---
title: Tunneling Spin Polarization
url: https://www.emergentmind.com/topics/tunneling-spin-polarization-tsp
type: topic
---

# Tunneling Spin Polarization

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 [1410.7494, 1101.5802]. 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 [2004.07010, 1909.02351]. 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 $P_z(U) \equiv q(U)$ [2004.07010]. 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 [1909.02351].

- **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 [1307.5485, 1404.2830].

- **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 [1012.4261, 2510.21416].

## 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 [2406.15290].

- **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 [2301.02156].

- **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 [1101.5802]. 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 [2004.07010, 1307.5485, 1404.2830].

- **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 [1802.02224, 1111.6442].

- **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 [1210.2280, 1012.4261, 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” [2510.21416].

- **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 [1112.3430].

## 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 [2004.07010]. 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.

Source: https://www.emergentmind.com/topics/tunneling-spin-polarization-tsp