Resonant Enhancement of Exchange Coupling for Voltage-Controlled Magnetic Switching

We predict that it is possible to achieve a purely voltage-driven switching of a ferromagnet using spin-dependent resonant tunneling. In a configuration of two exchange-coupled magnets through a resonant-tunneling barrier, application of a voltage leads to a resonant enhancement and an oscillatory nature of the exchange coupling. The peak equivalent exchange field is strong enough to switch typical ferromagnets used in scaled magnetic memory devices. The switched configuration is retained once the electric field is removed since the equilibrium exchange coupling is negligible, suppressed by large barriers. Bidirectional switching is possible with the same polarity of the voltage, unlike conventional magnetic memory devices where a bidirectional current or a magnetic field is necessary. Further, the threshold of switching is decoupled from the speed, due to the conservative nature of the exerted torque. This is very different from the conventional spin-torque devices that exhibit a trade-off due to the nonconservative nature of the switching torque. We further show that the structure shows an oscillation in the magnetoresistance (MR) stemming from the resonant tunneling. Interestingly, the MR is higher for smaller voltages while the exchange field is higher for larger voltages—this is promising for efficient read and write operations in potential memory applications.

Figure 1

(a) The proposed composite magnetic-tunnel-junction structure with two oxide barriers sandwiching a metallic spacer. The two barriers form a quantum well with discrete states within the metallic spacer. The structure can control the transmission coefficient between the two magnets via resonant tunneling, which results in a control on the IEC energy. (b) The bias-dependent IEC changes sign in a periodic manner and grows in magnitude for higher electric field. For simulation, barrier heights are 0.7 eV and widths are 1 nm each. The spacer thickness is 0.8 nm.

Figure 2

Materials parameter calibration. (a) NEGF simulation of the oscillatory equilibrium IEC (solid lines) as a function of metallic spacer thickness $d$. The parameters are such that the simulation agrees with experiments on a $\mathrm{Co}$$|$$\mathrm{Ru}$$|$$\mathrm{Co}$ system [27] (scatter points). The first peak occurs at approximately $6\AA$ with IEC approximately $5{\mathrm{mJ}/\mathrm{m}}^2$ and a periodicity ${\lambda }_{\mathrm{IEC}}\approx 11\AA$. (b) The periodicity of equilibrium IEC (${\lambda }_{\mathrm{IEC}}$) depends on the spin-dependent quantum well (with a depth ${\mathrm{\Delta }}_{\mathrm{sp}}$) formed below the Fermi level due to a $d$-orbital mismatch between the FM and the spacer. NEGF simulation (solid line) of (c) the equilibrium IEC across an oxide spacer. Thin oxide ($<5\AA$) exhibits a large IEC due to tunneling effect, which drastically reduces for thick oxides, similar to the experimental observations across $\mathrm{Mg}\mathrm{O}$ in Refs. [43, 44] (scatter points). (d) Bias-dependent nature of the dampinglike and fieldlike torques on the free layer in $\mathrm{Mg}\mathrm{O}$-based MTJs, compared with the experiments (scatter points) in Ref. [45].

Figure 3

(a) Voltage pulse applied across the structure in Fig. 1. The three voltage pulses applied induce IEC with strengths corresponding to $P_4$, $P_3$, and $P_2$, respectively, in Fig. 1. We observe the magnetization dynamics as a function of time, as a result of the applied voltage pulses: (b) $z$ component $m_z$, (c) $x$ component $m_x$, and (d) $y$ component $m_y$. Fixed magnet: $M_{s1}=1100$ emu/cc, $H_{k1}=300$ Oe, and $t_{f1}=10$ nm. Free magnet: $M_{s2}=1100$ emu/cc, $H_{k2}=150$ Oe, and $t_{f2}=1.5$ nm. Diameter of the device is 150 nm and the Gilbert damping is 0.01.

Figure 4

$M$-$H$ loop of the structure in Fig. 1 for different applied voltages $V_{\mathrm{in}}$: (a) 0 V [corresponds to $P_1$ in Fig. 1], (b) 1 V (corresponds to $P_2$ in Fig. 1], (c) 1.3 V [corresponds to $P_3$ in Fig. 1], and (a) 1.6 V [corresponds to $P_4$ in Fig. 1]. Fixed magnet: $M_{s1}$ = 1100 emu/cc, $H_{k1}=300$ Oe, and $t_{f1}=10$ nm. Free magnet: $M_{s2}=1100$ emu/cc, $H_{k2}=150$ Oe, and $t_{f2}=1.5$ nm. The diameter is 150 nm and the Gilbert damping is 0.01.

Figure 5

(a) Voltage periodicity ($V_{\mathrm{REC}}$) of the resonance-enhanced IEC, which scales with the equilibrium periodicity (${\lambda }_{\mathrm{IEC}}$) of the spacer (determined by ${\mathrm{\Delta }}_{\mathrm{sp}}$). (b) Effect of dephasing ($d_{\mathrm{ph}}$) on the resonance-enhanced IEC.

Figure 6

(a) Charge and $z$-polarized spin-current densities, $J_c$ and $J_z$, as a function of the applied voltage $V_{\mathrm{in}}$. (b) Magnetoresistance as a function of $V_{\mathrm{in}}$. (c) Effect of dephasing ($d_{\mathrm{ph}}$) on the current transport.

Figure 7

Voltage-dependent oscillatory resonance-enhanced IEC for different (a) QW heights ${\mathrm{\Delta }}_B$ and (b) QW widths $t_{\mathrm{QW}}$.

Figure 8

NEGF setup for the structure in Fig. 1.

Figure 9

Comparison of Eq. (6) with numerical simulations using the coupled LLG in Eqs. (B1a) and (B1b). We observe the switching time ($t_{\mathrm{sw}}$) as a function of (a) the resonance-enhanced IEC, $J_{\mathrm{ex}}$, (b) the Gilbert damping, ${\alpha }_g$, and (c) initial angle of the free magnet, ${\theta }_0$.

Figure 10

Comparison of write energy and delay of this work with existing memory technologies [15]: embedded static random access memory (eSRAM), embedded dynamic random access memory (eDRAM), ferroelectric random access memory and field-effect transistor (FeRAM, FeFET), resistive random access memory (RRAM), spin-transfer-torque random access memory (STT MRAM), phase-change random access memory (PCRAM), and embedded FLASH memory (eFLASH). **crossbar-RRAM. ***vertical-RRAM.