The Zeeman

Magnets change spectra.

It sounds like a claim you'd hear in a crackpot's email — a random person claiming that a magnet can alter the light from an atom — but it's one of the oldest and most robust effects in physics. Discovered in 1896 by Pieter Zeeman, a Dutch physicist who was testing an idea from his mentor, Lorentz. Lorentz had predicted that magnetic fields should split spectral lines. Zeeman built the experiment. He proved him right.

The Nobel Prize followed in 1902. But the story is in the splitting.

Here's what happens. Put an atom in a magnetic field, and its energy levels shift. Not uniformly. Different quantum states shift by different amounts. An electron with spin aligned with the field is at a different energy than one with spin opposed. An electron with angular momentum pointing along the field is different from one pointing perpendicular.

The magnetic field breaks the degeneracy. States that were at the same energy before — the same spectral line — now separate. The line splits.

Not into two. Often into more. The pattern depends on the transition, the quantum numbers, the strength of the field. The simplest case — a transition between two singlet states, where spin is zero — splits into exactly three components. This is the normal Zeeman effect. Three lines: one unshifted (the π component, polarized parallel to the field) and two shifted (the σ components, polarized perpendicular).

But most atoms have spin. And when spin is involved, the splitting is more complex. The anomalous Zeeman effect — "anomalous" only because it was anomalous before we understood spin. Now it's just Zeeman, the default. Multiple components, shifted by different amounts, with intensities governed by selection rules.

The splitting scale is straightforward. The energy shift is proportional to the magnetic field strength B. ΔE = μB · g · mJ · B, where μB is the Bohr magneton, g is the Landé g-factor (specific to each level), and mJ is the magnetic quantum number. A stronger field means wider splitting. A weaker field means tighter clustering.

And that proportionality is what makes the Zeeman effect useful. If you can measure the splitting, you know the field strength. You don't need to touch the star. You don't need to send a probe. You just look at the spectrum.

I measured my first Zeeman splitting in sunspots. A small telescope, a spectropolarimeter built from a birefringent filter and a rotating half-wave plate, and a CCD camera cooled to −40 °C. Sunspots are dark patches on the solar surface where the magnetic field is strong — thousands of gauss, compared to the Sun's average of about 1 gauss. And in those spots, spectral lines are clearly split.

The Fe I line at 525.02 nm is a classic Zeeman target. In a quiet region of the solar disk, it's a single line. In a sunspot, it splits into a triplet with a separation of about 0.015 nm at 5000 gauss. You can see it on a good spectrograph. You can measure it. And from the measurement, you calculate the field strength.

The Zeeman effect is how we know that sunspots have fields of 2000–4000 gauss. It's how we know that magnetic white dwarfs have fields of 10⁶–10⁹ gauss. It's how we know that magnetars — neutron stars, the most magnetized objects in the universe — carry fields of 10¹⁴–10¹⁵ gauss, so strong that they reshape atomic orbitals, binding electrons into cylinders along the field lines.

On the laboratory scale, the Zeeman effect is a calibration tool and a research instrument. Atomic clocks use it. Magnetometers use it. Quantum computing experiments with trapped ions use it to address individual transitions. The Zeeman shift is a nuisance when you want precise frequencies and a feature when you want to manipulate quantum states.

I've used the Zeeman effect to study magnetic Ap stars — chemically peculiar stars with fields of thousands of gauss. Their spectra show clean, well-separated Zeeman components because their atmospheres are stable and rotationally broadened lines stay sharp. I mapped the magnetic field geometry of a dozen Ap stars, watching the splitting change over their rotation periods. The field isn't aligned with the rotation axis. It's tilted. And as the star turns, different field lines sweep across our line of sight. The spectrum rotates with it.

The Zeeman effect also tells us about stellar activity. Cool stars with convective envelopes — like the Sun — have magnetic cycles. The splitting patterns in their spectra vary over years. Zeeman-Doppler imaging reconstructs maps of the surface magnetic field from polarized line profiles. It's like doing a solar magnetogram for a distant star.

The beauty of the Zeeman effect is that it turns magnetic fields — invisible, intangible, existing in regions you can't see — into spectral lines you can measure. A magnet can't be photographed. A magnetic field can't be touched. But its effect on an atom? That's light. And light we can measure to parts per billion.

Pieter Zeeman didn't just discover a splitting. He discovered a way to measure the invisible.

And every time I look at a split line, I think about him, standing in a lab in Amsterdam in 1896, watching sodium lines widen and separate as he turned on an electromagnet. The world's first magnetometer was a spectroscope. And the universe has been speaking its magnetic secrets ever since.