Metamagnetic transition self-propelled by spin injection

We study metamagnetic phase transition of itinerant electrons controlled by the spin-injection mechanism. The current flow between a ferromagnetic metal and a metamagnetic metal produces the nonequilibrium shift of chemical potential for spin-up and spin-down electrons. This shift acts as an effective magnetic field driving the metamagnetic transition between low and high magnetization states of the metamagnet in the vicinity to the contact with the ferromagnet. We show that high magnetization state of the metamagnet self propels into the bulk of the metamagnet and the length of this state has threshold dependence on the electrical current.

Figure 1

Free energy $F\left(H,M\right)$ dependence on the magnetization $M$ of the metamagnet shown schematically for different magnetic fields $H_2>H_1$. The state with high magnetization has lower energy at higher magnetic fields. Inset: dependence of the magnetization on magnetic field.

Figure 2

Ferromagnetic metal $x∊\left(-L/2,0\right)$—metamagnetic metal $x∊\left(0,L/2\right)$ contact. (p) defines the low magnetization state of the metamagnet and (m) stands for the high magnetization state induced by the spin injection from the ferromagnet (f). ${\ell }_{\text{F}},{\ell }_{\text{m}},{\ell }_{\text{p}}$ are the spin diffusion lengths in ferromagnet and metamagnet in high and low magnetization states.

Figure 3

Up: dependence of the effective magnetic field on coordinate for two values of the current density $\left|J_2\right|>\left|J_1\right|$. Effective magnetic field decreases in the metamagnet and the phase transition undergoes at $x=d\left(J\right)$ when $H^{\text{eff}}=H_{\text{m}}$. Down: magnetization profile, where $M_{\text{F}},M_{\text{m}},M_{\text{p}}$ are the corresponding magnetizations of the ferromagnet, high and low magnetization states of the metamagnet.