5.2 The Samples

The structure of the NbSe₂ single crystal used in this thesis is shown in Fig. 5.2. The precise chemical formula is 2H-NbSe₂. The numeral 2 indicates the number of layers in a unit cell, while the capital letter H indicates the type of crystal symmetry (i.e. H stands for hexagonal). Each layer is a ``sandwich'' of two layers of Se atoms with a layer of metallic Nb atoms between them. The Nb and Se atoms within a sandwich are covalently bonded, and these atoms form a 2D-hexagonal lattice. The NbSe₂ layers are weakly coupled by van der Waals forces. As a result, the mechanical and electrical properties of 2H-NbSe₂ are extremely anisotropic. For instance, this material is very easy to cleave along a plane parallel to the layers. This feature makes NbSe₂ ideal for studies of the vortex lattice using surface techniques (such as STM) since clean, fresh, smooth surfaces are easily obtained. The 2D nature of the electronic properties in NbSe₂ is similar to that in YBa₂Cu₃O$_{7-\delta}$. Electrons can move freely within the layers, however the overlap of the electron wave functions between the layers is small. Consequently, the conductivity perpendicular to the layers is several orders of magnitude smaller than that within the layers.

 

 

The NbSe₂ single crystal was grown by a standard vapour transport technique as discussed in Ref. [83]. The characteristics of this sample are listed in Table 5.1. The near zero-field T_c was 7.0 K with a transition width less than 0.1 K, determined from magnetization measurements. The upper critical field was also measured with magnetization and is roughly described by the relation $H_{c2} (T) \! = \! H_{c2} (0) \left[ 1-t^p \right]$, where $t \! = \! T/T_c$, $H_{c2} (0) \! = \! 3.5$ T and $p \! = \! 1.55$.

Figure 5.3 shows the unit cell of the fully oxygenated compound YBa₂Cu₃O₇. The unit cell is orthorhombic with dimensions $a \! = \! 3.83$ Å , $b \! = \! 3.88$ Å  and $c \! = \! 11.68$ Å . The layers containing the Cu(2) and O(3) sites are often referred to as the ``CuO<sub>2</sub> planes'', whereas the layers containing the Cu(1) and O(1) sites along the $\hat{b}$-axis are commonly referred to as the ``chain layers''. The O(2) and O(3) sites in the CuO₂ planes are almost always occupied. Deoxygenation involves the removal of oxygen primarily from the O(1) sites.

The most significant improvement in experimental studies of YBa₂Cu₃O$_{7-\delta}$ in recent years is the availability of high-quality single crystals. The single crystals used in the present study were grown at the University of British Columbia (UBC) by a flux method in yttria-stabilized-zirconia (YSZ) crucibles [203]. The purity of the UBC crystals has been determined to be greater than $99.5 \%$. The impurities which are present in the crystals originate from corrosion of the crucibles. The characteristics of the YBa₂Cu₃O$_{7-\delta}$samples used in the present study are summarized in Table 5.1. The transition temperatures were determined by low-field magnetization measurements. All samples were on the order of 0.1 mm thick. The high quality of these crystals has been verified by other characterization methods, namely resistivity, microwave surface resistance and heat capacity measurements (see Ref. [203]).

Hole doping in YBa₂Cu₃O$_{7-\delta}$ is primarily controlled by adding or removing oxygen in the O(1) sites in the CuO chain layers. The local oxygen configuration is highly sensitive to the temperature and oxygen partial pressure in the annealing process. Impurities tend to impede the mobility of some of the oxygen. Thus, the most uniform oxygen configuration can be achieved in the purest crystals. The highest value of T_c is obtained with $\delta \! \approx \! 0.05$,so that YBa₂Cu₃O_6.95 will frequently be referred to in this thesis as the ``optimally doped'' compound. Note that there are still some oxygen vacancies at this doping level which may act as pinning sites for vortex lines. At $\delta \! = \! 0.4$, every other CuO chain in a chain layer is essentially empty. The compound YBa<sub>2</sub>Cu<sub>3</sub>O<sub>6.60</sub> will often be referred to as the ``underdoped'' compound.

To remove the twin planes, some of the samples were mechanically detwinned and subsequently reannealed to set the oxygen doping level. Sample O3 was completely free of twins after this process. However, some of the twin planes reformed in sample U2 when reannealed. The separation between the twin boundaries in U2 was on the order of 10⁴ Å, which is substantially larger than the spacing between vortex lines for the field range considered in this study.

 

Name 4688center Chemical

Formula 4691center Number of

Crystals 4694center tex2html_wrap_inline$T_c$tex2html_wrap_inline

 [K]  4699center Total Mass

 [mg]  4702center Surface Area

 [mm²]  4705center Detwinned center 4708center Ref. center

O1 YBa₂Cu₃O_6.95 3 93.2(0.25) 53 36 no [2,3]

O2 YBa₂Cu₃O_6.95 1 93.2(0.25) 25 no [3]

O3 YBa₂Cu₃O_6.95 1 93.2(0.25) 25 yes

U1 YBa₂Cu₃O_6.60 3 59.0(<0.1) 53 36 no [5]

U2 YBa₂Cu₃O_6.60 2 59.0(<0.1) 30 yes [5]

NB NbSe₂ 1 7.0(<0.1) 43 30 no twins [4]