Conditions for ferromagnetic resonance in nanoparticles and microwave magnetization

[1] In order to access the ancient magnetic record in palaeomagnetic samples it is necessary to raise the temperatures of the magnetic carriers to temperatures close to their magnetic transformation temperature. If this is done thermally, in an oven, mineral alteration of the magnetic carriers results, (probably involving transport in the non-magnetic matrix) often rendering intensity results completely useless [Walton, 1984]. [2] Because it is reversal of the moments of the magnetic particles that is important it should be emphasized that it is the magnetic temperature which is important, and that an increase in the magnetic temperature is identical to an increase in the density of spin waves. [3] Microwaves are absorbed by generating spin-waves [Sparks, 1964], and this is a very efficient way to raise the temperature of ferromagnetic particles in a non-magnetic matrix [Walton et al., 1993]. Since microwaves are essentially only absorbed by the magnetic grains the matrix remains cool which eliminates the problem of mineral alteration. Under the right conditions the sample will absorb virtually all the microwave energy. However if conditions are not optimal hardly any absorption will occur. A key factor responsible for the failure of microwave magnetization is that the size of the magnetic particles has simple but important consequences for the spin wave spectrum. [4] Magnetite is an important magnetic carrier, and the dispersion relations for magnetite, determined by Alperin et al. [1967] are shown in Figure 1. [5] Spin waves whose wavelength exceeds about twice the size of the particle are not possible [Hendriksen et al., 1993] except for the uniform mode that involves the coherent rotation of the spins about the anisotropy field axis; so the dispersion relations for small particles are cut-off at the corresponding wave-vector. Direct absorption of microwaves is still possible by exciting the uniform mode, but this is uninteresting because its frequency is temperature dependent, and soon becomes lower than the microwave frequency as the particle's temperature rises. [6] For that reason a process is used whereby one microwave photon is absorbed by two spin waves of equal and opposite wave-vector (thereby satisfying quasi-momentum conservation since the photon wave-vector is essentially zero). Now it doesn't matter if the dispersion relations drop with temperature since two spin waves of equal and opposite wave-vector can always be found. But the gap in the spectrum has important consequences since the frequency of the microwave photon must be twice the spin wave frequency, and the minimum spin-wave wave-vector leads to a minimum frequency. If we are willing to wait 1 year for the moments to flip, the situation is not so bad, but if we wish to have them flip in seconds the microwave frequency must be about 24 GHz (assuming that the scale of grains whose blocking temperature is room temperature is 30nm) in order to flip the moments of the smallest grains at temperatures close to room temperature. [7] If a lower frequency is used some magnetization will occur because there are larger grains in the sample, that can absorb the microwave energy and heat the sample, thereby magnetizing the smaller grains that are unable to absorb the microwaves. If this process is restricted to grains whose relaxation time at room temperature is less than about one year it probably makes little difference to any palaeomagnetic information since the moments involved are uninteresting short term viscous ones. Some alteration is likely at this temperature [Walton, 1984, 1991], but the time at elevated temperature is only a few seconds; so its effect will be negligible [Walton, 1991]. [9] Microwave experiments are usually a variant of the Thellier method with a series of microwave power levels [Walton et al., 1996] replacing the temperature steps. Thus the moment carried by the unaffected grains which is being removed slowly by heating over the duration of the experiment can be a source of error. [10] A large body of published data exists that was obtained at a frequency of 8.2 GHz that would excite 4.1 GHz spin waves. On the basis of the arguments presented above, thermal magnetization of these grains now requires temperatures in excess of 400C where alteration is not just possible it is unavoidable. However, it should be borne in mind that these numbers are only estimates: the shape of the grains makes the major contribution to the anisotropy, and it is possible for the shape of the grains that can just absorb 8.2GHz photons, to lead to lower blocking temperatures. The experience has been that the microwave response of palaeomagnetic samples is very variable, some can be easily magnetized at low powers, and a very few cannot be magnetized at any power available. [11] Nevertheless the power and microwave times should be restricted to values that avoid alteration. In practice if the substrate temperature remains lower than 150C alteration does not appear to be a problem. This means that some samples may not magnetize completely. Consequently, if the magnetization is insufficient for a reliable result, they must be discarded. If this is not done, and the power, and, or, the time increased until complete magnetization is achieved, random and meaningless results may be obtained. [12] If the microwave frequency is too low another problem arises: if a secondary magnetic component exists in the sample, it will affect all those grains whose blocking temperature is lower than the temperature at which the secondary NRM was emplaced. However, if these are small grains that cannot absorb microwaves, and are being demagnetized thermally, the moment carried by the small grains will be removed as they are heated, but this will be a gradual process. Thus, the moment carried by the grains absorbing the microwaves will be removed as soon as their temperature reaches the temperature at which the secondary NRM was emplaced, but the other moment may continue to be removed as the matrix temperature continues to rise. This can lead to a “smearing” of the distinction between the primary and secondary NRM observed by Hill et al. [2002]. [13] Evidence for the increase in efficiency of the microwave technique with frequency is shown in Figure 2 that shows the power required to demagnetize two lava samples at 8.2 GHz and 16.5 GHz. [14] While the remarks above about the variability of palaeomagnetic samples should be remembered, it is clear that the results shown support the arguments presented here. They also suggest that it may not be necessary to go to 24 GHz to achieve demagnetization of all the grains. Whether this is due to the mineralogy of the grains, or because the sample temperature is raised to about 200 C is not clear. [15] To summarize: in order for microwave techniques to yield reliable results the frequency must be high enough for all the carriers of the remanence to be “on speaking terms” with the microwaves (Figure 1). [16] The author is grateful A. J. Biggin for providing the 16.5 GHz results, and to J. Shaw, M. J. Hill, and M. N. Gratton for useful discussions during the preparation of this paper.

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