Tunneling Spin Polarization

• Tunneling Spin Polarization is a measure of the spin imbalance in a tunnel junction, defined as P = (I↑ − I↓)/(I↑ + I↓).
• Experimental techniques like spin Hall spectroscopy, Meservey-Tedrow adaptation, and spin-ARPES extract both in-plane and out-of-plane components accurately.
• Its applications span spintronic devices, MTJs, and topological insulators, impacting tunneling magnetoresistance and enabling spin-charge conversion.

Tunneling Spin Polarization (TSP) is a fundamental quantitative descriptor of spin-dependent tunneling in magnetic and topological systems. Formally, it measures the net spin imbalance carried by the current traversing a tunnel barrier and is foundational for spintronic device operation, spin filtering, and spin-charge conversion in materials such as ferromagnetic metals, topological insulators, and semiconductors. TSP is defined generically as $$P = (I_\uparrow - I_\downarrow)/(I_\uparrow + I_\downarrow)$$, where $I_\uparrow$, $I_\downarrow$ are the spin-resolved current components. Contemporary research has focused on developing experimental protocols for extracting both in-plane and out-of-plane (vectorial) components of TSP, analyzing its physical origins via symmetry and quantum coherence, and quantifying its impact on tunneling magnetoresistance (TMR) and related device metrics.

1. Formal Definition and Fundamental Principles

Tunneling spin polarization quantifies the difference in transmission probability or current for spin-up and spin-down electrons in a tunnel junction. The most general definition is

$$P = \frac{I_\uparrow - I_\downarrow}{I_\uparrow + I_\downarrow}$$

where $I_\uparrow$, $I_\downarrow$ are the spin-resolved currents across the barrier (Liu et al., 2014, Schwab et al., 2011). In systems where spin is a good quantum number, this expression can be directly related to the spin-resolved density of states at the Fermi level, $D_\uparrow$, $D_\downarrow$, or to spin-resolved transmission probabilities, $T_\uparrow$, $T_\downarrow$. This makes TSP a material-dependent parameter set by the band structure, spin texture, and interface quality.

In topological insulators (TIs), TSP acquires additional complexity due to spin-momentum locking of surface states (Götte et al., 2020, Götte et al., 2019). Both in-plane and out-of-plane spin components are relevant, with the out-of-plane component central for hexagonal warping and device-level spin control.

2. Measurement Techniques and Experimental Extraction

Multiple experimental methodologies have been developed for measuring TSP:

• Spin Hall Effect Tunneling Spectroscopy: Utilizing a four-terminal FM/tunnel/TI junction, the out-of-plane component of TSP ($P_z$) is uniquely extracted from the ratio of in-plane and out-of-plane spin Hall signals. The analytic inversion is

$$q(U) = \sqrt{ 1 / \left[1 + \left( \frac{ \pi \Delta G_{\rm ip}(U) \Delta n_{\rm op} }{ 6 \sin\phi_F \Delta G_{\rm op}(U) \Delta n_{\rm ip} } \right)^2 \right] }$$

with $P_z(U) \equiv q(U)$ (Götte et al., 2020). The technique is robust, requiring no knowledge of tunnel prefactor and is validated against tight-binding simulations for Bi$_2$Se$_3$ and Sb$_2$Te$_3$.

• Meservey-Tedrow Technique Adaptation: For in-plane polarization, a superconducting Al electrode with Zeeman-split density of states acts as a spin filter. Spin polarization is extracted from the relative heights of four peaks at $eU = \pm(\Delta \pm \mu_B B)$ in conductance. The geometric acceptance of contacts can be controlled to access full momentum dependence of the TI spin texture (Götte et al., 2019).
• Spin-Resolved Photoemission (ARPES): For ultrathin TI films, spin-ARPES is used to directly measure momentum- and energy-resolved spin polarization. The gap opened by inter-surface tunneling suppresses $P(k)$ near the Dirac point; thick films recover the bulk polarization. These data precisely follow

$$P(k) = \frac{ \hbar v_F |k| }{ \sqrt{ (\hbar v_F |k|)^2 + t(L)^2 } }$$

where $t(L)$ is the thickness-dependent tunneling amplitude (Neupane et al., 2013, Neupane et al., 2014).

• Alternative Spin-Resolved Tunneling Systems: In magnetic semiconductors or atomic-scale RT-MTJs, the spin polarization is measured directly from the difference in current for parallel and antiparallel magnetic alignments; in RTDs, the polarization can reach values in excess of 90% in zero field due to bound magnetic polaron formation (Rüth et al., 2010, Bazarnik et al., 24 Oct 2025).

3. Theoretical Modeling and Symmetry Considerations

TSP is highly sensitive to the symmetry properties of electrode wavefunctions and interface states:

• Symmetry Filtering in Crystalline MTJs: In SrRuO$_3$/SrTiO$_3$/SrRuO$_3$ MTJs, TSP cannot predict TMR in the regime of perfect symmetry filtering, where evanescent barrier states select specific orbital symmetries (e.g., $\Delta_1$ Bloch states). Giant TMR ($\sim$3000%) is achieved not because of large $P$, but due to symmetry matching/mismatching of barrier and electrode wavefunctions. Only in the presence of defect-induced diffuse scattering (breaking $k_\parallel$ conservation) does TSP correlate with TMR via Jullière’s formula (Samanta et al., 2024).
• Decoherence and Chiral-Induced Spin Selectivity (CISS): Analytical solutions in Rashba-barrier models show that time-reversal symmetry enforces $P=0$ in truly coherent two-terminal devices. Introduction of a Büttiker dephasing probe destroys Onsager reciprocity, enabling sizable TSP by incoherent processes, a general scenario for CISS (Varela et al., 2023).
• Spin-Charge Locking: In helical metals (TIs), spin dynamics are entirely locked to charge. Tunneling resistance depends on the angle between FM magnetization and current direction, amplifying spin-charge conversion (Schwab et al., 2011). Addition of normal-metal overlayers further enhances spin accumulation by factors set by the density of states ratios.

4. Materials Systems and Applications

TSP measurement and control are central to multiple device classes:

• Topological Insulator Devices: Quantitative extraction of $P_z$ and $P_{\rm ip}$ is crucial for spintronic applications such as TI-based spin filters, spin Hall voltage generators, and gate-tunable spin switches (Götte et al., 2020, Neupane et al., 2013, Neupane et al., 2014).
• Magnetic Tunnel Junctions (MTJ): Device-level performance (TMR, STNO thresholds, MRAM endurance) is directly determined by the TSP of electrodes. Experimental protocols combining tunneling and spin Hall injection allow precise mapping of TSP (e.g., $p$ extracted as 58% at low bias by Jullière’s formula, falling with increasing bias), with direct links to auto-oscillator amplitude and device lifetime (Tarequzzaman et al., 2018, Gabor et al., 2011).
• Spin-Dependent Resonant Tunneling: In paramagnetic RTDs, tunable TSP arises from giant Zeeman effects, bound magnetic polarons, and bias-controlled population of quasi-bound states. Oscillatory regimes (THz frequency) offer promise for spin-polarized current generators; stable filtering requires avoiding these oscillations (Wojcik et al., 2012, Rüth et al., 2010, 0705.0237).
• Atomic-Scale Spin Filtering: RT mechanisms in SP-STM enable direct measurement and control of TSP at nanomagnet sites, with the sign and magnitude of STT tracking the spectral spin polarization. These concepts generalize to 2D van-der-Waals magnets and “altermagnets” (Bazarnik et al., 24 Oct 2025).
• Thermoelectric Spin Injection: Seebeck spin tunneling exploits the energy derivative of TSP to create pure thermal spin currents without charge flow. Spin accumulation $\Delta\mu/\Delta T$ is maximized for smaller tunnel resistance, avoiding the “impedance mismatch” that plagues electrical injection. Hanle magnetothermopower enables magnetic control of thermal voltages (Jansen et al., 2011).

5. Quantitative Trends, Limitations, and Outlook

Tables of representative TSP values extracted from the literature (TIs, MTJs, RTDs):

System	TSP Value	Method
Bi$_2$Se$_3$ TI (ARPES)	25–40%	Spin-ARPES, thickness, $k$-dep.
FM/MgO/TI junction	30% effective	Spin Hall voltage, tunneling geom.
MTJ (CoFe/MgO/CoFe)	58% (low bias)	Jullière formula, TMR
Co$_2$FeAl/MgO/CoFe (def.)	0.57	Extended-Glazman–Matveev model
II–VI DMS-RTD (zero field)	>90%	BMP-driven splitting
Atomic-scale RT-MTJ (STM)	20–30%	dI/dU spectroscopy

The main limitations arise from interface quality (defects suppress symmetry filtering, lowering TSP), quantum coherence (coherent channels may enforce $P=0$ unless TRS is broken), and bias/temperature dependence (TSP generally decreases at higher biases and temperatures).

The field continues to advance toward quantitative vectorial measurement (both $P_{\rm ip}$ and $P_z$), bias and geometry control, scaling to 2D and atomic-scale systems, and tight integration with advanced spintronic device platforms.

6. Future Directions and Generalizations

Current trends emphasize generalization of TSP measurement protocols to arbitrary spin textures, including Rashba systems, chiral-molecule junctions (CISS), and interface states in non-centrosymmetric heterostructures. The generic formula

$$P = \frac{G_\uparrow - G_\downarrow}{G_\uparrow + G_\downarrow}$$

or its energy-dependent analogue at $E_F$, can be applied to any spin-polarized junction by comparing differential conductances for opposite magnetizations or spin filter orientations (Götte et al., 2020). Experimental advances in spin Hall effect tunneling, spin-resolved STM, and spin-octane spectroscopy provide increasingly precise tools.

Furthermore, device-level control via gating, geometry modification, and interface engineering are paving the way for versatile spin-filtering, efficient spin-charge conversion, and robust operation under electrical and thermal drive. These advances underwrite next-generation room-temperature spin-based information technology.