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Article
Volume 11, Number 8
4 August 2010
Q08Z19, doi:10.1029/2010GC003182
ISSN: 1525‐2027
Quantifying the concentration of ferrimagnetic particles
in sediments using rock magnetic methods
Ioan Lascu, Subir K. Banerjee, and Thelma S. Berquó
Institute for Rock Magnetism, Department of Geology and Geophysics, University of Minnesota,
Twin Cities, 310 Pillsbury Drive SE, Minneapolis, Minnesota 55455, USA (lascu003@umn.edu)
[1]We have developed a quantification method that uses mainly room temperature rock magnetic measure-
ments to calculate concentrations of ferrimagnetic particles in sediments. Our method uses saturation mag-
netization (M
s
) as a total ferrimagnetic concentration proxy, the saturation remanence ratio (M
rs
/M
s
)asa
magnetic grain‐size proxy, the anhysteretic remanence ratio (c
a
/M
rs
)toestimateinter‐particle magneto-
static interactions, and the normalized susceptibility of the ferrimagnetic fraction (c
f
/M
s
) to calculate the
proportion of ultrafine, superparamagnetic particles. This approach eliminates the effect of dilution of
the magnetic properties by weakly magnetic matter, and allows the calculation of direct concentrations
(or fluxes for dated sedimentary profiles) of constituent ferrimagnetic components. We test our method
on a short sediment core from an urban Minnesota lake, for which we calculate ferrimagnetic fluxes of four
magnetic components, and compare their pre‐and post‐European settlement values. Our quantification
technique can be applied for reconstructing past environmental changes in a range of sedimentary environ-
ments, and is particularly useful for large sets of samples, where detailed magnetic unmixing methods are
unfeasible due to time or instrument constraints.
Components: 13,700 words, 7 figures, 2 tables.
Keywords: quantification; rock magnetism; sediments; magnetic unmixing; magnetostatic interactions.
Index Terms: 1512 Geomagnetism and Paleomagnetism: Environmental magnetism; 1540 Geomagnetism and
Paleomagnetism: Rock and mineral magnetism; 1594 Geomagnetism and Paleomagnetism: Instruments and techniques.
Received 26 April 2010; Revised 1 June 2010; Accepted 9 June 2010; Published 4 August 2010.
Lascu, I., S. K. Banerjee, and T. S. Berquó (2010), Quantifying the concentration of ferrimagnetic particles in sediments using
rock magnetic methods, Geochem. Geophys. Geosyst.,11, Q08Z19, doi:10.1029/2010GC003182.
Theme: Magnetism From Atomic to Planetary Scales: Physical Principles and
Interdisciplinary Applications in Geoscience
Guest Editors: J. Feinberg, F. Florindo, B. Moskowitz, and A. P. Roberts
1. Introduction
[2]Iron‐bearing minerals with characteristic mag-
netic properties are ubiquitous in sedimentary
environments, and are used in environmental
magnetism studies as indicators of past climatic
conditions [e.g., Geiss and Banerjee, 1997, 1999;
Dearing, 1999a; Paasche et al., 2004; Zillén and
Snowball, 2009; Haltia‐Hovi et al., 2010], soil
and vegetation development [e.g., Oldfield et al.,
2003; Geiss et al., 2003, 2008], erosion [e.g.,
Rosenbaum et al., 1996; van der Post et al., 1997;
Copyright 2010 by the American Geophysical Union 1 of 22
Reynolds et al., 2004; Rosenbaum and Reynolds,
2004a, 2004b], water and sediment (bio)geochem-
istry [e.g., Snowball, 1994; Snowball et al., 2002;
Kim et al., 2005], and diagenetic conditions [e.g.,
Peck and King, 1996; Dearing et al., 1998; Gibbs‐
Eggar et al., 1999; Snowball et al., 1999; Demory
et al., 2005; Ortega et al., 2006; Larrasoaña et al.,
2007]. Natural samples contain mixtures of mag-
netic phases of different origins, mineralogical
compositions, and grain sizes. The most important
magnetic carriers are ferrimagnetic minerals, such
as magnetite (Fe
3
O
4
), maghemite (g‐Fe
2
O
3
), and
greigite (Fe
3
S
4
). Antiferromagnetic minerals like
hematite (a‐Fe
2
O
3
) and goethite (a‐FeO[OH])
have weak ferromagnetism, and contribute signifi-
cantly to the total magnetization of sediments only
if the total antiferromagnetic material represents at
least 90% (by mass) of the ordered magnetic phases
[Frank and Nowaczyk, 2008]. Bulk magnetic
properties such as mass susceptibility (c), isother-
mal remanent magnetization (IRM), anhysteretic
remanent magnetization (ARM), saturation mag-
netization (M
s
), saturation remanence (M
rs
), coer-
civity (H
c
), remanent coercivity (H
cr
), and a
number of their interparametric ratios are used to
characterize magnetic mineral assemblages in terms
of concentration, mineralogy, and grain size.
Magnetic mineral assemblage characteristics are
used in turn to make inferences about the processes
that lead to the accumulation of these minerals in
the depositional environment [Evans and Heller,
2003].
[3]Magnetic components (ensemble of particles
with common origin, biogeochemical history, and a
characteristic array of magnetic properties [Egli,
2004]) have been successfully modeled using
magnetization spectrum methods, which exploit the
subtleties of entire magnetization curves, reducing
the non‐uniqueness of a bulk parameter approach
[e.g., Robertson and France, 1994; Roberts et al.,
2000; Carter‐Stiglitz et al., 2001; Kruiver et al.,
2001; Heslop et al., 2002; Egli, 2003, 2004,
2006a; Egli et al., 2010]. However, the relatively
involved methodology inherent to spectral techni-
ques poses the disadvantage of only being able to
process a limited number of samples in a given
time span. On the other hand, bulk magnetic
measurements are fast, inexpensive, non‐destructive,
and extremely sensitive to very small quantities of
magnetic material, but they sometimes lack the
ability to distinguish between different sedimentary
magnetic components. For the analysis of large
numbers of samples, such as typically encountered
in long core studies, a technique that makes use of a
limited number of spectral analyses on selected
samples to calibrate numerous bulk measurements
is particularly desirable.
[4]Several attempts have been made to quantify
the concentration of various magnetic components
using bulk parameters like c, ARM, or IRM. Lees
[1997] has quantified the concentration of magnetic
components in synthetic mixtures of up to six
sedimentary sources by using linear modeling
techniques, and has found cto be the most reliable
concentration‐dependent parameter in case of
complex mixtures. Large errors were encountered
in the deconvolution of mixtures with a large
number of components, implying that linearity
does not apply for complex source mixing due to
the extreme heterogeneity of considered samples,
in addition to effects of magnetic viscosity of ma-
terials, interactions between particles, and inter‐
instrument calibration issues. In an attempt to
unmix bulk cmeasurements, von Dobeneck [1998]
introduced the concept of partial susceptibilities,
which states that the bulk susceptibility of a sample
is the sum of the susceptibilities of its constituent
components. The method was subsequently devel-
oped in studies by Frederichs et al. [1999], Xie et
al. [1999], Bleil and von Dobeneck [2004], Funk
et al. [2004], and Xie et al. [2009]. The contribu-
tion of individual components to the bulk suscep-
tibility is calculated via multiple regression,
whereby each partial susceptibility term is related
by a proportionality factor to the value of a mag-
netic parameter that is diagnostic for that particular
component (e.g., ARM for fine‐grained particles).
The partial susceptibility method assumes linear
proportionality between the susceptibility of the
individual component and the magnetic parameter
used as diagnostic, an assumption that does not
always hold true. The method offers the advantage
of reducing everything to susceptibilities, and the
potential to eliminate the diagnostic parameter mea-
surements if an empirical proportionality factor is
universally found for every component considered
in the model.
[5]The property of linear additivity of individual
components that contribute toward a remanence
parameter was used by Dunlop [2002] in devel-
oping theoretical mixing curves of simple two‐
component numerical mixtures, based on hysteresis
properties. Linear additivity of remanence was
applied by Geiss and Zanner [2006] to understand
pedogenic enhancement in loessic soils in North
American Great Plains. Bulk ARM and IRM
measurements were used to quantify magnetite
formed as a result of biogeochemical processes
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occurring in the topsoil. The pedogenic fraction
obtained via this binary mixing model was found to
underestimate calculations based on hysteresis
parameter modeling, and coercivity spectra de-
convolution. One reason for this discrepancy is
their ARM‐IRM model ignores the effects of
magnetostatic interactions between particles in the
sediment matrix, which tend to lower ARM values
even for low ferrimagnetic concentrations [Egli,
2006b]. The decrease of ARM values as a result
of inter‐particle interactions was investigated by
Yamazaki [2008], who uses first‐order reversal
curve (FORC) diagrams in addition to bulk ARM
and IRM measurements, and coercivity analysis of
IRM acquisition curves to unmix sedimentary
components in North Pacific sediment cores. The
FORC analysis reveals the presence of a fine‐
grained non‐interacting component, a fine‐grained
interacting component, and a coarse‐grained
background component. The concentration of the
interacting particles is inversely related to the ARM
ratio (ARM normalized by saturation IRM), indi-
cating that interactions between particles are an
important ARM‐controlling factor. This is highly
significant because the ARM ratio is widely used as
a grain‐size indicator in enviromagnetic studies.
Since ARM is sensitive to magnetostatic interac-
tions between proximal particles, the ratio can be
artificially lowered if small particles occur in
clumps, as is the case of collapsed bacterial mag-
netite chains, or clusters of pedogenic magnetite
washed into a basin. Therefore, small‐scale varia-
tions in the ARM ratio could point to interactions
between particles rather than grain size changes,
potentially offering information about the packing
and arrangement of magnetic particles in the sedi-
ment matrix [Egli, 2006b; Kopp et al., 2006;
Yamazaki, 2008].
[6]In this paper we present a quantification method
that uses bulk rock magnetic measurements to
calculate mass fractions, mass per volume concen-
trations, and mass fluxes of ferrimagnetic particles
in sediments. Detailed rock magnetic and non‐
magnetic measurements are performed on represen-
tative samples to calibrate the modeling parameters.
The quantification method consists of three parts:
1) Calculation of total ferrimagnetic concentration
from in‐field magnetization parameters, 2) Model-
ing the remanence‐carrying fractions using rema-
nent magnetizations to gain information about
magnetic grain size and inter‐particle interactions;
this is tested on a selection of synthetic mixtures
of stable single domain (SD), pseudo single
domain (PSD), and multi‐domain (MD) magnetite
[Carter‐Stiglitz et al., 2001; Dunlop and Carter‐
Stiglitz, 2006], and 3) Calculation of the super-
paramagnetic (SP) fraction from ferrimagnetic
susceptibility and SP grain size distribution data.
The quantification method is applied to a short
sediment core from a Minnesota urban lake, but is
applicable to a range of environments, including
marine sediments, loess deposits, and soils.
2. Theoretical Considerations
2.1. Total Concentration of Ferrimagnetic
Material
[7]Magnetic susceptibility, remanent magnetiza-
tions (ARM and IRM), and saturation magnetiza-
tion are generally used to qualitatively assess the
amount of magnetic material present in sediments.
Saturation magnetization is an intrinsic property of
magnetic materials, so should theoretically offer
the most reliable concentration estimates. Suscep-
tibility‐based concentration estimates are wide-
spread due to low cost and ease of measurement,
but require information about magnetic mineral-
ogy, grain size, and grain shape. Remanence
measurements are accurate as concentration proxies
only when magnetic composition is uniform (with
respect to mineralogy and grain size) over the
sedimentary interval investigated, because of the
varying degree of remanence acquisition efficiency
for different categories of magnetic particles. In this
section we focus on cand M
s
, and discuss their use
as ferrimagnetic concentration proxies.
2.1.1. Magnetic Susceptibility as a
Ferrimagnetic Concentration Proxy
[8]Low‐field magnetic susceptibility (c
lf
) is the
most common magnetic property measured on
sediments, popularized by the use of multisensor
core loggers equipped with loop or point suscep-
tibility meters [Nowaczyk, 2001]. Large‐scale dril-
ling expeditions employ the use of core loggers to
measure unsplit sections of core immediately after
retrieval for initial characterization of the sedi-
ments. At this stage c
lf
is mainly used to strati-
graphically correlate between parallel cores from
the same basin, and to roughly estimate the con-
centration of magnetic minerals in the core sec-
tions. c
lf
is strongly controlled by the presence of
ferrimagnetic minerals, but this signature can be
diluted by contributions of diamagnetic, paramag-
netic, and antiferromagnetic materials [e.g.,
Dearing, 1999b]. Bulk c
lf
can be expressed as the
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sum of the magnetic contributions of all compo-
nents to the total susceptibility signal:
lf ¼X
n
i¼1
ifi;ð1Þ
where c
i
is the susceptibility of component i, and f
i
is the mass fraction of component i (Sf
i
= 1). This
expression equates to the partial susceptibilities
concept of von Dobeneck [1998], but expressed in
terms of fractions of pure substance susceptibilities.
Since the ferrimagnetic component exerts the major
control on c
lf
, its fraction (f
ferri
) is of interest for
calculating mass or volume based concentration
parameters. In order to determine f
ferri
, the contri-
bution of diluting sedimentary matrix must be
subtracted from the bulk value. Diamagnetic and
paramagnetic substances have weak suscept-
ibilities, but can amount to significant portions of
bulk c
lf
if they are present in abundance, as in the
case of water‐laden, organic, carbonate‐rich, or
siliciclastic sediments [Rochette, 1987]. Suscepti-
bility values for these substances are known from
experimental work (see compilations by Hunt et al.
[1995a] and Dearing [1999b]), and have average
values of ∼−9·10
−9
m
3
/kg for water and organic
matter, ∼−8·10
−9
m
3
/kg for calcite, ∼−6·10
−9
m
3
/kg
for feldspar and quartz, 0.1–7·10
−6
m
3
/kg for
paramagnetic and imperfect antiferromagnetic mi-
nerals. By comparison, ferrimagnetic mineral sus-
ceptibilities are on the order of 10
−4
‐10
−3
m
3
/kg.
Mass fractions f
i
can be obtained from geo-
chemical or mineralogical methods (e.g., loss on
ignition (LOI), X‐ray diffraction, etc.). After all
non‐ferrimagnetic contributions are determined and
subtracted from c
lf
, equation (1) is reduced to:
f¼fferriferri ;ð2Þ
where c
f
is the susceptibility corrected for non‐
ferrimagnetic contributions, and c
ferri
is the sus-
ceptibility of the ferrimagnetic component. Average
c
ferri
values are 0.2–1.2 · 10
−3
m
3
/kg for magnetite,
0.025–0.29 · 10
−3
m
3
/kg for titanomagnetite, 0.3–
0.5 · 10
−3
m
3
/kg for maghemite, and 0.026–0.194 ·
10
−3
m
3
/kg for greigite [Hunt et al., 1995a;
Dearing, 1999b; Peters and Dekkers, 2003]. For
SP grains these values are expected to be one order
of magnitude higher [Dunlop and Özdemir, 1997],
because they have very high intrinsic suscept-
ibilities, and are thermally unstable, thus being
easily and efficiently magnetized even in small
magnetic fields. They will dominate the c
ferri
signal
even when in low concentrations. The main chal-
lenge posed by the exercise of determining f
ferri
from c
f
is finding an appropriate value for c
ferri
,
which implies some a priori knowledge about the
ferrimagnetic mineralogy, grain size, and grain
shape. Alternatively, if f
ferri
can be determined from
measurements of saturation magnetization, c
ferri
can be calculated from equation (2). This scenario
is discussed below.
2.1.2. Saturation Magnetization as a
Ferrimagnetic Concentration Proxy
[9]Saturation magnetization M
s
is an intrinsic
property of a magnetic mineral, and provides a
more straightforward measure of f
ferri
than mag-
netic susceptibility. The only a priori information
necessary for f
ferri
calculation is knowledge of the
ferrimagnetic mineralogy. Ferrimagnetic mass
fraction is calculated as:
fferri ¼Ms
ferri
;ð3Þ
where bulk M
s
is obtained from hysteresis
measurements after correcting for high field non‐
ferrimagnetic contributions, and m
ferri
is the ferri-
magnetic saturation magnetization, which can be
written as a linear combination of the saturation
magnetizations of the ferrimagnetic constituents:
ferri ¼X
m
j¼1
pjj;ð4Þ
where p
j
is the fraction of total ferrimagnetic mass
represented by component j (Sp
j
= 1) and m
j
is its
intrinsic mass‐normalized saturation magnetiza-
tion. Ferrimagnetic mineral composition can be
determined either from magnetic or non‐magnetic
methods. Magnetic methods are based mainly on
thermal order‐disorder transitions (Curie or Néel
points) or spin reorientations and are semiquanti-
tative, while non‐magnetic methods, such as
Mössbauer spectroscopy and X‐ray diffraction on
magnetic extracts, permit a direct calculation of the
ferrimagnetic mineral fractions. The main ferri-
magnetic minerals found in lake and marine
sediments are magnetite (m
Mt
=92Am
2
/kg),
maghemite (m
Mh
=∼74.3 Am
2
/kg) [Dunlop and
Özdemir, 1997], and greigite (m
Gr
=∼59 Am
2
/kg)
[Chang et al., 2008]. Magnetite and maghemite are
by far the most common, so in the absence of
reliable methods of ferrimagnetic mineral determi-
nation, calculating concentrations both as magne-
tite and maghemite will set the concentration
interval boundaries, assuring accuracy of results,
although at the expense of reduced precision.
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[10]The slope correction applied to raw hysteresis
loop measurements also offers an alternative way
to determine the contribution of non‐ferrimagnetic
components to c
lf
, bypassing the need for sediment
composition information. The high field suscepti-
bility c
hf
is calculated from the slope of a loop at
magnetic fields larger than the saturating field,
which is typically a few hundred mT for important
ferrimagnets, and is equivalent to the sum of partial
susceptibilities of all non‐ferrimagnetic compo-
nents contributing of c
lf
. The ferrimagnetic con-
tribution to c
lf
can thus be expressed as:
f¼lf hf :ð5Þ
Having calculated f
ferri
and c
f
(from equations 3–5),
c
ferri
can now be obtained from equation (2). This
is done in order to calculate the SP particle fraction
contributing to the total ferrimagnetic concentration
(see section 2.3).
2.1.3. Expression of Total Ferrimagnetic
Concentration
[11]The fraction of ferrimagnetic material is in
effect a mass concentration, i.e., the mass ferri-
magnetic component of total sediment mass. Since
ferrimagnetic concentrations are on the order of
thousandths of the total sediment mass, it is more
convenient to express f
ferri
as a part per thousand
(ppt, mg/g, g/kg, etc.) concentration:
cferri ¼103fferri:ð6Þ
The concentration of ferrimagnetic minerals can
also be expressed as mass ferrimagnetic material
per unit volume sediment:
Cferri ¼fferri wet fsed ;ð7Þ
where C
ferri
is the total ferrimagnetic concentration
as mass per volume unit, r
wet
is the wet sediment
density, and f
sed
is the mass fraction sediment (i.e.,
the ratio of dry mass to wet mass). Wet sediment
density is a standard parameter measured during
initial core logging, but can also be calculated on
samples of known volume by dividing the wet
mass of a sample by its volume. If sample volume
is unknown, r
wet
can be obtained from composi-
tional analysis (e.g., LOI) as a sum of pure sub-
stance densities (e.g., 1000 kg/m
3
for water)
weighed by their respective mass fractions. C
ferri
is
of interest for calculating ferrimagnetic particle
fluxes in sediment cores with established chronol-
ogies. The mass flux of ferrimagnetic material F
ferri
to the sediment column is obtained from multiplying
C
ferri
by the sediment accumulation rate R
sed
(expressed in length units per time):
ferri ¼CferriRsed :ð8Þ
In order to separate the fluxes of various ferri-
magnetic components, an unmixing method is
necessary.
2.2. Concentration of Remanence‐Carrying
Ferrimagnetic Components
[12]In this section we present a three‐component
mixing model that makes use of bulk remanence
measurements to quantify the remanence‐carrying
fractions of f
ferri
. Unmixing models using either
hysteresis or bulk remanence parameters have been
used to analyze synthetic, natural, and numerical
mixtures of two components, and are based on the
linear additivity of remanence properties when the
mixture is monomineralic [Dunlop, 2002; Dunlop
and Carter‐Stiglitz, 2006; Geiss and Zanner,
2006]. The mixing model presented here com-
bines the remanence aspect of the hysteresis
approach of Dunlop [2002] and Dunlop and
Carter‐Stiglitz [2006] with the ARM‐IRM model-
ing of Geiss and Zanner [2006]. However, we use
the ARM ratio primarily to evaluate particle inter-
actions rather than grain size, essentially extending
two‐component models to mixtures of three end‐
members, here MD (including PSD), uniaxial non‐
interacting SD (UNISD) [Egli et al., 2010], and
interacting SD (ISD). Our model accounts for all
the remanence‐carrying contributors to f
ferri
, i.e.,
the non‐SP ferrimagnetic fraction.
[13]Bulk ARM and saturation IRM (or M
rs
) values
can be written as linear combinations of the ARM
and M
rs
values of the mixture end‐members. Since
the absolute remanence values of end‐member
components are not invariant, they are normalized
by M
s
(m
ferri
is constant across the mixture) in order
to obtain comparable ratios. The resulting system
of equations for the three‐component (MD,
UNISD, and ISD) mixing model is:
Mrs
Ms
bulk
¼X
3
i¼1
gi
Mrs
Ms
i
a
Ms
bulk
¼X
3
i¼1
gi
a
Ms
i
X
3
i¼1
gi¼1
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
;ð9Þ
where c
a
is the ARM susceptibility (ARM nor-
malized by acquisition bias field), (M
rs
/M
s
)
bulk
and
(c
a
/M
s
)
bulk
are ratios obtained from measured
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parameters, (M
rs
/M
s
)
i
and (c
a
/M
s
)
i
are the respec-
tive ratios of end‐member i, and g
i
is the fraction of
component i. The system is solved for g
i
. Since
c
a
/M
s
is not a commonly used ratio, the second
equation in (9) can be divided by the first in order to
obtain the expression for the ARM ratio (c
a
/M
rs
).
The system then becomes:
Mrs
Ms
bulk
¼X
3
i¼1
gi
Mrs
Ms
i
a
Mrs
bulk
¼X
3
i¼1
gi
a
Ms
i
X
3
i¼1
gi
Mrs
Ms
i
X
3
i¼1
gi¼1
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
>
:
:ð10Þ
Note that ARM and M
rs
combine in a nonlinear
fashion. Theoretical values for M
rs
/M
s
and c
a
/M
rs
can be predicted by varying the end‐member frac-
tions g
i
over the interval [0, 1] with the third con-
dition of the system always satisfied. The model
ratio values can be plotted in M
rs
/M
s
versus c
a
/M
rs
scatter diagrams at regular g
i
intervals (e.g., 0.1) as
“mixing grids,”and overlain with the experimental
values for comparison. The mixing grids are
equivalent to ternary diagrams in g
i
coordinates.
The choice of end‐member ratios will be discussed
in section 4.
2.3. Concentration of Superparamagnetic
Particles
[14]In order to calculate the absolute concentra-
tions of the remanence‐carrying components, the
SP concentration must be first subtracted from the
total ferrimagnetic concentration. Rearranging
equation (2) to solve for c
ferri
, and substituting f
ferri
with M
s
/m
ferri
(equation 3), we find that c
ferri
is
nothing but a multiple of c
f
/M
s
, where the multi-
plier is the ferrimagnetic saturation m
ferri
. The ratio
c
f
/M
s
has been used in a quantitative way to
express fluctuations in high susceptibility SP grains
relative to a non‐SP baseline for Chinese loess
plateau deposits [Hunt et al., 1995b]. SP con-
centrations obtained this way were found to be in
good agreement with concentrations calculated via
the more reliable thermal demagnetization of
low temperature remanence method [Hunt and
Banerjee, 1992], and are much easier to perform.
The non‐SP susceptibility (c
nonSP
), carried by SD
and MD grains, has values an order of magnitude
lower compared to the typical susceptibility of SP
particles (c
SP
). c
ferri
can be written as the linear
combination of c
SP
and c
nonSP
, an expression
which can be rearranged to solve for the SP fraction
(f
SP
):
fSP ¼ferri nonSP
SP nonSP
:ð11Þ
c
nonSP
is typically characterized by a narrow range
of values (0.4–0.8 · 10
−3
m
3
/kg for magnetite
[Dunlop and Özdemir, 1997]), while c
SP
can be
determined using information about the SP grain
size distribution. For very small particles (<10 nm)
the relationship between c
SP
and particle volume is
linear at room temperature, according to Néel [1949]
theory of thermally activated magnetization. Larger
SP particles (10–20 nm) exhibit frequency depen-
dence of susceptibility at room temperature,
because their magnetization relaxation times are
comparable to the observation times of the exper-
iment. Worm [1998] has investigated the nature of
the SP‐SD transition and the behavior of the
magnetic susceptibility across this boundary. The
relationship between c
SP
and particle volume is no
longer linear, and the transition to SD suscept-
ibilities is gradual, especially if the particles are
characterized by a distribution of coercivities [see
Worm, 1998, Figure 2]. In Worm’s [1998] approach,
frequency‐dependent susceptibility measurements
across a range of temperatures are necessary to
estimate the SP particle size distribution, and thus
c
SP
(which for magnetite is found to have values of
up to 8 · 10
−3
m
3
/kg). The choice of c
SP
depends
from case to case and will be discussed in context
in Section 4.
3. Materials and Methods
3.1. Samples and Non‐magnetic
Treatments
[15]The synthetic mixtures used for testing our
remanence model (Section 2.2) have been prepared
by Carter‐Stiglitz et al. [2001] by combining an
SD end‐member with PSD and MD end‐members
in incremental mass fractions. The SD particles are
freeze‐dried cells of vibroid magnetotactic bacte-
rium MV1, which produces prismatic magnetite
magnetosomes with mean volumes of 0.65 · 10
−22
m
3
and aspect ratios of 1.5, aligned in linear chains
(samples from the same batches have also been
used by Moskowitz et al. [1993]). The PSD and
MD phases are Wright Company magnetites 3006
and 041183 with grain sizes of 1.06 ± 0.71 mm and
18.3 ± 12 mm respectively [Yu et al., 2002]. The
non‐SD component was first dispersed in CaF
2
using a blender; the MV1 freeze‐dried cells were
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then added in the desired mixing proportions, and
gently mixed together using a mortar and pestle
[Carter‐Stiglitz et al., 2001].
[16]The natural samples used in this study are
lacustrine sediments from Brownie Lake, a small
urban water body in Minneapolis, Minnesota.
Brownie Lake has a surface area of ∼5·10
4
m
2
and
a maximum depth of 14.1 m (5.6% relative depth).
The lake has been meromictic (permanently strati-
fied) since the lake level was artificially lowered by
∼3 m in 1917 [Swain, 1984; Tracey et al., 1996]. A
139 cm core was retrieved in 2007 from 13 m water
depth, using a drive‐rod surface corer. The core
was logged and described at the University of
Minnesota Limnological Research Center, and
sampled at a resolution of 1 cm. Aliquots of ∼1cm
3
were used for LOI analysis, according to the pro-
cedure described by Dean [1974] and Heirietal.
[2001]. Separate subsamples were freeze‐dried,
weighed, and packed in plastic boxes for magnetic
analyses. On 15 September 2009 a water column
profile of dissolved oxygen (DO) was recorded
using a Hydrolab multisensor probe. Water sam-
ples were collected using a Van Dorn sampler at a
resolution of 0.5–1 m across the oxic‐anoxic
interface (OAI) and 1–1.5 m below the OAI.
Between 150 and 200 ml of each sample were
filtered in the laboratory using 0.1 mm filters,
which were then frozen and packed in plastic
straws. A surface sediment (top 10–15 cm of the
sediment column) sample was collected on the
same date from a water depth of 13.5 m using an
Ekman dredge. A subsample was disaggregated
with sodium hexametaphosphate (0.5 g to 100 ml
sediment slurry) and circulated through an in‐house
magnetic separator. The magnetic fraction was
extracted using a high‐gradient permanent magnet,
collected on a daily basis for a two‐week period,
and stored in isopropanol at 4°C. The extract was
then dried at 25°C for 24 h, and used for room
temperature
57
Fe Mössbauer spectroscopy. Möss-
bauer analysis was performed with a conventional
constant‐acceleration spectrometer in transmission
geometry with a source of
57
Co in an Rh matrix.
Hyperfine parameters such as magnetic hyperfine
field (B
HF
), isomer shift (IS) and quadrupole shift
(QS) have been determined by NORMOS program
[Brand, 1987], and a‐Fe at room temperature was
used to calibrate isomer shifts and velocity scale.
3.2. Magnetic Measurements
[17]All magnetic measurements were performed at
the University of Minnesota Institute for Rock
Magnetism. Magnetic susceptibility was measured
on a Kappabridge KLY‐2 susceptometer operating
at a frequency of 920 Hz. A D‐Tech 2000
demagnetizer was used for ARM acquisition,
which was imparted in a 0.1 mT steady field su-
perimposed on an AF field decaying from a peak
value of 200 mT, with a rate of 5 mT per half cycle.
Stepwise alternating frequency (AF) demagnetiza-
tion of the ARM was performed on the filtered
water samples using an automated 2G Enterprises
superconducting quantum interference device
(SQUID) magnetometer, with peak fields increas-
ing from 0.5 to 170 mT. The demagnetization
procedure contains one hundred measurement steps
spaced on a logarithmic scale. IRM was imparted
on the same samples by pulsing the samples in a
200 mT field using a 2G core pulse magnetizer.
This was done two times in order to remove any
viscous effects. The IRM was demagnetized fol-
lowing the same procedure as for the ARM. For
coercivity component analysis, first derivatives of
the demagnetization curves were fitted with
skewed generalized Gaussian distributions using
MAG‐MIX [Egli, 2003]. Hysteresis loops were
measured on a Princeton Measurements vibrating
sample magnetometer using a maximum applied
field of 1 T. The loop slopes at high fields (>0.7 T)
were used to correct raw M
s
values, and to calcu-
late the contribution of non‐ferrimagnetic minerals
to low field susceptibility. A Quantum Design
magnetic properties measurement system (MPMS‐2)
was used to perform low temperature demagneti-
zation experiments on representative lake sediment
samples. Thermal demagnetization of saturation
IRM (SIRM) acquired at 10 K in a 2.5 T field after
cooling the sample in zero magnetic field (the
so‐called ZFC treatment) was measured from 10 K
to room temperature at 5 K intervals. Room tem-
perature SIRM imparted in a 2.5 T field was par-
tially decayed by cooling the sample to 10 K
and rewarming it back to 300 K. Measurements
were performed in zero field at 5 K intervals. The
MPMS was also used to measure susceptibility as a
function of temperature and frequency on the
selected lake samples. AC susceptibility was
measured in 10 K steps from 10 to 300 K at fre-
quencies of 1, 10, and 100 Hz.
4. Results and Discussion
4.1. Synthetic Mixtures
[18]We use the synthetic samples of known end‐
member proportions to test the validity of our
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mixing model defined by system (9). The M
rs
/M
s
and c
a
/M
rs
values of the SD‐MD and SD‐PSD
mixtures are plotted in Figure 1a, together with
theoretical values for mixture bulk ratios deter-
mined from varying g
i
in (10). The measured values
fall on the PSD‐SD and MD‐SD mixing lines (i.e.,
two‐component mixtures; g
3
= 0), where the SD
end‐member ratio values are M
rs
/M
s
= 0.498, and
c
a
/M
rs
= 1.6 · 10
−3
m/A. For comparison,
Moskowitz et al. [1993] measured ARM ratios on
freeze‐dried MV1 cells and obtained values of
1.8–2.1 · 10
−3
m/A, while Kopp et al. [2006] report
ARM ratios of 1.59–1.79 · 10
−3
m/A for intact and
treated (with sodium dodecyl sulfate and/or ultra-
sonication followed by dilution in sucrose) freeze‐
dried MV1 cells. Moskowitz et al. [1993] have also
performed ARM acquisition experiments on wet
MV1 cell suspensions fixed with 1% glutaralde-
hyde, and obtained ARM ratio values of 3.1–3.5 ·
10
−3
m/A. Fragile bacterial cell membranes must be
partially ruptured or destroyed in the process of
freeze drying, which involves freezing the sample
and extracting the water fraction by sublimation
in vacuum. The partial destruction of the cell
Figure 1. (a) Crossplot of M
rs
/M
s
versus c
a
/M
rs
for MD‐SD (diamonds) and PSD‐SD (circles) mixtures. Number
next to each symbol represents fraction SD component added to mixture. Mixing lines (dashed) for theoretical mix-
tures of two end‐members were calculated using a nil fraction for the third component in system (10). The symbols on
the mixing lines represent theoretical values of M
rs
/M
s
and c
a
/M
rs
calculated at fraction increments of 0.1. The
continuous lines are outer contours of mixing grids calculated for three end‐members, where the SD component was
subdivided into UNISD and ISD (see text for discussion of end‐member ratios). (b) Ternary diagram of calculated
fractions for each component (UNISD, ISD, and MD or PSD) of the synthetic mixtures, according to the three end‐
member mixing model (g
i
are solutions to the system of equations). Shaded area is the interval 60–75% interacting
component in a ISD‐UNISD mixture. (c) Inverted fractions of end‐members UNISD, ISD, and MD (left) or PSD
(right) versus fractions SD (top) and non‐SD (bottom) added to each mixture.
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membranes results in magnetosome chain clump-
ing, which explains the lower ARM ratios of
freeze‐dried samples as the effect of interactions
between the disturbed magnetosomes. Transmis-
sion electron microscope (TEM) analysis of the
untreated, freeze‐dried MV1 samples of Kopp et al.
[2006] reveals that only about 10% of the magne-
tosomes are isolated from other crystals and chains,
while the bulk of the chains are either in side‐to‐
side arrangements, or collapsed into loop config-
urations [Kopp et al., 2006, Figure 2a]. Given the
ARM ratio value of 1.6 · 10
−3
m/A for the SD end‐
member component in our mixtures, we conclude
that the SD end‐member physically added to the
mixtures is in fact a combination of non‐interacting
and interacting particles and chains, which means
the synthetic samples can be modeled as mixtures
of three components.
[19]We first assign values to the remanence ratio
(M
rs
/M
s
) and ARM ratio of the non‐interacting SD
end‐member. For magnetite, M
rs
/M
s
has a value of
0.5 by definition of randomly oriented UNISD
particles [Stoner and Wohlfarth, 1948]. The deter-
mination of the value for the ARM ratio is not as
clear‐cut. Egli and Lowrie [2002] have developed
an analytical solution for the ARM of assemblages
of UNISD particles, and have found that the ARM
ratio of UNISD grains characterized by uniform
rotation depends chiefly on grain size and grain
shape, and only weakly on microcoercivity. They
calculate a maximum c
a
/M
rs
value of 3.7 · 10
−3
m/A
for prismatic crystals with volumes of 1.25–2.2 ·
10
−22
m
3
, and aspect (length to width) ratios of
1.43–2.5 [see Egli and Lowrie, 2002, Figure 11c].
Mean volumes of 0.65 · 10
−22
m
3
and aspect ratios
of 1.5 (as is the case with our MV1 samples) yield
ARM ratios of ∼2·10
−3
m/A according to the Egli
and Lowrie [2002] model, and yet c
a
/M
rs
values
obtained from wet suspensions of the same batches
of particles used in this study [Moskowitz et al.,
1993] are close to the maximum values predicted
by theory. This discrepancy can be explained by
the fact that Egli and Lowrie [2002] model ran-
domly oriented non‐interacting isolated particles,
and not magnetosome chains. The arrangement of
particles in linear chains should have the same
effect as particle elongation, namely to increase
dipole moment and coercivity. The increase in
chain magnetic moment would lead to a higher
chain ARM ratio than that of its isolated magne-
tosomes. Therefore having a UNISD end‐member
with a c
a
/M
rs
value of 3.7 · 10
−3
m/A is not an
unreasonable assumption.
[20]The ISD end‐member ratios (M
rs
/M
s
= 0.497
and c
a
/M
rs
= 0.47 · 10
−3
m/A) were determined so
that a) M
rs
/M
s
of the 100% SD mixture would fall
on the ISD‐UNISD mixing line; b) the correlation
between the (non) SD fraction added to the mixture
and the inverted (non) SD fraction obtained from
the solution to system (9) approaches a 1:1 rela-
tionship (i.e., the slope of a linear fit to the data is
close to 1); and c) Pearson’s correlation coefficient
R of the fits for each mixture is maximized (R =
0.999, Figure 1c). The ARM ratio of the ISD end‐
member is close to the value of 0.41 · 10
−3
m/A
measured by Kopp et al. [2006] on ultrasonicated
MV1 cells diluted at 1 ppt in sucrose (their sample
V2a). The ultrasonic treatment destroys the bacte-
rial cell membrane but keeps the magnetosome
organelles intact, while the dilution prevents the
particles from clumping. TEM images of V2a show
collapsed chains throughout, but there are no major
magnetosome clumps, and some of the particles
remain isolated [Kopp et al., 2006, Figure 2b].
According to the calculations of Egli [2006b] this
corresponds to an average spacing of three particle
diameters. The SD component of our mixtures is
therefore a combination of intact chains and iso-
lated magnetosomes (the UNISD end‐member),
and collapsed chains of particles that still preserve
their magnetosome membranes (the ISD end‐
member). The mixing grids between the three end‐
members are calculated using system (10), but we
plot only the outer contours of these grids (con-
tinuous lines Figure 1a) in order not to unneces-
sarily clutter the diagram. For reference, a similar
mixing grid, calculated at fraction increments of
0.1, is plotted in Figure 5a. We find that the ISD
component in our synthetic samples comprises 60–
75% of the total SD grains in the mixtures (shaded
area in Figure 1b), compared to the 90% visual
estimate of Kopp et al. [2006] from TEM analysis
of samples with equivalent ARM ratios.
4.2. Lake Sediments
4.2.1. Sedimentary Units and Chronology
[21]European settlement in the Brownie Lake area
began shortly after 1850. In the core it is expressed
as a change in sedimentary characteristics at a
depth of 65 cm, marking the boundary between the
post‐settlement sedimentary succession (Unit 1)
and the pre‐settlement sediments (Unit 2). Unit 1
(0–65 cm; ca. 1850‐present) is a laminated clayey
silt with authigenic calcite and diatoms. The lami-
nae are discontinuous, and of variable thickness of
up to 0.5 cm. Organic matter (mostly sapropel) and
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carbonate contents each average between 10 and
20% of the dry sedimentary matter. A tan sandy
layer that occurs at 50 cm marks an artificial low-
ering of the water level in 1917, the year a canal
connecting Brownie Lake with Cedar Lake to the
south was completed. Unit 2 (65–140 cm; <1850)
is a dark brown, massive, partly humic peat com-
posed of terrestrial mosses and aquatic plants.
Organic matter fluctuates between 30 and 60%,
while carbonate content is constant at ∼5%. The
chronology of the Brownie Lake core is based on
the correlation with the
210
Pb dated core of Swain
[1984]. The correlation is drawn from organic
matter concentration variations, and is aided by the
recognition of marker horizons such as the 1917
sand lens.
4.2.2. Room Temperature Magnetic Properties
[22]Sediment‐magnetic properties of the Brownie
Lake core are presented in Figure 2, and the mean
(m) and standard deviation (s) of each parameter
are listed for both sedimentary units in Table 1. The
standard deviation was calculated for the detrended
magnetic parameters, in order to remove variability
introduced by long‐term shifts in mean. In Table 1
is also computed the coefficient of variation (CV =
s/m) for each magnetic parameter within a sedi-
mentary unit. The concentration‐dependent para-
Figure 2. Bulk magnetic properties of the Brownie Lake sediment core: ARM susceptibility c
a
, low‐field suscep-
tibility c
lf
, saturation remanence M
rs
, saturation magnetization M
s
, ARM ratio c
a
/M
rs
, remanence ratio M
rs
/M
s
, and
c
f
/M
s
. The magnetic parameters define two sediment‐magnetic units (separated by dashed line): Unit 1 (1850‐present)
and Unit 2 (<1850).
Table 1. Mean, Standard Deviation, and Coefficient of
Variation Values for the Magnetic Properties of Brownie
Lake Sediment Units
a
Magnetic Parameter
Unit 1 Unit 2
msCV msCV
c
lf
(10
−7
m
3
/kg) 8.95 2.52 0.28 8.96 1.67 0.19
c
a
(10
−5
m
3
/kg) 0.71 0.2 0.28 3.32 0.7 0.21
M
rs
(10
−3
Am
2
/kg) 15.6 4.8 0.31 21.5 4.4 0.2
M
s
(10
−3
Am
2
/kg) 96.7 34.4 0.36 69.7 13.9 0.2
c
a
/M
rs
(10
−3
m/A) 0.48 0.15 0.31 1.71 0.18 0.1
M
rs
/M
s
0.16 0.02 0.1 0.31 0.02 0.06
c
f
/M
s
(10
−5
m/A) 0.87 0.06 0.07 1.16 0.11 0.09
a
Here, m is the mean, sis the standard deviation, and CV = s/mis
the coefficient of variation. Standard deviations are calculated after
subtracting the effect of any long‐term trends on the magnetic
parameters. CV is a unitless measure.
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meters c
lf
,c
a
,M
rs
, and M
s
show higher variability
in Unit 1 compared to Unit 2 (higher CVs), and a
general increase in values with the decrease in
depth in core over the past 150 years. In Unit 2 the
concentration‐dependent parameters exhibit a
larger shift in mean to lower values, but the de-
trended variance is lower, indicating a steady
decrease in concentration with time, up to the
European settlement horizon. The concentration‐
independent magnetic parameters M
rs
/M
s
,c
a
/M
rs
,
and c
f
/M
s
have weak increasing trends with
decreasing depth in Unit 1. In Unit 2 M
rs
/M
s
and
c
a
/M
rs
have weak decreasing trends and lower
variability than in Unit 1 (lower CV values), while
c
f
/M
s
has a weak increasing trend and slightly
higher variability.
4.2.3. Suspended Sediments
[23]ARM and IRM profiles of the water filtrates
are shown in Figure 3a, along with the DO profile.
Oxygen concentrations are close to saturation va-
lues in the epilimnion (7.6–8 mg/l), but then
decrease to 0.2 mg/l at 4m, with a maximum gra-
dient between 2.5 and 3 m. At the depth of 3 m DO =
1.3 mg/l, and both ARM and IRM values are
lowest in the profile. DO drops to 0.75 mg/l between
3 and 3.5 m, with a simultaneous increase in ARM
and IRM, which reach maximum values at 4m,
immediately below the OAI. Below 4 m oxygen
levels remain low, with a slight increase from 0.2 to
0.35 mg/l in the bottom waters. ARM and IRM are
still elevated at 5 m, but decrease significantly below
5 m. The ARM ratio peaks (2.6–2.7 · 10
−3
m/A) at
Figure 3. Magnetic properties of filtered water samples collected from Brownie Lake. (a) Profiles of dissolved oxy-
gen, ARM, IRM, and ARM ratio. (b) Component analysis of ARM (diamonds) and IRM (squares) demagnetization
curves showing three components defined by median coercivity and distribution width: D (detrital + dissimilatory),
BS (biogenic “soft”), and BH (biogenic “hard”). (c) ARM ratio of the bulk filtrates, individual components, and total
biogenic contribution (BS+BH).
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the OAI (3.5–4 m), is lowest (<1 · 10
−3
m/A)
between 7 and 9 m, and has values of 1–1.5 · 10
−3
m/A
for the rest of the filtrates.
[24]The biogenic contribution to both ARM and
IRM was separated by coercivity component
analysis from first derivatives of ARM and IRM
demagnetization curves, using the fitting model
proposed by Egli [2003, 2004]. Figure 3b shows
three coercivity components present below the
OAI, each defined by two distribution parameters:
median coercivity and dispersion. According to the
definitions of Egli [2004] the low coercivity com-
ponent comprises large detrital grains, and fine
extracellular particles mediated by dissimilatory
microorganisms (D); the intermediate coercivity
component is identified as biogenic “soft”(BS),
and the high coercivity component as biogenic
“hard”(BH). The ARM ratio of each component
is plotted in Figure 3c. The two biogenic com-
ponents have maximum ARM ratios at the OAI
(3.4 · 10
−3
m/A for BS; 3.82 · 10
−3
m/A for BH).
Below the OAI BS decreases to <1 · 10
−3
m/A at
8 m (where BH peaks at 3.2 · 10
−3
m/A), and
increases again toward the bottom (where BH < 1 ·
10
−3
m/A). Integrating BS and BH remanences over
the entire water column profile, we obtain average
ARM ratios of 2.44 · 10
−3
m/A for component BS,
and for 2.13 · 10
−3
m/A for component BH. The
ARM and IRM values of the two biogenic compo-
nents were respectively added for each sample in
order to calculate an average biogenic ARM ratio
(BS + BH in Figure 3c). At the OAI the ARM ratio
of BS + BH is 3.47 · 10
−3
m/A, while its integrated
value over the water column is 2.36 · 10
−3
m/A.
4.2.4. Total Ferrimagnetic Concentration
[25]To calculate the total mass concentration of
ferrimagnetic particles in a particular sample using
equation (3), the nature of the ferrimagnetic carrier
must first be identified. The low temperature
magnetization experiments reveal the presence of
partially oxidized magnetite in both sedimentary
units, with more pronounced maghemitization in
Unit 2. Zero field cooled (ZFC) 10 K SIRM
warming curves of typical samples for each sedi-
mentary unit are shown in Figure 4a. The Unit 1
sample demagnetization rate is highest between
10 and 50 K, where ∼30% of the SIRM is lost,
decreases between 50 and 100 K (10% loss), in-
creases again (20% loss) between 100 and 130 K
through the Verwey transition (T
V
), and is lowest
between 130 and 300 K, interval in which only
10% more is lost. The remanence retained at room
temperature is a little over 30%. By comparison,
the Unit 2 sample memory is almost double. The
initial remanence loss of this sample is steep but the
magnitude of loss (∼20%) is less than in Unit 1.
This is followed by a decrease in demagnetization
rate with a broad (10% loss over 30K) but still
distinct T
V
, shifted to lower temperatures (80–
110 K). Above T
V
the demagnetization rate
remains constant at ∼7% per 100 K. The depressed
and broadened T
V
, shifted to lower temperature is a
trait of non‐stoichiometric magnetite, while rema-
nence loss below and above T
V
have also been
attributed to magnetite oxidation in well charac-
terized starting material [Özdemir et al., 1993]. The
degree of oxidation also dictates the magnitude of
the demagnetization rate below and above T
V
.
The initial remanence loss is thus highest for
surface oxidized magnetite particles, while severely
maghemitized particles demagnetize at a higher
rate above T
V
[Özdemir and Dunlop, 2010].
However, this remanence loss can also occur due to
unblocking of magnetite SP particles during sample
warming. To avoid the effect of superposition of
the two phenomena, we examine the behavior of
room temperature remanence during low tempera-
ture cycling (Figure 4b). Typical Unit 1 curves
show a 1% increase in remanence with cooling
from 300 to 250 K, followed by a loss of ∼25% to
T
V
, and only a slight increase in remanence at
temperatures lower than 70 K. The cooling curve is
reversible from 10 to 60 K, temperature above
which the remanence recovery is incomplete.
Above T
V
, the warming curve peaks around 170 K,
followed by a steady decrease to room temperature.
The total remanence recovery is above 75%. The
Unit 2 cooling curve shows the same magnitude
increase in remanence between 300 and 250 K, but
is followed by a gradual decrease to 110 K
corresponding to a remanence loss <2%. Below T
V
there is a ∼2% increase in remanence, which is
reversible upon warming from 10 to 100 K. Above
100 K it steadily decreases to room temperature,
first gradually to ∼250 K and then more steeply
from 250 to 300 K. Compared to the Unit 1 sample,
only 5% of the room temperature SIRM is lost in
the low temperature cycling process. According to
Özdemir and Dunlop [2010] the hump‐shaped
cooling and warming curves above T
V
, together
with the high degree of room temperature rema-
nence memory are diagnostic for magnetite in the
advanced stages of maghemitization. Özdemir and
Dunlop [2010] have also proposed a semiquanti-
tative method for estimating the oxidation parameter
z[O’Reilly and Banerjee, 1967; Readman and
O’Reilly, 1971], by comparing the room tempera-
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ture memory loss (DM
c
) with the difference in
magnetization between 20 K and T
V
(DM
m
).
Although this method has not been extensively
tested on a range of particle size fractions (or
mixtures thereof), it can be useful as a first‐pass
estimate of the degree of maghemitization
[Özdemir and Dunlop, 2010]. In our case, Unit 2
DM
c
and DM
m
values fall in the range of PSD
magnetite characterized by zvalues of 0.8–0.9,
whereas in Unit 1 the small DM
m
value, deter-
mined by the predominance of a low coercivity MD
component [Muxworthy et al., 2003], does not
allow a comparison.
[26]The room temperature Mössbauer spectrum of
the surface sediment magnetic extract (Figure 4c)
gives us a quantitative measure of maghemite
concentration for Unit 1 in this case. The fitted
parameters correspond to the sextets of hematite,
maghemite, site A (tetrahedral) and site B (octa-
hedral) of magnetite, and doublets of Fe
2+
and Fe
3+
(Figure 4c and Table 2). The B
HF
of site A and B of
magnetite, maghemite and hematite are in agree-
ment with values from the literature and suggest
iron phases without presence of foreign elements
(e.g., Ti or Al substitutions) in their structure
[Murad and Cashion, 2004]. However, the mag-
netite site A/site B concentration ratio (Table 2) is
higher than 0.5, showings some deviation from a
stoichiometric form. The non‐stoichiometry is in-
terpreted as the combined effect of a stoichiometric
magnetite core, a non‐stoichiometric magnetite
transition zone (characterized by a distribution
of z), and an outer maghemite shell. The Fe
2+
doublet is associated with paramagnetic minerals
(e.g., iron phyllosilicates), and the Fe
3+
doublets
correspond to paramagnetic iron minerals (wide
Figure 4. (a) Thermal demagnetization of SIRM applied at 10 K after ZFC treatment of representative samples from
the two sedimentary units. (b) Behavior of room temperature SIRM with cooling to 10 K and warming back 300 K for
the same samples. (c)
57
Fe Mössbauer spectrum of magnetic extract from the surface sediment. (d) Time series of total
ferrimagnetic concentration by mass (c
ferri
) on a water‐free basis: thick line represents solution of equation (10) with
m
ferri
=88Am
2
/kg for Unit 1 and 78 Am
2
/kg for Unit 2, thin lines are solutions calculated for magnetite (lower bound)
and maghemite (upper bound) and delimit a solution space (shaded) for c
ferri
considering the entire range of z[0,1].
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Fe
3+
doublet), as well as to superparamagnetic
iron oxides (narrow Fe
3+
doublet). If we consider
only the magnetically ordered ferrimagnetic par-
ticles, then 91% of the iron is in contained in non‐
stoichiometric magnetite, and 9% is in maghemite.
If we assume the SP fraction is entirely ferrimagnetic
(i.e., no ferrihydrite) and fully oxidized, then only
81% of the iron is in contained in non‐stoichiometric
magnetite, and 19% is in maghemite. Since DM
c
of
Unit 1 samples is ∼0.25, the average remanence ratio
is 0.16 ± 0.02 (characteristic of generic PSD
behavior), and room temperature SIRM memory is
partially due to SD grains, an upper limit for zcan be
set at 0.5 for Unit 1, based on the model of Özdemir
and Dunlop [2010]. The Mössbauer‐based calcula-
tion helps lower this upper limit to 0.3. The oxida-
tion parameter is necessary for determining m
ferri
values for Units 1 and 2 from equation (4), where the
two components considered are magnetite (m
Mt
=
92 Am
2
/kg) and maghemite (m
Mh
= 74.3 Am
2
/kg),
and the weighing factor is none other than z,
according to the quasi‐linear relationship between z
and either end‐member fractions of the magnetite‐
maghemite oxidation series [Readman and O’Reilly,
1972]. For Unit 1 we find an average ferrimagnetic
component with m
ferri
=88Am
2
/kg (corresponding
to z= 0.3), while for Unit 2 the average m
ferri
=
78 Am
2
/kg (z= 0.8). The total mass concentration of
ferrimagnetic material (c
ferri
) is obtained by nor-
malizing bulk M
s
measurements by the respective
m
ferri
value (equation 3). Figure 4d shows c
ferri
delimited by total ferrimagnetic mass concentration
calculated as magnetite (lower limit) and maghe-
mite (upper limit).
4.2.5. Concentration of Remanence‐Carrying
Particles
[27]The sedimentary MD, UNISD, and ISD com-
ponents are modeled using system (9), which has
been successfully tested on the synthetic mixtures.
The choice for end‐member component ratios is
driven by the characteristics of the end‐member
components in the depositional environment
examined.
[28]The UNISD component comprises all SD
particles or chains of particles that are isolated from
other magnetic grains in the sediment matrix. These
particles can have various sources, but in lake se-
diments they are overwhelmingly biogenic [Egli et
al., 2010]. Lakes generally have diverse magneto-
tactic bacteria communities that live in specific
geochemical conditions [Moskowitz et al., 2008],
so it is expected that populations of magnetosomes
originating in different environmental stress zones
have characteristic magnetic properties, specifically
the ratios used in this model. The magnetosomes
present in our samples have been identified as non‐
stoichiometric magnetite, based on the Mössbauer
analysis and the presence of Verwey transition in
the low‐temperature experiments. The remanence
ratio of the UNISD component is therefore set to
0.5 [Stoner and Wohlfarth, 1948]. The ARM ratio
should reflect the average value of non‐interacting
magnetosomes and chains from all bacterial strains.
Since it is difficult to identify all the species that
produce magnetosomes in natural samples, and
there is little data for wild strain magnetic proper-
ties, the choice of UNISD ARM ratio should be
based on measurements of samples collected from
the horizons inhabited by magnetotactic bacteria.
The Brownie Lake water column ARM ratio of the
integrated biogenic coercivity component peaks at
the OAI (BS+BH in Figure 3c). The decrease of
the ARM ratio with depth is partially due to the
incipient breakdown during settling of some of the
chains produced at the OAI, and partially due to
possibly lower intrinsic ARM ratios of magneto-
some chains produced by some of the strains in the
low‐oxygen layers [Egli, 2004]. It is also plausible
Table 2. Magnetic Hyperfine Parameters at Room Temperature for the Brownie Lake Surface Sediment Magnetic Extract
Iron Phase B
HFa
(T) QS
b
(mm/s) IS
c
(mm/s) %Fe
d
Magnetite (site A‐tetrahedral) 49.0(2)
e
−0.04(2) 0.26(2) 28
Magnetite (site B‐octahedral) 45.8(4) 0.02(2) 0.67(1) 34
Hematite 51.3(3) −0.22(1) 0.38(2) 9
Maghemite 50.2(5) 0.03(2) 0.43(5) 6
Fe
3+
narrow doublet ‐0.51(1) 0.49(1) 9
Fe
3+
wide doublet ‐1.53(3) 0.70(2) 7
Fe
2+
‐2.72(3) 1.03(1) 7
a
Magnetic hyperfine field.
b
Quadrupole splitting.
c
Isomer shift.
d
Relative concentration.
e
Errors quoted in parentheses refer to the last decimal.
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that some of low coercivity particles are non‐in-
teracting pedogenic particles that also have lower
intrinsic ARM ratios [Geiss et al., 2008]. Coer-
civity spectra deconvolution does not discriminate
between interacting and non‐interacting particles,
but isolating the biogenic component in its imme-
diate environment is the most important step in
the process of choosing a representative ARM ratio
for UNISD. Based on the BS+BH ARM ratio value
at the OAI, the habitat of magnetotactic bacteria,
we use (c
a
/M
rs
)
UNISD
= 3.5 · 10
−3
m/A in our
model. The ISD end‐member ratios were chosen to
represent strongly interacting SD particles (M
rs
/M
s
=
0.41; c
a
/M
rs
=0.12·10
−3
m/A [Moskowitz et al.,
1993]), e.g., clumps of collapsed magnetosomes
from bacterial cells with totally degraded organic
membranes, or washed‐in pedogenic particle
aggregates. The MD component end‐member ratios
(M
rs
/M
s
= 0.05; c
a
/M
rs
= 0.1 · 10
−3
m/A) represent
average values for MD grains sensu lato (i.e.,
account for the presence PSD particles).
[29]Figure 5 illustrates the modeling results. Bulk
M
rs
/M
s
and c
a
/M
rs
are compared to theoretical
values in Figure 5a. A mixing grid is formed by the
lines connecting the three end‐member components
(defined above), which are calculated using system
(10). The fractions of the end‐members in each
sample are plotted in a ternary diagram (Figure 5b),
which is equivalent to the mixing grid, but in g
i
coordinates. On average, Unit 1 samples contain
60–80% MD, 20–30% ISD, and <10% UNISD
particles. Comparatively, pre‐settlement samples
contain only 30–50% MD grains, while ISD and
UNISD end‐members are well represented with
20–40% of the total ferrimagnetic mass each. In
Figure 5c we plot results from eight model runs that
used all possible combinations of the following
end‐member ratio pairs (M
rs
/M
s
,c
a
/M
rs
), which
represent boundaries defined for each component:
(0.5, 3 · 10
−3
m/A) and (0.5, 4 · 10
−3
m/A) for
UNISD, (0.41, 0.1 · 10
−3
m/A) and (0.45, 0.15 ·
10
−3
m/A) for ISD, (0.01, 0.05 · 10
−3
m/A) and
Figure 5. (a) Crossplot of M
rs
/M
s
versus c
a
/M
rs
for Brownie Lake Units 1 (triangles) and 2 (dots). Theoretical
values for bulk ratios were calculated from system (10) at 0.1 fraction increments of end‐member components (see
text for end‐member ratio values). (b) Ternary diagram of calculated fractions for each component (UNISD, ISD, and
MD or PSD) in Brownie Lake sediments, according to the three end‐member mixing model (g
i
are solutions to system 9).
(c) Time series of end‐member component fractions for model runs with eight different end‐member combinations.
Lines represent mean values, and uncertainty bars are two standard deviations in length (see text for error calculation
method).
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(0.05, 0.1 · 10
−3
m/A) for MD. The curves are
mean g
i
values of the model runs, and the length of
the error bars is two standard deviations.
4.2.6. Concentration of SP Particles
[30]A broad distribution of particle sizes was
inferred for the SP grains based on frequency
dependence of susceptibility across the whole
spectrum of measurement temperatures (Figure 6a).
This implies that the c
SP
value to be used in
equation (11) for the calculation of f
SP
must be the
average of SP susceptibilities over the entire range
of SP volumes. We calculate c
SP
following Worm
[1998], which assumes even coercivity distribu-
tions between 40 and 60 mT for of each grain size
fraction. For a measurement frequency of 100 Hz,
average c
SP
across the frequency‐dependence
interval is 4 · 10
−3
m
3
/kg. c
nonSP
was calculated
using an SD value of 0.4 · 10
−3
m
3
/kg, and an MD
value of 0.6 · 10
−3
m
3
/kg (average values for
nonstoichiometric magnetite [Dunlop and Özdemir,
1997]), weighed by their respective fractions as
obtained from system (9). SP fraction f
SP
is plotted
in Figure 6b (continuous line); Unit 1 SP fractions
are between 0.05 and 0.1, while Unit 2 values are
in the interval 0.1–0.2. For comparison, dashed
lines are f
SP
curves calculated using c
SP
values of
3·10
−3
m
3
/kg (higher values), and 5 · 10
−3
m
3
/kg
(lower values). Figure 6c illustrates the contribu-
tions of the SP and non‐SP fractions to c
ferri
. The
SP particles account for as much as 50% of c
ferri
in
some intervals, even though their concentration is
only ∼10%.The non‐SP baseline in Unit 1 has
slightly higher values than in Unit 2 because of the
prevalence of MD particles, but the average base-
line value is equivalent to the one used by Hunt et
al. [1995b]. Support for our method is provided by
the Mössbauer analysis of the magnetic extract.
The SP concentration given by the narrow Fe
3+
doublet in Figure 4c (representing paramagnetic
and SP iron oxides) is 12% of the ferrimagnetic
material (9% of total Fe). Given that not only fer-
rimagnetic SP material contributes to this doublet,
this value should be taken as a maximum SP con-
centration. By comparison, our ferrimagnetic SP
fraction calculation for the top 10–15 cm of the
core (equivalent to the surface sample from which
the extract was prepared) yields an average con-
centration of 8%.
4.2.7. Ferrimagnetic Flux Model
[31]In the previous sections we have calculated the
mass of ferrimagnetic material relative to the total
dry sediment mass (Figure 4d), and the partition
between its constituent components: UNISD, ISD,
MD (Figure 5c), and SP (Figure 6b). Knowing the
pre‐and post‐settlement sedimentation rates from
the Brownie Lake age model [Swain, 1984], sedi-
ment density from core logging, and composition
from LOI, the calculated mass fractions of the
ferrimagnetic components can be expressed as
sediment loads or fluxes (Figure 7) according to
equations (7) and (8). The full interpretation of the
Figure 6. (a) Frequency and temperature dependence
of susceptibility for representative samples of each sed-
imentary unit. Both samples are frequency dependent in
the interval 30–300 K, indicating a broad SP grain size
distribution. (b) SP fraction calculated for c
SP
=4·
10
−3
m
3
/kg (thick line), bracketed by calculations for
c
SP
values of 5 · 10
−3
m
3
/kg(left),and3·10
−3
m
3
/kg
(right). (c) SP and non‐SP contributions to c
ferri
.
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temporal fluctuations of the ferrimagnetic compo-
nents in terms of regional environmental and
anthropogenic forcing factors will be discussed in
detail elsewhere (I. Lascu et al., manuscript in
preparation, 2010); however, a synopsis follows.
The annual sedimentary ferrimagnetic flux before
European settlement is fairly constant at 0.01–
0.02 mg/cm
2
, and is dominated by the SD and SP
fractions (∼70%). After 1850 the total flux steadily
increases and by 1950 is an order of magnitude
higher than in pre‐settlement times. This tenfold
increase is observed in the MD, ISD, and SP
components. The 1917 lake level lowering is
marked by short‐lived abrupt increase in sediment
delivery from the surrounding catchment, marked
in Figure 7 by peaks in the MD and ISD compo-
nents. The annual UNISD flux is on the order of
2–6mg/cm
2
before, and 4–12 mg/cm
2
after settle-
ment, with the lowest values (<2 mg/cm
2
) occurring
in the eighteenth and nineteenth centuries. By
comparison to the other components, whose fluxes
are controlled by increased erosion rates, UNISD
post‐settlement values are only two times higher
than in pre‐settlement times, and are tied to an
increase in nutrient delivery brought by anthro-
pogenically driven eutrophication of the lake in the
twentieth century [Swain, 1984]. The low UNISD
values that predate the 1917 lake level lowering
are interpreted as a sign of the reductive dissolution
front migrating downward into the sediment column
after the establishment of meromictic conditions.
4.3. Discussion of Modeling Parameters
Selection
[32]We here focus on the significance of the choice
of modeling parameters in understanding ferri-
magnetic components in their sedimentary context.
The total ferrimagnetic mass calculation is based
on M
s
, an intrinsic property of ferromagnetic
materials [Dunlop and Özdemir, 1997]. The error
associated with f
ferri
(or c
ferri
) is strictly related to
the determination of ferrimagnetic mineralogy, and
has a maximum value of 19% in the general case of
non‐stoichiometric magnetite (i.e., unknown oxi-
dation parameter z). To decrease this error, low
temperature magnetization curves and Mössbauer
57
Fe spectroscopy have been employed to narrow
down possible zvalues for each of sedimentary
unit. The low temperature magnetic behavior of
Unit 1 samples and the Mössbauer analysis of the
surface sample indicate that the magnetite is only
oxidized at the particle surface. Brownie Lake has
been meromicitic since the 1920s, having anoxic
and reducing bottom waters that are rich in dis-
solved Fe
2+
and Mn
2+
[Swain, 1984; Tracey et al.,
1996], an unfavorable environment for oxidation of
magnetite particles. On the contrary, reductive
dissolution can potentially remove SP nanoparticles
and reduce the size of SD grains to SP [Anderson
and Rippey, 1988; Tarduno, 1995; Geiss et al.,
2004]. The magnetite particles must either have
been already oxidized before deposition and have
survived without being completely reduced, or
underwent oxidation during the laboratory storage
period of the core and samples, between collection
and measurement. Before settlement, the lake water
was only seasonally anoxic, complete mixing of
epilimnetic and hypolimnetic waters occurring at
spring and fall turnover events. Evidence for this
can be inferred from the lake’s reduced relative
depth, the absence of annually laminated sedi-
ments, higher sedimentary Fe/Mn ratio, and the
presence of a diatom flora in a higher‐trophic status
[Swain, 1984; Tracey et al., 1996]. Because of the
more oxic conditions, and of the one order of
magnitude lower sedimentation rate [Swain, 1984],
Unit 2 ferrimagnetic particles are in a more
advanced oxidation state. The average magnetic
grain size is also lower than in Unit 1, which means
an increased surface‐to‐volume ratio, making the
grains more susceptible to oxidation. The choice
of m
ferri
for each unit was therefore determined by a
combination of sediment‐magnetic characteristics
Figure 7. Model of annual ferrimagnetic flux of
UNISD, ISD, MD, and SP particles in Brownie Lake
(note that Units 1 and 2 are plotted on separate axes).
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and evidence of limnological conditions at the time
of deposition.
[33]The remanence‐carrying components have
been modeled by way of a three‐component mixing
model, using specific end‐member values for
remanence and ARM ratios. According to our
model, bulk M
rs
/M
s
and c
a
/M
rs
of a sample can be
translated into mass fractions for each component
considered, here UNISD, ISD and MD. The basis
for defining these particular components is the
ability of the two ratios to discriminate between
grain‐size categories (M
rs
/M
s
) and inter‐particle
interactions (c
a
/M
rs
). A judicious choice of end‐
member ratios will result in lower model errors. The
components for Brownie Lake were defined with the
knowledge that lake sediments in temperate‐climate
areas are characterized by a mixture of detrital and
endogenic magnetic particles [Snowball et al., 2002;
Geiss et al., 2003; Egli, 2004], and that non-
stoichiometric magnetite is the ferrimagnetic carrier
in our sediments. The detrital fraction is generally
dominated by MD particles, but can also contain
finer SD and SP grains (e.g., of pedogenic origin).
The MD component sensu stricto (no PSD grains)
has low remanence and ARM ratio values (M
rs
/M
s
<
0.05, c
a
/M
rs
∼0.1 · 10
−3
m/A). A PSD end‐member
would have a higher remanence ratio (e.g., 0.2 for
1mm grains), but a similar ARM ratio. We use
the cutoff M
rs
/M
s
value of 0.05 [Day et al., 1977;
Dunlop, 2002] as an average in our model, in
order to incorporate the effects of both true MD
and PSD grains. This value corresponds to an
average grain size of ∼20 mm[Yu et al., 2002]. The
0.01 M
rs
/M
s
value used in the error estimation for
the MD component (g
3
in Figure 5c) corresponds to
much larger particles (∼100–200 mm) [Day et al.,
1977; Dunlop, 2002], and would be a limit case.
The detrital SD grains can be transported into a
depositional basin either independently through
sorting, or in most cases as part of clay/organic
matter aggregates that also contain larger ferri-
magnetic particles. In both situations the SD par-
ticles are disturbed to a certain extent from their
original configuration (e.g., dispersion in a soil
matrix). It is then reasonable to assume that they
contribute to both ISD and UNISD end‐members.
The ISD component is characterized by SD‐like
remanence ratios, and MD‐like ARM ratios, and
was defined to represent the extreme case of strong
interactions between SD particles clumped in
aggregates [Moskowitz et al., 1993; Kopp et al.,
2006]. Both detrital (e.g., pedogenic) and endo-
genic (biogenic and inorganic) SD particles that
occur in such closely packed configurations are
expected to contribute to ISD. The UNISD com-
ponent is designed to include only isolated grains
or undisturbed linear chains of bacterial magneto-
somes [Yamazaki, 2008; Egli et al., 2010]. The
remanence ratio for magnetite UNISD particles is
0.5bydefinition[Stoner and Wohlfarth, 1948]. For
greigite magnetosomes the remanence ratio usually
exceeds 0.5, approaching a theoretical value of
0.83 as H
cr
/H
c
approaches unity, due to a [100]
easy axis of magnetization and the prevalence of
magnetocrystalline anisotropy over shape anisot-
ropy [e.g., Roberts, 1995; Sagnotti and Winkler,
1999; Chang et al., 2009]. The ARM ratio of
UNISD can be determined with the help of coer-
civity deconvolution of samples harvested from the
OAI, by calculating the ARM ratio of the biogenic
coercivity‐spectrum component (3.5 · 10
−3
m/A in
our model). The biogenic component defined by its
coercivity is likely to include interacting particles
from magnetosome clusters and bundled or col-
lapsed chains [Egli et al., 2010], which can artifi-
cially lower (c
a
/M
rs
)
UNISD
. On the other hand,
the detrital coercivity‐spectrum component may
include non‐interacting particles with lower initial
ARM ratios (e.g., 1–3·10
−3
m/A for pedogenic
particles [Egli, 2004; Geiss et al., 2008]), which
should truly lower (c
a
/M
rs
)
UNISD
. Our error esti-
mation for the UNISD end‐member (g
1
in Figure 5c)
was based on ARM ratios in the interval 3–4·
10
−3
m/A. The error is higher for Unit 2 samples,
indicating that the choice of ARM ratio for the
UNISD component is more critical for finer grained
magnetic assemblages.
[34]The SP component fraction is modeled using
the ferrimagnetic susceptibility c
ferri
(derived from
c
f
/M
s
) by subtracting the non‐SP baseline suscep-
tibility [Hunt et al., 1995b]. The critical parameter
in the calculation of f
SP
is the susceptibility of the
SP ferrimagnetic grains, which can vary over an
order of magnitude with SP grain size [Worm,
1998]. Frequency‐dependent susceptibility mea-
surements across a range of temperatures are
therefore necessary to characterize the SP particle
size distribution, as a preliminary step for calcu-
lating a representative c
SP
. Sediments usually
comprise magnetic particles characterized by a
wide grain‐size distribution in the SP realm
[Dearing et al., 1996], so an average c
SP
value
calculated over the SP size spectrum is a reasonable
assumption in most cases. This approach is pre-
ferred to the traditional room temperature suscep-
tibility measurements at two frequencies (c
fd
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parameter), which captures only a narrow interval
of the grain‐size distribution curve.
5. Conclusions
[35]1. We provide a quantitative model for calcu-
lating the concentrations of ferrimagnetic sedimen-
tary components using rock magnetic properties.
The quantification method is based mainly on bulk
room temperature measurements, and translates
raw magnetic parameters into ferrimagnetic mass
concentrations. This method eliminates dilution
effects on magnetic properties by weakly magnetic
substances in high concentrations, such as water,
organic matter, carbonates, clay minerals, etc., and
allows the calculation of ferrimagnetic particle
fluxes for dated sedimentary sequences. It can
be applied for reconstructing past environmental
changes in a range of sedimentary environments,
and is particularly useful for large sets of samples,
where detailed magnetic unmixing methods (espe-
cially low‐temperature techniques) are unfeasible
due to time or instrument constraints.
[36]2. Total ferrimagnetic concentration is most
accurately determined from in‐field magnetization
measurements. Saturation magnetization corrected
for non‐ferrimagnetic contributions (M
s
) is the
most reliable parameter, only ferrimagnetic miner-
alogy being needed for concentration calculations.
Susceptibility‐based concentrations are less reliable
because they require a priori knowledge about
ferrimagnetic grain size and shape in addition to
magnetic mineralogy. Remanence measurements
are useful as concentration proxies only when
magnetic composition is uniform with respect to
mineralogy and grain size, due to the varying
degree of remanence acquisition efficiency for
different categories of magnetic particles.
[37]3. Anhysteretic and saturation isothermal
remanences are used here to model the concentra-
tions of the remanence‐carrying ferrimagnetic
fractions via a three‐component mixing model,
which is tested on mixtures of SD and non‐SD
magnetite grains of known concentrations. The
use of the ARM ratio (c
a
/M
rs
) as a proxy for inter‐
particle magnetostatic interactions allows the sepa-
ration of SD particles into two separate components
(UNISD and ISD), which may have independent
origins. The remanence ratio (M
rs
/M
s
) is a true
grain‐size indicator, whereas c
a
/M
rs
should be used
in that capacity only when the proportion of inter-
acting particles is constant.
[38]4. For a robust quantification of the super-
paramagnetic fraction, we propose a technique that
corroborates ferrimagnetic susceptibility calcula-
tions with information about the SP particle size
distribution obtained from the frequency and tem-
perature dependence of magnetic susceptibility.
This approach is recommended, when possible, in
lieu of frequency‐dependent susceptibility mea-
surements at room temperature only.
Acknowledgments
[39]We thank the National Lacustrine Core Repository
(LacCore) at the University of Minnesota for access to the
Brownie Lake core and initial description data, Amy Chen
for help with water sampling and filtering, Bruce Moskowitz
and Brian “The Dude”Carter for access to the synthetic mix-
tures. Mike Jackson’s comments and suggestions significantly
improved the development of our methodology. Constructive
reviews by Christoph Geiss, Mike Jackson, Leonardo Sagnotti
and an anonymous referee have helped improve this manu-
script. I.L. has benefited from the support of a University of
Minnesota Doctoral Dissertation Fellowship. The Institute for
Rock Magnetism is funded by the National Science Founda-
tion, the Keck Foundation, and the University Of Minnesota.
This is IRM contribution 1003.
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