7.6 Experimental Techniques
173
known as second-harmonic generation (SHG) where the medium is excited by the
optical field E (ω) and generates light with a frequency double of initial one, i.e., 2ω.
The intensity of the second harmonic light in ferromagnets or antiferromagnets can
be found as
I (2ω) ∼ P|(2ω) |
2
=
χ i jk
(nl) E j (ω) E k (ω) + α i jkl
(nl) E j (ω) E k (ω)M(0) l
2
Or [χ ijk
(nl) E j (ω) E k (ω) + α ijkl
(nl) E j (ω) E k (ω)I(0) l ]
2 respectively.
Hence, the equation tells that the SHG can also be a measure of the magnetization
M(0) or antiferromagnetic vector l(0). Compared to linear magneto-optical effects,
the second harmonic is generated only in centrosymmetric media (in electric dipole
approximation). Consequently, the magnetic second-harmonic generation (MSHG)
technique can be used as a unique tool for probing surface and interface magnetism.
In the visible spectral range, the optical response of media is dominated by electric dipole transitions. Spin flip and the selection rules for such transitions are not
allowed. A strong spin–orbit interaction is required for the sensitivity of light to
magnetic order in case of both linear and non-linear magneto-optical (M–O) effects.
A strong coupling between spins and orbitals results in substantial values of α and β
components in Eq. (7.7). Hence, the magneto-optical effects can provide information
about the magnetic state of a medium.
The analysis of results obtained from M–O studies of solids is troublesome as
the optical transition in visible spectral region is relatively broad. Besides that,
magneto-optical effects are helpful only as indirect probes of spin ordering as they
are proportional to M and l. Therefore, the interpretations of time-resolved M–O
measurements bear a number of uncertainties. Laser-induced excitation can alter the
populations of the excited states and change the symmetry of the ground state. As a
result, the M–O response may be changed even without affecting its magnetic order
and magnetization vector. Thermo dynamical description is unsuitable for an explanation of femtosecond laser-induced effects in magnets in terms of time-dependent
tensors. Laser-induced M–O Kerr or Faraday effects should be described considering
non-linear effect.
7.6.3 Far-Infrared (F-IR) Probe
Far-infrared spectroscopy is used to measure low-energy optical excitations in high
magnetic fields such as various electron magnetic resonances (ESR, cyclotron resonance, antiferromagnetic resonance). The low excitations in the F-IR or THz region
are point of concern since the electronic properties of quantum materials are usually
determined by the low lying charge and magnetic excitations. Significantly, the
frequencies of magnetic resonance of most antiferromagnets and spin-flip transition of many rare-earth ions lie in the frequency range from 100 GHz to 3 THz. A
173
known as second-harmonic generation (SHG) where the medium is excited by the
optical field E (ω) and generates light with a frequency double of initial one, i.e., 2ω.
The intensity of the second harmonic light in ferromagnets or antiferromagnets can
be found as
I (2ω) ∼ P|(2ω) |
2
=
χ i jk
(nl) E j (ω) E k (ω) + α i jkl
(nl) E j (ω) E k (ω)M(0) l
2
Or [χ ijk
(nl) E j (ω) E k (ω) + α ijkl
(nl) E j (ω) E k (ω)I(0) l ]
2 respectively.
Hence, the equation tells that the SHG can also be a measure of the magnetization
M(0) or antiferromagnetic vector l(0). Compared to linear magneto-optical effects,
the second harmonic is generated only in centrosymmetric media (in electric dipole
approximation). Consequently, the magnetic second-harmonic generation (MSHG)
technique can be used as a unique tool for probing surface and interface magnetism.
In the visible spectral range, the optical response of media is dominated by electric dipole transitions. Spin flip and the selection rules for such transitions are not
allowed. A strong spin–orbit interaction is required for the sensitivity of light to
magnetic order in case of both linear and non-linear magneto-optical (M–O) effects.
A strong coupling between spins and orbitals results in substantial values of α and β
components in Eq. (7.7). Hence, the magneto-optical effects can provide information
about the magnetic state of a medium.
The analysis of results obtained from M–O studies of solids is troublesome as
the optical transition in visible spectral region is relatively broad. Besides that,
magneto-optical effects are helpful only as indirect probes of spin ordering as they
are proportional to M and l. Therefore, the interpretations of time-resolved M–O
measurements bear a number of uncertainties. Laser-induced excitation can alter the
populations of the excited states and change the symmetry of the ground state. As a
result, the M–O response may be changed even without affecting its magnetic order
and magnetization vector. Thermo dynamical description is unsuitable for an explanation of femtosecond laser-induced effects in magnets in terms of time-dependent
tensors. Laser-induced M–O Kerr or Faraday effects should be described considering
non-linear effect.
7.6.3 Far-Infrared (F-IR) Probe
Far-infrared spectroscopy is used to measure low-energy optical excitations in high
magnetic fields such as various electron magnetic resonances (ESR, cyclotron resonance, antiferromagnetic resonance). The low excitations in the F-IR or THz region
are point of concern since the electronic properties of quantum materials are usually
determined by the low lying charge and magnetic excitations. Significantly, the
frequencies of magnetic resonance of most antiferromagnets and spin-flip transition of many rare-earth ions lie in the frequency range from 100 GHz to 3 THz. A