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`Home » 2. Classes of Magnetic Materials
`
`2. Classes of Magnetic
`Materials
`
`The origin of magnetism lies in the orbital and spin motions of
`electrons and howthe electrons interact with one another. The best
`
`way to introduce the different types of magnetism is to describe
`how materials respond to magnetic fields. This may be surprising to
`some, but all matter is magnetic. It's just that some materials are
`much more magnetic than others. The main distinction is that in
`some materials there is no collective interaction of atomic magnetic
`moments, whereas in other materials there is a very strong
`interaction between atomic moments.
`
`The magnetic behavior of materials can be classified into the
`following five major groups:
`
`1. Diamagnetism
`
`2. Paramagnetism
`
`3. Ferromagnetism
`
`4. Ferrimagnetism
`
`5. Antiferromagnetism
`
`Materials in the first two groups are those that exhibit no collective
`magnetic interactions and are not magnetically ordered. Materials
`in the last three groups exhibit long-range magnetic order below a
`certain critical
`temperature. Ferromagnetic and ferrimagnetic
`materials are usually what we consider as being magnetic (ie.,
`behaving like iron). The remaining three are so weakly magnetic
`that they are usually thought of as "nonmagnetic".
`
`1. Diamagnetism
`
`TAl mane ere tie fe fee el nn etal wenn nets Af all we nttne alah nw.
`
`. eb Me
`
`Here we presentthe Hitchhiker's
`Guide to Magnetism written by
`Bruce M. Moskowitz for the
`
`Environmental Magnetism
`Workshop held 5-8 June 1991 at the
`Institute for Rock Magnetism. It is a
`great introduction to rock
`magnetism and something we have
`encouraged many students new to
`the field to read. Below arelinks to
`
`the -html version in several sections
`
`with some links to help you navigate
`through or jump to certain sections
`as you prefer. We also include a .pdf
`version. Both versions can be
`
`printed, however, if you print the
`.html version, we recommend to
`printit in landscape mode.
`
`
`Hitchhiker's Guide to Magnetism in
`a .pdf document
`
`More About
`
`Hitchhiker's Guide to
`Magnetism
`
`*
`
`e
`
`1. Definitions and Units
`
`3. Magnetic Anisotropy
`
`« 4. Domain Theory
`
`e
`
`*
`
`5. Thermally Activated
`Magnetizations
`
`6. Types of Remanence
`
`7. References
`
`APPLE 1037
`
`1
`
`APPLE 1037
`
`

`

`Ld MaBMEUSIID IS &@ TUNUaITMeETILal Properly Ul dil Maller, GILNIOUEIT IL Id
`
`is due to the non-cooperative behavior of
`It
`usually very weak.
`orbiting electrons when exposed to an applied magnetic field.
`Diamagnetic substances are composed of atoms which have no net
`magnetic moments(ie., all the orbital shells are filled and there are
`no unpaired electrons). However, when exposed to a field, a
`negative magnetization is produced and thus the susceptibility is
`negative. If we plot M vs H, we see:
`
`M
`
`Diamagnetisi
`
`Note that whenthe field is zero the magnetization is zero. The other
`characteristic behavior of diamagnetic materials
`is
`that
`the
`susceptibility is
`temperature independent. Some well known
`diamagnetic substances,in units of 10°m?/kg, include:
`
`quartz (SiO2)
`
`-0.62
`
`Calcite (CaCO3) -0.48
`
`water
`
`-0.90
`
`2. Paramagnetism
`
`This class of materials, some of the atoms or ions in the material
`have a net magnetic moment due to unpaired electrons in partially
`filled orbitals. One of the most important atoms with unpaired
`electronsis iron. However, the individual magnetic moments do not
`interact magnetically, and like diamagnetism, the magnetization is
`zero whenthefield is removed. In the presence of a field, there is
`now a partial alignment of the atomic magnetic moments in the
`direction of the field, resulting in a net positive magnetization and
`positive susceptibility.
`
`_“slope=y
`
`x
`
`x +
`
`M+
`
`<<»
`M=,H
`4 > 0
`
`-
`
`T
`
`2
`
`

`

`Paramagnetisi
`
`In addition, the efficiency of the field in aligning the moments is
`opposed by the randomizing effects of temperature. This results in
`a temperature dependent susceptibility, known as the Curie Law.
`
`At normal temperatures and in moderatefields, the paramagnetic
`susceptibility is small (but larger than the diamagnetic contribution).
`Unless the temperatureis very low (<<100 kK) or the field is very high
`paramagnetic susceptibility is
`independent of the applied field.
`Under these conditions, paramagnetic susceptibility is proportional
`to the total
`iron content. Many iron bearing minerals are
`paramagnetic at room temperature. Some examples, in units of 10°
`8 m?/kg, include:
`
`Montmorillonite (clay) 13
`
`Nontronite (Fe-rich clay) 65
`
`Biotite (silicate)
`
`79
`
`Siderite(carbonate)
`
`100
`
`Pyrite (sulfide)
`
`30
`
`The paramagnetism of the matrix minerals in natural samples can
`be significant if the concentration of magnetite is very small. In this
`case, a paramagnetic correction may be needed.
`
`3. Ferromagnetism
`
`When you think of magnetic materials, you probably think ofiron,
`nickel or magnetite. Unlike paramagnetic materials, the atomic
`moments in these materials exhibit very strong interactions. These
`interactions are produced by electronic exchange forces and result
`in a parallel or antiparallel alignment of atomic moments. Exchange
`forces are very large, equivalent to a field on the order of 1000
`Tesla, or approximately a 100 million times the strength of the
`earth'sfield.
`
`The exchange force is a quantum mechanical phenomenon due to
`the relative orientation of the spins of two electron.
`
`Ferromagnetic materials exhibit parallel alignment of moments
`resulting in large net magnetization even in the absence of a
`magneticfield.
`
`parallel alignment
`
`A
`
`
`
`4
`
`
`
`6A;
`
`
`
`A
`
`3
`
`

`

`|
`
`oA;
`
`|
`
`A
`
`A
`
`
`
`a
`
`
`
`Ferromagnetisn
`
`The elements Fe, Ni, and Co and many oftheir alloys are typical
`ferromagnetic materials.
`
`Twodistinct characteristics of ferromagnetic materials are their
`
`(1) Spontaneous magnetization and the existence of
`
`(2) magnetic ordering temperature
`
`Spontaneous Magnetization
`
`The spontaneous magnetization is the net magnetization that exists
`inside a uniformly magnetized microscopic volume in the absence
`of a field. The magnitude of this magnetization, at 0 K, is dependent
`on the spin magnetic momentsof electrons.
`
`the saturation magnetization which we can
`A related term is
`measure in the laboratory. The saturation magnetization is the
`maximum induced magnetic moment that can be obtained in a
`magnetic field (H<:); beyond this field no further increase in
`magnetization occurs.
`
`mm —
`
`a
`
`
`T
`T
`|
`T
`T
`|
`T
`az O04
`os
`Applied Magnetic Field (Tesla)
`
`1
`
`The difference between spontaneous magnetization and the
`saturation magnetization has to do with magnetic domains (more
`about domains later). Saturation magnetization is an intrinsic
`property,
`independent of particle
`size
`but dependent on
`temperature.
`
`There is a big difference between paramagnetic and ferromagnetic
`susceptibility. As
`compared to paramagnetic materials,
`the
`magnetization in ferromagnetic materials is saturated in moderate
`magnetic fields and at high (room-temperature) temperatures:
`
`a
`
`a a
`
`4
`
`
`
`Saturation Magnetization
`
`35 - 40 micron magnetite
`
`a
`
`4
`
`_mo
`
`=ts
`zo
`Qo
`=
`=ms
`az #7
`Ccnnoc
`=
`
`a4
`
`
`
`4
`
`

`

`paramagnets
`
`o
`
`Heat Tesla
`>10
`
`L T range (K)
`<<100
`
`L x 10°m?/kg
`~50
`
`o
`
`ferromagnet
`s
`
`~1
`
`~300
`
`1000-10000
`
`Curie Temperature
`
`Even though electronic exchange forces in ferromagnets are very
`large,
`thermal energy eventually overcomes the exchange and
`produces
`a
`randomizing effect. This occurs at
`a_ particular
`temperature called the Curie temperature (Tc). Below the Curie
`temperature, the ferromagnetis ordered and aboveit, disordered.
`The
`saturation magnetization
`goes
`to zero at
`the Curie
`temperature. A typical plot of magnetization vs temperature for
`magnetite is shown below.
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`MagnetrationM7)Ae
`
`
`
`eee 0
`
`100
`
`400
`300
`200
`Temperature (PC)
`
`200
`
`600
`
`The Curie temperature is also an intrinsic property and is a
`diagnostic parameter that can be used for mineral identification.
`However,it is not foolproof because different magnetic minerals,in
`principle, can have the same Curie temperature.
`
`Hysteresis
`
`In addition to the Curie temperature and saturation magnetization,
`ferromagnets can retain a memory of an applied field once it
`is
`removed. This behavior is called hysteresis and a plot of the
`variation of magnetization with magnetic field is called a hysteresis
`loop.
`
`tization
`
`MT
`
`5
`
`

`

`
` Magnetic Field
`
`Flysterests
`loop
`
`Anotherhysteresis property is the coercivity of remanence (Hr). This
`is the reverse field which, when applied and then removed, reduces
`the saturation remanence to zero.
`It
`is always larger than the
`coercive force.
`
`The initial susceptibility (yo) is the magnetization observed in low
`fields, on the order of the earth's field (50-100 pT).
`
`The various hysteresis parameters are not solely intrinsic properties
`but are dependent on grain size, domain state, stresses, and
`temperature. Because hysteresis parameters are dependent on
`grain size,
`they are useful for magnetic grain sizing of natural
`samples.
`
`4. Ferrimagnetism
`
`In ionic compounds, such as oxides, more complex forms of
`magnetic ordering can occur as a result of the crystal structure. One
`type of magnetic ordering is
`call
`ferrimagnetism. A simple
`representation of the magnetic spins in a ferrimagnetic oxide is
`shown here.
`
`Ox0-0REPRO
`BOReePEE
`
`Ferrimaguetism
`4. OM
`
`6
`
`

`

`The magnetic structure is composed of two magnetic sublattices
`(called A and B) separated by oxygens. The exchange interactions
`are mediated by the oxygen anions. When this happens,
`the
`interactions are called indirect or superexchange interactions. The
`strongest superexchange interactions result
`in an antiparallel
`alignment of spins betweenthe A andBsublattice.
`
`In ferrimagnets, the magnetic moments of the A and B sublattices
`are not equal and result in a net magnetic moment. Ferrimagnetism
`is therefore similar to ferromagnetism. It exhibits all the hallmarks
`of
`ferromagnetic behavior- spontaneous magnetization, Curie
`temperatures, hysteresis, and remanence. However,
`ferro- and
`ferrimagnets have very different magnetic ordering.
`
`Magnetite is a well knownferrimagnetic material. Indeed, magnetite
`was considered a ferromagnetuntil Néel in the 1940's, provided the
`theoretical framework for understanding ferrimagnetism.
`
`Crystal Structure of Magnetite
`
`A
`
`Pad
`
`prsegtee satin
`|
`
`hens inge” (_) oxygen
`
`&
`
`tetrahedral Fe
`A-site
`
`P
`
`
`octahedral Fe
`:
`===
`B-site
`tae att
`-*
`bicwnnrinncghtnn on eoad
`eeeeeeeee” after Banerjee and
`Moskowitz (1985)
`
`Magnetite, Fez0, crystallizes with the spinel structure. The large
`oxygen ions are close packed in a cubic arrangement and the
`smaller Fe ionsfill in the gaps. The gaps come in twoflavors:
`
`tetrahedral site: Fe ion is surrounded by four oxygens
`
`octahedralsite: Fe ion is surrounded bysix oxygens
`
`The tetrahedral and octahedral sites form the two magnetic
`sublattices, A and B respectively. The spins on the A sublattice are
`antiparallel to those on the B sublattice. The twocrystal sites are
`very different and result in complex forms of exchange interactions
`of the iron ions between and within the two typesofsites.
`7
`
`7
`
`€
`

`

`The structural formula for magnetite is
`
`[Fe>*]A [Fe**,Fe?*]B O4
`
`This particular arrangement of cations on the A andBsublattice is
`called an inverse spinel structure. With negative AB exchange
`interactions, the net magnetic moment of magnetite is due to the B-
`site Fe?*.
`
`5. Antiferromagnetism
`
`Antiferromagnetisn
`
`a
`
`4
`
`;
`
`If the A and B sublattice moments are exactly equal but opposite,
`the net momentis zero. This type of magnetic ordering is called
`antiferromagnetism.
`
`
`
`N
`
`The clue to antiferromagnetism is the behavior of susceptibility
`above a critical temperature, called the Néel temperature (Ty).
`Above Ty,
`the susceptibility obeys
`the Curie-Weiss
`law for
`paramagnets but with a negative intercept
`indicating negative
`exchangeinteractions.
`
`8
`
`

`

`Crystal Structure of Hematite
`
`Crystal Structure of Hematite
`C
`
`1
`
`T > -10°C
`
`T<-10°C
`
`after Fuffer (1937)
`
`Hematite crystallizes in the corundum structure with oxygen ionsin
`an hexagonal close packed framework. The magnetic moments of
`the Fe?* ions are ferromagnetically coupled within specific c-planes,
`but antiferromagnetically coupled between the planes.
`
`Me
`
`e
`
`CantedAntiferromagnetism
`
`Above -10°C, the spin moments lie in the c-plan but are slightly
`canted. This produces a weak spontaneous magnetization within
`the c-plan (o, = 0.4 Am2/kg).
`
`Below -10°C, the direction of the antiferromagnetism changes and
`becomes parallel
`to the c-axis;
`there is no spin canting and
`hematite becomesa perfect antiferromagnet.
`
`This spin-flop transition is called the Morin transition.
`
`Hematite
`
`Morin
`transition
`
`Curie
`—,
`—" Point
`\
`\
`
`a
`mh
`ow5
`=<w
`b
`
`oat
`
`ahs
`
`~
`
`ai
`
`9
`
`

`

`Temperature (°C)
`
`after Dunlop (1971)
`
`Magnetic Properties of Minerals
`
`Mineral
`
`Oxides
`
`Compositi
`on
`
`Magnetic
`Order
`
`T<(°C)
`
`Os
`(Am2/kg) L
`
`Magnetite
`
`Fes04
`
`ferrimagn
`etic
`
`575-585
`
`90-92
`
`Ulvospine
`
`FesTiO>
`
`AFM
`
`-153
`
`l H
`
`ematite
`
`dFe203
`
`canted
`
`675
`
`0.4
`
`v7
`
`51
`
`21
`
`-233
`
`~600
`
`300
`
`585
`
`AFM
`
`AFM
`
`ferrimagn
`etic
`
`ferrimagn
`etic
`
`ferrimagn
`etic
`
`ferrimagn
`etic
`
`ferrimagn
`etic
`
`ferrimagn
`etic
`
`320
`
`~333
`
`IImenite
`
`FeTiO>
`
`Maghemit
`
`yFe,03
`
`M nFe;04
`
`e J
`
`acobsite
`
`Trevorite
`
`NiFe,04
`
`MgFe2O,
`
`Magnesio
`ferrite
`
`Sulfides
`
`Pyrrhotite
`
`Fe7Sg
`
`Greigite
`
`FezSa
`
`Troilite
`
`FeS
`
`AFM
`
`305
`
`Oxyhydro
`xides
`
`Goethite
`
`aFeQOOH
`
`AFM, weak
`FM
`
`~120
`
`<1
`
`Lepidocro
`cite
`
`yFeOQOH
`
`AFM(?)
`
`-196
`
`Feroxyhyt
`
`5FeOOH
`
`ferrimagn
`etic
`
`~180
`
`<10
`
`Fe
`
`Ni
`
`Co
`
`FM
`
`FM
`
`FM
`
`770
`
`358
`
`1131
`
`55
`
`161
`
`10
`
`e M
`
`etals &
`
`Alloys
`
`Iron
`
`Nickel
`
`Cobalt
`
`10
`
`

`

`Awaruite
`
` NisFe
`
`Wairauite
`
`CoFe
`
`FM
`
`FM
`
`620
`
`986
`
`120
`
`235
`
`FM = ferromagnetic order
`AFM = antiferromagnetic order
`T, = Curie or Néel Temperature
`G, = saturation magnetization at room-temperature
`
`
`
`
`
`Institute for Rock Magnetism College of Science and)=Department of Earth andNational Science
`
`Foundation
`Engineering
`Environmental Sciences
`
`Department of Earth and Environmental Sciences,
`150 John T. Tate Hall, 116 Church St. SE, Minneapolis,
`MN 55455
`
`
`612-624-5274—irm@umn.edu Fi ao
`
`
`
`Institute for Rock Magnetism
`
`The IRM is made possible through the
`
`Instrumentation and Facilities program of
`the National Science Foundation, Earth Science
`
`Division, and by funding from the University of
`Minnesota. Recent NSF funding information and
`resulting publications by grant: NSF-EAR 2153786.
`
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`
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`
`11
`
`11
`
`

`

`Hitchhiker's Guide to Magnetism
`Bruce M. Moskowitz
`
`Definitions and Units
`
`Let's start with a few definitions. There are three magnetic vectors:
`
`(1) H
`(2) M
`(3) B
`
`Magnetic field
`Magnetization
`Magnetic induction
`
`There is some confusion in the literature over units. SI units are now the preferred units
`over the older CGS . Confusion prevails because there are two ways that magnetostatics is
`presented:
`
`1. fictitious magnetic poles
`2. current sources
`
`(CGS: centimeter, gram, second)
`(SI:
`systéme internationale)
`
`As a result, the form of many of the basic equations are different between the two systems.
`What this all means is that some arbitrary constant has units in one system but is equal to
`unity and dimensionless in the other system. There are also factors of 4 π floating around.
`
`The difference between the pole and current approach is only significant in the subject of
`units. The older (pre 1980) paleomagnetic and rock magnetic literature is primarily in CGS
`units.
`
`Because SI are now the units of choice, we begin with current loops. Consider a loop of
`radius r and current i, roughly equivalent to an atom with orbiting electrons.
`
`A magnetic field H will be produced at
`the center of the loop given by
`
`[Amperes/meter, A /m]
`
`i2
`
`r
`
`H =
`
`loop has a magnetic
`The current
`moment, m, associated with it
`
`m = i x Area [Am2]
`
`iiii
`
`HHHH
`
`Current Loop
`
`12
`
`

`

`The intensity of magnetization, M or J, is magnetic moment per unit volume
`
`[A/m]
`
`
`
`mv
`
`M =
`
`Note that M and H have the same units.
`
`13
`
`

`

`Magnetic moment per unit mass, σ, is
`
`σ=
`
`m
`mass
`
` [Am2/kg]
`
`Another fundamental quantity is the ratio of magnetization to magnetic field, which is
`called the susceptibility
`
`[dimensionless]
`
`
`
`MH
`
`κ=
`
`The mass susceptibility is
`
`[ m3/kg].
`
`κ
` = density
`
`
`
`σ H
`
`χ =
`
`Susceptibility is a measure of how magnetizable a substance can become in the presence of
`a magnetic field and can be used in a general way to describe the various classes of
`magnetic materials. A related quantity, denoted by µ, relates B to H and is called the
`permeability (Engineering types use permeability instead of susceptibility).
`
`In the SI system, the relationship between B, H and M is given by
`B= µo(H+M)
`
`
`
`[Tesla, T]
`
`The B unit is called the Tesla and the total B field is the sum of the H field and the
`magnetization M of the medium. The constant µo is called the permeability of free space. In
`SI it is equal to 4πx10-7 Henry/m.
`
`However, in CGS, µo is set equal to unity, which makes B and H, and M numerically equal
`to one another, but each have different unit names (arbitrarily chosen and named after
`famous dead people, Gauss, Oersted, and emu/cm3). The CGS equation is
`B=H+4πM
`
`14
`
`

`

`Herein lies some of the confusion, because in CGS, B and H are used interchangeably, but
`the unit conversions going to SI give different numerical values. For example, the earth's
`field is 0.5 Gauss or 0.5 Oe. However, in SI
`
`0.5 Gauss = 50 µT
`0.5 Oersted = 39.8 A/m
`
`[B fields]
`[H fields].
`
`As you can see from this example, it is much easier to convert Gauss to Tesla (move the
`decimal point 4 places) than to convert Oersted to A/m. So it is not too surprising that this
`is the current practice used by paleomagnetists to report all fields (B and H) in Tesla. We
`have not decided suddenly that the B field is more fundamental than the H field (neither
`field is any more fundamental than the other). Actually, when we talk about an alternating
`"field", or a magnetic "field", of say 100 milliTesla (mT), we really mean µoH=100 mT.
`However, this is rarely noted.
`
`I have summarized the comments about units in Table 1.
`
`Magnetic Term
`
`Symbol
`
` SI
` unit
`
` CGS
` unit
`
`conversion
` factor
`
`magnetic induction B
`
`Tesla (T)
`
`Gauss (G)
`
`1 T = 104G
`
`A/m
`
`A/m
`
`Am2/kg
`
`Am2
`
`Oersted (Oe)
`
`1 A/m =4π/103 Oe
`
`emu/cm3
`
`1 A/m = 10-3 emu /cm3
`
`emu/g
`
`emu
`
`1 Am2/kg = 1 emu/g
`
`1 Am2 = 103 emu
`
`dimensionless
`
`dimensionless
`
`4π(SI) = 1 (cgs)
`
`m3/kg
`
`H/m
`
`emu/Oe. g
`
`1 m3 /kg = 103/4π emu /Oe. g
`
`dimensionless
`
`4πx10-7 H/m = 1 (cgs)
`
`magnetic field
`
`magnetization
`
`mass magnetization
`
`magnetic moment
`
`volume
`susceptibility
`
`mass
`susceptibility
`
`permeability of
` free space
`
`H
`
`M
`
`σ
`
`m
`
`κ
`
`χ
`
`µ0
`
`A=
`cm=
`
`Ampere
`centimeter
`
`15
`
`

`

`emu=
`g=
`kg=
`m=
`H=
`
`electromagnetic unit
`gram
`kilogram
`meter
`Henry
`
`For more information on SI and CGS units in magnetism see:
`
`M.A. Payne (1981), Phys. Earth Planet Inter., 26, P10-P-16, with errata
`(1981), Phys. Earth Planet. Inter., 27, 233.
`P.N. Shive (1986), Transactions American Geophys. Union (EOS), 67, 25.
`
`Classes of Magnetic Materials
`
`The origin of magnetism lies in the orbital and spin motions of electrons and how the
`electrons interact with one another. The best way to introduce the different types of
`magnetism is to describe how materials respond to magnetic fields. This may be surprising
`to some, but all matter is magnetic. It's just that some materials are much more magnetic
`than others. The main distinction is that in some materials there is no collective interaction
`of atomic magnetic moments, whereas in other materials there is a very strong interaction
`between atomic moments.
`
`The magnetic behavior of materials can be classified into the following five major groups:
`
`1. Diamagnetism
`2. Paramagnetism
`3. Ferromagnetism
`4. Antiferromagnetism
`5. Ferrimagnetism
`
` Materials in the first two groups are those that exhibit no collective magnetic interactions
`and are not magnetically ordered. Materials in the last three groups exhibit long-range
`magnetic order below a certain critical temperature. Ferromagnetic and ferrimagnetic
`materials are usually what we consider as being magnetic (ie., behaving like iron). The
`remaining three are so weakly magnetic that they are usually thought of as "nonmagnetic".
`
`1. Diamagnetism
`
`Diamagnetism is a fundamental property of all matter, although it is usually very weak. It is
`due to the non-cooperative behavior of orbiting electrons when exposed to an applied
`magnetic field. Diamagnetic substances are composed of atoms which have no net
`magnetic moments (ie., all the orbital shells are filled and there are no unpaired electrons).
`However, when exposed to a field, a negative magnetization is produced and thus the
`susceptibility is negative. If we plot M vs H, we see:
`
`16
`
`

`

`M
`+
`
`-
`
`χ
`
`M=χH
`χ < 0
`
`H
`
`slope=χ
`
`Diamagnetism
`
`Τ
`
`χ = constant
`
`Note that when the field is zero the magnetization is zero. The other characteristic behavior
`of diamagnetic materials is that the susceptibility is temperature independent. Some well
`known diamagnetic substances, in units of 10-8 m3kg-1, include:
`
`quartz (SiO2)
`Calcite (CaCO3)
`water
`
`-0.62
`-0.48
`-0.90
`
`2. Paramagnetism
`
`This class of materials, some of the atoms or ions in the material have a net magnetic
`moment due to unpaired electrons in partially filled orbitals. One of the most important
`atoms with unpaired electrons is iron. However, the individual magnetic moments do not
`interact magnetically, and like diamagnetism, the magnetization is zero when the field is
`removed. In the presence of a field, there is now a partial alignment of the atomic magnetic
`moments in the direction of the field, resulting in a net positive magnetization and positive
`susceptibility.
`
`M
`+
`
`-
`
`slope=χ
`
`H
`
`χ
`
`1
`χ ∝ Τ
`
`M=χH
`χ > 0
`Paramagnetism
`
`Τ
`
`17
`
`

`

`In addition, the efficiency of the field in aligning the moments is opposed by the
`randomizing effects of temperature. This results in a temperature dependent susceptibility,
`known as the Curie Law.
`
`At normal temperatures and in moderate fields, the paramagnetic susceptibility is small
`(but larger than the diamagnetic contribution). Unless the temperature is very low (<<100
`K) or the field is very high paramagnetic susceptibility is independent of the applied field.
`Under these conditions, paramagnetic susceptibility is proportional to the total iron content.
`Many iron bearing minerals are paramagnetic at room temperature. Some examples, in
`units of 10-8 m3kg-1 include:
`
`Montmorillonite (clay)
`Nontronite (Fe-rich clay)
`Biotite (silicate)
`Siderite(carbonate)
`Pyrite (sulfide)
`
`13
`65
`79
`100
`30
`
`The paramagnetism of the matrix minerals in natural samples can be significant if the
`concentration of magnetite is very small. In this case, a paramagnetic correction may be
`needed.
`
`3. Ferromagnetism
`
`When you think of magnetic materials, you probably think of iron, nickel or magnetite.
`Unlike paramagnetic materials, the atomic moments in these materials exhibit very strong
`interactions. These interactions are produced by electronic exchange forces and result in a
`parallel or antiparallel alignment of atomic moments. Exchange forces are very large,
`equivalent to a field on the order of 1000 Tesla, or approximately a 100 million times the
`strength of the earth's field.
`
`The exchange force is a quantum mechanical phenomenon due to the relative orientation of
`the spins of two electron.
`
`Ferromagnetic materials exhibit parallel alignment of moments resulting in large net
`magnetization even in the absence of a magnetic field.
`
`18
`
`

`

`parallel alignment
`
`Ferromagnetism
`
`The elements Fe, Ni, and Co and many of their alloys are typical ferromagnetic materials.
`
`Two distinct characteristics of ferromagnetic materials are their
`
`(1) spontaneous magnetization and the existence of
`(2) magnetic ordering temperature
`
`Spontaneous Magnetization
`
`The spontaneous magnetization is the net magnetization that exists inside a uniformly
`magnetized microscopic volume in the absence of a field. The magnitude of this
`magnetization, at 0 K, is dependent on the spin magnetic moments of electrons.
`
`A related term is the saturation magnetization which we can measure in the laboratory. The
`saturation magnetization is the maximum induced magnetic moment that can be obtained
`in a magnetic field (Hsat); beyond this field no further increase in magnetization occurs.
`1.00
`
`between
`difference
`The
`spontaneous magnetization and
`the saturation magnetization has
`to do with magnetic domains
`(more
`about domains
`later).
`Saturation magnetization
`is an
`intrinsic property, independent of
`particle size but dependent on
`temperature.
`
`saturation magnetization
`
`0
`
`200
`
`600
`400
`Magnetic Field (mT)
`
`800
`
`1000
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`0.00
`
`Magnetization (Am Kg )
`-1
`
`2
`
`There is a big difference between paramagnetic and ferromagnetic susceptibility. As
`compared to paramagnetic materials, the magnetization in ferromagnetic materials is
`saturated in moderate magnetic fields and at high (room-temperature) temperatures:
`
`19
`
`

`

`Hsat(Tesla)
`
`T-range (K)
`
`χ(10-8m3kg-1)
`
`paramagnets:
`ferromagnets:
`
`>10
`(cid:31)1
`
`<<100
`(cid:31)300
`
`50
`
`1000-10000
`
`Curie Temperature
`
`Even though electronic exchange forces in ferromagnets are very large, thermal energy
`eventually overcomes the exchange and produces a randomizing effect. This occurs at a
`particular temperature called the Curie temperature (TC). Below the Curie temperature, the
`ferromagnet is ordered and above it, disordered. The saturation magnetization goes to zero
`at the Curie temperature. A typical plot of magnetization vs temperature for magnetite is
`shown below.
`
`1.00
`
`0.80
`
`0.60
`
`0.40
`
`0.20
`
`Because we are still dealing
`with atoms having magnetic
`moments,
`a
`ferromagnet
`above the Curie temperature
`is paramagnetic.
`
`T = 575°C
`c
`
`0.00
`
`0
`
`100
`
`400
`300
`200
`Temperature (ÞC)
`
`500
`
`600
`
`The Curie temperature is also an intrinsic property and is a diagnostic parameter that can be
`used for mineral identification. However, it is not foolproof because different magnetic
`minerals, in principle, can have the same Curie temperature.
`
`20
`
`

`

`Hysteresis
`
`In addition to the Curie temperature and saturation magnetization, ferromagnets can retain
`a memory of an applied field once it is removed. This behavior is called hysteresis and a
`plot of the variation of magnetization with magnetic field is called a hysteresis loop.
`
`Ms
`
`Magnetization
`
`The saturation
`magnetization
`(Ms) is measured
`in the laboratory
`by applying a
`magnetic field of
`1-2 Tesla. This
`field strength is
`usually sufficient
`to saturate most
`magnetic
`minerals. Upon
`reducing
`the
`field to zero, the
`magnetization
`does not go to
`zero but persists
`as a saturation
`remanence
`(Mr). Increasing
`the field in the
`negative direction, a point is reached where the induced magnetization becomes zero. The
`field at this point is called the coercivity (Hc). Increasing the field further in the negative
`direction results in saturation again but in the negative direction.
`
`Mr
`
`Hc
`
`Hr
`
`χχχχ 0000
`Magnetic Field
`
`
`Hysteresis Hysteresis
`
`Hysteresis Hysteresis
`looplooplooploop
`
`Another hysteresis property is the coercivity of remanence (Hr). This is the reverse field
`which, when applied and then removed, reduces the saturation remanence to zero. It is
`always larger than the coercive force.
`
`The initial susceptibility (χ0) is the magnetization observed in low fields, on the order of
`the earth's field (50-100 µT).
`
`The various hysteresis parameters are not solely intrinsic properties but are dependent on
`grain size, domain state, stresses, and temperature. Because hysteresis parameters are
`dependent on grain size, they are useful for magnetic grain sizing of natural samples.
`
`21
`
`

`

`4. Ferrimagnetism
`
`In ionic compounds, such as oxides, more complex forms of magnetic ordering can occur
`as a result of the crystal structure. One type of magnetic ordering is call ferrimagnetism. A
`simple representation of the magnetic spins in a ferrimagnetic oxide is shown here.
`
`The magnetic structure is composed of
`two magnetic sublattices (called A and
`B) separated by oxygens. The exchange
`interactions are mediated by the oxygen
`anions. When
`this happens,
`the
`interactions are called
`indirect or
`superexchange
`interactions.
`The
`strongest superexchange interactions
`result in an antiparallel alignment of
`spins between the A and B sublattice.
`
`
`FerrimagnetismFerrimagnetism
`
`FerrimagnetismFerrimagnetism
`
`In ferrimagnets, the magnetic moments
`of the A and B sublattices are not equal
`and result in a net magnetic moment.
`Ferrimagnetism is therefore similar to
`ferromagnetism.
`It exhibits all
`the
`hallmarks of ferromagnetic behavior-
`spontaneous magnetization, Curie temperatures, hysteresis, and remanence. However,
`ferro- and ferrimagnets have very different magnetic ordering.
`
`Magnetite is a well known ferrimagnetic material. Indeed, magnetite was considered a
`ferromagnet until Néel in the 1940's, provided the theoretical framework for understanding
`ferrimagnetism.
`
`Crystal Structure of Magnetite
`
`Let's take a closer look at the crystal structure of magnetite.
`
`22
`
`

`

`A
`
`A
`
`B
`
`A
`
`A
`
`A
`
`oxygen
`
`B
`
`B
`
`B
`
`A
`
`tetrahedral Fe
`A-site
`
`octahedral Fe
`B-site
`
`after Banerjee and after Banerjee and
`
`after Banerjee and after Banerjee and
`
`Moskowitz (1985)Moskowitz (1985)
`
`Moskowitz (1985)Moskowitz (1985)
`
`
`Magnetite, Fe3O4 crystallizes with the spinel structure. The large oxygen ions are close
`packed in a cubic arrangement and the smaller Fe ions fill in the gaps. The gaps come in
`two flavors:
`
`tetrahedral site:
`octahedral site:
`
`Fe ion is surrounded by four oxygens
`Fe ion is surrounded by six oxygens
`
`The tetrahedral and octahedral sites form the two magnetic sublattices, A and B
`respectively. The spins on the A sublattice are antiparallel to those on the B sublattice. The
`two crystal sites are very different and result in complex forms of exchange interactions of
`the iron ions between and within the two types of sites.
`
`The structural formula for magnetite is
`
`[Fe3+]A [Fe3+,Fe2+]B O2-4
`
`This particular arrangement of cations on the A and B sublattice is called an inverse spinel
`structure. With negative AB exchange interactions, the net magnetic moment of magnetite
`is due to the B-site Fe2+.
`
`5. Antiferromagnetism
`
`If the A and B sublattice moments are exactly equal but opposite, the net moment is zero.
`This type of magnetic ordering is called antiferromagnetism.
`
`23
`
`

`

`
`AntiferromagnetismAntiferromagnetism
`
`AntiferromagnetismAntiferromagnetism
`
`Antiferromagnetic materials also have zero remanence, no hysteresis, but a small positive
`susceptibility that varies in a peculiar way with temperature.
`The clue to antiferromagnetism is
`the behavior of susceptibility above
`a critical temperature, called the
`Néel temperature (TN). Above TN,
`the susceptibility obeys the Curie-
`Weiss law for paramagnets but with
`a negative
`intercept
`indicating
`negative exchange interactions.
`
`χ
`
`AF
`
`0
`
`ΤΝ
`
`Τ
`
`Slight deviations from ideal antiferromagnetism can exist if the anti-parallelism is not
`exact. If neighboring spins are slightly tilted (<1°) or canted, a very small net
`magnetization can be produced.
`
`P
`
`1χ
`
`χ
`
`24
`
`

`

`Μ
`
`
`Canted AntiferromagnetismCanted Antiferromagnetism
`
`Canted AntiferromagnetismCanted Antiferromagnetism
`
`This is called canted antiferromagnetism and hematite is a well known example. Canted
`antiferromagnets exhibit many of the typical magnetic characteristics of ferro- and
`ferrimagnets (e.g., hysteresis, remanence, Curie temperature).
`
`Crystal Structure of Hematite
`
`Hematite crystallizes in the corundum structure with oxygen ions in an hexagonal close
`packed framework. The magnetic moments of the Fe3+ ions are ferromagnetically coupled
`within specific c-planes, but antiferromagnetically coupled between the planes.
`Crystal Structure of Hematite
`
`3+
`Fe ion
`
`T > -10°C T < -10°C
`
`
`after Fuller (1987)after Fuller (1987)
`
`after Fuller (1987)after Fuller (1987)
`
`25
`
`

`

`Above -10°C, the spin moments lie in the c-plan but are slightly canted. This produces a
`weak spontaneous magnetization within the c-plan (σs =0.4 Am2/kg).
`
`Below -10°C, the direction of the antiferromagnetism changes and becomes parallel to the
`c-axis; there is no spin canting and hematite becomes a perfect antiferromagnet.
`
`The spin-flop transition is called the Morin transition.
`
`Hematite
`
`Morin
`transition
`
`Curie
`Point
`
`σ σ σ σ (Am kg )
`2-1
`
`s
`
`Temperature (°C)
`
`
`after Dunlop (1971)after