Measurement of standard samples

consistent to each other. The slope of P-E curves may be related to the relative permittivity by the following expressions:

P = Q

Where P is polarization, Q is the electric quantity calculated by the instrument, A is the area of the thin film, V is the applied voltage, C is the capacitance of the thin film,

d is the thickness of the thin film, E is the electric field, εr is relative permittivity and ε0 is vacuum permittivity. The slope of P-E curves derived from Fig. 4.14 matches the

relative permittivity shown in Fig. 4.13 very well.

4.3 Measurement of standard samples

For the check of our circuit, we used standard samples, which were provided by Radiant Technologies, to make sure of the ferroelectric hysteresis loop measurement of our system. The linear capacitance (1.004 nF) and the ferroelectric capacitance (PZT) are connected to our circuit and tested individually. The P-E curves are shown as the Fig. 4.17 and Fig. 4.18.

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Fig. 4.17 The result of linear capacitance test shows that the circuit is accuracy in capacitance test.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-30 -20 -10 0 10 20 30

P ( µC/ c m

)

Voltage (V)

PZT sample

Fig. 4.18 The P-E curve shows that the system can measure the ferroelectric hysteresis character.

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4.4 The correlation between strain, electric, and magnetic properties

10 20 30 40 50 60 70 80

Fig. 4.19 The plot shows the χ(T) curves with applied magnetic field(H=500 Oe and 1000 Oe) along b-axis, and the εr(T) curve by applying 1 kHz ac signal with amplitude of 10 mV (E//a).

Finally, we compare the results of χ(T) and εr(T). As shown in Fig. 4.19, the anomaly seen in εr(T) around 30K coincides with the second magnetic transition TSR. Thus, it is quite natural to correlate the observed εr(T) anomaly with the magnetism-induced ferroelectric transition as suggested theoretically by Sergienko et

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al. [5]. The missing of the expected P-E hysteresis is not understood at present.

However, we note that the strain effect of o-LuMnO3 thin film was not considered in the theory and the strain effect has been demonstrated to cause changes in the magnetic properties [4, 13, 28].

The epitaxial strain plays the essential roles, which are stabilizing the structure of o-LuMnO3 and affecting the magnetic properties. Considering the lattice distortion,

the crystal elastic energy is promoted to the higher level. Assume the elastic energy is the E∝x², which x is the displacement of ions, as shown in Fig. 4.20.

Fig. 4.20 The schematic illustration of relation between the ion displacement and the elastic energy.

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The red hollow circle is the state of the o-LuMnO3 thin film with no distortion caused by double exchange. The red full circle is the state considered double exchange. And the black is the o-LuMnO3 bulk, respectively. The bulk preparation is using the process of high temperature and high pressure, which may cause a little strain, so the black hollow circle is not at zero of x. The thin film is distortion by the epitaxial stress of substrate compared with the bulk, which is more strain than the bulk. Supposing the same hopping energy in the bulk and the thin film, the displacement is much different. The distortion of the thin film is rather small than that of the bulk, which may reduce the polarization very much, even totally.

Somehow it may also affect the correlation of magnetoelectric properties. In any case, further studies are certainly needed in order to clarify the discrepancies described above.

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Chapter 5 Summary

The a-axis oriented o-LuMnO3 films were successfully grown on NSTO (110) by PLD. X-ray diffraction and Φ-scan allowed us to confirm the structure of LuMnO3

was orthorhombic with specific growth directions. Using SQUID to measure the anisotropic magnetization, an antiferromagnetic transition of Mn moment were observed near 43K in each axis and the second transition (TSR) was observed around 30K only in b-axis. Furthermore, we probed the polarization and the relative permittivity with electric field applied along a-axis. The linear behavior of P-E curves at fixed temperature (T ranged from 13K to 50K) indicates the absence of spontaneous polarization. The temperature dependent relative permittivity revealed the anomaly around 30K may have correlation with the second magnetic transition (TSR) in b-axis. The difference between the experiment and theoretic prediction is presumably due to the strain effect, but need further investigations to clarify.

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