Magnetic Tunnel Junction

Intuition

Replace the non-magnetic metal spacer of a GMR spin valve with a thin insulator (typically MgO, $\sim 1$ nm). The conduction electrons can no longer cross classically; they must tunnel. The tunneling probability depends sensitively on whether the wavefunctions of the two electrodes overlap — and because each electrode is ferromagnetic with an asymmetric DOS at the Fermi level, the tunneling current ends up depending on the relative orientation of the two magnetizations.

The result is tunnel magnetoresistance (TMR): a low resistance when both ferromagnets are aligned (lots of matching states) and a high resistance when they are antiparallel (the majority of one electrode finds only minority states in the other). Effects of 600 % at room temperature are routinely measured in MgO-based stacks — an order of magnitude beyond what GMR can deliver, and large enough that a single MTJ can serve as a non-volatile memory bit.

Formal definition

A magnetic tunnel junction (MTJ) is a three-layer stack:

$${\text{FM}}_1/\text{insulator}/{\text{FM}}_2,$$

with the insulator thin enough ($\sim 1$–$2$ nm) for quantum tunneling to dominate. The TMR ratio is

$$\mathrm{TMR}\equiv \frac{R_{\text{AP}}-R_{\text{P}}}{R_{\text{P}}},$$

where $R_{\text{P}}$ and $R_{\text{AP}}$ are the resistances when the magnetizations are parallel and antiparallel.

In the Jullière model (1975), tunneling is spin-conserving and spin-channel resistances add in parallel. This gives

$$\boxed{\mathrm{TMR}=\frac{2P_1{P}_2}{1-P_1{P}_2}}$$

in terms of the spin polarizations $P_1$ and $P_2$ of the two electrodes. Two consequences are immediate:

• A half-metal ($P=1$) electrode gives infinite Jullière TMR.
• TMR is always positive in the Jullière model — the parallel configuration is always more conducting.

Key results

1. Three generations of barrier

Barrier	Year	TMR @ 300 K	Mechanism
Ge, amorphous	1975 (Jullière)	14 % @ 4 K	proof-of-principle
AlO${}_x$	1995 (Moodera, Miyazaki)	30–70 %	first room-temperature MTJ
MgO (001), crystalline	2004 (Yuasa, Parkin)	up to 600 %	symmetry filtering of ${\Delta }_1$ Bloch states

Crystalline MgO does much more than the Jullière model predicts: its band structure filters the tunneling wavefunctions by symmetry. Only the ${\Delta }_1$ Bloch states of bcc Fe and CoFeB couple to the ${\Delta }_1$ evanescent state in MgO, and those states are completely spin-polarized — so the effective $P$ approaches unity for the relevant channel, sending TMR sky-high.

2. The MTJ as a memory cell

An MTJ has exactly two stable states (P and AP), separated by a controllable energy barrier set by the anisotropy of the free layer:

• One layer is pinned (its magnetization is fixed by an adjacent antiferromagnet through exchange biasing).
• The other layer is free and stores one bit by pointing parallel (“0”) or antiparallel (“1”) to the pinned reference.

Reading the bit is just a resistance measurement. Writing the bit is the difficult part — see STT for the modern solution.

3. MRAM — non-volatile DRAM-class memory

A Magnetoresistive Random-Access Memory (MRAM) array is a 2D grid of MTJs, one per cell. Each cell stores a non-volatile bit in the free-layer magnetization and is read out by sensing $R_{\text{P}}$ vs $R_{\text{AP}}$.

	SRAM	DRAM	Flash	MRAM (STT-MRAM)
Speed (R/W)	very fast	fast	slow (W)	fast
Density	low	high	high	medium
Endurance	$\to \infty$	$\to \infty$	$\sim 10^5$ writes	$\gtrsim 10^{15}$ writes
Volatility	volatile	volatile	non-volatile	non-volatile
Power	high (leakage)	refresh power	high (writes)	very low

MRAM combines DRAM-class density and SRAM-class speed with Flash-class non-volatility — the long-standing memory holy grail. Commercial STT-MRAM has been shipping since around 2018 (Everspin, Intel, Samsung, TSMC) and is now found in last-level caches and IoT microcontrollers.

4. Limits and trade-offs

• Thermal stability: a smaller cell shrinks $K_{u}V$, eventually losing the data to thermal noise. Practical cells need $K_{u}V\gtrsim 60k_{B}T$ for a 10-year retention.
• Write current: STT writing requires $J\sim 10^6$–$10^8$ A/cm${}^2$ through the (high-resistance) tunnel barrier, which must be thin enough not to break down.
• Read-disturb: read currents must be safely below the switching threshold to avoid accidentally flipping the bit.

The compromise between read signal, write current, retention, and barrier reliability is what makes MTJ engineering a multi-decade research field.

Summary

An MTJ is two ferromagnets separated by a thin insulator. Spin-conserving tunneling makes its resistance depend on the relative orientation of the two magnetizations:

$$\mathrm{TMR}=\frac{R_{\text{AP}}-R_{\text{P}}}{R_{\text{P}}}=\frac{2P_1{P}_2}{1-P_1{P}_2}.$$

In crystalline MgO MTJs, symmetry filtering pushes TMR above 600 % at room temperature. The MTJ has become the storage element of STT-MRAM, a non-volatile, fast, high-endurance memory that is already a billion-dollar industry and the most likely successor to embedded SRAM/Flash.

Connections

• spin-valve — metallic predecessor of the MTJ; lower MR ratios
• spin-polarized-current — the $P_1,P_2$ that enter Jullière
• spin-transfer-torque — how MRAM cells are written
• stoner-model — the asymmetric DOS that ultimately produces TMR
• hysteresis — the bistable free-layer loop that stores the bit

References

• M. Jullière, Phys. Lett. A 54, 225 (1975).
• S. S. P. Parkin et al., Nat. Mater. 3, 862 (2004) — MgO MTJ.
• S. Yuasa et al., Nat. Mater. 3, 868 (2004) — MgO MTJ.
• A. D. Kent & D. C. Worledge, Nat. Nanotechnol. 10, 187 (2015) — STT-MRAM review.