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Geophys. J. Int. (2023) 235, 2268–2284 https://doi.org/10.1093/gji/ggad360
Advance Access publication 2023 September 15
Geomagnetism and Electromagnetism
Tracing titanomagnetite alteration with magnetic measurements at
cryogenic temperatures
Andrei Kosterov ,
1 Leonid Surovitskii,
1 , 2 Valerii Maksimochkin,
3 Svetlana Yanson
1 and
Aleksey Smirnov
2 , 4
1
St Petersburg University, 7 - 9 Universitetskaya Embankment 199034 , St Petersburg, Russia. E-mail: a.kosterov@spbu.ru
2
Department of Geological and Mining Engineering and Sciences, Mic hig an Tec hnological University, 1400 Tow ns e nd Drive, Houghton, MI 49931 , USA
3
Faculty of Physics, Moscow State University, 1 , bld. 2 Leninskie Gory 119991 , Moscow, Russia
4
Department of Physics, Mic hig an Te c hnological Univer sity, 1400 To wn s en d Drive , Houghton, MI 49931 , USA
Accepted 2023 September 7. Received 2023 September 6; in original form 2023 June 12
S U M M A R Y
Titanomagnetite containing up to 0.6–0.7 Ti atoms per formula unit is a primary magnetic
mineral phase in submarine basalts and in some terrestrial volcanic rocks. On a geologi-
cal timescale, it often undergoes alteration, forming new magnetic phases that may acquire
(thermo)chemical remanent magnetization. The initial stage of this natural process can be
modelled by prolonged laboratory annealing at moderately elevated temperatures. In this
study, our goal is to characterize the alteration products resulting from annealing a submarine
basalt containing homogeneous titanomagnetite Fe
3 −x
Ti
x
O
4
( x ≈0.46) at temperatures of 355,
500 and 550
◦C for up to 375 hr, by examining their magnetic properties over a wide range of
temperatures.
The effect of extended annealing is most apparent in the low-temperature magnetic prop-
erties. In the fresh sample, a magnetic transition is observed at 58 K. Below the transition
temperature, the field-cooled (FC) and zero-field-cooled (ZFC) saturation isothermal remanent
magnetization (SIRM) curves are separated by a tell-tale triangular-shaped area, characteristic
for titanomagnetites of intermediate composition. The room-temperature SIRM (RT-SIRM)
cycle to 1.8 K in zero field has a characteristic concave-up shape and is nearly reversible. For
the annealed samples, the magnetic transition temperature shifts to lower temperatures, and
the shape of the curv es abov e the transition changes from concave-up to concave-down. The
shape of the RT-SIRM cycles also pro gressi vel y changes with increasing annealing time. The
SIRM loss after the cycle increases up to ∼30 per cent for the samples annealed for 375 hr at
355
◦C, and for 110 hr at 500 and 550
◦C.
The Curie temperatures of the ne wl y formed magnetic phases exceed the Curie temper-
ature of the fresh sample (205
◦C) by up to 350
◦C. While this effect is most commonly
attributed to e xtensiv e single-phase oxidation (maghemitization), the behaviour observed at
cryogenic temperatures appears incompatible with the known properties of highly oxidized
titanomaghemites. Therefore, we propose that, at least in the initial stage of the ‘dry’, that is,
not involving hydrothermalism, alteration of titanomagnetite, temperature- and time-controlled
cation reordering is the primary mechanism driving changes in both low- and high-temperature
magnetic properties.
Key words: Magnetic mineralogy and petrology; Marine magnetics and palaeomagnetics;
Rock and mineral magnetism; Titanomagnetite.
1 INTRODUCTION
T itanomagnetite (Fe
3 −x
T i
x
O
4
, thereafter TMX, where X = 100 ·x )
with Ti content x up to 0.6–0.7 is a primary magnetic mineral
phase present in submarine basalts and some terrestrial volcanic
rocks. On a geological timescale, it is believed to undergo slow
oxidation—a process that is likely widespread and occurs via
different mechanisms such as burial heating, baking by intrud-
ing magma, hydrothermal alteration, etc. Titanomagnetite alter-
ation results in the acquisition of secondary magnetization in the
ne wl y formed magnetic phase(s), producing a potent mechanism
for remagnetization. Understanding which magnetic phases, and
2268 C
The Author(s) 2023. Published by Oxford University Press on behalf of The Royal Astronomical Society.
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Tracing titanomagnetite alteration 2269
in what conditions, are formed during chemical alteration of ti-
tanomagnetites is crucial for further assessing how these ne wl y
formed phases affect the primary magnetization and distinguish it
from possible secondary overprint(s). Since oxidation typically oc-
curs at ele v ated temperatures, this secondary magnetization can
often be classified as thermochemical remanent magnetization
(TCRM). TCRM has been the subject of study since the early
days of palaeomagnetism (Nagata & Kobayashi 1963 ; Creer &
Pete rsen 1969 ; Wasilewski 1969 ; Kellogg et al. 1970 ), and more
recently gained further attention because of its presumably ad-
verse role in absolute palaeointensity determination with the Thel-
lier method (Yamamoto et al. 2003 ; Smirnov & Tarduno 2005 ;
Draeger et al. 2006 ; Yamamoto 2006 ; Fab ia n 2009 ; Shcherbakov
et al. 2019 ). Ho wever , so far , no clear-cut criteria have been de-
vised for detecting TCRM in rocks. In addition, the laboratory
heatings used in Thellier-type (Thellier & Thellier 1959 ) or Shaw-
type (Shaw 1974 ) palaeointensity experiments often result in ad-
ditional magneto-mineralogical changes, further complicating data
interpretation.
The initial stages of the natural oxidation process may be mod-
elled, to some extent, by prolonged annealing at moderatel y ele v ated
temperatures. Numerous experiments of this kind have been carried
out on synthetic titanomagnetites (Ozima & Larson 1970 ; Ozima
& Sakamoto 1971 ; Readman & O’Reilly 1972 ; Keefer & Shive
1980 , 1981 ; Nishitani & Kono 1983 , 1989 ; Brown & O’Reilly
1988 ), and on rocks bearing titanomagnetites and separated ti-
tanomagnetite grains (Creer & Petersen 1969 ; Ozima & Larson
1970 ; Marshall & Cox 1971 ; Johnson & Merrill 1973 ; Walder-
haug et al. 1991 ). The common belief is that annealing of inter-
mediate ( x ≥0.04) titanomagnetites at moderate, < 400
◦C, tem-
peratures, causes vacancies to enter the spinel lattice, forming ti-
tanomaghemites. The latter would have considerably higher Curie
temperatures than their stoichiometric counterparts and, therefore,
could serve as a medium for TCRM acquisition. Ho wever , recently
an alternative mechanism for Curie temperature enhancement with
annealing has been suggested (Bowles et al. 2013 , 2019 ; Jackson
& Bowles 2018 ), inferring that the Curie temperature increase in
annealed samples is due to increasing ionic order in the spinel
lattice.
Magnetic measurements at cryogenic temperatures have been
used e xtensiv ely to characterize both synthetic titanomagnetites
(Schmidbauer & Readman 1982 ; Radhakrishnamurty & Likhite
1993 ; Moskowitz et al. 1998 ; Carter-Stiglitz et al. 2006 ; Engel-
mann et al. 2010 ; Church et al. 2011 ; Almeida et al. 2014 ) as well
as titanomagnetite/titanomaghemite phases in subaerial (Moskowitz
et al. 1998 ; Kosterov 2001 ;
¨
Ozdemir & Dunlop 2003 ; Kosterov et al.
2009 , 2018 ; Vigliotti et al. 2022 ) and submarine volcanic rocks
(Matzka et al. 2003 ; Doubrovine & Tarduno 2004 , 2005 , 2006a , b ;
Kr
´
asa et al. 2005 ; Kr
´
asa & Matzka 2007 ; Wan g et al. 2021 ). In-
termediate titanomagnetites do not show the Verw ey ( 1939 ) phase
transition at 125 K (Walz 2002 ), characteristic of stoichiometric
magnetite (Arag
´
on et al. 1985 ; K
akol & Honig 1989 ). Instead,
their magnetic properties show an anomalous behaviour in the
30–80 K temperature range manifesting itself in (i) a pronounced
loss of remanence given at a temperature below this range af-
ter cooling in a zero magnetic field (ZFC); (ii) an even faster
decrease of remanence given at a low temperature after cooling
in a strong magnetic field (FC) and (iii) a frequency-dependent
peak of initial magnetic susceptibility. This behaviour is believed
to be caused primaril y b y sharpl y decreased magnetocrystalline
anisotropy in this temperature range (Syono 1965 ; K
akol et al.
1991 ).
In this study, we employ magnetic measurements at cryogenic
temperatures to e v aluate the changes produced b y prolonged an-
nealing at 355, 500 and 550
◦C in a titanomagnetite-bearing subma-
rine basalt. Our experimental setup mainly pertains to laboratory-
produced alteration. Ho wever , one may hope that prolonged heating
at high temperatures could somewhat emulate alterations occurring
naturally at moderately lower temperatures.
2 MATERIALS AND METHODS
Sample P72/4, a submarine basalt ( < 500 ka), was dredged from
the Holocene bed in the Red Sea during the 30th cruise of the R/V
Akademik Kurchatov in 1985. The basalt contains homogeneous ti-
tanomagnetite with an approximate TM46 composition and a Curie
temperature of 205
◦C (Maksimochkin & Grachev 2019 ). Material
from this basalt block has pre viousl y been used to model chemical
(CRM) and TCRM acquired during annealing at, or slow cooling
from, temperatures ranging from 350 to 570
◦C (Gribov et al. 2019 ;
Shcherbakov et al. 2019 ; Maksimochkin et al. 2020 ; Gribov et al.
2021 ).
To investigate changes induced by prolonged heating in air, we
annealed multiple fragments of the sample in a Nabeltherm furnace
(Research Centre Geomodel, St. Pete rsburg State University) for
4, 40, 110, and 375 hr at a nominal temperature of 355
◦C, and
for 4 and 110 hr at 500 and 550
◦C. Once the annealing cycle was
complete, the samples were promptly transferred to a shielded room
(residual field ∼400 nT) to allow them to cool naturally.
Micromineralogical studies have been carried out at the Centre for
Microscopy and Microanalysis, Science Park of St. Petersburg State
University, using a scanning electron microscope (SEM) Quanta 200
3D (FEI, The Netherlands) with an analytical comple x Pe gasus 4000
(EDAX, USA) in the backscattered and secondary electron modes.
For the SEM study, the samples were embedded in epo xy b locks,
washed in an ultrasonic bath, dried in a flo w dryer , and sprayed with
carbon. Electron probe microanalysis was performed on an energy
dispersi ve dif fractometer of the Quanta 200 3-D microscope under
high vacuum conditions at an accelerating voltage of 15–20 kV.
The temperature dependencies of the mass specific magnetic sus-
ceptibility for fresh and annealed fragments have been determined
between −192 and 700
◦C in air and an argon atmosphere using
an MFK-1FA susceptibility bridge (A GICO , Czech Republic) con-
nected to the CS-L cryostat and the CS4 furnace. Fo r the fresh sam-
ple, susceptibility has been measured in three consecutiv e c ycles to
300, 500 and 700
◦C, respecti vel y; for annealed samples, a single
cycle to 700
◦C has been measured. Hysteresis loops in a maximum
field of 7 T and backfield curves of saturation isothermal remanent
magnetization (SIRM) acquired in a 5 T field have been measured
at 295 K with an MPMS 3 SQUID VSM (Quantum Design, US).
For these loops, a paramagnetic correction has been calculated by
extrapolating the differential susceptibility dM / dH dependence on
1/ H to a 20 T field (Starunov et al. 2019 ). Also, hysteresis loops
and backfield curves in a 1.8 T maximum field have been measured
using a Princeton Measurements Corporation 3900 Model vibrat-
ing sample magnetometer (Institute of Physics of the Earth RAS,
Moscow). The same instrument was also used to measure first-order
rev ersal curv es (FORCs). Between 210 and 340 FORCs with the
1.25 or 1.5 mT uniform field step have been traced depending on the
sample. FORC distributions have been computed using a ne wl y de-
veloped FORCtool software ( https://forctool.com/ ; Surovitskii et al.
2022 ). Fo r the fresh sample, smoothing (SF) and damping ( λ) fac-
tors for the VARIFORC algorithm (Egli 2013 ) have been selected
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2270 A. Kosterov et al .
by a trial-and-error search for an optimal solution as outlined in
Heslop et al. ( 2020 ). FORC distributions for the annealed samples
have been calculated with the same SF and damping factor as for
the fresh sample for the sake of consistenc y; howev er, these may
not be optimal in the sense of Heslop et al. ( 2020 ).
Low-temperature magnetic measurements have been carried out
at the Centre for Diagnostics of Functional Materials for Medicine,
Pharmacology and Nanoelectronics, Science Park of St. Petersburg
State University. Magnetization measurements carried out using an
MPMS 3 SQUID VSM included the following. SIRM acquired in a
5 T field at 1.8 K after cooling at zero (zero-field cooling, ZFC) and
in a strong (5 T, field cooling, FC) magnetic field, have been traced
during warming to 300 K in a zero field. SIRM (5 T) acquired at
300 K (referred to thereafter as RT-SIRM) has been measured dur-
ing a cooling–warming cycle between 300 and 1.8 K, also in a zero
field. All measurements have been carried out in the vibration mag-
netometer mode with the temperature change rate of 2 K min
−1
,
allowing to record the magnetic moment value every 0.05 K. The
temperature and frequency dependencies of the mass specific com-
plex magnetic susceptibility k = k
−i ·k
, where k
and k
are the
in-phase and out-of-phase susceptibilities, respecti vel y, have been
determined between 2 and 300 K at 2 K increment between 2 and
80 K, and 5 K between 80 and 300 K, using a PPMS instrument
(Quantum Design). Measurements have been performed in a driv-
ing field of 250 μT at seven frequencies between 11 and 9500 Hz
selected so that the increment in log frequency would be approxi-
mately uniform.
3 RESULTS
3.1 Characterizing fresh P72/4 sample
Backscatter electron (BSE) imaging of the fresh sample reveals
the presence of skeletal titanomagnetite grains typical for rapidly
cooled submarine basalts (Fig. 1 a). No exsolution structures within
the grains were observ ed. Howev er, the fine size of titanomagnetite
grains did not allow one to determine their precise composition
from microprobe data. Magnetic hysteresis properties (Fig. 1 b and
Tab le 1 ) indicate that the sample is in a pseudo-single domain (PSD)
magnetic state. Wo r th noting is a relati vel y low value of H
cr
/ H
c
of
1.25, which is sometimes encountered in submarine basalts (Gee &
Kent 1999 ). The central part of the FORC diagram (Fig. 1 c) has an
arrowhead shape centred at about 15 mT, while the outer contours
are clearly onion-like, the 90 per cent density contour extending to
about 55 mT along the μ0
H
c
axis. Both features are characteristic of
small PSD grains (Roberts et al. 2014 ). The maximum of the hys-
teron distribution appears to be slightl y, b y about 1.2 mT, displaced
down relative to the μ0
H
b
= 0 line, suggesting that magnetostatic
interactions are non-negligible in this sample. This is a well-known
property of strongly interacting magnetic particles such as those
used in magnetic recording media (Pike et al. 1999 ), considered
as an indication of a ne gativ e mean interaction field. In addition,
an increased hysteron density in the vicinity of the μ0
H
b
axis may
also be due to interactions (Muxworthy et al. 2006 ). Indeed, non-
negligible magnetostatic interactions are expected to act between
the close segments of abundant skeletal titanomagnetite grains as
re vealed b y BSE images (Fig. 1 a).
Measurements on duplicate specimens show that the concentra-
tion of the ferrimagnetic phase in the rock can vary within ±15 per
cent of the mean value, as attested by the respective saturation mag-
netization values. At the same time, the M
rs
/ M
s
ratio, coercive force,
Figure 1. P72/4 fresh sample. (a) Backscattered electron image of a titano-
magnetite grain; (b) central part of a hysteresis loop measured at 295 K in
a 7 T maximum field. The measured loop is shown in black, corrected for
high-field slope according to the extrapolation method of Starunov et al.
( 2019 ) in red. Inset shows full ±7 T loops; (c) FORC distribution (smooth-
ing factors, SFc = SFb = 2 and damping factors, λc = λb = 0.04). Contours
are drawn every 10 per cent of maximum hysteron density. Bold dashed lines
mark the location of the maximum.
coercivity of remanence, and coercivity ratio H
cr /
H
c are constant
within 1 per cent. The basalt sample can thus be considered suffi-
cientl y homo geneous to justify comparison of the results obtained
by annealing different duplicate specimens.
The temperature dependence of low-field susceptibility deter-
mined on a fresh sample in argon show that the sample is stable up
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Tracing titanomagnetite alteration 2271
Tab le 1. Parameters of hysteresis loops measured in a maximum field of 7 T at 295 K, for the fresh and annealed samples of
P72/4 submarine basalt. The last two columns list the coordinates of the FORC distribution maxima.
Sample
M
s
(Am
2
kg
−1
)
M
rs
(Am
2
kg
−1
) M
rs
/ M
s
μ0
H
c
(mT)
μ0
H
cr
(mT) H
cr
/ H
c
μ0
H
c FORC
(mT)
μ0
H
u FORC
(mT)
Fresh sample
No. 1 Fresh 1.035 0.3223 0.3114 17.70 22.24 1.257 15.5 −1.20
No. 2 Fresh 1.211 0.3761 0.3106 17.18 21.55 1.254
No. 3 Fresh 0.9434 0.3036 0.3218 17.31 21.63 1.250
Annealed at 355
◦C
4 hr 1.202 0.3423 0.2848 15.26 19.91 1.305 13.1 −1.44
40 hr 1.370 0.3285 0.2398 12.74 17.98 1.411 10.2 −0.94
110 hr 1.390 0.3112 0.2239 12.57 18.72 1.489 11.9 −0.24
375 hr 1.320 0.2834 0.2147 14.29 22.88 1.601 13.1 −0.94
Annealed at 500
◦C
4 hr 1.290 0.4208 0.3262 29.37 40.91 1.392 27.6 −2.07
110 hr 1.437 0.4838 0.3367 42.70 60.42 1.415 50.5 −2.80
Annealed at 550
◦C
4 hr 1.410 0.5400 0.3830 49.14 63.29 1.288 51.2 −3.30
110 hr 1.092 0.3317 0.3038 37.08 54.28 1.464 39.2 −2.40
to 500
◦C (Fig. 2 a), in agreement with the previous work (Maksi-
mochkin & Grachev 2019 ). The Curie temperature, e v aluated from
the minimum of the deri v ati ve of the war ming cur ve to 300
◦C,
is 205
◦C. When heated to 700
◦C, a minor phase with the Curie
temperature of ∼550
◦C is seen in both heating and cooling curves.
While it is impossible to determine whether this phase is primary
or forms due to heating, its contribution to the magnetic properties
of the sample is negligible. On the contrary, when heated in air, the
sample (fresh aliquot was used) begins to alter between 350 and
400
◦C, and after heating to 500
◦C produces two distinct magnetic
phases with Curie temperatures of about 480 and 300
◦C (Fig. 2 b).
Further heating to 700
◦C transforms these two phases into a sin-
gle phase with a Curie temperature of ∼550
◦C and possibly also
into a continuous range of phases with Curie temperatures down to
400
◦C.
For fresh P72/4 material, the ZFC and FC remanences exhibit
rather complex behaviour (Figs 3 a and b). About a quarter of these is
demagnetized already at 5 K. This property, albeit less pronounced,
has pre viousl y been observed in subaerial volcanic rocks containing
titanomagnetites with compositions ranging from pure magnetite to
approximately TM10-15 (K osterov 2001 ; K osterov et al. 2009 ). It
may be due to a mineral with very low magnetic ordering tem-
perature, or else to extremely fine superparamagnetic grains. The
titanomagnetite phase manifests itself in a magnetic transition at
58 K. Below this temperature, the FC and ZFC curves sharply di-
v erge, as observ ed for titanomagnetites of intermediate composition
(Kosterov et al. 2009 , 2018 ; Almeida et al. 2014 ; Wang et al. 2021 ;
Vigliotti et al. 2022 ). Also, an accelerated magnetization decay
at 30–35 K is observed in the FC curve (see the deri v ati ve curve
d FC/ d T, Fig. 3 b). The origin of this feature remains unclear.
The in-phase AC magnetic susceptibility k
(Fig. 3 c) shows a
fivefold decrease up to ca . 50 K, apparently due to the contribu-
tion of the paramagnetic mineral matrix. Between 50 and 150 K,
frequency-dependent behaviour is seen, manifesting itself also in
the characteristic peaks of the out-of-phase susceptibility (Fig. 3 d).
Similar behaviour has been observed for synthetic titanomagnetites
(Radhakrishnamurty & Likhite 1993 ; Church et al. 2011 ) and more
recently also in titanomagnetite-bearing rocks (Kosterov et al. 2018 ;
Wan g et al. 2021 ; Vigliotti et al. 2022 ).
3.2 Samples annealed at 355
◦C
Fig. 4 summarizes temperature dependencies of magnetic suscep-
tibility measured in argon atmosphere for the samples annealed at
355
◦C. Annealing for only 4 hrs already results in the formation of
new magnetic phases (phases 1 and 2 thereafter) with Curie temper-
atures of 420 and 590
◦C, respecti vel y (Fig. 4 a). At the same time,
a phase close to the initial titanomagnetite survives in a notable
amount, although its Curie point also shifts towards high tempera-
tures (Figs 4 a and e). With increasing annealing duration, the initial
titanomagnetite completely disappears, the Curie temperature of
phase 1 increases, reaching 500
◦C after 375-hr annealing, and the
Curie temperature of phase 2 remains largely unchanged (Figs 4 b–
d). Phase 1 is however unstable to heating to 700
◦C in argon, which
reduces it to essentially the initial titanomagnetite in samples an-
nealed for up to 110 hr (Fig. 4 f). In the sample annealed for 375 hr,
the complete reduction of the initial titanomagnetite is not reached,
traces of phase 1 remain, and the Curie temperature of the reduced
phase is 250
◦C, rather than 205
◦C. The ne wl y formed phase 2
survives the heating to 700
◦C almost unchanged.
The parameters of the hysteresis loops for the annealed samples
are listed in Table 1 , and plotted on a Day–Dunlop diagram (Fig. 5 ).
FORC diagrams for samples annealed at 355
◦C are shown in Fig. 6 .
Increasing annealing time results in a gradual decrease of M
rs
/ M
s
and a matching increase of H
cr /
H
c
ratio. Bearing in mind that grains
are unlikely to grow physically during annealing, this could be due to
relieving internal stress initially present in the fresh material. Along
the same line, inspection of FORC diagrams shows that at the first
stages of annealing, hysteron density distribution narrows, so that
for the sample annealed for 40 hr, the 90 per cent density contour
only reaches about 45 mT (Fig. 6 b) as compared to 65 mT for the
fresh sample. In contrast, at longer annealing times the whole hys-
teron distribution expands significantly (Figs 6 c and d), suggesting
that magnetostatic interactions grow with increasing annealing time.
Increase of interactions would also explain the pro gressi ve reduc-
ing of the bulk coercive force for the samples annealed for 110 and
375 hr. Overall, it may be hypothesized that upon the increase of the
annealing duration, single-domain-like magnetic states would have
an ample amount of time to relax into a more PSD-like states, en-
hancing the hysteron density close to the μ0
H
b
axis (Figs 6 c and d).
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2272 A. Kosterov et al .
Figure 2. Magnetic susceptibility cycles for the fresh P72/4 sample to 300, 500 and 700
◦C in (a) argon atmosphere and (b) in air.
Figure 3. Magnetic properties of the fresh P72/4 sample at cryogenic temperatures. (a) Decay of SIRM given at 1.8 K after ZFC and FC (5 T), respecti vel y,
on warming in a zero field (black and red curves, left ordinate axis), and a zero-field cycle of SIRM given at 300 K (blue curve, right ordinate axis). Note
the different scales on the two ordinates axes. (b) Deri v ati ves of ZFC and FC SIRM decay curves showing magnetic transitions at 58 and 32 K (FC curve
onl y). Deri v ati v e curv es are presented as 51-point adjacent av erages. (c) and (d) Temperature dependencies of the in-phase and out-of-phase AC magnetic
susceptibility, respecti vel y, measured at seven frequencies between 11 and 9500 Hz. Inset in (c) shows a detailed view of frequency-dependent behaviour
between 50 and 140 K.
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Tracing titanomagnetite alteration 2273
Figure 4. (a)–(d) Temperature dependencies of magnetic susceptibility for samples annealed at 355
◦C for 4, 40, 110 and 375 hr, respecti vel y, and deri v ati ves
of (e) heating and (f) cooling curves showing the evolution of Curie temperatures with increasing annealing time.
The effect of prolonged annealings is clearly seen in low-
temperature magnetic properties. For the annealed samples, the
shape of the ZFC and FC SIRM demagnetization curves and the
ratio between them (Fig. 7 ) remain similar to those observed for
the fresh sample, but with some notable differences. At the initial
annealing stage (4 hr), the 58 K transition in the ZFC curve shifts
to about 50 K, and a second transition emerges at about 40 K. On
further annealing, the two transitions coalesce into a single one
at 45 K. The magnetization decay rate below the transition grad-
ually increases (Figs 7 e and f). In the FC curves, the magnetic
transition at 30–35 K gradually disappears with annealing, leav-
ing the single transition at 45 K. The shape of the demagnetization
curv es abov e the transition changes from concav e up to concav e
down, as illustrated by their temperature derivative curves chang-
ing the slope above ca . 60 K from initially ne gativ e to near-zero
for 110 hr annealing time and further to positive for 375 hr (Figs
7 e and f).
The RT-SIRM cycle to 1.8 K in the zero field for the fresh sample
has a characteristic conv e x shape and is almost reversible. Magne-
tization at 1.8 K is about 20 per cent higher than the initial value
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2274 A. Kosterov et al .
Figure 5. Extended view of Day plot (Day et al. 1977 ), showing figurative points for fresh and annealed samples. The first number on the labels is the annealing
temperature in
◦C, second is the annealing time in hours. Solid and dashed lines are SD–MD mixing lines for magnetite (Dunlop 2002 ). Arrow marks directions
towards parameter ranges corresponding to SD and MD grains, respectively.
at 300 K, and magnetization loss after the cycle is only 2–3 per
cent. With increasing annealing time, the shape of RT-SIRM cy-
cles changes pro gressi vel y and the irre v ersibility de gree (defined
here as a loss of SIRM given at 300 K after a cycle to 1.8 K in a
zero field) increases to about 30 per cent for the sample annealed
for 375 hr, in agreement with magnetic softening seen in hysteresis
properties.
In contrast to the remanence, the change in AC magnetic sus-
ceptibility due to annealing manifests itself most strongly above
50 K, where the temperature dependencies of the in-phase sus-
ceptibility k
change the shape dramatically (Figs 8 a, c, e and
g), remaining, ho wever , frequency-dependent between 50 and
150 K. Some what surprisingl y, characteristic peaks of the out-of-
phase susceptibility occur at nearly the same temperatures for
all annealing times, gradually increasing in intensity (Figs 8 b,
d, f and h).
3.3 Samples annealed at 500 and 550
◦C
Annealing at 500 and 550
◦C for 4 hr produces two magnetic phases
with Curie temperatures of about 500 and 560–570
◦C (Figs 9 a, c,
e and g). At a more prolonged annealing for 110 hr at the same two
temperatures, a seemingly single phase is produced with Curie tem-
peratures of 575 and 550
◦C, respecti vel y. Howe ver, the annealed
samples are not entirely stable to heating to 700
◦C in an argon
atmosphere. For samples annealed for 4 hr, Curie temperature de-
termined from the cooling curves is significantly lower than those
obtained from the heating curves (compare Figs 9 e and g, and 9 f and
h). In samples annealed for 110 hr, a single phase seen in heating
curv es disinte grates into two phases with close but distinct Curie
temperatures on cooling.
FORC diagrams for samples annealed at 500 and 550
◦C are
shown in Fig. 10 . All diagrams extend to nearly 150 mT along
the μ0
H
c axis, more than twice compared to those measured for
the fresh sample and samples annealed at 355
◦C. The spread of
the FORC distribution along the μ0
H
b axis is also notably larger,
whereas the downward shift of the distribution maximum relative
to the μ0
H
c = 0 line increases. Overall, hysteron density distri-
bution appears more single-domain-like in these samples, in line
with considerably enhanced coercive force and coercivity of re-
manence (compare Figs 1 c and 5 , on one hand, and Fig. 10 on
the other). Increased downward shift of the distribution maxi-
mum with respect to the μ0
H
c = 0 line may indicate a more sig-
nificant magnetostatic interaction between SD-like regions. How-
ever, the details var y depending on the annealing temperature. At
500
◦C, coercivity increases with annealing time and the M
rs
/ M
s
ratio changes only slightly compared to the fresh sample, while
at 550
◦C both the M
rs
/ M
s ratio and coercivity are maximal af-
ter 4 hr of annealing and decrease considerably after 110 hr of
annealing.
The properties at cryogenic temperatures exhibit pro gressi ve
changes with annealing temperature and duration. The magnetic
transition shifts to still lower temperatures, 38–39 K for the sam-
ples annealed at 500
◦C, and 34–36 K for those annealed at 550
◦C
(Fig. 11 ). The difference between the ZFC and FC curves persists,
but the slope of the ZFC curve below the transition is significantly
greater than for the samples annealed at 355
◦C. The sample an-
nealed at 500
◦C for 110 hr also exhibits a broad Ve r w ey transition
centred at 95 K, indicating that in this case, the ne wl y formed phase
is close to magnetite. Zero-field RT-SIRM cycles develop fairly
strong irreversibility, similar to that previously observed in rocks
containing titanomagnetite of TM10–TM30 composition (Kosterov
et al. 2009 , 2018 ).
The shape of susceptibility temperature dependencies in the
2–300 K range evolves to develop well-pronounced frequency-
dependent maxima of the in-phase susceptibility (Figs 12 a, c, e
and f). On the other hand, the maxima of the out-of-phase sus-
ceptibility (Figs 12 b, d, f and h) decrease in magnitude and shift
to considerably lower temperatures ( ca . 45–60 K) compared to the
samples annealed at 355
◦C.
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Tracing titanomagnetite alteration 2275
Figure 6. FORC distributions for samples annealed at 355
◦C. Smoothing factors, SFc = SFb = 2 and damping factors, λc = λb = 0.04 have been used to
calculate all distributions. Contours are drawn every 10 per cent of maximum hysteron density. Dashed lines mark the location of the maximum.
4 DISCUSSION
4.1 Low-temperature magnetic properties of intermediate
titanomagnetites
Temperature-dependent behaviour of remanence and AC mag-
netic susceptibility in magnetic materials is governed b y se v-
eral factors, of which magnetic phase transitions, if present,
are by far the most significant ( cf. Dunlop & ¨
Ozdemir 1997 ).
Temperature variation of the intrinsic material properties such
as magnetocrystalline anisotropy and magnetostriction also plays
an essential role. All of these factors are, in turn, affected
by the stoichiometry of the material and the degree of crys-
tallinity. On top of this, the low-temperature variation of rema-
nence and magnetic susceptibility is in most cases grain-size
dependent.
T itanomagnetites Fe
3 −x
T i
x
O
4
with x > 0.035 do not exhibit the
Verwe y transition (Kozłowski et al. 1996 ), resulting in a major
change in their low-temperature magnetic behaviour, compared to
magnetite. The signature of the Ve r wey transition disappears from
demagnetization curves of remanence given below the transition
temperature (typicall y, 2–20 K); howe ver, irre versibility of zero-
field cycles of remanence given at 300 K persists in some cases
(
¨
Ozdemir & Dunlop 2003 ; Kosterov et al. 2009 , 2018 ) though not
uni versall y ( cf. Wan g et al. 2021 ). This beha viour ma y be due to
the temperature dependence of the magnetocrystalline anisotropy
that remains qualitati vel y similar to that of magnetite for a wide
range of compositions, approximately up to x ∼0.4. For such ti-
tanomagnetites, the first constant of magnetocrystalline anisotropy
K
1 is ne gativ e at 300 K. Upon temperature decrease, its absolute
value first increases and then starts to decrease, approaching zero
at the so-called isotropic point. With increasing Ti content, the
isotropic point temperature first shifts to ward lo wer temperatures,
to below 77 K for the material with x = 0.18–0.36 (Syono 1965 ;
K
akol et al. 1991 ), and then starts to increase again, so that titano-
magnetite with the nominal composition TM41 has an isotropic
point of about 125 K, very close to that of magnetite (K
akol et al.
1991 ). For still more Ti-rich compositions, K
1
turns positive at all
temperatures below 300 K (Syono 1965 ; K
akol et al. 1991 ), and
is strongly temperature-dependent increasing sharply to very high
values below 200 K.
The variation of magnetostriction with temperature for inter-
mediate titanomagnetites is known only in the 100–300 K range
(Klerk et al. 1977 ). Unlike that of the magnetocrystalline anisotropy,
temperature dependence of magnetostriction changes significantly
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2276 A. Kosterov et al .
Figure 7. (a)–(d) Decay of SIRM given at 1.8 K after ZFC and FC (5 T), respecti vel y, on w arming in a zero field (black and red curves, left ordinate axis), and
a zero-field cycle of SIRM given at 300 K (blue curve, right ordinate axis) for samples annealed at 355
◦C. Note the different scales on the two ordinates axes.
Annealing time is indicated in the figures. (e) and (f) Evolution of deri v ati v e curv es of ZFC and FC SIRM decay, respecti vel y, with increasing annealing time.
Deri v ati v e curv es for the fresh sample are plotted for reference. Deri v ati v e curv es are presented as 51-point adjacent av erages.
with increasing Ti content. Both λ100 and λ111 constants rapidly
increase and develop a notable temperature dependence for com-
positions with x > 0.2. For example, at 100 K, λ111 is a factor
of 5, and λ100 is a factor of 20 higher for TM40 titanomag-
netite than for magnetite. Magnetostriction is considered to be
a primary factor that controls the magnetic behaviour of both
magnetite- (Hodych 1982a ) and TM60-bearing rocks (Hodych
1982b ) between 100 and 300 K. Therefore, it may be inferred
that the properties of the fresh P72/4 sample containing titano-
magnetite of an average TM46 composition are also governed by
magnetostriction.
ZFC/FC remanence decay curves of the fresh P72/4 basalt show
a characteristic pattern. Below the magnetic transition, which in
our case occurs at 58 K, the remanence in the FC state is consid-
erably higher than the remanence in the ZFC state, but decreases
with increasing temperature at a much higher rate. As a result,
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Tracing titanomagnetite alteration 2277
Figure 8. Temperature dependencies of (a), (c), (e) and (g) in-phase and (b), (d), (f) and (h) out-of-phase AC magnetic susceptibility measured at seven
frequencies between 11 and 9500 Hz for samples annealed at 355
◦C. Annealing time is (a) and (b) 4 hr, (c) and (d) 40 hr, (e) and (f) 110 hr and (g) and (h)
375 hr. Insets in (a) and (c) show detailed views of frequency-dependent behaviour.
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2278 A. Kosterov et al .
Figure 9. (a) and (b) Temperature dependencies of magnetic susceptibility for samples annealed at 500
◦C for 4 and 110 hr, respecti vel y; (c) and (d) the same
for samples annealed at 550
◦C; (e) and (f) deri v ati ves of heating and cooling susceptibility curves for samples annealed at 500
◦C for 4 and 110 hr, respecti vel y
and (g) and (h) the same for samples annealed at 550
◦C.
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Tracing titanomagnetite alteration 2279
Figure 10. FORC distributions for samples annealed at (a) and (b) 500
◦C and (c) and (d) 550
◦. Smoothing factors, SFc = SFb = 2 and damping factors, λc
= λb = 0.04 have been used to calculate all distributions. Contours are drawn every 10 per cent of maximum hysteron density. Dashed lines mark the location
of the maximum.
the area between the FC and ZFC remanence decay curves has a
recognizable triangular shape. This behaviour has previously been
observed in synthetic titanomagnetites (Almeida et al. 2014 ) and in
titanomagnetite-bearing rocks (Kosterov et al. 2009 , 2018 ; Wa ng
et al. 2021 ). It should be noted that Curie temperatures of these sam-
ples vary widely, from < 200
◦C (Sample S3 of Almeida et al. 2014
and Sample 39I-TVG02 of Wan g et al. 2021 ) to > 500
◦C (Sample
P15 of Kosterov et al. 2009 ), implying that the above pattern only
weakly depends on the composition of titanomagnetite. Ho wever , it
seems that in more Ti-rich titanomagnetites the decay rate of ZFC
remanence is lower than in their Ti-poor counterparts (compare, e.g.
our P72/4 sample and sample 39I-TVG02 of Wa ng et al. 2021 ), but
this observation needs further confirmation on a larger number of
samples.
Unlike the remanence given at a low temperature, zero-field
300 K—LT—300 K SIRM cycles of intermediate titanomagnetites
show a variety of behaviours, from nearly reversible (sample P15,
Kosterov et al. 2009 ; sample S3, Almeida et al. 2014 ; sample 39I-
TVG02, Wan g et al. 2021 ; sample P72/4, this study) to highly irre-
versible (e.g. sample S2, Almeida et al. 2014 ; most samples in Kos-
terov et al. 2018 ). Again, there seems to be a trend that more Ti-rich
samples show a higher degree of reversibility, but it is by no means
uni versal, as demonstrated b y the example of sample P15 having the
Curie temperature of 535
◦C (Kosterov et al. 2009 ). With increasing
Ti content in titanomagnetite, magnetostriction increases faster than
magnetocrystalline anisotropy. It may be conjectured therefore that
in more Ti-rich titanomagnetites magnetostriction is a dominant
factor controlling remanence behaviour at cryogenic temperatures.
Ho wever , if stress is sufficiently high, magnetostriction may gov-
ern remanence even in relatively Ti-poor titanomagnetite, like one
in the P15 sample of Kosterov et al. ( 2009 ). Given the above, in
fresh P72/4 basalt, remanence behaviour appears to be controlled
by magnetostriction.
4.2 How does alteration affect the low-temperature
magnetism of P72/4 basalt?
A comparison of the magnetic properties of the samples annealed
at 355 and 500 or 550
◦C shows that the alteration follows sig-
nificantl y dif ferent paths depending on the annealing temperature.
Annealing at 355
◦C produces two magnetic phases with Curie tem-
peratures ranging from 420
◦C to approximately 500
◦C for phase
1, and about 580–590
◦C for minor phase 2. No signs of the Ver -
wey ( 1939 ) transition are observed in low-temperature experiments
(Figs 7 and 8 ) ruling out the possibility that phase 2 can be a sto-
ichiometric magnetite. Phase 1 could be either titanomagnetite or
titanomaghemite. Ho wever , an increase in the Curie temperature by
nearl y 300
◦C would impl y a v ery high de gree of o xidation cor -
responding to values of the oxidation factor z > 0.8 (Readman &
O’Reilly 1972 ). Titanomaghemites in this composition range show
completel y re v ersible zero-field SIRM c ycles between 300 and 5 or
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2280 A. Kosterov et al .
Figure 11. (a) and (b) Decay of SIRM given at 1.8 K after ZFC and FC (5 T), respecti vel y, on w arming in a zero field (black and red curves, left ordinate axis),
and a zero-field cycle of SIRM given at 300 K (blue curve, right ordinate axis) for samples annealed at 500
◦C. Note the different scales on the two ordinates
axes. Annealing time is indicated in the figures. Panel (c) displays an enlargement of the plot in panel (b) with overlapped FC deri v ati ve curve showing a broad
Verw ey transition centred at 95 K; and (d) and (e) Same as (a) and (b), but for samples annealed at 550
◦C.
10 K, and magnetization may even self-reverse at the lowest tem-
perature (Doubrovine & Tarduno 2004 , 2006a , b ; Kr
´
asa & Matzka
2007 ). In our samples, an entirel y dif ferent behaviour is observed,
with the irreversibility of SIRM cycles increasing with increas-
ing annealing time. This resembles the properties observed in vol-
canic rocks containing titanomagnetites of TM10–TM30 composi-
tion (Kosterov et al. 2009 , 2018 ). Therefore, maghemitization does
not appear a viable explanation for the observed low-temperature
magnetic properties of annealed P72/4 samples.
Bearing this in mind, we prefer a hypothesis put forward by
Bowles and co-authors (Bowles et al. 2013 , 2019 ; Jackson & Bowles
2018 ) that shift of titanomagnetite Curie temperatures to higher
values after annealing at a relatively moderate (355
◦C) tempera-
ture could be at least partly due to increasing ionic order in the
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Tracing titanomagnetite alteration 2281
Figure 12. Temperature dependencies of (a), (c), (e) and (g) in-phase and (b), (d), (f) and (h) out-of-phase AC magnetic susceptibility measured at seven
frequencies between 11 and 9500 Hz for samples annealed at 500 and 550
◦C. Annealing time at 500
◦C (a) and (b) 4 hr, and (c) and (d) 110 hr, at 550
◦C (e)
and (f) 4 hr, and (g) and (h) 110 hr. Out-of-phase susceptibility is essentially constant above 140 K, and so the respective plots are truncated at this temperature
to show frequency-dependent behaviour. Insets in (a) and (e) show detailed views of frequency-dependent behaviour of the in-phase susceptibility.
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2282 A. Kosterov et al .
titanomagnetite spinel lattice. Fur ther more, this process appears
to be reversible to some extent, as indicated by restoring close to
original Curie temperatures after heating to 700
◦C in an argon at-
mosphere (Figs 4 a–d). For the samples annealed for up to 110 hr,
the Curie temperatures deduced from cooling susceptibility versus
temperature curves are about 220
◦C, and for the sample annealed
for 375 hr—260
◦C (Fig. 4 f). The increase of Curie temperatures of
the phase produced by annealing is also accompanied by changes
in the shape of temperature dependencies of AC susceptibility at
cry ogenic temperatures (F ig. 8 ). At the same time, magnetic soft-
ening of titanomagnetite grains occurs with increasing annealing
time, as indicated by (i) points in the Day plot moving towards
the multidomain (MD) range (Fig. 5 ), (ii) appearance of MD-like
signal in FORC diagrams particularly for the samples annealed for
110 and 375 hr (Figs 6 c and d), and (iii) increase of irreversibil-
ity of low-temperature zero-field cycles of SIRM given at 300 K
(Figs 7 a–d). Taken together, these obser vations fur ther confir m that
prolonged annealing at 355
◦C results in a considerable lessening
of the internal stress in titanomagnetite grains, and magnetostric-
tion becomes less important in controlling remanence properties at
cryogenic temperatures.
By contrast, annealing at 500 and 550
◦C first produces two mag-
netic phases with Curie temperatures of about 500 and 560
◦C,
respecti vel y (Fig. 9 ). Upon longer (110 hr) annealing, these phases
coalesce into a single phase. Interestingly, the Curie temperature
of the product phase is somewhat higher (577
◦C) for the sample
annealed at 500
◦C than for the sample annealed at 550
◦C (553
◦C).
The former sample is the only one exhibiting the Ve r wey transition,
characteristic of magnetite with Ti content < 3.5 at. per cent per
formula unit (Kozłowski et al. 1996 ); howe ver, e ven in this sam-
ple the signature of the Verwe y transition is faint and occurs on
the tail of remanence surviving above 40 K. In some cases, further
heating to 700
◦C in an argon atmosphere during the susceptibility
v ersus temperature e xperiment produces a Ve r we y transition-like
response in low-temperature susceptibility curves measured after
completing the high-temperature cycle ( cf. Figs 9 b and c). The un-
derlying process in both cases appears to be the high-temperature
exsolution, similar to that observed in the same basalt cooled from
570 to 569
◦C at a rate of 1
◦C h
−1
and then quickly cooled to room
temperature (see figs 2 d and f in Shcherbakov et al. 2019 ). It is
w orth noting ho wever that the Curie temperature of about 300
◦C,
which we ascribe to a titanomagnetite phase subjected to a partially
reversible ionic reordering, is clearly seen in a susceptibility vs. tem-
perature cooling from 500
◦C curve of the fresh sample (Fig. 2 b)
and in the cooling curve of the sample annealed at 500
◦C for 4 hr
(Fig. 9 f).
At the same time, the general shape of low-temperature rema-
nence (Fig. 11 ) and AC susceptibility curves (Fig. 12 ) remain sim-
ilar to those typical for more Ti-rich intermediate titanomagnetites
(Kosterov et al. 2009 , 2018 ; Almeida et al. 2014 ). The two most
prominent features in remanence curves are: (i) a characteristic tri-
angular shape separating FC and ZFC curves, and (ii) cooling and
warming branches of the RT-SIRM zero-field c ycle conv erging be-
tween 50–70 K. A possible explanation of this conundrum might
be that an e xsolv ed phase with near-magnetite Curie temperatures
but without the Ve r we y transition is a titanomaghemite with both
moderate Ti content (say, 0.10–0.15 Ti atoms per formula unit) and
a moderate degree of oxidation such as not to modify the behaviour
at cryogenic temperatures significantly. If the Curie temperature of
this phase and its magnetic hysteresis properties were to be like
those of magnetite, it would be impossible to distinguish the two
phases without performing measurements at cryogenic tempera-
tures. A similar explanation may also apply to the absence of the
Verwe y transition in archaeological ceramics that often contain a
magnetically soft phase with Curie temperatures extending up to
560–580
◦C (Kosterov et al. 2021 ; Troyano et al. 2021 ).
5 CONCLUSIONS
Comparison of the magnetic properties of basalt samples annealed at
355 and 500 or 550
◦C shows that alteration of the initial relati vel y
high-Ti titanomagnetite follows two significantly different paths
depending on the annealing temperature, clearly reflected in the
magnetic properties of samples at cryogenic temperatures.
In the first case, two magnetic phases are formed with Curie
temperatures ranging from 420 to about 500
◦C for phase 1 and about
580–590
◦C for a minor phase 2. The latter cannot be magnetite
because of the absence of a Verwe y transition. An increase in the
Curie temperature of phase 1 with increasing annealing time is
likely associated with an increase in the degree of ionic order in the
spinel lattice of titanomagnetite (Bowles et al. 2013 ), and not with
maghemitization.
At the initial stage of annealing at 500 and 550
◦C, two magnetic
phases are formed with Curie temperatures of about 500 and 560
◦C,
respecti vel y. At a longer (110 hr) annealing, these phases appear to
coalesce into a single one. The shape of the low-temperature mag-
netization and susceptibility curves of the annealed samples is how-
ever reminiscent of more Ti-rich titanomagnetites of composition
TM10–15, whose Curie temperatures are several tens of degrees
lower. The explanation for this discrepancy may be that the phase
with a Curie temperature close to magnetite but not showing the
Verwe y transition is a titanomaghemite with a moderate Ti content
and a relati vel y low degree of oxidation not sufficient to signifi-
cantly alter the behaviour at cryogenic temperatures characteristic
for stoichiometric titanomagnetite.
The results of this study contradict the generally accepted
idea that upon the initial stage of annealing, titanomagnetite
is oxidized according to a single-phase mechanism, forming ti-
tanomaghemite. Indeed, the magnetic properties of highly oxidized
titanomaghemites at cryogenic temperatures (Doubrovine & Tar-
duno 2004 , 2006a , b ; Kr
´
asa & Matzka 2007 ) are known to be entirely
dif ferent. For moderatel y oxidized ( z < 0.5) titanomaghemites, there
are practically no data, but it is difficult to envisage a pathway how
a sample such as one annealed for 375 hr at 355
◦C in this study
would, with further oxidation, develop the low-temperature mag-
netic properties like described by Doubrovine & Tarduno ( 2004 ,
2006a ; 2006b) and Kr
´
asa & Matzka ( 2007 ). Therefore, we sug-
gest that under ‘dry’ heating conditions, titanomagnetite oxidation
does not occur, at least at short timescales, while the correspond-
ing change in magnetic properties is controlled by the reordering
of Ti ions in the titanomagnetite lattice (Bowles et al. 2013 , 2019 ;
Jackson & Bowles 2018 ).
Overall, the magnetic properties of P72/4 basalt samples an-
nealed for different times at different temperatures show significant
variation, resulting from the neoformation of different magnetic
phases with distinct Curie temperatures. These results highlight the
importance of carefully controlling the heating temperature and
time when conducting palaeointensity determinations using con-
ventional methods that involve multiple temperature steps. The oc-
currence of multiple titanomagnetite and titanomaghemite phases,
both original and ne wl y formed, can complicate the interpretation of
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Tracing titanomagnetite alteration 2283
palaeointensity data and would require additional analytical tech-
niques to accurately characterize the magnetic properties of the
samples.
ACKNOWLEDGMENTS
This study has been supported by Russian Foundation for Basic
Research, grants 19–05-00471 to AK and 20–05-00573 to VM.
Experimental studies have been performed using the facilities of
the Scientific Park of St Petersburg University at the Centre for
Diagnostics of Functional Materials for Medicine, Pharmacology
and Nanoelectronics, the Centre for Geo-Environmental Research
and Modelling (GEOMODEL) and the Centre for Microscopy and
Microanalysis. FORC measurements have been carried out at the
Institute of Physics of the Earth RAS, Moscow. AK thanks Vladimir
Pavlov for hosting his visit, and Pavel Minaev for help with mea-
surements. This paper has benefitted from the re vie ws b y Thomas
Berndt and anonymous reviewer, and from editorial comments by
Eduard Petrovsk
´
y.
DATA AVAILABILITY
The data underlying this paper will be shared on reasonable request
to the corresponding author.
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