**ESR Techniques for the Detection of Seismic Frictional Heat**

Tatsuro Fukuchi *Yamaguchi University Yoshida, Yamaguchi, Japan* 

#### **1. Introduction**

316 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

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The contribution of seismic frictional heat to the total earthquake energy budget is an important topic to elucidate earthquake rupture process. However, the frictional heat has been hardly estimated from fault rocks except melting-originated pseudotachylytes but calculated from seismological or frictional test data. The frictional heat calculated often gives a large component of the total energy budget although the San Andreas fault heat flow paradox suggests that the contribution of frictional heat may be rather small (Kanamori et al., 1998; Kanamori & Heaton, 2000; Lachenbruch & Sass, 1980, 1992). Thus, we had required any new technique to directly estimate frictional heat from fault rocks. Recent ESR (electron spin resonance) and magnetic studies of fault zones revealed that fault rocks may have been magnetized due to the thermal decomposition of iron-bearing paramagnetic or antiferromagentic minerals included in host rocks into ferrimagnetic ones by frictional heating (Fukuchi, 2003; Fukuchi et al., 2005, 2007; Ferré et al., 2005; Han et al., 2007). Since ferrimagnetic minerals commonly show huge ESR absorption due to their spontaneous magnetization, we can detect them as FMR (ferrimagnetic resonance) signals using the ESR technique. Detailed ESR analyses showed that the growth process of FMR signals during heating may fundamentally follow the zero-order reaction kinetics (Fukuchi, 2003; Fukuchi et al., 2005). Therefore, we can use FMR signals as an effective index of frictional heat. In this chapter, I will explain the basis and application of ESR techniques for the detection of seismic frictional heat using FMR signals. According to one-dimensional equations on frictional heating (McKenzie & Brune, 1972; Cardwell et al., 1978), the frictional heat strongly depends on the width of heat generation, which is equivalent to the thickness of the slip zone but not to the thickness of a pseudotachylyte vein. The thickness of the slip zone is considered to be commonly an order of millimeters or less (Kanamori and Heaton, 2000; Sibson, 2003). To actually estimate the frictional heat from a fault rock, we must sequentially detect FMR signals at a resolution of 1 mm or less. From this point of view, I develop the scanning ESR microscopic technique for sequential high-resolution measurements of FMR signals. I will introduce the case of the Nojima fault rocks in Japan.

### **2. Principles of ESR and FMR**

A number of vacancies, interstitials and impurities exist in natural minerals. These point defects often trap unpaired electrons such as electrons ionized or holes formed in the valence energy band by natural radiation. Some transition elements such as Fe or Mn originally have unpaired electrons at the *d*-orbit. Classical physically, an electron with negative charge may be considered to be a rotating sphere, so that the rotation of an electron, that is, the electron spin generates a circular current. Since the circular current causes a magnetic field around the electron due to the electromagnetic induction, every unpaired electron has the magnetic moment. Paired electrons in materials show no magnetic moment due to the neutralizing effect of the pairing electron spins on the basis of the Pauli exclusion principle. The electron spin is responsible for all sorts of magnetism. In this section, I will explain the principles of ESR and FMR.

#### **2.1 Electron spin resonance**

Electron spin resonance is a spectroscopic technique to detect unpaired electrons in materials. Fig. 1 shows the principle of ESR. In case of paramagnetic materials, when no external magnetic field exists around, the unpaired electrons, that is, the internal electron spins are distributed at random and as a whole show no magnetic moment. On the other hand, when the external magnetic field exits, the spins are arranged in parallel or antiparallel with the magnetic field and separate into two energy levels (*E*1 and *E*2). This phenomenon is called the Zeeman splitting or Zeeman effect. Consequently, the paramagnetic materials as a whole show the magnetic moment. The difference in energy level △*E* (=*E*2-*E*1) caused by the Zeeman splitting is expressed by △*E*=*gβH*, where *g* is a spectroscopic splitting factor (g-value), *β* is the Bohr magneton and *H* is the magnetic field. If microwaves are added to the materials under the Zeeman splitting, parallel spins with the lower energy *E*1 absorb microwave power and shift to the higher energy level *E*2, and

Fig. 1. Principle of electron spin resonance.

valence energy band by natural radiation. Some transition elements such as Fe or Mn originally have unpaired electrons at the *d*-orbit. Classical physically, an electron with negative charge may be considered to be a rotating sphere, so that the rotation of an electron, that is, the electron spin generates a circular current. Since the circular current causes a magnetic field around the electron due to the electromagnetic induction, every unpaired electron has the magnetic moment. Paired electrons in materials show no magnetic moment due to the neutralizing effect of the pairing electron spins on the basis of the Pauli exclusion principle. The electron spin is responsible for all sorts of magnetism. In this

Electron spin resonance is a spectroscopic technique to detect unpaired electrons in materials. Fig. 1 shows the principle of ESR. In case of paramagnetic materials, when no external magnetic field exists around, the unpaired electrons, that is, the internal electron spins are distributed at random and as a whole show no magnetic moment. On the other hand, when the external magnetic field exits, the spins are arranged in parallel or antiparallel with the magnetic field and separate into two energy levels (*E*1 and *E*2). This phenomenon is called the Zeeman splitting or Zeeman effect. Consequently, the paramagnetic materials as a whole show the magnetic moment. The difference in energy

spectroscopic splitting factor (g-value), *β* is the Bohr magneton and *H* is the magnetic field. If microwaves are added to the materials under the Zeeman splitting, parallel spins with the lower energy *E*1 absorb microwave power and shift to the higher energy level *E*2, and

△

*E*=*gβH*, where *g* is a

*E* (=*E*2-*E*1) caused by the Zeeman splitting is expressed by

section, I will explain the principles of ESR and FMR.

**2.1 Electron spin resonance** 

Fig. 1. Principle of electron spin resonance.

level △ simultaneously anti-parallel spins with the higher energy *E*2 emit microwaves and shift to the lower energy level *E*1 when the energy *hν* of microwaves are equal to the difference in energy level; *E gH h* , where *h* is Planck's constant and *ν* is the frequency of microwaves. This phenomenon is called electron spin resonance.

Since the number of the parallel spins is commonly larger than that of the anti-parallel ones, the paramagnetic materials as a whole cause the absorption of microwave power, that is, the ESR absorption. The ESR absorption is measured by sweeping the magnetic field under a fixed microwave frequency and power, and is recorded as an absorption curve using an ESR spectrometer (Fig. 2). Every paramagnetic material shows the largest absorption at the resonant magnetic field and the area of the absorption curve is proportional to the total number of the internal spins. Recent ESR spectrometers have an additional 100 kHz modulation of magnetic field to improve the S/N ratio and the rectified output is recorded as the first derivative line of the absorption curve on the recorder. We commonly call this first derivative line ESR spectrum and detect the unpaired electrons with the Zeeman energy (*E*1 or *E*2) as an ESR signal in the ESR spectrum (Fig. 3). Every ESR signal has an intrinsic g-value calculated from the resonant magnetic field *Hr* and microwave frequency *ν<sup>0</sup>* (*g*=*hν0*/*βHr*), so that we can identify the ESR signal by its g-value; the g-value of free electrons is 2.0023. Moreover, the linewidth and lineshape of the signal are also important physical parameters. There are two types of lineshape, the Gaussian and Lorentzian lines, in

Fig. 2. X-band ESR spectrometer

the absorption curve and the first derivative line. The relationship between the peak-to-peak linewidth *ΔHpp* and the spin-spin relaxation time *T2* are expressed by *H T pp* /2 /( ) <sup>2</sup> (Gaussian) and 2 1/( 3 ) *H T pp* (Lorentzian), respectively, where *γ*=*gβ/(h/2π*) (Alger, 1973). On the other hand, the peak-to-peak length of the signal is proportional to the total number of the internal spins.

Fig. 3. ESR absorption curve and its first derivative line.

#### **2.2 Ferrimagnetic resonance**

Electron spin resonance is classified into electron paramagnetic resonance (EPR), ferromagnetic resonance, ferrimagnetic resonance, antiferromagnetic resonance (AFMR), etc. on the basis of the magnetism of the materials studied (e.g. Kittel, 2005). The principle of ferrimagnetic resonance is essentially similar to that of ferromagnetic resonance as far as the opposing magnetic moments of two sublattices in ferrimagnets precess in a magnetic field retaining their antiparallel state. In addition to this mode of precession, there is another mode that the two magnetic moments in an imperfectly antiparallel state precess on easy axes of magnetization in ferrimagnets (Kittel, 2005; Smit & Wijn, 1965). Thus, I use the term "FMR" as the abbreviation for ferrimagnetic resonance in this chapter.

In general, ferrimagnets have two sublattices consisting of different magnetic ions such as Fe3+ and Fe3+Fe2+ ions in magnetite. The magnetic moments of the two sublattices are opposed due to the negative exchange interaction and unequal, so that a spontaneous magnetization as a whole remains. When an external magnetic field exits, the magnetic field exerts a torque on the opposing magnetic moments and causes them to precess in one body. In case of ferromagnets, the magnetic moments are aligned in the same direction due to the

the absorption curve and the first derivative line. The relationship between the peak-to-peak linewidth *ΔHpp* and the spin-spin relaxation time *T2* are expressed by *H T pp*

1973). On the other hand, the peak-to-peak length of the signal is proportional to the total

Electron spin resonance is classified into electron paramagnetic resonance (EPR), ferromagnetic resonance, ferrimagnetic resonance, antiferromagnetic resonance (AFMR), etc. on the basis of the magnetism of the materials studied (e.g. Kittel, 2005). The principle of ferrimagnetic resonance is essentially similar to that of ferromagnetic resonance as far as the opposing magnetic moments of two sublattices in ferrimagnets precess in a magnetic field retaining their antiparallel state. In addition to this mode of precession, there is another mode that the two magnetic moments in an imperfectly antiparallel state precess on easy axes of magnetization in ferrimagnets (Kittel, 2005; Smit & Wijn, 1965). Thus, I use the term

In general, ferrimagnets have two sublattices consisting of different magnetic ions such as Fe3+ and Fe3+Fe2+ ions in magnetite. The magnetic moments of the two sublattices are opposed due to the negative exchange interaction and unequal, so that a spontaneous magnetization as a whole remains. When an external magnetic field exits, the magnetic field exerts a torque on the opposing magnetic moments and causes them to precess in one body. In case of ferromagnets, the magnetic moments are aligned in the same direction due to the

(Gaussian) and 2 1/( 3 ) *H T pp*

number of the internal spins.

Fig. 3. ESR absorption curve and its first derivative line.

"FMR" as the abbreviation for ferrimagnetic resonance in this chapter.

**2.2 Ferrimagnetic resonance** 

(Lorentzian), respectively, where *γ*=*gβ/(h/2π*) (Alger,

 /2 /( ) <sup>2</sup> positive exchange interaction, so that the external magnetic field causes the aligned moments to precess in one body. As mentioned above, in ferrimagnetic resonance there is another mode that the two magnetic moments in an imperfectly antiparallel state precess on the easy axes of magnetization. The precession in an imperfectly antiparallel state occurs in antiferromagnets as well, where the magnetic moments of two sublattices are opposed due to the negative exchange interaction and equal, so that the precession is responsible for antiferromagnetic resonance. However, the ESR absorption due to antiferromagnetic resonance is much weaker than that due to ferrimagnetic one. On the other hand, in paramagnetic resonance, every electron's magnetic moment (electron spin) is caused to precess by the magnetic field. The frequency of precession is called the Larmor frequency. Regardless of the types of magnetism, the ESR absorption occurs when the Larmor frequency is the same as the resonant frequency, that is, the frequency of microwaves added (Kittel, 2005). In magnetic resonance, the energy *hν* of electromagnetic waves with the Larmor frequency coincides with the difference in the Zeeman energy levels (Fig. 1). Since the whole of the opposing moments in ferrimagnets has much larger energy level in the magnetic field than every electron's moment, ferrimagnets show much larger ESR absorption than paramagnets. Moreover, the resonant frequency in ferrimagnetic resonance and the linewidth of the ESR absorption curve strongly depend on the orientation of the material and the magnitude of the magnetic field due to the large demagnetizing field arising from the spontaneous magnetization. The ESR signals obtained from ferrimagnets are especially called FMR (ferrimagnetic resonance) signals.
