# Does Barkhausen noise affect the measurement of magnetic particle based qubits?

Q1: I've tried to find out if Barkhausen noise affects the measurement of spin-wave excitations in magnetic particle material based qubits.

I prefer implementations such as those described in "Magnetic qubits as hardware for quantum computers", rather than a true hybrid system such as described in "Coherent coupling between a ferromagnetic magnon and a superconducting qubit" or "Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet"; which relies on the coherent coupling between a single-magnon excitation in a millimeter-sized ferromagnetic sphere and a superconducting qubit.

I'm asking about the situation where the magnetic particle is the qubit and not simply part of a magnon-qubit coupling scheme.

Q2: Is Barkhausen noise a factor that is not considered relevant?

After several hours of research the closest search I could find, for a paper of quantum computing hardware, Mesoscale and Nanoscale Physics, and Barkhausen noise, was this paper: "The Theory of Spin Noise Spectroscopy: A Review".

"Barkhausen noise

Studies of fluctuations in magnetic systems take roots in the work of Heinrich Barkhausen who proved already in 1919 that the magnetic hysteresis curve is not continuous, but is made up of small random steps caused when the magnetic domains move under an applied magnetic field. This noise can be characterized by placing a coil of a conducting wire near the sample. The motion of ferromagnetic domain walls produces changes in the magnetization that induces noisy electrical signals in the coil. Studies of Barkhausen noise have been used in practice as a nondemolition tool to characterize the distribution of elastic stresses and the microstructure of magnetic samples".

It would seem that Barkhausen noise can affect even very small magnetic particles subjected to an external magnetizing field, as might be encountered during measurement, but nowhere (it would seem) is there research on it's effect on quantum noise of the system.

It appears to be a difficult or unanswered question.

An answer was offered stating:

The Barkhausen effect has to do with domain wall motion. The magnetic qubit discussed in the first reference is based on nm sized magnetic particle, which we can assume to be single domain, and therefore would not exhibit Barkhausen noise. This paper by Kittel [Theory of the Structure of Ferromagnetic Domains - 1946] discusses domains in magnetic particles.

There are different limits stated as to what constitutes a single-domain magnetic particle, I've found upper limits ranging from 30-100 nm, with lower limits somewhat more consistent around 10 nm.

While it's not precisely stated what the exact size of the particles are in that paper, and we might assume others using similar methods could utilize particles of a different size, let's assume for the sake of that one answer only that the particles in question are single domain.

There are five main mechanisms due to which magnetic Barkhausen emissions occur [Jiles (1988)]:

1. Discontinuous, irreversible domain wall motion

2. Discontinuous rotation of magnetic moments within a domain

3. Appearance and disappearance of domain walls (Bloch or Neel). Domain walls are narrow transition regions between magnetic domains. They only differ in the plane of rotation of magnetization. For Bloch walls the magnetization rotates through the plane of the domain wall whereas for Neel walls the magnetization rotates within the plane of the domain wall.

4. Inversion of magnetization in single-domain particles

5. Displacement of Bloch or Neel lines in two 180$$°$$ walls with oppositely directed magnetizations

There are a number of papers on the measurement of Barkhausen noise in single-domain magnetic particles:

"The fundamental Barkhausen noise generated by the magnetization reversal of individual particles within a particulate magnetic medium has been observed using the anomalous Hall effect (AHE) as a sensitive magnetization probe. This is the first time the reversal of individual interacting single or nearly single domain particles has been detected. The jumps correspond to magnetic switching volumes of ~3×10$$^{-15}$$ cm$$^3$$ with moments around 10$$^{-12}$$ emu.".

"These observations thereby demonstrate that nucleation becomes increasingly more dominant as the particles become smaller, a manifestation of the random distribution of active nucleation sites. Nucleation may therefore account for much of the magnitude and grain size dependence of hysteresis parameters in the PSD range as well as resulting in a gradual transition between multidomain and PSD behavior. Fine particles completely controlled by nucleation during hysteresis behave in a strikingly parallel manner to classical single domains and are therefore quite appropriately described as being pseudo‐single‐domain.".

That paper goes as far as to state:

"We will show that here Barkhausen Noise has nothing to do with the movement of domain walls nor with Self Organized Criticality nor with fractal domains nor with thermodynamic criteria."

The first paper you mention, by Tejada et al, does not actually refer to conventional nanoparticles as such, but rather to single molecule magnets. This other paper by Loss, Quantum computing in molecular magnets, is about the same systems but perhaps more clear in quantum computing terms, since it gives more details on the underlying Hamiltonian and gives a suggestion for a quantum algorithm. Magnetic molecules do present decoherence (see for example Decoherence in crystals of quantum molecular magnets), but their mechanisms are different from those of magnetic nanoparticles, at least in the details, meaning Barkhausen noise is not be a sufficient description for those. In any case, you may want to check the supporting information of this latter reference by Stamp et al, since it includes methodological details on how to estimate the different decoherent sources.

• Thanks for writing. The other answer said: "... based on nm sized magnetic particle, which we can assume to be single domain, and therefore would not exhibit Barkhausen noise." - IE: 'Single domains do not have Barkhausen noise', I disagreed. There's no requirement in the question for full decoherence, measurement error would be enough. – Rob Apr 9 '18 at 5:29
• I'm more used to a description involving the spin energy level structure. In these terms, magnetic molecules such as the one presented by Tejada and Loss have an extremely simple and clean energy level structure (e.g. the Hilbert space consisting of a subset of the 21 levlels of a collective spin S = 10, with the rest of the spectrum being gapped), whereas even small nanoparticles have complicated, more dense spectra. This is why Berkhausen is typically not invoked in those systems to describe the source and influence of magnetic noise, which indeed does happen. – agaitaarino Apr 9 '18 at 5:36

The Barkhausen effect has to do with domain wall motion. The magnetic qubit discussed in the first reference is based on nm sized magnetic particle, which we can assume to be single domain, and therefore would not exhibit Barkhausen noise.

This paper by Kittel discusses domains in magnetic particles.

• Thank you for offering an answer, do you have a source? -- On the Wikipedia page it says that the noise occurs in thin films (< nm), there's my source in the question, and I've found another source: aip.scitation.org/doi/pdf/10.1063/1.118032 which with respect to "nm scale" sized particles says: "Rotation of the net array magnetization at low temperatures (20 K) occurs by both reversible and irreversible modes, the latter revealed by Barkhausen jumps.". – Rob Mar 26 '18 at 7:46
• I added a link to a paper by Kittel. – Ofer Naaman Mar 26 '18 at 16:44
• Yes but it's 1946, and unsearchable. Is there a page number and a specific quote? – Rob Mar 26 '18 at 16:46
• The question has additional information about single-domain magnetic particles. – Rob Mar 27 '18 at 5:41