How Much Spin “Leaks” Each Cycle? The QTT Story Behind a Surprisingly Universal Number

Attar, A. (2025). Quantum Traction Theory (QTT). Zenodo. 10.5281/zenodo.17527179

What if wildly different magnetic materials — from iron to fancy spintronic alloys — all leaked roughly the same tiny fraction of their spin “capacity” every time their magnetization precesses?

That’s exactly what the Quantum Traction Theory (QTT) spin–damping test looks at. And the punchline is simple enough to say in plain language:

Every time the magnetization vector goes around once (one precession cycle), only a small, almost universal percentage of its “spin capacity” is lost.

Spins as Tiny, Tired Tops

Imagine a bunch of tiny spinning tops inside a magnetic material. These tops are the electron spins. When you hit the material with a microwave field, the spins start to wobble around the external magnetic field direction — this is called ferromagnetic resonance (FMR).

But nothing wobbles forever. The wobble slowly dies down. In standard language, that decay is described by a number called the Gilbert damping, written as α. Bigger α means the wobble (precession) dies out faster.

Traditionally, people look at α and say “this material has higher damping than that one.” QTT says: that’s only half the story.

QTT’s Twist: Don’t Look at α Alone

QTT tells us to ask a much more “capacity-like” question:

When the spins go around once, what fraction of their precession capacity do they lose in that single cycle?

That’s a different question than simply “how fast does it die in time?” It’s a question about loss per cycle, not just loss per second.

To capture that, QTT defines a dimensionless number called the leak per cycle, written as η_LLG. It takes α and combines it with the other experimental knobs:

• γ : the gyromagnetic ratio (how fast the spins precess per unit magnetic field)
• H_res : the resonance field where FMR occurs
• f_FMR : the precession frequency at resonance

The result is a clean, unitless “leak fraction per turn” — exactly the sort of quantity QTT cares about.

What the Test Shows (Layman Summary)

Across many different ferromagnets — Fe, Co, NiFe, CoFeB, Heuslers, and others — experimental data show that:

• For ordinary 3d metallic ferromagnets, the leak per cycle η_LLG is only a few percent per precession cycle.
• For cleaner, more “spin-filtered” systems (like some Heusler alloys), η_LLG drops to sub-percent levels.
• Inside each “class” (ordinary metals vs special spintronic alloys), the values of η_LLG cluster tightly — they don’t jump all over the place from one material to another.
• When η_LLG is unusually large, there’s a clear physical reason: extra loss channels like impurities, interfaces, or strong spin–orbit scattering.

In other words, once you measure the damping in the right dimensionless way — as leak per cycle, not just as α — different materials suddenly look much more alike than you might expect. They fall into a few universal “bands” rather than an arbitrary scatter of unrelated numbers.

Why This Matters for QTT

Quantum Traction Theory is built around the idea that physical systems have a kind of “capacity ledger” that tracks how much can be stored and how much leaks per cycle. The spin–damping test is a direct, real-world example of that:

• η_LLG is a capacity leak fraction per cycle.
• It’s dimensionless and nearly universal within a given dissipation channel class.
• You don’t need to tune a separate free parameter for each material; once you group by channel, the numbers line up.

This is exactly the kind of behavior QTT also uses when it talks about more exotic things, like organizing lepton masses or neutrino mass splittings. The spin–damping test shows that the “capacity per cycle” idea is not just philosophical — it actually matches how real ferromagnets behave in the lab.

For the Curious: The Key Equations

Here is the core QTT definition of the leak per cycle in proper WordPress LaTeX shortcode form.

1. Dimensionless leak per cycle

The QTT leak-per-cycle parameter is defined as

Equation

η_LLG equiv (α γ H_res)/(f_FMR).

Meaning in words:

• α: Gilbert damping (how fast the wobble decays in time)
• γ: gyromagnetic ratio (relates magnetic field to precession frequency)
• : resonance field at which FMR occurs
• : resonance precession frequency

The combination is unitless and answers the question: “What fraction of spin precession capacity is lost each cycle?”

2. Approximate relation: leak per cycle vs damping

In the common situation where the resonance condition gives

Equation

γ H_res ≈ 2π f_FMR,

the leak per cycle simplifies to

Equation

η_LLG ≈ 2π α.

So in many practical cases, QTT says:

Leak per cycle ≈ 2π × (Gilbert damping).

This is why α alone is not the most natural quantity — tells you directly the fraction of spin capacity lost each turn, which is exactly the kind of bookkeeping QTT is built to do.

If you’re comfortable with ordinary magnetism and want to test QTT yourself, start with any FMR paper: extract α, γ,

Equation

H_res

,

Equation

f_FMR

, compute

Equation

η_LLG

, and see which universal “band” your material lives in.