"Magnetic Magic in Nature"

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Unregistered Submission:

( April 7th, 2016 10:01am UTC )

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Unregistered Submission:

( April 8th, 2016 8:07am UTC )

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The preprint states without reference that ferritin is paramagnetic. What is the evidence for this? I can see that a solution of ferritin must be paramagnetic, because individual molecules will not interact and will be subject to strong thermal agitation. But what about the properties of individual ferritin cores? I've found papers describing ferritin as superparamagnetic - if I understand correctly that means ferromagnetic with polarity flip-flopping thermally. For ferritin those transitions are thought to occur too quickly to be exploitable in this situation anyway, but I believe paramagnetic implies total magnetic disorganisation, which isn't exactly the same thing.

Peer 2:

( April 10th, 2016 9:38pm UTC )

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Thanks for the comment. Yes, ferritin does have superparamagnetic properties, meaning that the spins within a small grain can flip collectively. In addition, there is antiferromagnetic alignment among those spins that reduces the effective moment of the particle. For the present treatment two aspects are important: (1) At room temperature ferritin has no permanent moment. The blocking temperature (transition to superparamagnetism) is around 40K. So the magnetization is strictly induced by the external field. (2) My first stab at estimating the susceptibility to the field assumed no interaction between the iron spins, and so ignored both superparamagnetic and antiferromagnetic effects: a first-order approximation that a student (or a reviewer) could do without having to absorb the literature. The second stab compares that to actual measurements of the susceptibility at room temperature, which is a factor of 10 *lower*. So the antiferromagnetic effects seem to be strong, such that within each ferritin particle only a few iron spins remain uncompensated. I will address this in a revised version.

Frankel, RB, Papaefthymiou, GC, Watt, GD (1991) Variation of superparamagnetic properties with iron loading in mammalian ferritin. Hyperfine Interactions 66:71-82.

Mohie-Eldin, MEY, Frankel, RB, Gunther, L (1994) A comparison of the magnetic-properties of polysaccharide iron complex (PIC) and ferritin. Journal of Magnetism and Magnetic Materials 135:65-81.

Frankel, RB, Papaefthymiou, GC, Watt, GD (1991) Variation of superparamagnetic properties with iron loading in mammalian ferritin. Hyperfine Interactions 66:71-82.

Mohie-Eldin, MEY, Frankel, RB, Gunther, L (1994) A comparison of the magnetic-properties of polysaccharide iron complex (PIC) and ferritin. Journal of Magnetism and Magnetic Materials 135:65-81.

Unregistered Submission:

( April 10th, 2016 10:38pm UTC )

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Thanks for the additional explanation!

I did have one further question. Does a ferritin "core" have a preferred axis of magnetisation (anisotropy)? If so, wouldn't some torque be generated if the magnetisation by the external field tended to be along that axis?

I did have one further question. Does a ferritin "core" have a preferred axis of magnetisation (anisotropy)? If so, wouldn't some torque be generated if the magnetisation by the external field tended to be along that axis?

Peer 2:

( April 12th, 2016 6:37am UTC )

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Good question. I can't find a good measurement of magnetic anisotropy for native ferritin. But let's suppose it was infinite, i.e. the particle can be magnetized only along the "easy" direction. Then the interaction energy with the magnetic field is M * B when the particle is oriented with the easy direction along the field and zero when orthogonal, where M is the induced magnetic moment. Using the susceptibility values quoted in my article and the magnetic field strength of 0.05 T, this energy difference will be 1.58e-25 J = 3.85e-5 kT. So it would be impossible to get any significant orientation of the particle out of this because of thermal fluctuations. Again the effects are about 5 log units too weak.

Unregistered Submission:

( April 12th, 2016 7:29pm UTC )

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It's not immediately clear which equation you are referring to, but I wonder whether you haven't implicitly used the atomic magnetic moment rather than that of the whole ferritin particle, which - I think - is what should be used in the superparamagnetic case.

If so, a "best case" calculation for the maximum torque energy might go something like this (taking your generous parameters):

4000 iron atoms * 4.5 Bohr Magnetons per atom * field

= 4000 * 4.5 * 1E-23 * 0.05

= 9e-21 J = 2kT

One could presumably even increase the field a bit. If this is correct, the maximum torque would not be so trivially negligible. Of course, the reduced moment caused by the cancellation of spins you cited and finite anisotropy would likely reduce this back below the threshold for usefulness, but it could be annoyingly close.

If so, a "best case" calculation for the maximum torque energy might go something like this (taking your generous parameters):

4000 iron atoms * 4.5 Bohr Magnetons per atom * field

= 4000 * 4.5 * 1E-23 * 0.05

= 9e-21 J = 2kT

One could presumably even increase the field a bit. If this is correct, the maximum torque would not be so trivially negligible. Of course, the reduced moment caused by the cancellation of spins you cited and finite anisotropy would likely reduce this back below the threshold for usefulness, but it could be annoyingly close.

Peer 2:

( April 12th, 2016 9:00pm UTC )

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No this isn't correct. In your picture the particle has a permanent magnetic moment equal to all spins aligned, as in a ferromagnet. Instead: (1) The interactions within the particle seem to be antiferromagnetic, so that most of the spins cancel. (2) The particle is much smaller (~5 nm) than the minimum size for a stable single domain (~30 nm). So it exhibits superparamagnetism, meaning the spins act coherently but flip thermally among all possible orientations. Without an external field the particle has no permanent magnetic moment. In a steady magnetic field, the spin orientation gets biased in the direction of the field and that makes the induced magnetic moment:

M = chi_mol * B

Where chi_mol is the single ferritin susceptibility per molecule, which has been measured at:

chi_mol = 6.33e-23 J/T^2

The energy between that induced moment and the field is

U = M * B = chi_mol * B^2 = 6.33e-23 J/T^2 * (0.05 T)^2 = 1.58e-25 J

where physics sticklers would reduce this by another factor of 1/2 but who's counting...

M = chi_mol * B

Where chi_mol is the single ferritin susceptibility per molecule, which has been measured at:

chi_mol = 6.33e-23 J/T^2

The energy between that induced moment and the field is

U = M * B = chi_mol * B^2 = 6.33e-23 J/T^2 * (0.05 T)^2 = 1.58e-25 J

where physics sticklers would reduce this by another factor of 1/2 but who's counting...

Unregistered Submission:

( April 12th, 2016 9:37pm UTC )

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"(1) The interactions within the particle seem to be antiferromagnetic, so that most of the spins cancel."

I should have put that factor of 10 directly into the calculation (I mentioned it at the end of the comment). That point was understood.

"(2) The particle is much smaller (~5 nm) than the minimum size for a stable single domain (~30 nm). So it exhibits superparamagnetism, meaning the spins act coherently but flip thermally among all possible orientations."

Yes, but doesn't that still leave open the question of anisotropy (all possible directions but not with equal probability)? The (likely unrealistic) case I was trying to model was where the axis of magnetisation but not the direction was constrained - the best case assumption of infinite anisotropy. Wouldn't the application of a strong field bias the flip-flopping? And a strong enough field actually then lead to a situation resembling a ferromagnet (reduced by that factor of 10) with polarity aligned along the axis constrained by anisotropy? It seemed that the threshold for stabilising the flip-flopping ought to be around kT. However, I didn't consider whether it would be feasible to induce the required degree of magnetisation, which I believe is another way of viewing your last calculation - it isn't feasible.

I'll leave it at that as I'm really not expert. Thanks for contributing to the discussion of these papers.

I should have put that factor of 10 directly into the calculation (I mentioned it at the end of the comment). That point was understood.

"(2) The particle is much smaller (~5 nm) than the minimum size for a stable single domain (~30 nm). So it exhibits superparamagnetism, meaning the spins act coherently but flip thermally among all possible orientations."

Yes, but doesn't that still leave open the question of anisotropy (all possible directions but not with equal probability)? The (likely unrealistic) case I was trying to model was where the axis of magnetisation but not the direction was constrained - the best case assumption of infinite anisotropy. Wouldn't the application of a strong field bias the flip-flopping? And a strong enough field actually then lead to a situation resembling a ferromagnet (reduced by that factor of 10) with polarity aligned along the axis constrained by anisotropy? It seemed that the threshold for stabilising the flip-flopping ought to be around kT. However, I didn't consider whether it would be feasible to induce the required degree of magnetisation, which I believe is another way of viewing your last calculation - it isn't feasible.

I'll leave it at that as I'm really not expert. Thanks for contributing to the discussion of these papers.

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