Long-Range Phase Coherence in Double-Barrier Magnetic Tunnel Junctions with a Large Thick Metallic Quantum Well

Double-barrier heterostructures are model systems for the study of electron tunneling and discrete energy levels in a quantum well (QW). Until now resonant tunneling phenomena in metallic QWs have been observed for limited thicknesses (1–2 nm) under which electron phase coherence is conserved. In the present study we show evidence of QW resonance states in Fe QWs up to 12 nm thick and at room temperature in fully epitaxial double ${\mathrm{MgAlO}}_x$ barrier magnetic tunnel junctions. The electron phase coherence displayed in this QW is of unprecedented quality because of a homogenous interface phase shift due to the small lattice mismatch at the $\mathrm{Fe}\text{−}{\mathrm{MgAlO}}_x$ interface. The physical understanding of the critical role of interface strain on QW phase coherence will greatly promote the development of spin-dependent quantum resonant tunneling applications.

Figure 1

(a) Energy profile in DMTJ structure and QW states at different energy levels. (b) Stack structure of DMTJ and setup of measurement.

Figure 2

Normalized conductance as a function of bias voltage in the (a) P and (b) AP state, respectively. (c) DTMR dependence with bias voltage. (d) QW thickness dependence of $d^{2}I/d{V}^2$ curves in the P state (measured at 16 K). The dashed lines indicate the resonant peak positions. (e) QW peak positions for the experimental results (circles), PAM simulation results (lines), and ab initio calculation results (squares). The three numbers $n$ in the figure represent the QW node number just below $E_F$ for the three samples with different QW thickness.

Figure 3

$d^{2}I/d{V}^2$ curves in the P and AP states for DMTJs with (a) $\mathrm{MgO}(3\mathrm{MLs})/\mathrm{Fe}/{\mathrm{MgAlO}}_x(12\mathrm{MLs})$ and (b) $\mathrm{MgO}(3\mathrm{MLs})/\mathrm{Fe}/\mathrm{MgO}(12\mathrm{MLs})$ structures, respectively. Insets: schematics of tunneling of electrons with ${\mathrm{\Delta }}_1$ symmetry in the AP configuration in samples with a thick ${\mathrm{MgAlO}}_x$ and MgO barrier, respectively. (c) Electrostatic potentials and structures of Fe-MgO and $\mathrm{Fe}\text{−}{\mathrm{MgAl}}_2{\mathrm{O}}_4$ layers. The width (Å) between potential valleys in the Fe layers is shown for the Fe-MgO (black) and $\mathrm{Fe}\text{−}{\mathrm{MgAl}}_2{\mathrm{O}}_4$ (red) interface. The lattice constant and length of the Fe–O bond are also shown in the structure. (d) Schematics of the DOS in the QW with a large and small interface phase shift distribution. ${\mathrm{\Phi }}_1$, ${\mathrm{\Phi }}_2$ represent the phase shift on reflection at the interface and ${\mathrm{\Phi }}_{\inf }$ stands for the interface phase shift.