We used the NMR technique to study the doping effect of the Bi2-xPbxSrzCo2Oy, which the Pb-doped sample have larger temperature independent magnetic susceptibility than un-doped sample. The frequency shift of Co3+ site in Fig.3-8, suggests that the enhanced temperature independent magnetic susceptibility is due to the orbital susceptibility of Co4+. Therefore, we can understand that the larger temperature independent magnetic susceptibility in Pb-doped samples is because the Pb-doped samples have larger Co4+ concentration.
Next, we study the topological insulator (Bi0.25Sb0.75)2 (Se2.35Te0.65). We measured 209Bi and 121Sb NMR spectra, spin-spin relaxation time, and spin-lattice relaxation time. The broad spectra of 209Bi and 121Sb suggest that the substitution of Te and Sb is randomly distributed in the crystal.
Both 209Bi and 121Sb spectrum could be separated into the slow and fast T2
components, it means that they are bonding with Se and Te two atoms. In addition, the nuclear quadrupolar splitting of (Bi0.25Sb0.75)2(Se2.35Te0.65) is larger than that of Bi2Se3 is because of the strong lattice distortion by doping. Finally, the spin lattice relaxation rate of 209Bi and 121Sb are telling us the weak temperature dependence susceptibility is related to the temperature dependent band parameters. Summary, the NMR result shows the (Bi0.25Sb0.75)2(Se2.35Te0.65) has the strong lattice distortion, but the surface states still can existence in this material. This fact tell us the topological insulator surface state is not vanish by lattice distortion as long as not breaking the time reversal symmetry.
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measurements. Therefore, the ac susceptometer offers the opportunity to study the magnetic susceptibility as a function of frequency and temperature. The main concept of ac susceptibility is the magnetization of the sample is changing to response an applied ac filed [28], and ac susceptometer design is based on the mutual inductance method [29].5-2 Theoretical background
AC susceptibility is the magnetization of the sample follows the applied ac field either in-phase or with some phase lag. Therefore, we use the ac inductive method to measurement ac susceptibility [30-32]. For the ac susceptometer described below, we will give some information about ac susceptibility in this section.
The susceptibility is defined as
(5.1)
where, is the magnetic susceptibility, M is volume magnetization, and H is magnetic field.
Consider a sample in the applied ac magnetic field , but the magnetic field in the sample will show a phase different behind an applied ac magnetic field. So the magnetization is
37
The physical meaning of is: the time average of the magnetic energy stored in the volume occupied by the sample [31] is
(5.4)
The physical meaning of is: The energy converted into heat during one cycle of the ac field [31] is
2
(5.5)
As we have seen, both parts of the complex ac susceptibility characterize the energy exchange between the sample and the applied ac magnetic field. The reflects the screening properties expressed as a difference between the energy in the normal state and the superconducting state. The corresponds to the amount of ac magnetic field energy converted to heat[28].
5-3 AC Susceptometer Design
The ac susceptometer typically consists of primary coil, pick-up coils, lock-in amplifier, and sample holder, and a typical circuit is shown in Fig.5-1(a). The ac suceptometer probe illustrated in Fig.5-1(b), includes a primary solenoid coil which produces an ac magnetic field. Inside the primary coil are the two pick-up coils which are wound in opposite
38
directions and electrically connected in series. The sample is placed in one of the pickup coils while the other pickup coil is left empty.
Fig. 5-1 (a)Experimental setup of the ac susceptometer (b) AC suceptometer probe illustrated [32]
The magnetic flux through the N turn pick-up coil of radius a (see Fig.5-1) is [32]
(5.6) The induced voltage V(t) across the pick-up coils is:
computer controlled lock-in amplifier (model SR830), and the lock-in amplifier measured voltage Vs is:
sensing coil
a
b
Primary coil pickup coils Sample
39
(5.8)
Since Vs(t)=V0(t), where
(5.9)
The lock-in amplifier can direct measures of Vx and Vy.
The Fig.5-3 shows the dimensions of primary coil, pick-up coils, and sample holder. The pick-up coils are inserted into the primary coil and the sample holder is inserted into the lower pick-up coil.
(a) Primary Coil
Wire gauge: 38(AWG) Total number of turns: 1500 Units: mm
45
40
(b)
(c)
Fig.5-3 (a) Primary coil, (b) pick-up coils, and (c) sample holder geometry
Secondary Coil
Wire gauge: 42(AWG) Total number of turns: 420 Units: mm
Sample holder Units: mm
13
6
41
current, and l is length of the solenoid.The first step is found the current in the primary coil but we use the get the magnetic field by equation (5.10).
The signal from the pick-up coils is proportional to the susceptibility of the sample, and depends on experimental parameters. We get their relationship is [30]
(5.13)
where V is the measured voltage (units V), α is the calibration constant of the susceptometer (units A.m2.V− 1.s− 1), Vs is the sample volume (units
42
temperature measured. The blue point is representation the sample holder with sample, and the read point is meaning the sample holder without sample. We can see that our homemade ac susceptometer is able to work, and transition temperature for YBCO is about 97K. In this chapter, we reported the principle and geometry of ac susceptometer. And finally, it is shown our homemade ac susceptometer is could be work.43
Fig.5-5 Real part of susceptibility ( ) vs temperature.
Fig.5-6 Imaginary part of susceptibility (
) vs temperature.
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