Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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electronic structure has particle–hole symmetry in the

close vicinity of the FS point considered.

Earlier ARPES studies of the self-energy focused

on the ðp; 0Þ point which, however, is masked by

bilayer splitting. Recently, a number of investigations

(cf. Damascelli et al. 2003) at the nodal point k

¼ k

revealed a linear temperature dependence of the im-

aginary part of the self-energy at optimal doping,

which seems to correspond to the linear temperature

dependence of the scattering rate in normal state re-

sistivity, but which, in the ARPES results, extends

deep into the superconducting state. This would be

consistent with the marginal FL model (Varma 1997).

The interest into the self-energy around ðp; 0Þ came

from the strong effect a magnetic mode at Q ¼ðp; pÞ

would have in this region (Eschrig and Norman

2000). It would lead to the peak-dip-hump structure

of the energy distribution functions measured in

ARPES around ðp; 0Þ. Much but very likely not all of

this structure is now attributed to the bilayer split-

ting. It remains a challenge for further studies to dis-

entangle these features.

4. Summary

The electronic structure of cuprate superconductors is

more or less settled in the cases of undoped ðdE0Þ and

overdoped ðjdj\0:2Þ material. In the former case it is

that of an AF charge transfer insulator which can

theoretically be described by a t–J model Hamiltonian.

It might be necessary to incorporate in-plane O-2p

orbitals into this model for certain considerations. In

the overdoped case, a weakly renormalized LDA band

structure of a Cu-3d

y

2 2O-2p

band is experimen-

tally found in the vicinity of the FL in ARPES.

At optimal doping (d E

) for superconductivity,

experimental evidence seems to accumulate for a

marginal FL state at elevated temperature, which is

masked by the d-wave superconducting state at low

temperature.

Still largely unclear is the situation in the under-

doped region where several interactions seem to be

interwoven leading to a complex behavior.

See also: High-temperature Superconductors, Cuprate:

Magnetic Properties by NMR/NQR; High-temperature

Superconductors: Thin Films and Multilayers; High-

temperature Superconductors: Transport Phenomena;

Superconducting Materials, Types of

Bibliography

Andersen O K, Liechtenstein A I, Jepsen O, Paulsen F 1995

LDA energy bands, low-energy Hamiltonians, t

, t

(k),

and J

. J. Phys. Chem. Solids 56, 1573–91

Baskaran G, Zhou Z, Anderson P W 1987 The resonating va-

lence bond state and high-T

superconductivity—a mean ﬁeld

theory. Solid State Commun. 63, 973–6

Dagotto E 1994 Correlated electrons in high-temperature

superconductors. Rev. Mod. Phys. 66, 763–839

Damascelli A, Hussain Z, Shen Z-X 2003 Angle-resolved pho-

toemission spectroscopy of the cuprate superconductors. Rev.

Mod. Phys. 75, 473–542

Ding H, et al. 1996 Angle-resolved photoemission spectroscopy

study of the superconducting gap anisotropy in Bi

CaCu

8 þx

. Phys. Rev. B 54, 9678

Eschrig H, Koepernik K, Chaplygin I 2003 Density functional

application to strongly correlated electron systems. J. Solid

State Chem. 176, 482–95

Eschrig M, Norman M R 2000 Neutron resonance: modeling

photoemission and tunneling data in the superconducting

state of Bi

8 þ d

. Phys. Rev. Lett. 85, 3261–4

Fink J, Nu

cker N, Pellegrin E, Romberg H, Alexander M,

Knupfer M 1994 Electron energy-loss and x-ray absorption

spectroscopy of cuprate superconductors and related com-

pounds. J. Electron Spectrosc. Relat. Phenom. 66, 395–452

Johnston D C 1997 Normal-state magnetic properties of single-

layer cuprate high-temperature superconductors and related

materials. In: Buschow K H J (ed.) Handbook of Magnetic

Materials. Elsevier, Amsterdam, Vol. 10, Chap. 1, pp. 1–237

Maekawa S, Tohyama T 2001 Charge and spin in low-dimen-

sional cuprates. Rep. Prog. Phys. 64, 383–428

Mori M, Tohyama T, Maekawa S 2002 Electronic states and

superconductivity in multilayer high-T

cuprates. Phys. Rev.

B 66, 064502-1–7

ller-Buschbaum H 1977 Oxometalates with planar coordi-

nation. Angew. Chem. Int. Ed. 16, 674–87

Norman M R, Ding H, Fretwell H, Randeira R, Campuzano

J C 1999 Extraction of the electron self-energy from angle-

resolved photoemission data: application to Bi

8 þ x

. Phys. Rev. B 60, 7585–90

Pickett W 1989 Electronic structure of the high-temperature

oxide superconductors. Rev. Mod. Phys. 61, 433–511

Ronning F, Kim C, Shen K M, Armitage N P, Damascelli A,

Lu D H, Feng D L, Shen Z-X, Miller L L, Kim Y-J, Chou F,

Terasaki I 2003 Universality of the electronic structure from

a half ﬁlled CuO

plane. Phys. Rev. B 67, 035113-1–16

Tohyama T, Maekawa S 2000 Angle-resolved photoemission in

high-T

cuprates from theoretical viewpoints. Supercond. Sci.

Technol. 13, R17–32

Varma C 1997 Non-Fermi-liquid states and pairing instability

of a general model of copper oxide metals. Phys. Rev. B 55,

14554–80

Zhang F C, Rice T M 1988 Effective Hamiltonians for the

superconducting Cu oxides. Phys. Rev. B 37, R3759–561

H. Eschrig

Institute of Solid State and Materials Research

Dresden, Germany

High-temperature Superconductors,

Cuprate: Magnetic Properties

by NMR/NQR

One of the peculiar properties of cuprate high-tem-

perature superconductors (HTSC) is their descent

from antiferromagnetic (AF) parent compounds

290

High-temperature Superconductors, Cuprate: Magnetic Properties by NMR/NQR

whose magnetic order arises from Cu

2 þ

spins in the

CuO

planes. For instance, YBa

7d

is obtained

by doping YBa

with oxygen while La

2x

CuO

results from Sr substitution in La

CuO

Both processes create electron holes in the CuO

planes and eventually destroy the AF long-range

order. However, AF short-range order is still present

in the superconductors and even in the supercon-

ducting regime. These properties make cuprate

HTSC a unique class of superconductors quite

different from conventional superconductors and

metals. (see Superconducting Materials, Types of ).

NMR–NQR spectroscopy has explored many as-

pects of HTSC and several papers have reviewed

these studies: Pennington and Slichter (1990), Alloul

(1991), Brinkmann and Mali (1994), Berthier et al.

(1996), Rigamonti et al. (1998). The present article

will update results related to magnetic properties of

cuprate HTSC: relaxation and Knight shift data in

the normal state, the dynamic susceptibility, the

single-spin ﬂuid model, the spin–gap effect, and some

experiments in the superconducting state.

1. Relaxation Rates and Magnetic Shifts

The information on the microscopic magnetic be-

havior of cuprate HTSC is contained in the spin sus-

ceptibility wðq; oÞ which depends on frequency o and

wavevector q . w is mainly probed by measuring re-

laxation times and magnetic frequency shifts. In most

NMR studies of HTSC, the external magnetic ﬁeld B

is sufﬁciently large to render the quadrupole interac-

tion a small perturbation of the Zeeman interaction

thus leading to a splitting of the NMR signal. In the

case of NQR, internal magnetic ﬁelds may give rise to

Zeeman perturbed NQR transitions. In nearly all

cuprate HTSC, the measured NQR frequencies for

both isotopes of in-plane Cu(2) are pure NQR fre-

quencies, thus revealing the absence of long-range

magnetic order in these compounds (on the time scale

of NQR).

The hyperﬁne interaction of the nuclear magnetic

moment with the local magnetic ﬁeld contains a static

part that induces a magnetic shift of the NMR line,

and a dynamic part that causes relaxation (see Solids,

Nuclear Magnetic Resonance of ). The shift tensor

consists of an orbital part being predominantly tem-

perature independent in HTSC, and a spin part, usu-

ally called the Knight shift K

spin

, that is temperature

dependent and is expected to vanish in the supercon-

ducting state due to singlet spin pairing. Each com-

ponent of K

spin

can be expressed by the hyperﬁne

interaction tensor, A

, and the static spin susceptibil-

ity: K

spin

¼ 1=g m

ðÞ



The ﬂuctuating part of the hyperﬁne interactions is

the source of relaxation processes. The main contri-

bution to the copper, oxygen, and yttrium spin–

lattice relaxation in HTSC compounds arises from

electron spin ﬂuctuations. This contribution is rela-

ted to the imaginary part of the dynamical spin

susceptibility wðq; o

Þ and it is given by the Moriya

formula:





2 m

q;a

ðÞ

q; o

ðÞ

where F

ðqÞ¼

j ;aa

exp iq  r





is the form fac-

tor, o

is the nuclear resonance frequency, a denotes

the direction of quantization, i.e., the direction of ei-

ther the maximum component of the electric ﬁeld

gradient tensor V

in NQR or of B

in NMR exper-

iments, and a

is the direction perpendicular to a. A

the on-site (r

¼ 0) and transferred (r

a0) hyperﬁne

coupling tensor for the nuclei under consideration.

Therefore, the spin–lattice relaxation time T

better (T

T )

1

provides information about the q av-

eraged imaginary part of wðq; o

Þ. Another relaxation

time, the spin–spin relaxation time T

, is related to

the real part of w ðq ; oÞ. In many HTSC, the domi-

nating part of 1/T

, called 1/T

2G,ind

, is due to an en-

hanced indirect nuclear–nuclear spin coupling

mediated by the electronic spin system; this leads to

a Gaussian contribution to the spin-echo decay sig-

nal. The numerical values of the coupling tensors A

which may range up to several thousand oersteds,

have been derived from various NMR experiments,

in particular from magnetic shift studies (see review

papers listed above).

If ﬂuctuating electric ﬁeld-gradients are present

(at the Larmor frequency), additional terms would

appear in the Moriya formula. Since these terms

are usually small in HTSC, they are neglected; how-

ever, as will be discussed in Sect. 3, the presence

of quadrupole interactions may have important

consequences.

Relaxation times and Knight shift behave quite

differently from corresponding data in conventional

superconductors or metals. For instance, W has a

nonlinear temperature dependence and K is temper-

ature dependent. Furthermore, different nuclei (Cu,

O, Y) display different temperature dependences

which, in turn, depend on the doping level of the

substance. More recent results are discussed by

Berthier et al. (1996) and Rigamonti et al. (1998).

Figure 1 sketches the general behavior of W,

1/T

2G,ind

and K for Cu(2), where the temperature

characterizes the spin–gap to be discussed in

Sect. 4. When interpreting these data, one usually

chooses the Mila–Rice Hamiltonian (Rigamonti et al.

1998) as the starting point. Then, the different tem-

perature dependences of W are attributed to differ-

ences in the form factors F

ðqÞ that ﬁlter the magnetic

ﬂuctuations at different points of the Brillouin zone.

This explains, for instance, the striking difference of

the W values for copper and oxygen.

291

High-temperature Superconductors, Cuprate: Magnetic Properties by NMR/NQR

2. Calculations of the Dynamic Spin Susceptibility

The quality of calculating 1/T

is based on the

knowledge of the imaginary part of the dynamic spin

susceptibility w

þ

q; o

ðÞ

. Several models have been

employed to calculate 1/T

for the normal state of

HTSC. Among these are the nearly antiferromagnetic

Fermi liquid (NAFL) description of HTSC and

the 2DQHAF scaling model which regards a cuprate

HTSC as a disordered 2-dimensional quantum

Heisenberg AF (Berthier et al. 1996, Rigamonti

et al . 1998). In the NAFL model, the dynamic spin

susceptibility is written, in a phenomenological ap-

proach, as the superposition of two terms, one for

itinerant quasiparticles and the other for localized

2 þ

magnetic moments. It seems that the NAFL

model is rather well obeyed in overdoped cuprates

while the 2DQHAF model describes underdoped

cuprates (Berthier et al. 1996, Rigamonti et al. 1998).

Usually, calculations of the dynamic spin suscep-

tibility start from the t–J model (Rigamonti et al.

1998) where t denotes the hopping energy of the holes

and J represents the strong repulsion between holes

residing on the same square. Then, the susceptibility

is usually calculated by using various methods.

However, in spite of considerable progress, all theo-

ries have some disadvantages which are mainly

connected with their phenomenological character.

For example, in these theories, the temperature and

doping dependence of the AF correlation length, x,

which is the essential parameter that governs the

temperature and doping dependence of 1/T

, are

postulated or, at best, are taken from a comparison

with experiment. Expressions used for the dynamic

spin susceptibility are good approximations only for

wave vectors in the vicinity of the AF wave vector,

thus the models provide reliable results for 1/T

if x is

large. In YBa

7d

, for instance, x is small and

therefore a more detailed theoretical analysis of the

NMR data is required.

This has been done, for instance, in an approach

where w

þ

q; o

ðÞis calculated within a constraint-

free theory based on the presentation of the t–J

model in terms of Hubbard operators (Brinkmann

and Zavidonov 2002). Both electron and AF spin

correlations were taken into account. The model is

able to reproduce the main features of the temper-

ature and doping dependences of x in both the pure

Heisenberg AF (e.g. La

CuO

) and doped com-

pounds La

2x

CuO

ðÞ. Starting form these results,

the factors F q

ðÞ

þ

q; o

ðÞ

=o and hence 1/T

were

calculated for

Cu,

O, and

Y in YBa

7d

Figure 2 demonstrates the good agreement with

experimental data.

3. The Single-spin Fluid Model

One of the central issues in understanding the cuprate

HTSC has been to determine the minimal number of

electronic degrees of freedom which are necessary to

describe the physics at the atomic scale of these

structures. Adopting the picture of the spin-resonant

singlet state with quasi-localized holes at copper

(Rigamonti et al. 1998), only one spin degree of free-

dom would be necessary; this is the single-spin ﬂuid

(SSF) scenario. However, as was discussed by various

Figure 1

Schematic behavior of relaxation times (a) and Knight

shift (b) of planar Cu in optimally (O) and underdoped

(U) cuprate HTSC (reproduced by permission of

Rigamonti et al. 1998).

Figure 2

Calculated temperature dependence of the

spin–lattice relaxation rates of

Cu,

O, and

Yin

YBa

(solid lines) compared with experimental

data (Brinkmann and Zavidonov 2002).

292

High-temperature Superconductors, Cuprate: Magnetic Properties by NMR/NQR

authors (e.g. Berthier et al. 1996), this model might be

an oversimpliﬁcation.

NMR provides information about oxygen and cop-

per independently. Studies of the uniform spin suscep-

tibility Refwðq ¼ 0; o ¼ 0Þg, i.e., of the Knight shift,

are in favor of the SSF model. On the other hand,

oxygen and copper show a very different temperature

dependence of the spin–lattice relaxation, that is of

the dynamic spin susceptibility, Imfwðq; o

Þg,thus

suggesting independent spin degrees of freedom. How-

ever, the hyperﬁne ﬁeld, due to antiferromagnetically

correlated copper spins, could cancel at the oxygen

site and this would explain the different temperature

dependences within a SSF model.

There is, however, evidence that this view is in-

complete. The

O NMR in Y-based cuprate HTSC

has extensively been studied by various groups. In

particular, the pronounced temperature depen-

dence of the anisotropy of the plane oxygen spin–

lattice relaxation rate,

W, is still puzzling (e.g.,

Suter et al. 1997) while the SSF model predicts an

almost temperature independent rate anisotropy.

Suter et al. (1997) pointed out that it is also very

difﬁcult to explain, within a simple SSF model, the

ratio of the oxygen and the yttrium rate, namely

W. Furthermore, a comparison of

O and

Cu NMR results from La

2x

CuO

with inelastic

neutron scattering data suggested that a single-band

picture is inadequate (Walstedt and Cheong 1995).

Further support of this conclusion came from a

study of the spin–lattice relaxation of plane oxygen in

YBa

below 200 K (Suter et al. 2000): there is a

considerable contribution of quadrupolar ﬂuctua-

tions (i.e., low-frequency charge ﬂuctuations) to the

total ﬂuctuating ﬁelds. Two degrees of freedom are

involved in the low-energy excitations of the elec-

tronic system, one of them is the single-spin degree,

implying that the single-spin ﬂuid model is partially

correct, whereas the other one is the charge degree of

freedom with predominantly oxygen character, since

it is not observed at the copper sites.

4. The Spin-gap Effect

A dominant characteristic of the normal state of op-

timally doped and underdoped cuprate HTSC is the

occurrence of the so-called pseudogap; its origin still

remains unclear. The pseudogap refers to the transfer

of low-energy excited states to higher energy. In

NMR and neutron scattering experiments, the pseu-

dogap reveals itself as a spin–gap (Brinkmann and

Mali 1994, Berthier et al. 1996, Rigamonti et al.

1998). For instance, in YBa

¼81 K),

T )

1

of Cu(2) increases with falling temperature

(see Fig. 1) and reaches a maximum at T

(E150 K),

which serves as a convenient scale for the temperature

dependence of the spin–gap onset temperature. Pos-

sible relations between the spin–gap and the super-

conducting gap are still under debate.

A hint to the interdependence of these gaps may be

found in the fact that several structure related anom-

alies have been observed in YBa

around a

temperature T

¼180 K. Based on NMR–NQR stud-

ies, the anomalies were interpreted as an electronic

crossover involving enhanced charge ﬂuctuations in

planes and chains (Suter et al. 1997). Because of the

proximity of T

and T

, Eremin et al. (1997) suggest-

ed that the spin–gap effect in YBa

is caused

by a transition due to a charge density wave insta-

bility. The authors explained, among others, the

strong temperature dependence of the magnetic shift

of Cu(2) nuclei and predicted a dependence of T

the isotope mass.

Such an isotope effect has been found in a high-

accuracy NQR T

study of the

Cu(2) nuclei, supple-

mented by susceptibility measurements, on

O and

O exchanged YBa

samples (Raffa et al. 1998).

The isotope exponents, deﬁned as a ¼Dln T



ðÞ=

Dln m

ðÞ

for T

and correspondingly for T

, are

¼0.061(8) and a

¼ 0:056ð12Þ. The agreement

of the exponents, within the experimental error,

suggest a common origin, or at least a relation, for

the superconducting and the spin-gap. This result

is contrary to a recent

Y magnetic shift study in

YBa

which reported the absence of an isotope

effect in the pseudogap (Williams et al. 1998). How-

ever, Mali et al. (2001), by extending the work of

Raffa et al. (1998) to the

Cu(2) Knight shift, again

found an isotope effect on the spin–gap; both expo-

nents have the same sign. Hence, the controversy on

this topic continues.

When T

is approached from above, one expects

enhanced superconducting pairing ﬂuctuations which

may, in the presence of strong magnetic ﬁelds, inﬂu-

ence various normal-state properties, including spin–

lattice relaxation (Rigamonti et al. 1998). These

effects can be used to clarify the origin of the pseu-

dogap (Eschrig et al. 1999). Previous experimental

results and the corresponding conclusions on the

Cu(2) relaxation rate in YBa

7d

have been

controversial (Rigamonti et al. 1998, Gorni et al.

2001). Latest high-precision measurements (Gorni

et al. 2001) found the relaxation rate to be ﬁeld in-

dependent (from 0 T up to 14.8 T) in the normal

state; a ﬁeld dependence develops only below T

A ﬁeld independent

Cu(2) relaxation has also

been observed in the normal state of YBa

(Brinkmann and Mali 1994).

5. The Superconducting State

Again, as in the normal state, magnetic properties of

the HTSC are probed mainly via the magnetic shift K

and relaxation rates, in particular W and 1/T

. The

temperature dependence of K below T

is in accord

with a carrier pairing into singlet-spin states and sup-

ports the model of d wave pairing. The temperature

293

High-temperature Superconductors, Cuprate: Magnetic Properties by NMR/NQR

dependence of 1/T

is also in accord with this model.

The temperature dependence of W is close to a T

behavior. The anisotropy of wðq; oÞ is studied by

measuring W with the magnetic ﬁeld parallel and

perpendicular to the c axis; the ﬁeld dependence is

explored by comparing NQR and NMR values. The

theoretical interpretations are mostly based on models

of phenomenological character. Special magnetic ef-

fects arise from substituting Cu(2) by diamagnetic Zn

and lead to deviations from the T

law.

The lattice and dynamics of ﬂux lines (FL) in the

superconducting state have attracted special atten-

tion. A summary of related NMR experiments is

found in Rigamonti et al. (1998). NMR spectra and

the relaxation times T

and T

are employed to study

statics and dynamics of the FL and their ﬁeld and

temperature dependence. For instance, the tempera-

ture dependence of the ﬁeld distribution inside the

bulk YBa

, together with a partial melting of

the FL lattice, can be inferred from the

Y linewidth.

O spectra demonstrate, for a certain temperature

range, the coexistence of liquid and solid vortex be-

havior, e.g., in YBa

. The ideal tool to study

the FL motion is spin–lattice relaxation: correlation

times and pinning barriers can be estimated, for in-

stance in YBa

Very promising are recent studies to explore the

vortex core structure by site-selective and spatially

resolved experiments. For instance, 1/T

and 1/T

increase for nuclei close to the vortex core. An NMR

imaging experiment has spatially resolved the elec-

tronic structure inside and outside vortex cores in

near-optimally doped YBa

7d

: strong AF ﬂuc-

tuations are found outside the cores whereas inside

unusual electronic states are detected (Mitrovic

et al.

2001). Site-selective 1/T

measurements in YBa

illustrate that the simple interpretation of

the data by the density of states of the Doppler-

shifted quasiparticles of a d superconductor is prob-

lematic (Kakuyanagi et al. 2002).

6. Conclusion

NMR and NQR have proven to be suitable tools to

investigate the dynamic susceptibility in cuprate

HTSC. Experimental results quite often agree with

phenomenological models of the susceptibility; but

the theoretical approaches still need further reﬁne-

ments to interpret details satisfactorily. The problems

of the single-spin ﬂuid model are not yet settled and

the spin–gap is still a matter of debate, in particular

its relation to other characteristic temperatures of the

HTSC. NMR–NQR studies of the superconducting

state seem to be an expanding and promising ﬁeld of

research.

See also: High-T

Superconductors: Electronic Struc-

ture; High-temperature Superconductors: Thin Films

and Multilayers; Nuclear Magnetic Resonance Spec-

trometry; Superconducting Thin Films: Materials,

Preparation, and Properties

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D. Brinkmann

University of Zurich, Switzerland

High-temperature Superconductors: Thin

Films and Multilayers

Since 1986, when high-T

superconductivity was dis-

covered, stunning achievements have been made in

the fabrication of ﬁlms and multilayers based on

these superconducting cuprates despite their complex

crystal structures (see also Superconducting Thin

Films: Materials, Preparation, and Properties, Super-

conducting Thin Films: Multilayers). In this article

the key morphologic and electronic properties of

high-T

superconducting thin ﬁlms, particularly of

YBa

7d

, and multilayers are described.

Efforts to produce thin ﬁlms of cuprate super-

conductors rapidly followed their discovery. The ﬁrst

polycrystalline ﬁlms of a high-T

superconductor,

(La,Sr)

CuO

, were deposited by sputtering in Feb-

ruary, 1987 (Koinuma et al. 1987, Nagata et al.

1987). In March, 1987 epitaxial (La,Sr)

CuO

ﬁlms

were prepared by sputtering on (100)SrTiO

subst-

rates (Suzuki and Murakami 1987). Although the

latter ﬁlms were superconducting as grown, their T

improved greatly after a high-temperature anneal.

Later that same month the ﬁrst superconducting ﬁlms

with a zero resistance critical temperature T

exceeding the boiling point of nitrogen, 77 K, were

grown (Laibowitz et al. 1987). These were poly-

crystalline YBa

7d

ﬁlms deposited by e-beam

evaporation and annealed at high temperatures. In

April 1987, the ﬁrst epitaxial YBa

7d

ﬁlms

were fabricated (Chaudhari et al. 1987). This was

accomplished by depositing amorphous Y-Ba-Cu-O

ﬁlms via e-beam evaporation on a (100)SrTiO

subst-

rate and subsequently crystallizing the YBa

7d

ﬁlm by solid-phase epitaxial regrowth during a high-

temperature annealing step.

These were the ﬁrst superconductors in any form

with critical current densities J

exceeding 10

Acm

2

at 4.2 K, thereby demonstrating the commercial utility

of high-T

superconductivity as well as the importance

of epitaxy in producing high-T

ﬁlms with useful elec-

trical transport properties. The progress did not stop

there. Soon, epitaxial ﬁlms with good electrical prop-

erties, of YBa

7d

(Terashima et al. 1988) and

other high-T

superconductors were grown in situ,di-

rectly in their crystalline state (i.e., without the need of

an ex situ annealing step following deposition) on a

wide variety of substrates including sapphire, silicon,

GaAs, and even on polycrystalline substrates such as

stainless steel and alumina, through the use of a high-

ly-textured, intermediate buffer layer. Today, excel-

lent ﬁlms of a multitude of high T

compounds are

produced by a variety of vapor-phase techniques (see

also Superconducting Thin Films: Materials, Prepara-

tion, and Properties, Superconducting Thin Films: Mul-

tilayers). Wafer sizes have reached diameters of 8

inches (20.32 cm), and ﬁlms are deposited in scalable

and continuous processes over lengths of up to a

meter (Foltyn et al. 1999, Park et al. 1999).

Due to their outstanding electrical transport char-

acteristics (high T

, high J

, low surface resistance

), epitaxial ﬁlms and multilayers, incorporating in

some cases Josephson junctions, are very useful for

applications involving high-T

superconductors, in-

cluding microwave ﬁlters, magnetometers, digital cir-

cuits, and fault current limiters. Films have also been

used with remarkable success to investigate funda-

mental properties and application-related aspects of

high-T

superconductivity, e.g., analysis of the order

parameter symmetry (Tsuei et al. 1994, Chaudhari

and Lin 1994, Mannhart et al. 1996) and measure-

ments of the transport properties of grain boundaries

(Hilgenkamp and Mannhart 2001). In addition, the

technology developed for the growth of cuprate su-

perconductor ﬁlms has enabled rapid progress in the

deposition of ﬁlms of other multicomponent oxides

including ferroelectrics (Waser et al. (eds.) 2001) and

manganates that exhibit colossal magnetoresistance

(Helmolt et al. 1993).

As it is impossible to provide a complete overview

of the ﬁeld within the space available, we have re-

stricted our discussion of the ﬁeld of high-T

ﬁlms

and focus on a few illustrative examples based mainly

on YBa

7d

. We regret that it is impossible to

include all of the important work contributed by the

large number of groups active in this relatively new

and rapidly progressing ﬁeld (see also Supercon-

ducting Thin Films: Materials, Preparation, and Pro-

perties, Superconducting Thin Films: Multilayers).

Additional information can be found in other review

papers on high-T

ﬁlms and multilayers (Humphreys

et al. 1990, Lemberger 1992, Somekh et al. 1992,

Matijasevic and Bozovic 1996, Bozovic and Eckstein

1996, Triscone and Fischer 1997, Wo

rdenweber

1999).

1. Substrates for Superconducting Films

A crucial starting point in the growth of high-T

thin

ﬁlms and multilayers is the selection of the substrate

material and its preparation. As large-area single

crystal substrates of high-T

superconductors, a

necessity for homoepitaxial growth, are not commer-

cially available, other substrate materials must be

used. The ideal substrate is both chemically and

structurally compatible with the epilayer. Other

295

High-temperature Superconductors: Thin Films and Multilayers

factors, including commercial availability, cost, the

potential for integration with other device techno-

logies, thermal expansion coefﬁcient, dielectric

constant, and the dielectric loss tangent at micro-

wave frequencies (for high-frequency operation of

superconducting circuits) must also be considered

(Hollmann et al. 1994, Phillips 1996). Unlike the

heteroepitaxial growth of semiconductors, where it is

imperative to choose a well lattice-matched substrate

in order to avoid undesired dislocations in the grown

structures, dislocations in superconductors and espe-

cially in high-T

superconductors are effective vortex

pinning sites and lead to significantly higher critical

current densities (Mannhart et al. 1992, Dam et al.

1999). Thus, a relatively large lattice mismatch be-

tween high-T

superconductors and substrate mate-

rials is, in principle, permissible. Thermal expansion

mismatches on the other hand, particularly those that

lead to the ﬁlm being in a state of tension upon

cooling (i.e., substrates with smaller thermal expan-

sion coefﬁcients), can lead to ﬁlm cracking.

The perovskites SrTiO

, LaAlO

, and NdGaO

have good structural and chemical match to the cop-

per-containing high-T

superconductors. The excel-

lent structural and chemical match of SrTiO

to the

cuprate superconductors immediately made it the

substrate of choice for epitaxial growth (Suzuki and

Murakami 1987, Chaudhari et al. 1987), and for

many purposes it remains the reference substrate.

However, the high loss tangent of SrTiO

bars it from

high-frequency applications. LaAlO

has the lowest

loss tangent of these perovskite substrates and is

available in diameters as large as 100 mm. MgO has

even lower dielectric loss, but the multiple in-plane

epitaxial orientations that often exist in oxide super-

conductor ﬁlms grown on MgO causes undesirable

high-angle grain boundaries in the ﬁlms. This results

in lower critical currents and higher surface resist-

ances (Laderman et al. 1991).

The extremely low dielectric loss of sapphire

(Al

) makes it an attractive material for high fre-

quency applications, especially when a device struc-

ture with a high quality factor Q is desired. It also has

high thermal conductivity at low temperature and is

available in large sizes. However, its anisotropic di-

electric properties complicate device design and the

direct growth of high-T

superconductors on sapphire

is plagued by chemical reactions. Several barrier lay-

ers, including SrTiO

, CaTiO

, MgO, Y

-ZrO

, and

CeO

, have been implemented to circumvent this

reaction. Of these, CeO

and CaTiO

barrier layers

on sapphire appear to be the most promising. The

surface resistance at microwave frequencies of

YBa

7d

ﬁlms grown on these latter barrier lay-

ers on sapphire is comparable to the best values ob-

tained on any other substrate (Merchant et al. 1992).

The integration of high-T

superconductor layers

with silicon and GaAs substrates is desirable to form

superconductor-semiconductor hybrid electronics

and monolithic microwave integrated circuits

(MMIC). The direct growth of cuprate superconduc-

tors on silicon or GaAs results in an interface reac-

tion and significant diffusion tails into both substrate

and ﬁlm. However, suitable barrier layers have been

found. Critical current densities exceeding 10

Acm

2

at 77 K have been achieved in YBa

7d

–

ZrO

/Si and YBa

7d

/MgO/GaAs ﬁlms (Fork

1994). Due to the higher thermal expansion coefﬁ-

cient of GaAs compared to silicon, crack-free

YBa

7d

ﬁlms may be prepared up to a thick-

ness about ﬁve times greater than on silicon subst-

rates, where the onset of cracking is about 50 nm

(Fork 1994). Another way to overcome the thermal

expansion problem when integrating with silicon is

to grow on silicon-on-sapphire, where crack-free

YBa

7d

ﬁlms more than 400 nm thick and crit-

ical current densities of 4.6 10

Acm

2

at 77 K have

been demonstrated (Fork et al. 1991). In light of the

desirable high-frequency properties of sapphire subst-

rates and the progress that has been made in inte-

grating them with high-T

superconductors, sapphire

substrates may be the best substrate choice for mon-

olithic superconductor–semiconductor electronics.

Epitaxial growth of high-T

ﬁlms on single crys-

talline substrates used to be the only way to realize J

values in excess of 10

Acm

2

at 77 K. However, the

ion-beam-assisted deposition (IBAD) process (Iijima

et al. 1992) and the rolling-assisted, biaxially-tex-

tured, substrates (RABiTS) process (Goyal et al.

1996, Norton et al. 1996) now allow comparable J

be achieved in YBa

7d

ﬁlms deposited on ei-

ther roll-textured strips of metals (e.g., nickel alloys)

using RABiTS or on polycrystalline or amorphous

substrates using IBAD. This freedom from single

crystal substrates offers incredible ﬂexibility in the

integration of high-T

superconductors ﬁlms with

other materials.

SrTiO

was not only the ﬁrst substrate on which

epitaxial high-T

superconductor ﬁlms were grown

(Suzuki and Murakami 1987), it has also become the

best studied and most advanced perovskite substrate

in terms of substrate preparation. As the results be-

low describe, it is possible to prepare atomically ﬂat

(100)SrTiO

substrates with relatively straight unit-

cell-high steps, where the entire surface is terminated

at the TiO

layer (Kawasaki et al. 1994, Koster et al.

1998). Initiating growth on a ﬂat substrate of known

termination is key to understanding and eventually

controlling the nucleation and growth of high-T

su-

perconductor ﬁlms and crucial to the preparation of

high-T

multilayers with structural control at the

atomic-layer level.

The surfaces of chem-mechanically polished

(100)SrTiO

substrates (as received from the vendor)

and imaged by atomic force microscopy (AFM) and

reﬂection high-energy electron diffraction (RHEED)

are shown in Figs. 1(a) and 2(a), respectively. These

images are indicative of the untreated SrTiO

surfaces

296

High-temperature Superconductors: Thin Films and Multilayers

on which most high-T

ﬁlms and multilayers have

been grown to date. (100)SrTiO

can terminate with

either the SrO layer or the TiO

layer and the co-

axial impact-collision ion scattering spectroscopy

(CAICISS) spectrum in Fig. 3(a) reveals that chem-

mechanically polished substrates have mixed SrO and

TiO

termination. The mixed termination remains

even after annealing the as-received (100)SrTiO

surface in oxygen at high temperatures, as shown

in Fig. 3(b). However, etching the (100)SrTiO

in buffered-HF results in a fully TiO

-terminated

(100)SrTiO

surface as revealed by the CAICISS

spectra in Fig. 3(c). This buffered-HF process (Kawa-

saki et al. 1994), which has since been enhanced

(Koster et al. 1998), also makes the surface smoother

and more regular as can be seen in the AFM image in

Fig. 1(b) and inferred from the RHEED pattern in

Fig. 2(b).

Figure 1

AFM images of (100)SrTiO

substrate surfaces (a) as-

received, following a brief heating to B650 1Cin

vacuum, and (b) following water soak, buffered-HF etch,

and oxygen anneal surface preparation. The vendor of

both substrates was ESCETE Single Crystal Technology

(reproduced by permission of the American Institute of

Physics from Appl. Phys. Lett., 1998, 73, 2920–2).

Figure 2

RHEED images taken at B650 1C in 15 Pa oxygen of

(100)SrTiO

substrate surfaces (a) as-received and (b)

following water soak, buffered-HF etch, and oxygen

anneal surface preparation. The vendor of both

substrates was ESCETE Single Crystal Technology

(reproduced by permission of the American Institute of

Physics from Appl. Phys. Lett. , 1998, 73, 2920–2 and

of Elsevier Science from Appl. Surf. Sci., 1999, 138–9,

17–23, respectively).

297

High-temperature Superconductors: Thin Films and Multilayers

2. Properties of YBa

7d

2.1 Structural Characterization

Improvements in electronic and photonic materials are

usually associated with lower defect densities, e.g.,

lower concentrations of unwanted impurities, disloca-

tions, grain boundaries, twin boundaries, stacking

faults, and inclusions, and improved crystalline order.

High-T

superconductors are an exciting case in which

defects—of the right kind—are often desired to dra-

matically improve properties. A clear example of the

beneﬁcial potential of such defects is the enhancement

of the self-ﬁeld J

of single crystals of YBa

7d

(as well as single crystals of all other high-T

super-

conductors studied to date) by over ﬁve fold at 4 K

and over ten fold at 77 K by subjecting them to heavy-

ion irradiation (Civale et al. 1991). Although im-

proved, the self-ﬁeld J

values of these bombarded

single crystals are still an order of magnitude lower

than the best ﬁlms at 77 K, indicating that the ﬁlms are

riddled with even more defects that enhance J

Unraveling which of the defects in the ﬁlms are

beneﬁcial and which are detrimental to a particular

property has been accomplished by correlating trans-

port measurements with structural characterization.

In this section we describe some of the defects that

exist in high T

thin ﬁlms and multilayers, focusing

on YBa

7d

ﬁlms in which the c-axis is oriented

normal to the plane of the substrate (c-axis

YBa

7d

ﬁlms). We concentrate on YBa

7d

as it is the best studied of all high-T

super-

conductors and on c-axis ﬁlms as this is generally the

most relevant orientation for applications. Note,

however, that for most studies and applications there

is no obvious reason why yttrium should be the

best rare earth (Re) to utilize in superconducting

ReBa

7d

ﬁlms. Indeed, the usage of NdBa

7d

and SmBa

7d

ﬁlms is increasing as

they tend to have smoother surfaces and can have

slightly higher T

values than YBa

7d

(a) Transmission electron microscopy (TEM)

A cross-sectional transmission electron micrograph

of a c-axis YBa

7d

ﬁlm grown by PLD on

(100)SrTiO

is shown in Fig. 4 (Eibl and Roas 1990).

The dark lines running vertically in this bright-ﬁeld

TEM image are threading dislocations. These dislo-

cations originate in the vicinity of the interface and

extend through the ﬁlm. Although the Burgers vector

of the dislocations in Fig. 4 was not determined,

subsequent TEM studies of the threading dislocations

in YBa

7d

ﬁlms grown by PLD on (100) MgO

found similar dislocation densities and suggested

the Burgers vector to be either [101], [011], or [111]

(Aindow and Yeadon 1994, Yeadon et al. 1995). Note

that when such a threading dislocation intersects the

ﬁlm surface its Burgers vector has a screw component.

As described in the next section, atomic force micro-

scopy (AFM) and scanning tunneling microscopy

(STM) studies reveal that YBa

7d

ﬁlms typi-

cally contain comparable densities of dislocations

with a screw component at the ﬁlm surface; thus it is

likely that the threading dislocations imaged in Fig. 4

have a Burgers vector with a screw component.

Another important issue that TEM studies have

clariﬁed is the chemistry of the interface between high-

ﬁlms and various substrates (Wen et al. 1993). Due

Figure 3

CAICISS time-of-ﬂight spectra taken at an incident

angle of 351 along the [110] azimuth of (100)SrTiO

substrate surfaces (a) as-received, (b) following a

1000 1C anneal in 1 atm. oxygen for 10 h, and (c)

following a buffered-HF etch surface preparation. The

geometry of the measurement is shown schematically in

the upper inset for a SrTiO

(100) surface terminated by

SrO as well as TiO

monolayers. The vendor of all three

substrates was Shinkosha (reproduced by permission of

the American Institute of Physics from Appl. Phys. Lett.,

1994, 65, 3197–9 and of the American Institute for

the Advancement of Science from Science, 1994, 266,

1540–2, respectively).

Figure 4

Cross-sectional transmission electron micrograph of a

YBa

7d

ﬁlm epitaxially grown on (100)SrTiO

PLD showing B10

threading dislocations cm

2

(reproduced by permission of Materials Research

Society from J. Mater. Res., 1990, 5, 2620–32).

298

High-temperature Superconductors: Thin Films and Multilayers

to the layered structure of all cuprate supercon-

ductors, it is unclear at which specific layer(s)

growth will be initiated, and whether this depends

on the type of substrate or deposition method. A

high-resolution TEM image of the interface between a

c-axis YBa

7d

ﬁlm and the (100)SrTiO

subst-

rate upon which it was epitaxially grown is shown in

Fig. 5. Analysis of the interface using TEM image

simulations allowed the starting layer sequence of

the YBa

7d

ﬁlm to be determined. For c-axis

YBa

7d

grown on TiO

-terminated (100)Sr

TiO

, the YBa

7d

starts with the BaO mono-

layer followed by the CuO

, Y, CuO

, BaO,

CuO, y monolayers of the YBa

7d

structure,

respectively. This result was found to be independent

of the type of codeposition method used to deposit the

YBa

7d

ﬁlm (Wen et al. 1993). However, the

initial monolayer of a c-axis YBa

7d

ﬁlm does

depend on the substrate—both the material and its

terminating monolayer.

Due to the narrow composition range within which

the YBa

7d

phase exists, YBa

7d

ﬁlms

often contain impurity phases. CuO, Y

, and

YCuO

are often seen in epitaxial ﬁlms produced

by in situ methods (Catana et al. 1993). Other impu-

rity phases including BaO, ‘‘YBa

’’ (which is

probably either YBa

8.5 þd

or YBa

10 þd

and Y

BaCuO

have also been reported. Some of

these inclusions can be quite small and epitaxially

oriented to the surrounding YBa

7d

matrix as

is the case for the Y

precipitates shown in Fig. 6.

(b) AFM and STM

The morphologies of c-axis oriented YBa

7d

ﬁlms grown by different vapor phase methods on a

variety of substrates exhibit remarkable similarity,

indicating that the same growth mechanisms are op-

erative (Hawley et al. 1991, Gerber et al. 1991, Ra-

istrick and Hawley 1994, Schlom et al. 1994). The

growth process may generally be described as ledge

growth, emphasizing the energetic preference of the

depositing species to attach to existing ledges (step

edges), which propagate laterally across the substrate

surface as they accommodate species. Depending on

the substrate, its misorientation, the YBa

7d

ﬁlm thickness, and growth conditions, three different

growth modes are seen in c-axis YBa

7d

ﬁlms:

spiral growth, layer-by-layer growth, and step-ﬂow

growth. In all three cases STM and AFM reveal a

surface morphology containing closely spaced steps.

These steps, which have a height equal to the c-axis

length of YBa

7d

(1.17 nm), or an integral

multiple of it, separate (001)YBa

7d

terraces.

These terraces are typically only a few tens of nano-

meters wide, indicating the length scale over which

such c-axis YBa

7d

ﬁlms are atomically ﬂat.

The steps expose (100) and (010) YBa

7d

faces,

which often account for 5–10% of the surface area of

c-axis oriented YBa

7d

ﬁlms.

Figure 5

High-resolution cross-sectional TEM of the

(001)YBa

7d

/(100)SrTiO

interface showing the

TiO

-termination layer of the (100)SrTiO

substrate and

the BaO-CuO

-Y- y starting layer sequence of the

YBa

7d

ﬁlm. The arrows indicate the position of

the interface. Regions a, b, and c are the observed image,

the averaged image, and the calculated image

(reproduced by permission of Elsevier Science from

Physica C, 1993, 205, 354–62).

Figure 6

TEM image of a Y

precipitate in sputtered

YBa

7d

ﬁlm. A planar-view image in which the

B10

precipitates per cm

give rise to the Moire

fringes (reproduced by permission of the American

Institute of Physics from Appl. Phys. Lett., 1992, 60,

1016–18).

299

High-temperature Superconductors: Thin Films and Multilayers