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CHEM313 > Claridge - magnetic properties of solids > Flashcards

Claridge - magnetic properties of solids Flashcards

1
Q

How do magnetic moments arise?

A

The orbital angular momentum of an electron generates a magnetic moment μl

The spin of an electron generates a magnetic moment μs

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2
Q

What quantum number represents the orbital angular momentum?
What does it describe ab the e-?

A

lowercase L

which subshell it’s in

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3
Q

Principle quantum number?
What does it describe ab the e-?

A

n = which shell the e- is in

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4
Q

Magnetic quantum number?
What does it describe ab the e-?

A

ml (l is subscript L)

gives the allowed orientations of the orbital angular momentum in an applied magnetic field, also how many orbitals in a subshell

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5
Q

What is the magnetic susceptibility?

A

how responsive a material is to an applied magnetic field
(per unit of molar volume if molar magnetic susceptibility - must be molar to compare them)

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6
Q

Difference between diamagnetic susceptibilities and paramagnetic?

A

diamagnetic = small magnitude, negative, temp independent, often closed shell semiconductors, no unpaired e-

paramagnetic = positive and temp dependent, includes most metals

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7
Q

Describe diamagnetism

A

no unpaired e-, so no orbital or spin angular momentum

weakly repelled by an applied field as:
- the orbital motion of the e- in the filled shells is changed
- induced magnetisation opposes the field

the repulsion due to a reduction in density of the magnetic field lines passing through

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8
Q

how does the number of e- affect diamagnetism?

A

more e- gives a larger repulsion effect

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9
Q

What is the magnetic susceptibility of a perfect diamagnet?

A

1, completely expels the magnetic field = superconductors

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10
Q

Describe paramagnetism

A

unpaired e-, net magnetic moment

applied magnetic field induces magnetisation to align the field and gives positive susceptibility

weak attraction to the applied field as the density of the field lines passing through is increased

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11
Q

is Curie’s law for paramagnets or diamagnets?

A

paramagnets

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12
Q

How can the Curie constant be found from a graph?

A

the gradient of the plot of inverse molar susceptibility (1/Xm) against temp (x axis)

C = 1/gradient

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13
Q

What is the magnetocaloric effect?

A

the reversible change in temperature of a paramagnetic material when magnetised or demagnetised with application or removal of an applied magnetic field, respectively

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14
Q

What is magnetic refrigeration?

A

magnetisation by applied field lines the moments up, heat is removed by a heat sink, demagnetisation leads to cooling, cycle repeats

larger magnetic moment leads to stronger magnetocaloric effect

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15
Q

Describe the Brillouin function

A

the saturated magnetisation gives the maximum magnetisation obtainable when all the magnetic moments in the sample align with the applied field

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16
Q

What is the saturated magnetic moment?

A

in large fields when the magnetic moments adopt the lowest energy state by aligning with the field

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17
Q

Hund’s first rule? Why does it act?

A

arrange e- in their orbitals to maximise S,

to minimise repulsive Coulomb interactions between e- with the same spin

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18
Q

Hund’s second rule? Why does it act?

A

given the spin arrangement from rule 1, now arrange the e- to maximise L

to reduce the overall energy of an atom by minimising Coulomb repulsion between e-

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19
Q

Hund’s third rule? Why does it act?

A

For atoms with a less than half full subshell J = |L-S|
For atoms with a more than half full subshell J = L+S as the lowest energy states.

To minimise spin-orbit coupling interaction

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20
Q

in what circumstances is Hund’s 3rd rule only correct?

A

spherical

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21
Q

Which two ions have discrepancies between the calc and experimental values for effective moments? Why?

A

Eu^3+ and Sm^3+ because they are low-lying excited states and Hund’s rules only work for ground states,

low-lying excited states can become thermally populated at high temps, changing the magnetic moment

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22
Q

How does μsat compare with μeff?

A

μsat is always smaller than μeff

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23
Q

For which elements do μcalc and μexp often disagree?

A

3d transition metals apart from 3d5 and 3d10 where the total orbital angular momentum L = 0

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24
Q

When are the spin-only and spin-only saturated magnetic moment eq used?

A

for 3d transition metals

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25
Q

What is orbital quenching?

A

When a strong crystal field lifts orbital degeneracy, causing the orbital angular momentum to be quenched (=0) for many 3d ions, gives spin-only magnetic moments

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26
Q

in which ion is orbital restoration possible?

A

high-spin Co^2+ 3d7 in an octahedral crystal field

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27
Q

Describe orbital restoration in an example

A

the d (3x) orbitals in the t2g set are degenerate and related by 90degree rotation symmetry

one electron hole in the t2g^5 config so allows movement of e- which partially restores the orbital angular momentum of Co2+ in a weak octahedral crystal field

giving an μexp of 1μB larger than spin-only

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28
Q

When to use the T term for 3d transition metals?

A

when the t2g level is neither half full not completely full, so there’s a degree of freedom in filling the t2g level

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29
Q

When to use the E term for 3d transition metals?

A

when the eg level is neither half full not completely full, so there’s a degree of freedom in filling the eg level

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30
Q

When to use the A term for 3d transition metals?

A

when the eg and t2g levels are either empty, full, or half-full so there are no other degeneracies

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31
Q

Example of a spin transition material

A

LaCoO3
at low temp = low-spin 1A
at higher temp = high spin 5T

so has a temp-dependent μeff

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32
Q

How to get total μeff?

A

calculate for each cation, then do sum of squares

= sqrt[ (μeff A)^2 + (μeff B)^2]

33
Q

Which term symbols are quenched and which are not?

A

T not quenched, A and E quenched

34
Q

Triplet state vs singlet state

A

Triplet = both e- in overlapping paramagnetic ions are spin up, Stot = 1

singlet = both e- in overlapping paramagnetic ions are spin down, Stot=0

35
Q

When is the triplet state energetically favoured?

A

when Jex > 0, Es> Et

36
Q

When is the singlet state energetically favoured?

A

when Jex < 0, Es < Et

37
Q

Which transition metal ion is an exception for paramagnetic metal centre overlap for transition metal oxides?

A

V4+

38
Q

Singlet state Goodenough-Kanamari rule?

A

If two e- of two magnetic metal ions interact with the same anion orbital, then Jex<0

the neighbouring magnetic moments align antiparallel to give the singlet state

39
Q

Singlet state relation to anti/ferro magnetism?

A

180degrees interaction gives rise to antiferromagnetism

40
Q

Triplet state Goodenough-Kanamori rule?

A

If two e- of two magnetic metal ions interact with two orthogonal intermediate non-magnetic anion orbitals, then Jex>0

the neighbouring magnetic moments align parallel to give the triplet state

41
Q

Triplet state relation to anti/ferro magnetism?

A

90degree interaction gives rise to ferromagnetism

42
Q

Which orbitals interact in the singlet state diagram?

A

2pz with two dz^2 ones

42
Q

Which orbitals interact in the triplet state diagram?

A

2py with two dx^2-y^2 ones

43
Q

ferromagnetic v antiferromagnetic

A

ferromagnetic: the magnetic moments align parallel

antiferromagnetic: the magnetic moments align antiparallel

44
Q

paramagnet v ferromagnet v antiferromagnet

A

paramagnet: weakly interacting, randomly orientated neighbouring magnetic moments

ferromagnet: strongly interacting, parallelly ordered neighbouring magnetic moments

antirferromagnet: strongly interacting, antiparallelly ordered neighbouring magnetic moments

45
Q

What is required for a material to enter its ferromagnetic or antiferromagnetic state?

A

cooling below its critical magnetic ordering transition temperature, the Curie temperature Tc

46
Q

What is the state between paramagnet and ferromagnet called?

A

cooperative paramagnet (in the liquid state)

47
Q

Define the Weiss constant

A

the sum of all of the exchange interactions in any magnetic system

48
Q

What is the sign of the Weiss constant for antiferromagnets?

A

negative

49
Q

What is the sign of the Weiss constant for ferromagnets?

A

positive

50
Q

What is ferrimagnetism?

A

When the neighbouring magnetic moments align antiferromagnetically

but the moment sizes are different so the magnetisation is only slightly cancelled and occurs below Tc

strong interaction, antiparallel ordering

51
Q

What is Hm?

A

the internal molecular field used in mean field theory

52
Q

What does a positive value of theta mean for mean field theory?

A

the molecular field acts in the same direction as the applied field, alignment of moments is parallel = ferromagnetism

53
Q

When will magnetic susceptibility diverge according to mean field theory? What does this cause?

A

at T= theta

causes phase transition

54
Q

Why do ferromagnets not behave as magnets until magnetised?

A

bc the sample will break into ferromagnetic domains to minimise the total energy, moments are aligned ferromagnetically in each domain, but the domains are randomly aligned,

magnetisation aligns the domains

55
Q

What are hard/soft magnets?

A

soft: small remanence, small coercivity

hard: large remanence, large coercivity

56
Q

What is coercivity?

A

how difficult a magnet is to magnetise/demagnitise, small coercivity = easily magnetised and demagnetised

57
Q

What is remanence?

A

the remaining magnetic field after demagnetisation

58
Q

Describe doped perovskite manganites

A

two antiferromagnetic insulators

doping Sr2+ into LaMnO3 oxidised Mn3+ to 4+

eg electron can move between Mn ions so the material becomes metallic below Tc = metal-insulator transition

also has magnetoresistance

59
Q

What is magnetoresistance?

A

change in resistance of a material when a field is applied

giant magnetoresistance is used to detect magnetic fields

60
Q

what is the critical ordering temperature for antiferromagnets?

A

Neel temp TN (subscript N)

61
Q

What does a negative value for theta mean for mean field theory?

A

negative molecular field, acts in the opposite direction as the applied field

causes neighbouring moments to align anti-parallel = anti ferromagnetism

62
Q

Why is pi-type 180 degree superexchange weaker than sigma type?

A

less orbital overlap

63
Q

What are the two different superexchange interactions for LaMnO3? What type of structure does this give?

A

sigma-type 90degrees and pi-type 180degrees

antiferromagnetically coupled ferromagnetic layers

64
Q

Why are neutrons better at determining the positions of lighter atoms within a crystal structure?

A

neutral charge prevents interaction with electrons so deeper penetration is possible

neutrons have a spin so the magnetic moment interacts with unpaired e- and gives magnetic structure info

65
Q

what is powder neutron diffraction used for?

A

antiferromagnet analysis

66
Q

What causes magnetic diffuse scattering in the powder neutron diffraction pattern?

A

the magnetic correlations are only short-range

67
Q

General formula for ferrites?

A

MFe2O4 where M is a 2+ cation

68
Q

Describe normal spinel ferrite structure

A

cubic spinel, FCC, M2+ occupy 1/8 tetrahedral and Fe3+ 1/2 octahedral sites,

dominant interaction = AFM but bc Zn2+ and Cd2+ are diamagnetic = paramagnetic overall

69
Q

Describe inverse spinel ferrite structure

A

M2+ occupy 1/4 tetrahedral and Fe3+ 1/4 octahedral sites and 1/8 tetrahedral

dominant interaction = AFM

examples = NiFe2O4, CoFe2O4, Fe3O4

70
Q

Describe magnetite

A

Fe3O4, strong antiferromagnetic superexchange interactions between Fe3+ ions = net moment of 0μB

ferromagnetic double exchange interactions between Fe3+ and Fe2+ ions = net moment of 4μB

71
Q

Use of ferromagnetism? Why?

A

memory storage, magnetisation can be switched with an applied field to give magnetisation up/down

72
Q

What is a multiferroic material?

A

where two or more primary ferroic orderings occuring spontaneously

73
Q

Describe the 3 primary ferroic orders in solids

A

Ferromagnetic: spontaneous magnetisation develops below Tc, switchable by applied magnetic field

Ferroelectric: spontaneous electric polarisation develops below Tc, switchable w/ applied electric field

Ferroelastic: spontaneous strain develops in crystal structure below Tc, switchable by applied mechanical stress

74
Q

Describe an example of a ferroelectric

A

BaTiO3

the cooperative displacement of the Ti4+ 3d0 ions in the TiO6 network gives electric polarisation and tetragonally distorts the cubic perovskite

75
Q

Where do ferroelastics occur?

A

in materials that have 2 or more orientations of crystal structures which are energetically equivalent when without stress

76
Q

Describe example of ferroelastic

A

NiTi

high temp cubic phase
low temp monoclinic phase

ferroelastic formed during cooling phase transition in the absence of stress

77
Q

Piezoelectric material? use and eg?

A

combination of ferroelectric and ferroelastic, generates electric charge under pressure, used in sensors and motors

perovskite lead zirconate titanate (PZT)

CHEM313 (6 decks)

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