P. Robinson’s research while affiliated with Norges geologiske undersøkelse and other places
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The spin orientation in synthetic hematite-ilmenite samples and in a sample of natural hematite was studied from room temperature to above the antiferromagnetic-paramagnetic phase transition (the Néel temperature; ≈ 600 − 950 K ) by neutron powder diffraction and at room temperature by Mö ssbauer spectroscopy. The usually assumed magnetic structure of hematite within this temperature range is antiferromagnetic with the spins confined to the basal plane of the hexagonal structure , however, an out-of-plane spin component is allowed by the symmetry of the system and has been observed in recent studies of synthetic hematite samples. We find the spins in the antifer romagnetic sublattices to be rotated out of the basal plane by an angle between 11 (2)° and 22.7(5)° in both synthetic hematite-ilmenite samples and in the natural hematite sample. The spin angle remains tilted out of the basal plane in the entire temperature range below the Néel temperature and does not depend systematically on Ti-content. The results indicate that the out-of-plane spin component is an intrinsic feature of hematite itself, with an origin not yet fully understood, but consistent with group theory. This represents a major shift in understanding of one of the two main mineral systems responsible for rock magnetism.
A spatially averaged mean-field model for fully or partially ordered members of the ilmenite–hematite solid solution series is rigorously derived from the Heisenberg Hamiltonian by first assuming no temporal correlation of atomic spins, and then by spatially averaging over spins at equivalent atomic positions. The model is based on the geometry of exchange interactions between nearest and next-nearest neighbours and predicts magnetization curves in homogenous solid solutions with variable degree of order. While the general framework presented can also be applied to atomic scale models, and to other solid solution series, here the symmetries of the ilmenite–hematite lattice are exploited to show that four different sublattice magnetizations and six independent combinations of exchange constants determine the temperature variation of the magnetization curves. Comparing measured Curie temperatures T C and M s ( T ) curves to model predictions results in accurate constraints for these combinations. It is also possible to calculate predictions for high-field magnetization slopes χ HF , which not only improve accurate experimental determination of the Curie temperature but also provide a new magnetic method to estimate the order parameter for ilmenite–hematite solid solution samples.
New experimental and computational approaches to interpret orientation
and intensity of natural remanent magnetization (NRM) carried by
lamellar magnetism are applied to historic magnetic measurements on a
collection of 82 massive hemo-ilmenite samples from the Allard Lake
District in the Grenville Province, Quebec. The anisotropy of magnetic
susceptibility (AMS), together with declination and inclination of NRM,
indicate a systematic deflection β of the NRM vector away from the
unit vector v that represents the Mesoproterozoic magnetizing field
direction. The deflection β is caused by a statistical
lattice-preferred orientation (LPO) of the individual (0001) basal
planes, to which the NRM is confined in hemo-ilmenite crystals. Here, we
study a second deflection ψ that is the angle the NRM makes with the
statistical (0001) basal plane of the crystal assemblage, in relation to
the angle α between the statistical (0001) basal plane and v. The
relation between these two angles depends on the scatter of the
distribution of crystal platelets, which also influences the AMS of the
assemblage. For a Fisher distribution of basal planes, the distribution
parameter K can be determined from ψ and α. It is then further
possible to infer the single-crystal anisotropy of individual platelets.
Typical crystals of hemo-ilmenite turn out to have a relatively weak AMS
so that samples with a narrow Fisher distribution of platelets
nevertheless can have a weak AMS. This has been confirmed in two samples
by measurement of the (0001) basal plane distribution of crystals using
electron backscatter diffraction, and in one of these two samples by
measuring AMS and NRM of a single hemo-ilmenite crystal. Based on our
estimated K values for selected samples, we calculate values of β,
NRM intensity and ψ for any value of α. These data provide
striking examples of the influence of the orientation of the crystal LPO
on the intensity of lamellar magnetism, and explain the large variation
of observed NRM intensities by varying orientation with respect to the
magnetizing field, without requiring large variations of the
paleomagnetic field intensity. This relation between NRM and LPO is also
important for anomaly interpretation in areas with strong foliation.
In the 1950's, rocks containing ferri-ilmenite solid solutions with
compositions X FeTiO3 = 0.53-0.71 were discovered to self-reverse during
cooling in a weak field. Such samples played a vexing early role in the
history of geomagnetism, because they demonstrably acquire a
thermoremanent magnetization (TRM) inverse to the external field,
strengthening a common opinion, at that time, that reversed lavas result
from a rock-magnetic self-reversal process, while the geomagnetic field
polarity itself is constant in time. Early self-reversal models
postulated two distinct phases, a subsidiary phase with weak
magnetization, and higher Fe content, Curie temperature, and coercivity,
referred to as "the x phase", and a dominant phase with a strong
magnetization, lower Fe content, Curie T temperature, and coercivity.
The "x phase" magnetizes first at higher temperature parallel to the
Earth field, and the dominant phase acquires a stronger magnetization at
a lower temperature in an orientation opposite to the Earth field,
either by direct antiferromagnetic coupling, or as a magnetostatic
response to the previously acquired mineral magnetization. Landmark
work by Nord and Lawson, on quench and annealing experiments with TEM,
showed that, during quench, the solid solution starts to order, but with
alternate A and B positioning of Fe and Ti layers. With coarsening, the
alternately and chaotically positioned domains merge along antiphase
domain boundaries (APBs) that are inherently unstable. With further
annealing, boundaries move and are eliminated due to coarsening of some
domains and shrinking of others. They showed that quenched, or slightly
annealed samples, show self-reversed TRM, but further annealing results
in a coarse simple ferrimagnetic phase. They suggested that the "x
phase" is represented by the disordered regions along the chemical
antiphase boundaries. Harrison visualized a solid solution sample,
after quench and coarsening after annealing, which consisted of two
kinds of regions, one dominated by A-ordering containing smaller regions
of B-ordering and the other dominated by B-ordering with smaller regions
of A-ordering. The key feature for self-reversal is that small and
shrinking domains became progressively Fe-enriched compared to their
larger neighbors, and the elusive "x-phase" is explained as a less
strongly ordered Fe-enriched phase near APBs during coarsening. We
pursued these studies further with TEM of the APB's and demonstrating
chemical phase separation in a synthetic composition FeTiO3 = 0.61.
Subsequent annealing of this sample showed self-reversed TRM and
room-temperature magnetic exchange bias. Analysis of charge balance
across APB's showed the significant role of contact layers and
disordered layers. Monte Carlo simulations demonstrated the necessity
for Fe-enrichment in the diminishing phase. A theoretical approach to
the ferri-ilmenite phase diagram showed potential for metastable
chemical phase separation over a wide composition range, related to the
order parameter Q, at temperatures well above phase separation over a
limited composition range related to a chemical solvus. A key feature
of the new perspective is the recognition of simple antiferromagnetic
coupling across the APBs. Evidence suggests negative magnetic
(antiferromagnetic) coupling required for magnetic self-reversal can
only be maintained when the antiphase domains are smaller than ~ 50 nm.
Magnetic anomalies on Earth are being measured with increasing accuracy
over a wide range of length scales and elevations, from near surface to
satellites. Crustal anomalies, which are deviations from Earth's
planetary field, reflect the magnetic minerals, the geographic locations
where these minerals were magnetized, and the intensity of the planetary
magnetic field at the time of magnetization. Anomalies are also
influenced by the geometry of the geological bodies, their fabric, the
magnetic and mineralogical properties of the rocks, and any subsequent
change, such as metamorphism or alteration following initial
magnetization. Magnetism of the continental crust is commonly described
in terms of bulk ferrimagnetism of crustal minerals, and most anomalies
are attributed to induced magnetization. Remanent magnetization proved
crucial for dating the ocean floor, yet the contribution of remanence to
continental magnetic anomalies is still underestimated. In the study of
the mineral sources of continental anomalies, we have explored the
nature of different exsolution intergrowths and microstructures, which
enhance the remanent component, either by providing additional
magnetizations, such as lamellar magnetism, or by enhancing stability
due to fine-scale intergrowths. Here we show that lamellar magnetism is
responsible for numerous remanent continental magnetic anomalies.
Anomalies may differ depending on whether multi-domain magnetite
coexists with one or more lamellar magnetic phases, or whether the rock
only contains lamellar magnetic phases. Due to its high thermal and
magnetic stability, lamellar magnetism can be an important contributor
to deep-seated anomalies on Earth, and to anomalies on other planets,
like Mars. Understanding of the fundamental nature and stability of
magnetic minerals in direct relation to their geological setting will
continue to expand in importance with the growing demand for mineral
exploration by magnetic methods.
Magnetic anomalies from crustal sources are measured over a wide range
of scales and elevations, from near-surface to satellites. They reflect
magnetic minerals in rocks, which respond to the changing planetary
magnetic field. Anomalies are influenced by the geometry of the
geological bodies, and magnetic properties of the minerals. Commonly,
magnetism of continental crust has been described in terms of bulk
ferrimagnetism of minerals, and much attributed to induced
magnetization. Though remanent magnetization was crucial for dating the
ocean floor, and is important in mineral exploration, its contribution
to continental magnetic anomalies is commonly ignored. Over the last
decade studying remanent anomalies in crustal rocks, we discovered a new
type of remanence, 'lamellar magnetism'. This is due to layers of mixed
Fe2+/Fe3+ valence at (001) contacts between exsolution lamellae and
hosts of ilmenite and hematite. The mixed-valence contact layers are
placed by chemistry between hematite Fe3+ layers and ilmenite Ti4+
layers, where they provide reduction of ionic charge imbalance.
Placement requires that the uncompensated spin of contact layers on
opposite sides of a lamella be in-phase magnetically. This produces a
net ferrimagnetic moment per lamella of ~4 uB per formula unit,
regardless of lamella thickness, thus net moment is greatest with the
greatest density of magnetically in-phase fine lamellae created during
slow cooling. We can show that in-phase magnetization of lamellae is
greatly enhanced in foliated samples, where the statistical (001) plane
is parallel to the Earth field at the time of exsolution. Strictly
speaking, the resulting magnetization is a chemical remanence with very
high stability. Lamellar magnetism is responsible for numerous remanent
magnetic anomalies in continental rocks we present here. We highlight
some bodies with NRMs > 20 A/m which are possible analogs for sources
of remanent anomalies on Mars.
The theory of lamellar magnetism arose through search for the origin of the strong and extremely stable remanent magnetization (MDF>100 mT) recorded in igneous and metamorphic rocks containing ilmenite with exsolution lamellae of hematite, or hematite with exsolution lamellae of ilmenite. Properties of rocks producing major remanent magnetic anomalies could not be explained by PM ilmenite or CAF hematite alone. Monte Carlo modeling of chemical and magnetic interactions in such intergrowths at high temperature indicated the presence of "contact layers" one cation layer thick at (001) interfaces of the two phases. Contact layers, with chemical composition different from layers in the adjacent phases, provide partial relief of ionic charge imbalance at interfaces, and can be common, not only in magnetic minerals. In rhombohedral Fe-Ti oxides, magnetic moments of 2 Fe2+Fe3+ contact layers (2 x 4.5µB) on both sides of a lamella, are balanced by the unbalanced magnetic moment of 1 Fe3+ hematite layer (1 x 5µB), to produce a net uncompensated ferrimagnetic "lamellar moment" of 4µB. Bulk lamellar moment is not proportional to the amount of magnetic oxide, but to the quantity of magnetically "in-phase" lamellar interfaces, with greater abundance and smaller thickness of lamellae, extending down to 1-2 nm. The proportion of "magnetically in-phase" lamellae relates to the orientation of (001) interfaces to the magnetizing field during exsolution, hence highest in samples with a strong lattice-preferred orientation of (001) parallel to the field during exsolution. The nature of contact layers, ~0.23 nm thick, with Fe2+Fe3+ charge ordering postulated by the Monte Carlo models, was confirmed by bond-valence and DFT calculations, and, their presence confirmed by Mössbauer measurements. Hysteresis experiments on hematite with nanoscale ilmenite at temperatures below 57 K, where ilmenite becomes AF, demonstrate magnetic exchange bias produced by strong coupling across phase interfaces. Interface coupling, with nominal magnetic moments perpendicular and parallel to (001), is facilitated by magnetic moments in hematite near interfaces that are a few degrees out of the (001) plane, proved by neutron diffraction experiments. When a ~b.y.-old sample, with a highly stable NRM, is ZF cooled below 57 K, it shows bimodal exchange bias, indicating the presence of two lamellar populations that are magnetically "out-of-phase", and incidentally proving the existence of lamellar magnetism. Lamellar magnetism may enhance the strength and stability of remanence in samples with magnetite or maghemite lamellae in pure hematite, or magnetite lamellae in ilmenite, where coarse magnetite or maghemite alone would be multi-domain. Here the "contact layers" should be a complex hybrid of 2/3-filled rhombohedral layers parallel to (001) and 3/4-filled cubic octahedral layers parallel to (111), with a common octahedral orientation confirmed by TEM observations. Here, because of different layer populations, the calculated lamellar moment may be higher than in the purely rhombohedral example.
Lamellar magnetism is a type of magnetic remanence, carried by uncompensated magnetic moments in monolayers at interfaces between nanoscale exsolution structures of antiferromagnetic hematite and paramagnetic ilmenite. Lamellar remanence is commonly found in rocks which have a very low susceptibility, implying a low concentration of magnetic oxides. Remanence in these rocks is considerably higher than the induced magnetization, resulting in high Q-ratios which can be larger than 100. During recent years, lamellar magnetism has advanced from a hypothesis into an experimentally and theoretically verified theory. The main steps of this development will be outlined in this presentation, and possible implications for other mineral systems will be discussed. There remain a number of open questions. Most important for paleomagnetic studies is the acquisition of lamellar NRM during cooling and the exsolution process. Experiments indicate that this NRM acquisition is extremely efficient, which poses strong constraints on the physical processes involved. Studies on several magnetic anomalies have shown that, when coexisting MD magnetite is present, it increases rather than decreases coercivity, intensity, and even Q-values. A possible explanation is magnetostatic coupling between the highly efficient lamellar NRM and the magnetically soft MD magnetite.
Magnetic exploration on local and global scale is focused on interpreting magnetic anomalies in terms of induced magnetization in today's geomagnetic field. However, numerous anomalies in Norway, Sweden and USA originate from rocks with oxide exsolution intergrowths with an overwhelmingly dominant magnetic remanence. In these rocks different magnetic minerals control induced versus remanent magnetization. Although, different types of magnetic interaction control the details of their potential to create anomalies, little is known about the detailed interplay between them. Using a newly developed giant-magnetoresistance micro-scanner, it is now possible to map remanent and induced magnetization at the mineral size scale from 10 micron up to several millimeters. In case studies presented here, Lamellar Magnetization (LM) accounts for the strong and stable magnetic signal in the rhombohedral oxides which produces significant large-scale negative anomalies. We explore experimentally and theoretically how the co-existing multi-domain magnetite and LM contributes to these anomalies, and correlate the mineral-scale maps with ground-magnetic traverses and high- resolution airborne surveys. This combination of methods provides a new paradigm for interpretation of remanence -dominated magnetic anomalies in Earth and planetary applications.
Citations (32)
... E Motion recognition is an important part of affective computing, which focuses on identifying and understanding human emotions from facial expressions [1], body gestures [2], speech [3], physiological signals [4], etc. It has potential applications in healthcare and human-machine interactions, e.g., emotion health surveillance [5] and emotion-based music recommendation [6]. ...
... Spins at Fe ions in the same Fe-Fe double atomic layers are ferromagnetically aligned; those in the adjacent Fe-Fe double atomic layers are antialigned. Recently, an out-of-plane spin component from the (0001) basal plane in pure α-Fe 2 O 3 was reported by neutron diffraction 17 . Below T M , the magnetic order is still antiferromagnetic but spins at each Fe ion in the adjacent Fe-Fe double atomic layers rotate to point in opposite ⟨0001⟩ directions. ...
... The prediction works in the following way If a user has tremor in hand or less than 10 Kg Grip Strength The predicted adaptation will be Gravity Well and Exponential Average Else The predicted adaptation will be Damping and Exponential Average In the first case, the adaptation will remove jitters in movement through exponential average and then attract the pointer towards a target when it is near by using the gravity well mechanism. Details about the gravity well algorithm can be found in a different paper [3] [10] ...
... These exsolved rhombohedral oxides have astonishing magnetic properties which have been related either to unbalanced magnetic moments at nanoscale exsolution interfaces observed in these mineral phases Robinson et al., 2002Robinson et al., , 2004McEnroe et al., 2004a;Kasama et al., 2004), or to a chemical locking of a high-temperature mono-mineralic singledomain remanence (Kletetschka et al., 2002). ...
... Exsolved opaques are common in the silicates: McEnroe, Skilbrei, et al. (2004) describe lamellae of hemo-ilmenite in the orthopyroxenes, and magnetite blades with ilmenite lamellae in the clinopyroxenes (Frandsen et al., 2004). McEnroe et al. (2000) and Robinson et al. (2001) describe the chemical and petrographic oxide phases in Unit IVe from Heskstad. The aim of this study is to investigate the source of the exceptionally high remanent magnetization of the study sample. ...
... More precise data of the field are currently being collected by the three SWARM satellites (Sabaka et al. 2020 ). These satellite data sets spurred research on the magnetic properties of the lithosphere (Schlinger 1985(Schlinger , 2001Kelso et al. 1993 ;McEnroe et al. 1996McEnroe et al. , 2001aMcEnroe et al. , b , 2004aMcEnroe et al. , b , 2018Pilkington & Perci v al 2001 ;Brown & McEnroe 2008 ;Schmidt et al. 2007 ;Dunlop et al . 2010 ;Brown et al. 2011 ;Liu et al. 2012 ;ter Maat et al. 2019 ). ...
... Magmatic iron-titanium-vanadium (Fe-Ti-V) oxide deposits are the most important source of Ti and V globally (Kelley et al. 2017;Woodruff et al. 2017), but the processes required to accumulate oxides into massive layers/lenses remains a debate (Cameron 1980;Wilson et al. 1996;Robinson et al. 2003;Charlier and Grove 2012;Charlier et al. 2015;Maier et al. 2013;Zhou et al. 2013;Howarth and Prevec 2013). Fe-Ti-V deposits can be subdivided into two types, namely those hosted in layered mafic-ultramafic intrusions (e.g., Bushveld Complex, South Africa: Klemm et al. 1985;Panzhihua, China: Pang et al. 2008), and those hosted in Proterozoic massif-type anorthosites (e.g., Lac-Saint-Jean: Grant 2020; Northwest River: Valvasori et al. 2020;Suwalki: Charlier et al. 2009). ...
... Here we use an atomistic mean-field model based on an approach previously used for analyzing complex magnetic structures [16] and apply it to nanoscale systems. The model was applied to a number of crystal structures; simple synthetic systems with uniform spin and exchange energies and a model of magnetite (Fe 3 O 4 ). ...
... Research [38], [57] reveals two characteristics of subtle affective states. The first characteristic is that different vocal features and metrics (attributes) distinguish between the expressions of different affective states, i.e. a set of attributes x may distinguish between class A and class B, while a different set y distinguishes between class A and class C. ...
... Synthetic studies on the magnetic implications of lamellae have been conducted because the anisotropic magnetic susceptibility of lamellae will affect both the shape and amplitude of magnetic anomalies (Biedermann & McEnroe, 2017). This is particularly important when oxide lamellae with a strong crystallographic preferred orientation are abundant (Robinson, Heidelbach et al., 2006;Robinson et al., 2002Robinson et al., , 2013Robinson et al., , 2016. Here, magnetism may be strongest when: (a) the proportion of exsolved lamellae material is large, (b) the total area of the exsolution interfaces is large, and (c) host planes are parallel to the magnetizing field (Robinson, Harrison, & McEnroe, 2006;Robinson et al., 2013Robinson et al., , 2021. ...