CrSBr. This sample geometry allows not only efficient detection, but also electrical control of the antiferromagnetic resonance through spin-orbit torque from the PtTe 2 electrode. The ability to efficiently detect and control antiferromagnetic resonance provides the means to make detailed studies of the physics governing these high-frequency dynamics and to pursue applications including radiation sources, modulators, and detectors.
Manipulation of spin dynamics within antiferromagnets is attractive for future applications due to the potential for high-frequency (GHz-THz) operation and insensitivity to small magnetic fields, but because antiferromagnets have no net magnetic moment, it is challenging to efficiently detect and control these dynamics (1,2,3). The field of antiferromagnetic spintronics has made recent progress in demonstrating that the antiferromagnetic Néel vector can be reoriented using current pulses (4,5,6,7,8,9,10,11,12) and in achieving large magnetoresistance in tunnel junctions made with metallic antiferromagnet electrodes (13,14,15).
High-frequency antiferromagnetic resonance modes have been detected using resonant absorption (16,17,18), optical (19,20,21,22), and spin-pumping techniques (23,24,25). However, the previous electrical approaches of resonant absorption and spin pumping focused on millimeterscale or larger samples. In order to utilize GHz-THz antiferromagnetic dynamics for applications such as radiation sources, modulators, and detectors, it will be necessary to develop much more compact electrical devices which are capable of both (1) detecting and (2) manipulating these dynamics in low-damping antiferromagnets. Here, we demonstrate micron-scale 3-terminal PtTe 2 /bilayer CrSBr/graphite tunnel junctions which realize both functions. The devices achieve direct read-out of antiferromagnetic resonance in the CrSBr tunnel barrier using spin-filter tunneling (26,27,28), and at the same time allow the resonance damping to be tuned via spin-orbit torque (29,30,31,32) from the PtTe 2 electrode (33,34). The measurements reveal that the spin-orbit torque acts selectively only on the spin sublattice within the CrSBr layer adjacent to the PtTe 2 electrode.
The antiferromagnet we employ, CrSBr (35,36,37,38,39), is an orthorhombic van der Waals (vdW) material in which spins within each layer are ferromagnetically aligned, while spins in adjacent layers are antiferromagnetically coupled. The bulk Néel temperature is 132 K and the magnetic anisotropy is triaxial, with a hard axis along the out-of-plane crystal c ˆaxis, an easy axis along the crystal b ˆaxis, and an intermediate axis along the crystal a ˆaxis (35,36,37). We will measure antiferromagnetic resonances for the case where a magnetic field is applied along or near the in-plane intermediate a ˆaxis, for which the equilibrium state of the two spin sublattices is a spin-flop configuration and the resonances have the form of in-phase (i.e., acoustic) or out-of-phase (i.e., optical) precession of the spin sublattices. Antiferromagnetic resonances in CrSBr have been measured previously both by resonant absorption in bulk samples (18) and by optical pump-probe methods in samples down to bilayer thicknesses (20,21).
The spin-orbit-torque material we use, PtTe 2 , is a vdW type-II Dirac semi-metal with an electrical conductivity of order 100 µΩcm and a spin-orbit torque efficiency per unit current density at room temperature of 0.05-0.15, comparable to Pt (33,34).
Our device geometry is shown in Fig. 1A,B (see also materials and methods). It consists of a bottom PtTe 2 channel which makes contact to pre-formed Pt electrodes, a bilayer CrSBr flake on top of the PtTe 2 oriented so that the easy b ˆaxis of the crystal is 45 • from the direction of current flow, and a narrow graphite top contact. The entire structure is encapsulated with a hexagonal boron nitride layer on top. All transport measurements to be reported in this paper were peformed in a liquid-nitrogen flow cryostat at 85 K, below the Néel temperature of CrSBr.
The low-bias magnetoresistance of the PtTe 2 /bilayer CrSBr/graphite tunnel junction is shown in Fig. 2A. The behavior differs in two critical ways from previous measurements which studied spin-filter tunneling between two graphite electrodes through antiferromagnetic CrI 3 (27,28) or CrCl 3 (40). First, the use of PtTe 2 instead of graphite for one of the electrodes reduces the overall tunnel-junction impedance, which is important for enabling high-frequency experiments. We measure a resistance of roughly 700 Ω for the PtTe 2 /bilayer CrSBr/graphite device, whereas a comparable graphite/bilayer CrSBr/graphite device (not shown) had a resistance of 2000 Ω. The second important difference is that CrSBr has significant within-plane magnetic anisotropy whereas CrI 3 and CrCl 3 have negligible anisotropy within their vdW planes. This magnetic anisotropy causes the magnetoresistance of the CrSBr junction to differ for in-plane magnetic fields applied parallel and perpendicular to its easy axis.
When an applied magnetic field H is increased from zero in the direction parallel to the easy magnetic axis (the CrSBr b ˆaxis), we see an abrupt transition from a higher resistance into a lower resistance state at 0.1 Tesla that corresponds to a spin-flip transition of the CrSBr spin sublattices from an antiparallel state to a parallel state (Fig. 2A). With H swept parallel to the intermediate anisotropy axis (the CrSBr a ˆaxis), there is instead a gradual transition from high to low resistance, corresponding to a gradual canting of both spin sublattices away from the easy axis. The ability to control the angle between the spin sublattices using a magnetic field applied along the intermediate axis allows us to maximize the sensitivity of the tunnel junctions for reading out the antiferromagnetic resonance and and also to tune the magnetic damping using spin-orbit torque.
Antiferromagnetic resonance can be excited and detected electrically via a 3-terminal version of the spin-torque ferromagnetic resonance technique, which for an antiferromagnetic resonance we will refer to as ST-AFMR (41), via the circuit diagram shown in Figure 1C. We apply a pulsed fixed-frequency microwave current (P ≤ 5 dBm) to the PtTe 2 channel through contact T1.
Most of this current flows out through contact T2, but a small leakage current also flows through the tunnel junction to the top contact T3. The microwave current excites antiferromagnetic resonance through a combination of spin-orbit torque and the Oersted magnetic field, which results in an oscillating tunnel-junction resistance on account of spin-filter tunneling. Mixing between this oscillating resistance and an oscillating leakage current flowing through the tunnel junction results in a pulsed dc voltage at contact T3 that is measured using a lock-in amplifier.
By sweeping an applied field through the resonant condition, the frequency of the resonance can be determined (Fig. 2B). Figure 2D shows the frequency vs. field dependence for magnetic-field orientations near the intermediate anisotropy axis. In our devices, the leakage current through the tunnel junction is sufficient to produce a mixing signal with a large signal-to-noise ratio. If that had not been the case, we could also have applied a separate microwave current directly through the tunnel junction to achieve an even larger signal.
Of the two antiferromagnetic resonance modes, the measurement is sensitive only to the optical mode, because this is the mode in which the relative angle between the two spin sublattices undergoes large changes at the precession frequency to produce a substantial oscillating resistance. Assuming a simple exchange field H E between the spin sublattices in CrSBr, the field dependence for the optical-mode frequency for a magnetic field along the intermediate axis should have the form ( 18)
where µ 0 is the magnetic permeability, γ is the gyromagnetic ratio, H is the external field strength, and H a and H c are the anisotropy parameters along the a ˆand c ˆaxes respectively.
From simultaneous fits to the resonance spectra in Figure 2D and the spin-flip transition in the tunneling magnetoresistance (Fig. 2A), we obtain exchange and anisotropy parameter values µ 0 H a = 0.33(6) T, µ 0 H E = 0.096(1) T and µ 0 H c = 0.77(2) T (supplementary text section 2.1, Fig. S2A,B). The in-plane and out-of-plane anisotropy parameters are not far from the values reported previously for bulk CrSBr at 85 K (18) (µ 0 H bulk a ≈ 0.22, µ 0 H bulk c ≈ 0.75 T), but the exchange parameter is less than half the bulk value (µ 0 H bulk E ≈ 0.27 T). This may be due to the reduced number of adjacent layers in a bilayer. As we rotate the field away from the intermediate anisotropy axis (Fig. 2D) we see a scaling of the mode to smaller resonant fields, in agreement with previous measurements on bulk crystals (18).
Our 3-terminal device geometry allows for manipulation of the antiferromagnetic resonance in addition to simple detection of the resonance. If a direct charge current is applied within the PtTe 2 channel together with the microwave current, the dc current exerts an anti-damping or damping spin-orbit torque (depending on the sign of the direct current) on the CrSBr that tunes the resonance linewidth. In conventional ferromagnetic spin-orbit torque devices, the effectiveness of anti-damping torque for tuning the linewidth is proportional to cos θ, where θ is the angle between the precession axis of the magnetization and the anti-damping spin-orbittorque vector σ ˆ, which lies in-plane and perpendicular to the current (30,42). Next we analyze how the effects of anti-damping torque depend on the orientations of the two spin sublattices in antiferromagnetic CrSBr.
Figure 3 shows how a direct current affects the linewidths, for a microwave frequency of 13.65
GHz and a magnetic field sweep along the intermediate axis of CrSBr. The resonant magnetic field at this frequency causes the two spin sublattices to be canted at a relative angle of 18). Since the CrSBr crystal is situated with the intermediate axis oriented approximately 45 • from the direction of current in the PtTe 2 channel, this means that near the resonance one of the spin sublattices is oriented approximately parallel to the applied current and the other approximately perpendicular to the current and hence parallel or antiparallel to the spin-orbit torque vector, σ ˆ(see Fig. 3, A and B). For the field direction depicted in Fig. 3A, we find the results in Fig. 3C: a negative dc current yields a linewidth significantly narrower than a positive current. For the opposite sign of magnetic field (Fig. 3B), there is negligible dependence of the linewidth on dc current (Fig. 3D). We can quantify the linewidths by fitting each resonance to a sum of a symmetric and an antisymmetric Lorentzian (41,30), with an additional linear term to account for a non-resonant background (41); we define ∆ as the half width at half maximum of the Lorentzians. The overall dependences of ∆ on current for the two signs of magnetic field are summarized in Fig. 3E.
From these results we conclude that the anti-damping spin-orbit torque from the PtTe 2 layer acts selectively on one of the spin sublattices in the CrSBr, the sublattice adjacent to the PtTe 2 interface (we will call this spin sublattice 1). For the field configuration corresponding to Fig. 3A and C, spin sublattice 1 is aligned with the axis of the spin-orbit torque vector σ ˆ, giving the maximum applied anti-damping torque with the maximum current-induced modulation of the linewidth. For the opposite sign of applied field (Fig. 3B and D), spin sublattice 1 is parallel to the current channel and hence perpendicular to σ ˆ, yielding negligible anti-damping torque.
Spin sublattice 2 in this second case is parallel to σ ˆand hence in the orientation favorable to receive an anti-damping torque, but our measurements indicate that nevertheless little of the spin current from the PtTe 2 penetrates to this second layer so there is little effect on the overall linewidth. To our knowledge, this is the first technique that allows an individual spin sublattice within an antiferromagnet to be addressed selectively.
We can model these effects quantitatively using a coupled two-lattice Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation ( 43) (supplementary text section 2.3). Assuming that the anti-damping spin-orbit torque acts only on sublattice 1, the dependence of the optical-resonance linewidth on the dc bias current I dc for magnetic fields applied along the intermediate axis should have the approximate form:
where we define the expressions
In these equations, θ 1 is the angle between σ ˆand spin-sublattice 1, f is the driving frequency, γ is the electron gyromagnetic ratio, α is the intrinsic damping parameter, h is the reduced Planck's constant, ξ SH is the spin-Hall efficiency, e is the electron charge, M s is the saturation magnetization, W = 3 µm is the width of the PtTe 2 channel, t m = 0.79 nm is the thickness of one CrSBr monolayer, t nm = 93 nm is the thicknesses of the PtTe 2 layer, and H 0 is the resonant magnetic field.
A linear fit to ∆ against 2πf γ ω 2 ω 1 at zero bias gives α = 0.066(2) (Fig. S3C). Based on Eq. ( 2), the slope of the current-modulated linewidth, normalizing for frequency and field dependencies, should have a cosine dependence on θ 1 :
By changing the microwave frequency we can shift the resonance magnetic field and hence tune the canting angle of the spin sublattices near the resonance condition. Figure 4C shows how the current dependence of the damping of the optical mode depends on the orientation of spin sublattice 1 relative to the direction of the spin-orbit torque vector σ ˆ(i.e., the angles θ H- 1 and θ H+ 1 ). For a magnetic field H applied along the intermediate anisotropy axis (i.e., 45
we calculate these angles based on the previously-determined parameters µ 0 H E = 0.096 T and µ o H a = 0.33 T (18):
The measured dc-bias-modulated linewidth slopes at different angles in Fig. 4C agree well with the cos θ 1 dependence expected from Eq. ( 4), with no detectable dependence on θ 2 . We also verified Eq. ( 4) by performing LLGS numerical calculations as a function of H and I dc (Fig.
). Using an estimated saturation magnetization value for bilayer CrSBr at 85 K of µ 0 M s = 0.28 T (supplementary text section 2.7, Fig. S3D), a fit of the measurements to Eq. ( 4) yields a value for the anti-damping spin-orbit torque efficiency of ξ SH = 0.29 (2), somewhat larger than previous room temperature measurements for PtTe 2 which ranged from 0.05 to 0.15 (33,34). We suspect the reason for this larger value may be that µ 0 M s is reduced by heating to make ξ SH appear larger and/or the torque efficiency of PtTe 2 may be higher near 85 K than at room temperature. The substantial anti-damping spin-orbit torque we measure acting on the fully-uncompensated CrSBr interface is in contrast to a very small value measured previously for a spin-compensated α-Fe 2 O 3 interface (44).
It is possible to reverse the Néel vector hysteretically by applying a magnetic field larger than 0.1 T along the magnetic easy axis of the CrSBr. This might be due to a small asymmetry in the magnetizations of the two layers, perhaps due to differences arising from the PtTe 2 /CrSBr interface versus the CrSBr/graphite interface. After the initial Néel vector is reversed relative to the configuration for the data in Fig. 3E, the asymmetry of the current-dependent damping with respect to the sign of the applied magnetic field is also reversed (Fig. 3F), as expected based on our assertion that only the spin sublattice at the PtTe 2 interface is affected by the anti-damping spin-orbit torque.
The ability to both (1) detect and (2) control antiferromagnetic resonance using a tunnel-junction structure opens the door to both fundamental studies of antiferromagnetic dynamics and potential high-frequency applications. With spin-filter tunneling, we achieve sensitive detection of antiferromagnetic resonance in a compact device geometry. The measurements we present represent only a first step in exploring the physics of antiferromagnetic spin dynamics; for example, studies with applied magnetic field in other directions than along the high-symmetry intermediate anisotropy axis should allow examination of the acoustic mode as well as the optical mode, control over the degree of hybridization between modes (18), and studies of angular momentum flow between the spin sublattices (which has been shown to be important in synthetic antiferromagnets) (45). Another future goal is to create antiferromagnetic nano-oscillators for use as high-frequency sources -this will require using anti-damping torque to drive the effective damping of the antiferromagnetic resonance to negative values (46,47,48,49). In our existing devices, we achieve a maximum damping reduction of ≈ 12% at a current density of 10 10 A/m 2 , beyond which heating limits further decrease. Negative effective damping might be achieved by reducing the thickness of the PtTe 2 layer to minimize heating, optimizing the ratio between antiferromagnetic parameters d∆ dI ∝ 2H E +Ha H 0 Hc , decreasing the intrinsic damping α, patterning the oscillator into a nanowire (50), or applying spin-orbit torque to both the top and bottom interfaces of the antiferromagnet. Uncertainties in the dc-bias modulated linewidth d∆ dI were determined from the standard deviation errors of linear fits to ∆ vs. I. Uncertainties in θ 1 were determined from the width in magnetic field of the corresponding resonance. (51,52,53,54,55,56,57,58,36,18,59,60,61,17,30,41,39)