Symmetry and the macroscopic dynamics of antiferromagnetic materials in the presence of spin-polarized current

Antiferromagnetic (AFM) materials with zero or vanishingly small macroscopic magnetization are nowadays the constituent elements of spintronic devices. However, the possibility to use them as active elements that show nontrivial and controllable magnetic dynamics is still discussible. In the present paper we extend the phenomenologic theory [Andreev and Marchenko, Sov. Phys. Usp. 23, 21 (1980)] of macroscopic dynamics in AFM materials for the cases typical for spin-valve devices. In particular, we consider the solidlike magnetic dynamics of AFM materials with strong exchange coupling in the presence of a spin-polarized current and give the general expression for the current-induced Rayleigh dissipation function in terms of the rotation vector for different types of AFMs. Based on the analysis of linearized equations of motion we predict the current-induced spin reorientation and AFM resonance, and find the values of critical currents in terms of AFMR frequencies and damping constants. The possibility of a current-induced spin-diode effect and second-harmonic generation in the AFM layer is also shown.

Figure 1

Effect of spin-transfer torque on the AFM layer. (a) Element of spin-valve structure consisting of FM (hard) and AFM (soft) layers and NM spacer. The FM layer polarizes the spin current $\mathbf{J}$ along the ${\mathbf{M}}_{\mathrm{pol}}$ direction. The positive-valued current flows from the FM to the AFM layer. (b) Macroscopic current-induced dynamics of an arbitrary AFM material with strong exchange coupling. The equilibrium magnetic structure is characterized by the three mutually orthogonal magnetic vectors ${\mathbf{L}}_1$, ${\mathbf{L}}_2$, and ${\mathbf{L}}_3$ (solid arrows). Any deflection from equilibrium (dash arrows) can be viewed as a solidlike rotation around the instantaneous axis $\mathbf{e}$ through the angle $\theta$.

Figure 2

Magnetic structure of the cubic noncollinear AFM materials. (a) Magnetic structure of the disordered FeMn. Magnetic atoms (circles) form fcc lattice; vectors ${\mathbf{M}}_k$ of sublattice magnetizations (arrows) point to $\langle 111\rangle$ directions. (b) This structure can be equivalently described in terms of three mutually orthogonal AFM vectors ${\mathbf{L}}_k$ [see Eq. (23)]. (c) Planar magnetic structure of IrMn${}_3$ and some of the antiperovskites Mn${}_3$MN, where M   Ni, Ga, Ag, Zn. Magnetic moments ${\mathbf{M}}_k$ (arrows) are localized on Mn atoms (circles). (d) Planar magnetic structure can be described by two mutually orthogonal AFM vectors ${\mathbf{L}}_k$ [see Eq. (25)]. The plane of AFM ordering is described by the unit vector $\mathbf{n}\parallel {\mathbf{L}}_1\times {\mathbf{L}}_2$.

Figure 3

Current-induced rotation of AFM structure. (a) Magnetic structure represented by three AFM vectors ${\mathbf{L}}_k$ is rotated through the fixed angle ${\varphi }_{\parallel }$ under the action of dc current. Rotation axis $\mathbf{e}$ (not shown) is parallel to the vector of current polarization ${\mathbf{p}}_{\mathrm{curr}}$. (b) Overcritical ($J\ge J_{\mathrm{cr}}^{\mathrm{AFM}}$) current induces instability with respect to rotation around the axis $\mathbf{e}\perp {\mathbf{p}}_{\mathrm{curr}}$.