---
title: 'Spin PN Junctions: Mechanisms & Applications'
url: https://www.emergentmind.com/topics/spin-pn-junctions
type: topic
---

# Spin PN Junctions: Mechanisms & Applications

Searching arXiv for relevant papers on spin PN junctions and closely related architectures.
Spin PN junctions are p–n junctions or pn-like interfaces in which spin becomes an active transport variable through spin-split band edges, spin-dependent recombination, spin-selective tunneling, spin–orbit coupling, spin–momentum locking, or depletion-controlled spin transport. In current usage, the term spans several technically distinct objects: magnetic semiconductor junctions that rectify charge and magnetization, quantum Hall tunnel diodes in which spin selection rules replace an electrostatic depletion barrier, graphene and topological-insulator interfaces that convert chirality or Klein filtering into spin manipulation, and semiconductor Hall structures in which a reverse-biased depletion front amplifies spin-to-charge readout [2603.02506], [1701.04463], [2303.05833], [1410.5823], [1605.04109].

| Platform | Spin-selective ingredient | Representative signature |
|---|---|---|
| Circular graphene pn junction | Rashba SOC, Zeeman coupling, chiral zero modes | Sweet spot $\omega_Z=\omega_0/2$ with fully in-plane, radially polarized spin [2303.05833] |
| 3D TI pn junction | Spin–momentum locking and chiral mode network | Mach–Zehnder conductance $G=(e^2/h)\sin^2(\phi/2)$ [1410.5823] |
| Magnetic p-AMS/n-Si junction | Exchange-split p-AMS and space-charge modulation | $\Delta M/M_0 \approx 24.36\%$ at $-5$ mA [2603.02506] |
| FGT/p-GaSe/n-InSe/FGT junction | Built-in depletion field and spin-dependent tunneling | Zero-bias SVE $\approx 32{,}230\%$ at $35$ K [2509.04206] |
| Quantum Hall spin diode | Spin-conserving tunneling and Pauli blocking | $R \gtrsim 100$ at $50$ mK [1701.04463] |

## 1. Definition and conceptual scope

In the magnetic-semiconductor formulation, a spin p–n junction is a semiconductor junction in which at least one side is magnetic, causing spin-dependent band structure and transport so that the device rectifies, switches, and amplifies both electrical charge and spin signals. The canonical charge relations remain the usual p–n expressions,
$$
V_{bi} = \frac{k_B T}{q}\ln\!\left(\frac{N_A N_D}{n_i^2}\right),\qquad
W=\sqrt{\frac{2\epsilon_s}{q}\frac{N_A+N_D}{N_A N_D}V_{bi}},
$$
and
$$
J(V)=J_s\left[e^{qV/k_B T}-1\right],
$$
but the transport variables become spin resolved through
$$
P=\frac{n_\uparrow-n_\downarrow}{n_\uparrow+n_\downarrow},\qquad
J_\sigma=q\mu n_\sigma E+qD\nabla n_\sigma,
$$
with a spin continuity equation containing spin relaxation time $\tau_s$ and spin diffusion length $L_s=\sqrt{D\tau_s}$ [2603.02506].

A more explicit magnetic-semiconductor construction introduces spin-split conduction and valence edges,
$$
E_{c\uparrow}=E_{c0}-\xi_n,\quad E_{c\downarrow}=E_{c0}+\xi_n,\quad
E_{v\uparrow}=E_{v0}+\xi_p,\quad E_{v\downarrow}=E_{v0}-\xi_p,
$$
which produce spin-dependent built-in barriers
$$
V_{n\uparrow}=V_0+\xi_{n,N}-\xi_{n,P},\qquad
V_{n\downarrow}=V_0-\xi_{n,N}+\xi_{n,P},
$$
and similarly for holes,
$$
V_{p\uparrow}=V_0+\xi_{p,P}-\xi_{p,N},\qquad
V_{p\downarrow}=V_0-\xi_{p,P}+\xi_{p,N}.
$$
In this picture, the depletion region is still central, but the built-in potential is spin selective rather than purely electrostatic [2509.16904].

A common misconception is that the term always implies a conventional depletion-layer diode. The quantum Hall realization instead treats a “Spin PN Junction” as a two-terminal element in which the roles of p- and n-type regions are played by layers with opposite spin magnetizations at the Fermi level. Rectification then arises from spin-conserving tunneling and Pauli blocking rather than minority-carrier recombination across a depletion barrier [1701.04463]. This broader usage is now intrinsic to the literature.

## 2. Spin-selective transport mechanisms

In magnetic-semiconductor homojunction theory, the central microscopic ingredient is spin-dependent recombination. A spin-resolved Shockley–Read–Hall channel is written as
$$
U_{\sigma,\sigma'}=
\frac{n_\sigma p_{\sigma'}-n_{i,\sigma}^2}
{\tau_{p,\sigma'}(n_\sigma+n_{i,\sigma})+\tau_{n,\sigma}(p_{\sigma'}+p_{i,\sigma'})},
$$
with lifetimes
$$
\tau_{n,\sigma\sigma'}=\frac{1}{r_{\sigma\sigma'}p_{\sigma'}},\qquad
\tau_{p,\sigma\sigma'}=\frac{1}{r_{\sigma\sigma'}n_\sigma},
$$
and an exponential recombination probability
$$
r_{\sigma\sigma'}=r_0
\exp\!\left(
\frac{(E_{c\sigma}-E_{v\sigma'})-(E_{c0}-E_{v0})}{k_B T}
\right).
$$
Because $r_{\sigma\sigma'}$ depends exponentially on the spin-split interband separation, the effective lifetime $\tau_{\mathrm{eff}}(B)$ acquires exponential field sensitivity, leading to
$$
J(V,B)\approx J_0 e^{-\gamma B}\left(e^{qV/k_B T}-1\right),\qquad
MR(B)=e^{\gamma B}-1,
$$
and a reported near-100× enhancement in magnetoresistance sensitivity under small forward bias [2509.16904].

A different mechanism operates in the room-temperature magnetic p-AMS/n-Si junction. There, the ferromagnetic p-AMS hosts extended, spin-polarized hole states, and the space-charge region acts as a spin-selective modulator. Forward bias is dominated by majority hole drift, small reverse bias by minority electron drift, and reverse breakdown by electron tunneling from spin-polarized Co valence states in p-AMS into n-Si. The device-specific DPC/iDPC profile yields a “triplet built-in electric field state” with negative charges concentrated at the interface and weaker positive charge accumulations on both sides; this barrier asymmetry governs the direction-dependent spin response [2603.02506].

A third mechanism appears in two-dimensional magnetic tunnel p–n junctions based on FGT/p-GaSe/n-InSe/FGT. Here the depletion-region field itself produces asymmetric spin diffusion at zero external bias. The interfacial tunneling probabilities satisfy
$$
T_\sigma\propto e^{-2\kappa_\sigma d},
\qquad
\kappa_\sigma=\sqrt{\frac{2m^*}{\hbar^2}(\Phi_\sigma-E)},
$$
while the steady-state spin density follows
$$
D\nabla^2 s-\frac{s}{\tau_s}=0.
$$
Under open-circuit conditions the net charge current vanishes but a finite spin accumulation remains, with spin voltage
$$
V_s=\frac{\mu_\uparrow-\mu_\downarrow}{2e}.
$$
DFT-informed drift-diffusion modeling gives an interfacial energy difference $\Delta U\approx 1.17$ meV for 5 nm GaSe/5 nm InSe and a predicted measurable voltage difference between antiparallel and parallel states of $\approx 690~\mu$V, in the same order as observed [2509.04206].

These mechanisms are not interchangeable. Some devices are recombination limited, some are tunneling limited, some are drift-diffusion limited, and some are governed by topological selection rules. The unifying feature is not a single transport equation, but spin-selective asymmetry built into the junction.

## 3. Graphene realizations

The most explicit graphene spin PN junction in the supplied literature is the circular junction defined by
$$
V(r)=V_0\,\mathrm{sign}(R-r),
$$
with a p-doped dot for $r<R$, an n-doped region for $r>R$, and a perpendicular magnetic field. The low-energy Hamiltonian is
$$
H_0=v_F(\tau\sigma_x\Pi_x+\sigma_y\Pi_y)+V(r),
$$
augmented by
$$
H_{\mathrm{spin}}=
\lambda_Z s_z+\frac{\lambda_R}{2}(\tau\sigma_x s_y-\sigma_y s_x)
+\lambda_I\tau\sigma_z s_z+\lambda_{VZ}\tau s_z .
$$
Projection onto the spin-degenerate zero-energy radial state at the interface yields the effective one-dimensional Hamiltonian
$$
\tilde H_{\mathrm{eff}}=\omega_0(L_z+\Phi)+(\omega_Z-\omega_0/2)s_z-\omega_R s_x,
$$
or, in the original basis,
$$
H_{\mathrm{eff}}=\omega_0(L_z+\Phi)+\omega_Z s_z-\omega_R s_r .
$$
The zero-mode dispersion is
$$
E_{m,\pm}=\omega_0(m+\Phi)\pm\sqrt{(\omega_Z-\omega_0/2)^2+\omega_R^2}.
$$
The crucial result is the exact sweet spot
$$
\omega_Z=\omega_0/2\;\Rightarrow\;\gamma=\pi/2,
$$
at which the spin is fully in-plane and radially polarized for any $\omega_R$. The corresponding interferometric conductance phase is
$$
\phi_S=2\pi\sqrt{(Q_Z-1/2)^2+Q_R^2},
$$
so at the sweet spot $\phi_S=2\pi Q_R$ and the Berry phase reaches $\varphi_g=-\pi$ without requiring large Rashba SOC. This is the paper’s “shortcut” relative to semiconductor Rashba rings, where in-plane alignment typically requires $\omega_R\gg \omega_0$ [2303.05833].

A complementary graphene result concerns gradual pn junctions with intrinsic SOC, Rashba SOC, and stagger potential,
$$
H=v_F(\tau_z\sigma_x p_x+\sigma_y p_y)+\Delta\sigma_z
+\lambda_I\tau_z s_z\sigma_z
+\lambda_R(\tau_z s_y\sigma_x-s_x\sigma_y)+U(x).
$$
In the negligible-Rashba regime the uniform-spectrum mass is
$$
m_{s,\tau}=\Delta+s\tau\lambda_I,
$$
and the WKB transmission becomes
$$
T_{s,\tau}(k_y)\approx
\exp\!\left[-\frac{m_{s,\tau}^2}{\beta^2}\right]
\exp\!\left[-\frac{(\hbar v_F k_y)^2}{\beta^2}\right],
\qquad
\beta=\left(\frac{\hbar v_F F}{\pi}\right)^{1/2}.
$$
At $E_F=0$, sweeping the stagger potential produces two Gaussian peaks,
$$
G_0^{K}(\delta)\propto
\exp\!\left[-\frac{(\delta-\Delta_{SO})^2}{\beta^2}\right],\qquad
G_0^{K'}(\delta)\propto
\exp\!\left[-\frac{(\delta+\Delta_{SO})^2}{\beta^2}\right],
$$
one per valley. The paper emphasizes that this enables valley detection without double-interface resonant devices. It also states that with intrinsic SOC only, $G_\uparrow=G_\downarrow$; spin–valley coupling does not by itself produce a net spin-polarized total conductance when $\lambda_R=0$ [1601.01275].

Taken together, these graphene results show two distinct spin PN junction regimes: curved, chiral, Landau-quantized interfaces whose zero modes act as spin interferometric channels, and smooth one-dimensional pn barriers whose SOC-modified masses encode valley-resolved transmission.

## 4. Topological-insulator pn junctions

In a 3D topological-insulator film, a p–n junction under perpendicular magnetic field reconfigures the chiral surface-mode network into a Mach–Zehnder interferometer. The surface Dirac Hamiltonian is
$$
H=v_F(\sigma\times \hat n)\cdot (p+eA)-\mu,
$$
and the slab representation can be written as
$$
H=-iv_F \hat s_\theta(\partial_x+i e A_x)
+iv_F \hat s_x \frac{2\pi}{P}\left(\partial_\theta+i\frac{\phi}{2\pi}\right)-\mu .
$$
Because the top and bottom surfaces carry opposite half-integer Hall responses in the $n=0$ Landau level, gating one half of the film from n to p creates two coherent paths on the top and bottom surfaces. The beam splitters are spin rotations,
$$
S_{v1}=S_{v2}=\frac{\sigma_x+\sigma_z}{\sqrt 2},
$$
the path transfer matrix is
$$
T=e^{i(kW+\phi/2)}e^{i(\phi/2)\sigma_z},
$$
and the conductance becomes
$$
G=\frac{e^2}{h}\sin^2(\phi/2).
$$
The paper describes the visibility as virtually perfect and identifies the same structure as a spin filter, because the path is tied to the direction of spin propagation by spin–momentum locking [1410.5823].

A distinct topological-insulator pn junction appears in the analysis of nanomagnetic switching on a 3D TI surface. There, the junction acts as a gate-tunable angular filter based on Klein tunneling. Reflection at the pn barrier suppresses charge current while modifying the spin distribution on the TI surface. Using NEGF quantum kinetic modeling, the work finds an intrinsic longitudinal spin-to-charge ratio on the TI surface that can exceed unity and reach $J_{sy}^{TI}/J_q>20$. However, it also states that this does not translate into external gain when the nanomagnet is the source contact, because the injected interfacial spin current remains bounded by the total charge current, with $J_{sy}^{FM-TI}/J_q\approx 100\%$. The surface current density itself is limited by the TI bulk band gap; for Bi$_2$Se$_3$ at 0.2 V bias, the current localized within approximately the top 2 nm carries only approximately 30% of the total current [2110.02641].

This distinction is important. A large intrinsic spin response on a Dirac surface does not automatically imply large spin torque on an attached ferromagnet. In the TI literature, the pn junction is simultaneously a momentum filter, a spin filter, and a constraint imposed by bulk shunting.

## 5. Magnetic semiconductor and magnetic tunnel junction implementations

The room-temperature magnetic p–n junction diode based on p-type amorphous magnetic semiconductor and n-type Si is a direct charge-and-spin diode realization. The p-AMS is oxygenated Co–Fe–Ta–B, specifically p-type CoFeTaBOx with $x\approx 0.485$ and a variant with $x\approx 0.55$, deposited by RF magnetron sputtering; the main vertical devices are In/p-AMS ($\sim 600$ nm)/n-Si ($\sim 500~\mu$m)/In. The p-AMS is single-phase amorphous, shows robust ferromagnetism with Curie temperature exceeding 600 K, and forms a space-charge region on the p-AMS side of width $\sim 10$ nm. The diode has turn-on voltage $V_t\approx 0.5$ V at 300 K, increasing to $\sim 0.8$ V at 200 K and $\sim 1.0$ V at 100 K, and reverse breakdown at $V_{br}\approx -6.5$ V. Magnetization is modulated by current alone, with $\Delta M/M_0\approx 6.01\%$ at $+1$ mA and 300 K under 50 Oe, $\Delta M/M_0\approx 4.24\%$ at $+1$ mA and 0 Oe, and a giant enhancement to $\Delta M/M_0\approx 24.36\%$ at $-5$ mA. Thin p-AMS-0.55 on highly conducting n-Si reaches saturation magnetization $\approx 509$ emu/cm$^3$, a 29-fold increase relative to p-AMS-0.55/p1 [2603.02506].

The van der Waals magnetic tunnel p–n junction FGT/p-GaSe/n-InSe/FGT realizes a different operating point: zero-bias spin-voltage generation rather than current-driven magnetic switching. The semiconductor spacer is a p-GaSe/n-InSe junction with typical thicknesses of GaSe 5–15 nm and InSe 5 nm, with the strongest effect in 5 nm GaSe + 5 nm InSe. No separate crystalline tunnel barrier is inserted; the depletion region itself acts as the tunneling and built-in-field barrier. The active overlap area is approximately $5~\mu$m$^2$, and the device is encapsulated by approximately 15 nm hBN. The zero-bias spin-voltage effect is defined as
$$
SVE=\frac{|V_{AP}-V_P|}{V_P},
$$
and reaches $\approx 32{,}230\%$ at 35 K in an FGT/p-GaSe(5 nm)/n-InSe(5 nm)/FGT device, with persistence from 10 K up to $T_c\approx 220$ K. The effect decreases as GaSe thickness increases, vanishes at 15 nm GaSe with 5 nm InSe, and is absent at zero bias in devices containing only a single p- or n-type spacer layer [2509.04206].

A third strand is theoretical: magnetic semiconductor homojunctions with spin splitting-induced band offsets. In this model, the forward-bias current remains Shockley-like but the saturation current inherits exponential sensitivity through spin-dependent recombination probabilities. The same framework predicts magnetically tunable circularly polarized luminescence,
$$
P_c=\frac{I_{\sigma^+}-I_{\sigma^-}}{I_{\sigma^+}+I_{\sigma^-}}
\approx \eta\tanh\!\left(\frac{\Delta}{2k_B T}\right),
$$
with near-half polarization when only one band is split in both neutral regions. Under reverse bias it further predicts a “spin Zener filter,” with spin-resolved tunneling
$$
T_\sigma=
\exp\!\left[
-\frac{4\sqrt{2m^*}E_{g,\sigma}^{3/2}}{3q\hbar E_\sigma}
\right],
$$
and, for $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$-like parameters, a $\sim 1$ V window where $P_j\approx 100\%$ [2509.16904].

These three cases illustrate the breadth of magnetic spin PN junctions: one is a room-temperature charge-and-spin diode on Si, one is a zero-bias spin-voltage tunnel junction in an atomically thin heterostructure, and one is an extended Shockley design paradigm for magnetoresistance, polarized emission, and Zener filtering.

## 6. Quantum Hall and depletion-front semiconductor realizations

The quantum Hall spin diode is implemented in a GaAs/AlGaAs double-layer 2DES with two 18 nm GaAs quantum wells separated by a 10 nm Al$_{0.9}$Ga$_{0.1}$As barrier and center-to-center spacing $d=28$ nm. Independent density tuning sets one layer to $\nu=5/2$ and the other to $\nu=7/2$ in the $N=1$ Landau level, giving antiparallel spin magnetizations at the Fermi level. Spin-conserving tunneling is allowed for one bias polarity and Pauli blocked for the other. Experimentally, the antiparallel configuration shows a forward-bias peak at $V\approx +0.5$ mV, a very weak reverse peak at $V\approx -0.25$ mV, and reverse peak current below 1% of the forward peak at 50 mK. The rectification ratio
$$
R(T,V)=\frac{I_{\mathrm{forward}}}{I_{\mathrm{reverse}}}
$$
satisfies $R\gtrsim 100$ at 50 mK near the resonance. The exchange-driven spin-flip alignment energy is $E_{sf}\approx 0.25$ meV, much larger than the bare Zeeman energy $E_Z\approx 0.021$ meV at $B_\perp=0.84$ T. The diode character degrades rapidly with temperature because thermally excited long-wavelength spin waves populate opposite-spin states and lift Pauli blocking [1701.04463].

A very different semiconductor implementation uses a reverse-biased planar pn junction in a GaAs/AlGaAs Hall-bar microdevice to amplify the inverse spin Hall effect. The p-region is a carbon-doped GaAs cap, the n-region is the underlying 2DEG, and reverse bias expands the depletion zone laterally into the Hall bar by at least approximately $10~\mu$m at 10 K. Three Hall crosses are placed at 2, 5, and 8 $\mu$m from the pn edge, and the depletion front can be moved through them sequentially. When the depleted zone reaches a Hall cross, the transverse spin Hall voltage $V_{xy}$ increases abruptly by more than an order of magnitude; at the same dc current $I_{dc}=10~\mu$A, $V_{xy}$ is amplified by a factor $\approx 30$ in the depleted regime relative to the normal regime. The average drift field rises from $E_{xx}\approx 4\times 10^3$ V m$^{-1}$ in the undepleted regime to $E_{xx}\approx 1\times 10^5$ V m$^{-1}$ in the depleted regime, while the conductivity drops from $\sigma_{\mathrm{normal}}=1.2\times 10^{-3}\ \Omega^{-1}$ to $\sigma_{\mathrm{depleted}}=9.0\times 10^{-5}\ \Omega^{-1}$. The inferred spin lifetime is $\tau_s<13$ ps and the effective spin Hall angle decreases from $\tilde\alpha_{SH,\mathrm{normal}}=(7\pm 2)\times 10^{-2}$ to $\tilde\alpha_{SH,\mathrm{depleted}}=(2.7\pm 0.6)\times 10^{-3}$ even as the measured voltage increases [1605.04109].

These two examples clarify a useful distinction. In the quantum Hall device, “spin PN junction” refers to a diode defined by spin-resolved tunneling asymmetry. In the planar Hall-bar device, the pn junction acts as a local electrostatic gate that amplifies spin-to-charge conversion by moving a depletion front. Both belong to the same topic because both use pn electrostatics or a pn analogue to control spin selectivity, but the transport observables are fundamentally different.

## 7. Applications, limitations, and open questions

The application space is correspondingly heterogeneous. Circular graphene pn junctions were proposed as spin interferometers exploiting the sweet spot for robust, low-RSOC manipulation of spin geometric phases and in-plane textures, as spin filters/selectors using polarity to choose inward versus outward radial spin orientation, and as reconfigurable spin waveguides based on gate-defined curved pn channels and chiral zero modes [2303.05833]. The room-temperature p-AMS/n-Si junction suggests spin logic and reconfigurable diodes with magneto-rectification and gain under reverse bias, nonvolatile or memory-adjacent functions via current-induced magnetization states, and hybrid charge–spin circuits enabling in-memory computing primitives or neuromorphic elements [2603.02506]. The 2D FGT/GaSe/InSe/FGT junction suggests nonvolatile memory elements, low-power spin logic and amplification, spin interconnects, and magnetic sensors, specifically because the readout occurs at zero bias or at nA-scale bias currents [2509.04206]. The quantum Hall spin diode functions as a spectroscopic probe of spin polarization in correlated $N=1$ Landau-level states such as $\nu=5/2$ and $7/2$ [1701.04463].

The limitations are equally platform specific. In curved graphene pn junctions, the analysis assumes a continuum Dirac model, circular symmetry, and adiabatic projection that neglects RSOC-induced coupling to higher Landau levels; valley-Zeeman SOC shifts $\omega_Z\to \omega_Z+\tau\lambda_{VZ}$ and spoils exact in-plane alignment unless $\lambda_R\gg\lambda_{VZ}$ [2303.05833]. In TI pn junctions, the surface spin response is limited by bulk shunting once the applied bias exceeds the bulk gap; the intrinsic conversion can remain large while the usable interfacial torque stays bounded by the surface current density [2110.02641]. In the p-AMS/n-Si diode, AMS composition control, interface quality, long-term reliability under repeated breakdown-current cycles, direct measurement of $P$, $\tau_s$, and $L_s$, and integration beyond indium contacts remain open engineering issues [2603.02506]. In the vdW magnetic tunnel p–n junction, the effect is thickness sensitive, decreases with increasing resistance-area product, and is presently limited by the Curie temperature of FGT, so room-temperature operation requires higher-$T_c$ 2D ferromagnets or alternative spin-control mechanisms [2509.04206]. In the quantum Hall diode, strong rectification requires high mobility, weak effective Landau-level mixing, and cryogenic temperatures; long-wavelength spin waves degrade the diode above approximately 0.1–0.5 K [1701.04463].

Several open questions recur across platforms. The graphene work explicitly identifies robustness of the sweet spot to disorder and shape imperfections, valley mixing at sharper interfaces, and dynamic control of $\omega_0$ via time-dependent gates as unresolved [2303.05833]. The p-AMS/n-Si work raises questions about thermal behavior under sustained breakdown currents and thickness scaling near the $\sim 10$ nm space-charge width [2603.02506]. The vdW tunnel junction literature leaves wafer-scale growth, controlled doping in ultrathin GaSe/InSe, and CMOS back-end compatibility as open challenges [2509.04206]. A plausible implication is that “spin PN junctions” are better regarded as a design class than as a single device archetype: the common element is a junction-induced asymmetry that acts differently on distinct spin channels, while the microscopic realization may be recombinative, tunneling, topological, interferometric, or depletion controlled.

Source: https://www.emergentmind.com/topics/spin-pn-junctions