Magnetite is both a common inorganic rock-forming mineral and a biogenic product formed by a diversity of organisms. Magnetotactic bacteria produce intracellular magnetites of high purity and crystallinity (magnetosomes) arranged in linear chains of crystals. Magnetosomes and their fossils (magnetofossils) have been identified using transmission electron microscopy (TEM) in sediments dating back to ∼510–570 Ma, and possibly in 4 Ga carbonates in Martian meteorite ALH84001. We present the results from two rock magnetic analyses—the low-temperature Moskowitz test and ferromagnetic resonance (FMR)—applied to dozens of samples of magnetite and other materials. The magnetites in these samples are of diverse composition, size, shape, and origin: biologically induced (extracellular), biologically controlled (magnetosomes and chiton teeth), magnetofossil, synthetic, and natural inorganic. We confirm that the Moskowitz test is a distinctive indicator for magnetotactic bacteria and provide the first direct experimental evidence that this is accomplished via sensitivity to the magnetosome chain structure. We also demonstrate that the FMR spectra of four different strains of magnetotactic bacteria and a magnetofossil-bearing carbonate have a form distinct from all other samples measured in this study. We suggest that this signature also results from the magnetosomes' unique arrangement in chains. Because FMR can rapidly identify samples with large fractions of intact, isolated magnetosome chains, it could be a powerful tool for identifying magnetofossils in sediments

Kim, Soon Sam

Kirschvink, Joseph L.

Kobayashi, Atsuko

Komeili, Arash

Kopp, Robert E.

Sankaran, Mohan

Weiss, Benjamin P.

Caltech Authors - Main

 1
Supplementary Information for: Weiss, B. P., S. S. Kim, J. L. Kirschvink, R. E. 
Kopp, M. Sankaran, A. Kobayashi, and A. Komeili (2003) Ferromagnetic resonance 
and low temperature magnetic tests for biogenic magnetite, Earth Planet. Sci. Lett., 
submitted 
 
A. Introduction 
Here we briefly review the ways in which FMR spectra can be used to infer the 
crystal and compositional properties of natural samples.  Since all of our samples are 
composed of many tiny, randomly oriented crystallites, we restrict the rest of the 
discussion on FMR spectra to the polycrystalline case.  The FMR spectrum of such 
polycrystalline samples is known as a “powder pattern”.  There is a well developed 
theory for rapidly obtaining magnetic and compositional parameters from such powder 
patterns using simple analytic expressions.  Except where noted, the following discussion 
focuses on FMR measurements at room temperature only. Also except where noted, the 
discussion assumes that the crystallites are non-interacting, SD, and sufficiently small in 
size such that eddy current effects can be neglected.  Eddy current effects in FMR 
spectra, which only become important for magnetite crystal diameters >~5 µm [1], 
should be unimportant for our samples.  However, some of our samples, particularly the 
extracellular magnetites and synthetic magnetites, do have strong self-interactions.   
 
B.  FMR Parameters 
As described in the main manuscript, we classified the FMR spectra of each of 
our FMR spectra using three of the following parameters: the polycrystalline effective g-
factor, geff, the linewidth (∆B and ∆BFWHM), and the asymmetry ratio, A (see Fig. 2a).  
The true g-factor is defined g ≡ hυ/βBrfe where h is Planck's constant, υ is the X-band 
microwave frequency (9.3 GHz), β is the Bohr magneton, and Brfe is the applied field at 
which maximum absorption occurs assuming the sample has no magnetic anisotropy (for 
magnetite g = 2.12 [2]).  Samples with anisotropy fields will have a peak absorption at a 
field Beff different from Brfe, which we use to define an effective g-factor, geff ≡ hυ/βBeff. 
Therefore, geff is specified by both the zero-crossing in the derivative spectrum and the 
peak absorption in the integrated spectrum (Fig. 2a).  The effective g-factor was first 
defined by Okamura [3], but is not widely used in the modern literature because simple 
 2
relations between geff and the anisotropy constants are only known for a small a few types 
of anisotropy fields (for instance, cubic magnetocrystalline [4]).   We report geff because 
the relationship between geff and g gives valuable information about the identify of the 
sample’s anisotropy and crystal size. 
The linewidth is a characteristic measure of the spread in field values over which 
resonance is observed to occur.  It can be defined in several ways, including the distance 
between the maximum positive and negative peaks in the derivative spectrum (∆B), or as 
the full-width at half maximum of the integrated (e.g., true absorption) spectrum 
(∆BFWHM) (Fig. 2a).  In this paper, except where otherwise noted we use the former 
definition, although we report both values (Table 2).  Following early workers in FMR 
[4, 5], we define the asymmetry ratio as A ≡ ∆Bhigh/∆Blow, where ∆Bhigh is the linewidth 
on the high-field side of the absorption peak (which is at Beff) and ∆Blow is the linewidth 
on the low-field side of Beff (Fig. 2a).  Both ∆Bhigh and ∆Blow are half-linewidths at half 
maximum in the integrated spectrum, such that ∆BFWHM = ∆Bhigh + ∆Blow, but are not 
usually equal since most spectra have an asymmetric shape.    
It is important to remember that these four parameters do not always have a 
simple physical meaning.  They are used here only to summarize the defining 
characteristics of a large number of spectra such that general features of each spectrum 
can be quickly compared.  For detailed interpretation of the FMR properties of individual 
samples, there is no substitute for direct examination of the FMR spectrum.  The sizes of 
geff, ∆B, and A give information about the strength and orientation of a sample’s 
anisotropy fields, crystal size and composition.   
 
C. Dependence of FMR on magnetic anisotropy 
1. Overview.  For equant crystals with cubic structure like magnetite and other ferrites, 
the peak-to-peak linewidth is (assuming only first order contributions to the anisotropy) 
[4, 6, 7]:  
                     ∆Ba ~ 5/3HK = 5/3 (2K1/Ms)                      (1) 
for the microscopic coercivity, HK, the first order cubic magnetocrystalline anisotropy 
constant, K1, and saturation magnetization, Ms.  Cubic ferromagnets with negative 
(positive) K1, have a {111} ({100}) magnetocrystalline easy axis and a {100} ({111}) 
 3
hard axis.  For cubic samples, the resonance field of the free electron in the absence of 
anisotropy fields, Brfe, is given by Brfe ~ Bmax - 3/5∆Ba (when K1 < 0) and Brfe ~ Bmax - 
2/5∆Ba (when K1 > 0), where Bmax is the high-field absorption peak [1].  The latter two 
relations allow one to obtain the true g-factor using g = hυ/βBrfe.  They imply that cubic 
samples with negative (positive) K1 will have A > 1 (A < 1) (for a graphical visualization 
of this, see [4-7]).  Computer modeling also shows that cubic samples with negative 
(positive) K1 will have geff greater (less) than the mineral’s g-factor [6, 7].   
Following Griscom [1] and using equation (5.35) of ref. [8], the peak-to-peak 
linewidth of samples dominated by uniaxial anisotropy (which can result from shape, 
crystal structure, or magnetoelasticity), is given by:  
∆Bu   ~ 3/2HK 
            = 3/2µ0(Nb – Na)Ms (shape anisotropy)           (2) 
        = 3/2(2Ku/Ms) (magnetocrystalline anisotropy)                     (3) 
        = 3/2(3λsσ/Ms) (magnetoelastic anisotropy)         (4) 
where Ku is the uniaxial magnetocrystalline anisotropy constant, Nb and Na are the 
demagnetizing factors perpendicular and parallel to the shape axis of rotational 
symmetry, λs is the isotropic magnetostriction, σ is the stress, and µ0 is the permeability 
of free space.  Crystals with ∆Bu > 0 are said to have positive uniaxial anisotropy, while 
samples with ∆Bu < 0 are said to have negative uniaxial anisotropy.  Examples of positive 
uniaxial anisotropy of the former are prolate spheroids, which have Nb > Na, minerals like 
goethite, which have uniaxial magnetocrystalline anisotropy with Ku > 0, and minerals 
like hematite, which are dominated by magnetostriction for which λs > 0. Examples of 
negative uniaxial anisotropy are oblate spheroids, which have Nb < Na.   It is easy to show, 
following similar calculations for cubic anisotropy [7, 9], that Brfe ~ Bmax - 1/3∆Ba (for 
positive uniaxial anisotropy) and Brfe ~ Bmax - 2/3∆Ba (negative uniaxial anisotropy) 
which again permits estimation of the true g-factors.  These relations imply that uniaxial 
samples with positive (negative) uniaxial anisotropy have A < 1 (A > 1) (for a graphical 
visualization of this, see [1, 10-12]).    
The minimum linewidth of magnetite and maghemite crystals will be obtained for 
non-interacting equant grains that only have magnetocrystalline anisotropy.  In this case, 
using equation (1) and Ms and K1 from [8], magnetite will have ∆B ~ ∆Ba ~ 94 mT and 
 4
maghemite will have ∆Ba ~ 40 mT.  Each of these equations will underestimates the true 
linewidths for crystal assemblages that are magnetostatically interacting and/or have 
multiple forms of anisotropy.  We also note that the above equations are only strictly true 
for very weak anisotropy: samples with large enough absolute anisotropy (regardless of 
its sign and angular dependence) will show enhanced secondary absorption peaks on the 
low-field side of the mineral’s g-factor because the anisotropy will divert the crystal 
moments away from the applied field [1, 6, 10-14]. 
 
2. FMR theory and modeling for uniaxial anisotropy.  Surig et al. [13, 14] directly 
computed the FMR spectra of polycrystalline materials with positive and negative 
uniaxial anisotropy for a wide range of saturation magnetization values.  Their results 
show how the FMR spectra of minerals with positive (negative) uniaxial anisotropy have 
A > 1 (A < 1) (see above).  Elongate magnetite crystals, which have Ms = 480 kA m-1 
would have an FMR spectrum intermediate between curves B and C of Fig. 3 of [14].  
This shows how magnetites with prolate shapes (oblate shapes) should have geff slightly 
less than 2.12 (greater than 2.12), A < 1 (A > 1) and might also have a low-field 
absorption peak in the derivative spectrum. Elongate magnetites should also have ∆B up 
to three times that of magnetite with only magnetocrystalline anisotropy.   
The extended low-field (high-field) absorption property of materials with positive 
(negative) uniaxial anisotropy can also be directly observed from the resonance condition 
[15] 
2
rfe
2
s0
2
bas0babb0,
rfes0baa0,
)()(
4
1)(
2
1
)(
BMNNMNNNB
BMNNB
+−+

 +−=
+−=
µµ
µ
                    (5) 
where B0,a and B0,b are, respectively, the resonance field for a single uniaxial crystal with 
the applied field parallel and perpendicular to the axis of symmetry (e.g., axis elongation 
or flattening).  For the powder pattern of elongate magnetite ellipsoids with axial ratios of 
0.1, using the ellipsoidal demagnetizing factors as given by [16] we find from equation 
(5) that B0,a = 19 mT and B0,b= 490 mT.  This predicts that ∆B ~ B0,b - B0,a = 470 mT and 
A ~ (B0,b - Brfe)/(Brfe - B0,a) = 0.6, in good agreement with equation (2) which gives ∆B ~ 
 5
420 mT. This demonstrates why direct numerical modeling [13, 14] gives A < 1 for these 
types of positive uniaxial materials. 
  
D. Dependence of FMR on crystal size 
FMR spectra also give information on the size of the ferromagnetic crystals.  Compared 
to single domain assemblages of the same mineralogy, superparamagnetic crystals of will 
have narrower linewidths (small ∆B), nearly symmetric absorption (A ~ 1), and geff closer 
to the mineral’s g-factor [17, 18].  Superparamagnetic assemblages of magnetites will 
show broader, more asymmetric linewidths (e.g, larger ∆B and A farther from 1) and 
higher geff at 77 K compared to room temperature (e.g., [19, 20]).  However, because 
FMR absorption and linewidth are smooth functions of particle size with no 
discontinuities across the single domain superparamagnetic boundary, there is no concept 
of “blocking temperature” in FMR [9].  Multidomain assemblages will typically have 
large ∆B [7] with very large geff (typically well above the free electron value of 2), A >1, 
and a high-field absorption peak near the field value at which saturation occurs (for 
equidimensional crystals, this would be at ~1/3µ0Ms, which is 200 mT and 160 mT for 
magnetite and maghemite, respectively) [9, 21].  The large geff and A > 1 of these coarse 
grained samples is a natural geometric consequence of their large ∆B: because the first 
derivative of the absorption with respect to field is an odd function of the field (see [22]), 
samples with large linewidths have enhanced low-field absorption due to absorption by 
crystals magnetized in directions different from that of the applied field.  
 
E. Dependence of FMR on composition 
Measurements of the sign and magnitude and angular dependence of the anisotropy (see 
Section A) can be used as compositional indicator.  This can be enhanced by FMR 
measurements at low temperatures, which can identify remanence transitions and 
behavior characteristic of mineralogy and stoichiometry as in standard low-temperature 
magnetometry [7, 23].   
Paramagnetic ions can be rapidly distinguished from ferromagnets by their 
characteristic fine and hyperfine structure and characteristic g-factors [24-26].   Their g-
factors are usually temperature-independent while their absorption intensity is inversely 
 6
proportional to temperature [7, 23, 27].   For ferromagnetic minerals, geff, ∆B, and the 
line intensity each have a wide variety of dependencies on temperature by which these 
minerals can often be distinguished [9, 17, 23, 28].  For instance, magnetite has a 
characteristic discontinuous change in its FMR spectrum when cooled or warmed across 
its ~125 K Verwey transition. 
 
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Ferromagnetic resonance and low-temperature magnetic tests for biogenic magnetite

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Ferromagnetic resonance and low-temperature magnetic tests for biogenic magnetite

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