnAs/Pt interface. Both effects would result in a non-staggered interfacial spin-polarisation p oriented along the y-axis when the current flows along the x-axis. In this case, the antidamping-like torque, which is driven by the sub-lattice magnetisation dependent staggered antidamping fields, in principle, efficiently act on the antiferromagnetic state 1,4 . However, in case of CuMnAs, this interfacial spin-orbit torque remains inefficient. It cants the sub-lattice magnetisations towards the in-plane orientation perpendicular to the applied current direction and the resulting exchange torques would then trigger Néel vector reorientation towards the outof-plane direction. This is inefficient, however, due to the strong, out-of-plane hard-axis anisotropy in tetragonal CuMnAs.