Interaction of matter with magnetic fields

Transcription

1 LN07-1 Interaction of matter with magnetic fields All substances have magnetic properties, which can be determined by examining their behaviour in the presence of an external magnetic field, H. N S When a substance is placed in a magnetic field with strength H, the electrons in the substance respond with a magnetic contribution of its own: B = H + ΔH ΔH = 4πM

2 LN07-2 Magnetic susceptibility B = H + 4πM B/H = 1 + 4πM/H Magnetic susceptibility is an inherent property of a substance; a dimensionless quantity that is constant at any given temperature. Other magnetic susceptibility expressions acquire units: g = gram susceptibility = V / cm 3 g -1 rho = density M = molar susceptibility = ( g ) (MW) cm 3 mol -1 Allows us to correlate the amount of susceptibility with a substance of a specific formula via its molecular weight. Magnetic measurements typically come from mass of substance in and out of field.

3 LN07-3 Types of magnetic interactions (i) The interaction of the magnetic field (H) with electrons as charged particles causes an internal field ( I ) that opposes the external field. H H The induced internal field is negative, as is the associated susceptibility, This is diamagnetism. It is is inherent in all substances. essentially temperature independent (ii) Spin and orbital angular momenta (S, L) give electrons the properties of a magnetic dipole, which tends to align with the external, applied field. H H the induced internal field is positive, as is associated susceptibility, This is paramagnetism. It occurs only in substances with incompletely filled orbitals. Paramagnetism is temperature-dependent

4 LN07-4 Simplest room temperature techniques use variants on Gouy or Faraday methods. Examines change in mass of a sample both in and out of a magnetic field. Measuring magnetic properties The change in measured mass (Δm) with/without magnetic field is proportional to the magnetic susceptibility, χ, of the sample. Diamagnetic materials are repelled by the magnetic field. Paramagnetic materials are pulled into the magnetic field. Temperature dependent measurements require more sophisticated instruments, e.g. a Superconducting quantum interference device (SQUID)

5 LN07-5 Paramagnetism [Cu(H 2 O) 6 ] 2+ SO 4 2- H - H individual spins are randomly oriented spins tend to align with an external field (H) H induces a net magnetization, M, in the sample

6 LN07-6 M vs H for paramagnet M sat M H At H = 0, M = 0 At low values of H, M increases linearly with H At higher values of H, M plateaus reaches a maximum value known as saturation

7 LN07-7 The Curie Law The magnetic properties of a substance depends on the strength of the external field AND temperature. At a given value of H, the magnetic susceptibility is inversely proportional to temperature magnetic susceptibility, χ (= M/H) = (Nβ 2 g 2 )S(S+1) 3kT = C T C = Curie constant = (Nβ 2 g 2 )S(S+1) 3k N = Avogadro s number Β = Bohr magneton k = Boltzmann constant g = gyromagnetic ratio: a property of the substance, usually around 2 S= total spin quantum number for the compound

8 LN07-8 Magnetic moments We use magnetic moments, µ, to take into account temperature, when quantifying the susceptibility of a substance. The expression for an experimentally measured magnetic moment simplifies down to: μ = χt = 4S(S+1)

9 LN07-9 Magnetic moments There is a fairly simple relationship then between the predicted magnetic moment and S. It turns out there are complicating factors.some of the time. Spin-only magnetic moment, µ spin-only (μ s ): an estimate of what µ eff should be, if only the unpaired electrons spin angular momentum determines susceptibility. μ s = 4S(S+1) = 2 S(S+1) = n(n+2) n S μ s ½ / /2 5.92

10 LN07-10 The Curie Law [Cu(H 2 O) 6 ] 2+ SO 4 2- S = 1/2 [Ni(H 2 O) 6 ] 2+ SO 4 2- S = 1 [Mn(H 2 O) 6 ] 2+ SO 4 2- S = 5/2 8 χ μ eff (BM) T (K) T (K)

11 LN07-11 There is a fairly simple relationship then between the predicted magnetic moment and S. It turns out there are complicating factors.some of the time. (ochahedral and high spin, where relevant): µ s : µ eff : Table 20.11, p.701

12 LN07-12 Orbital contributions to magnetic moment The magnetic dipole properties of electrons come from both the spin (S) and the orbital (L) angular momentum. An expression for the theoretical magnetic moment is: μ = 4S(S+1) + L(L+1) This formula can works if S and L operate independently (LS, or Russell-Saunders coupling): recall this is true of most first row metals. Less valid for heavier metals where JJ coupling is operative. For d n for which L = 0, there is no orbital contribution, so µ reduces to µ S.

13 LN07-13 Orbital contributions to magnetic moment What about when L 0? From H&S pp : for an electron to have orbital angular momentum, it must be possible to transform the orbital it occupies into an entirely equivalent and degenerate orbital by rotation. For octahedral complexes: d n configuration ground state term orbital contribution predicted? 1 (t 2g ) 1 2 T 2g 2 (t 2g ) 2 3 T 1g 3 (t 2g ) 3 4 A 2g 4(HS) (t 2g ) 3 (e g *) 1 5 E 2g 4(LS) (t 2g ) 4 3 T 1g 5(HS) (t 2g ) 3 (e g *) 2 6 A 1g 5(LS) (t 2g ) 5 2 T 2g 6 (HS) (t 2g ) 4 (e g *) 2 5 T 2g 6(LS) (t 2g ) 6 1 A 1g 7(HS) (t 2g ) 5 (e g *) 2 4 T 1g 7(LS) (t 2g ) 6 (e g *) 1 2 E g 8 (t 2g ) 6 (e g *) 2 3 A 2g 9 (t 2g ) 6 (e g *) 3 2 E g

14 LN07-14 Spin-orbit coupling H&S p. 703: Spin-orbit coupling is a complicated subject. (sigh) Nevertheless, it happens, and it can affect the size of µ eff. For first-row metals, the contribution of spin-orbit coupling to µ eff is usually small. In these cases S and L operate independently. There are exceptions, though. Most examples of noticeable spin-orbit coupling for first row TMs occur for complexes with T ground states. Can also see it in complexes where ground state is not T but there are T excited states. Normally only states that are identically labelled can mix. Spin-orbit coupling permits some mixing of states (ground and excited) That are not the same. Even taking orbital angular momentum (L) into account, experimental magnetic moments (μ eff ) can deviate from the calculated values based on μ = 4S(S+1) + L(L+1) T 1(g) T 1(g) T 2(g) A 2(g) P F

15 LN07-15 Spin-orbit coupling Cobalt provides the most common examples of observable spin-orbit coupling contributions to µ eff among first row metals. [Co(H 2 O) 6 ] 2+ µ eff = 5.0µ B [CoCl 4 ] 2 µ eff = 4.4 µ B For the heavier second- and third-row metals spin-orbit coupling is usually large. Again, can see spin-orbit coupling even for complexes with L=0. This can lead to big discrepancies between µ S and experimental µ eff e.g. cis-[nbbr 4 (NCMe) 2 ] d 1 µ eff = 1.27 µ B cis-[tacl 4 (NCMe) 2 ] d 1 µ eff = 0.45 µ B

16 Rationalizing µ eff values for some first row metal complexes Metal salt µ S µ eff (80K) µ eff (300K) KCr(SO 4 ) 2 12H 2 O d 3 (Oh) 4 A 2g 3.87 µ B 3.8 µ B 3.8 µ B Cr(SO 4 ) 6H 2 O Cr 2+ d 4 (Oh, HS) 5 E g 4.90 µ B 4.8 µ B 4.8 µ B Cs 2 VCl 6 V 4+ d 1 (Oh) 2 T 2g 1.73 µ B 1.4 µ B 1.8 µ B (Et 4 N) 2 NiCl 4 Ni 2+ d 8 (Td) 3 T µ B 3.2 µ B 3.8 µ B A and E ground states give µ eff close to μ s that do not vary with temperature (no orbital contributions (L(L+1)) to the magnetic moments, and no spin-orbit coupling contributions). For Oh V 4+, which has a T ground state, the room temperature µ eff is close to the spin-only value, and there is some temperature sensitivity of this value: consistent with very small orbital contribution and some spin-orbit coupling For Td Ni 2+,also with a T ground state, see µ eff values higher than spin-only value and temperature sensitive: consistent with independent contribution of L (which increases µ eff ) and spin-orbit coupling (raises µ eff for d n >5).

17 LN07-17 High spin vs low spin Magnetic measurements allow us to distinguish between high spin and low spin complexes. For some of these complexes, the difference in energies between oct and P is relatively small, which makes it possible for the two spin states to coexist, in equilibrium. The degree to which each state is represented in the sample will depend on the temperature. < P > P

18 LN07-18 Spin crossover 5 4 μ eff / BM From: Real et al., Dalton Trans. 2005, 2062

19 LN07-19 Interactions Between Unpaired Electrons Bridging ligands can facilitate coupling of electron spins located on different metal ions via a superexchange pathway. This leads to antiparallel (antiferromagnetic) alignment of unpaired electron spins on adjacent metal centres. M 1 µ-l M 2 It s also possible for the unpaired electrons to prefer to align with the same spin (ferromagnetic)

20 LN07-20 Interactions Between Unpaired Electrons S = 1 S = 0 2J S = 0 J < 0: antiferromagnetic Singlet is ground state 2J S = 1 J > 0: ferromagnetic Triplet is ground state R.G. Hicks, Radical approaches to magnetism, 2002

21 LN07-21 Interactions Between Unpaired Electrons Robin Hicks: X x = 2Ng 2 b 2 kt(3 + exp(-j/kt)) (m = T ) 3 J > 0 m (BM) 2 1 J = 0 J < 0 T (K)

22 LN07-22 Intermolecular Magnetic Interactions Even in simple complexes, there can be weak interactions between magnetic ions. These interactions can lead to deviations from the Curie Law. = C T - q Curie-Weiss Law q = Weiss constant 4 [Cu(H 2 O) 6 ] 2+ SO 4 2- m (BM) 3 2 q = +5K q = 0K q = -5K T (K)

23 LN07-23 bulk magnetic properties The paramagnetic complexes we ve discussed so far are all magnetically dilute: in the bulk phase, the unpaired electrons do not interact with each other or do so only weakly. When paramagnetic ions are very close together or are separated by species that can transmit magnetic interactions, they may couple magnetically throughout the solid. Ferromagnetic materials contain large domains of magnetic dipoles aligned in the same direction. Antiferromagnetic materials contain large domains of neighbouring magnetic dipoles aligned in opposite directions. paramagnetism ferromagnetism antiferromagnetism Fig 20.32, p.706 (ferrimagnetism = magnetic moments are opposed, but unequal in size or number - more complex to diagnose)

24 LN07-24 Magnetic Ordering T > Tc: paramagnet T < T c : Ferromagnet T < T c : Antiferromagnet Fe (T c = 1043K) Ni (T c = 631K) Cr (T c = 313K) Mn (T c = 95K) CrO 2 (T c = 387K) CrBr 3 (T c = 33K) NiO (T c = 523K) MnO (T c = 120K)

25 LN07-25 Below TC, ferromagnets behave as permanent magnets. (i.e. they retain a non-zero magnetization M even when the external field, H, is zero. The M vs H behaviour of a ferromagnet is a hysteresis loop: R M = remanent magnetization: H C (ignore this) H C = coercive field:

26 LN07-26 Types of magnets and uses The most important magnets are based on d- and f-elements. Ferrite Fe 2 O 3 + BaCO 3 or SrCO 3 AlNiCo alloys of these elements SmCo alloys of these elements NdFeB alloys of these elements Uses of magnets Magnetic recording media televisions and computer monitors: Electric guitars Medicine: magnetic resonance imaging refrigerator magnet. Art: Vinyl magnet sheets Magnetic levitation transport. Credit, debit, and ATM cards Speakers and microphones: Electric motors and generators: Chemistry: NMR, Compasses: toys. automobiles