Chemical, magnetic and electronic properties of NaxCoO2 and related compounds

Uni e sidad de San iago de Compos ela
Depa amen o de Química Física
Chemical, magne ic and elec onic
p ope ies o NaxCoO2 and ela ed
compounds.
Memo ia p esen ada po D. Manuel Bañob e López
Pa a op a al g ado de Doc o en Química
Uni e sidad de San iago de Compos ela
Ab il, 2011
ISBN 978-84-9887-753-3 (Edición Digi al PDF)
D. Manuel A u o López Quin ela, ca ed á ico del depa amen o de
Química Física de la Uni e sidad de San iago de Compos ela; D. José
F ancisco Ri adulla Fe nández, p o eso i ula del depa amen o de
Química Física de la Uni e sidad de San iago de Compos ela y D. Ca los
Vázquez Vázquez, con a ado doc o del depa amen o de Química Física
de la Uni e sidad de San iago de Compos ela,
Ce i ican:
Que el abajo desc i o en la memo ia i ulada “Chemical, magne ic
and elec onic p ope ies o NaxCoO2 and ela ed compounds” ha sido
ealizado bajo nues a di ección po D. Manuel Bañob e López y eúne
odos los equisi os necesa ios pa a se p esen ado como Tesis Doc o al.
San iago de Compos ela, 8 de Ab il de 2011.
Fdo.:P o . D. M. A u o Fdo.:P o . D. J. F ancisco Fdo.:P o . D. Ca los
López Quin ela Ri adulla Fe nández Vázquez Vázquez
Fdo.: Manuel Bañob e López
El doc o ando

Ag adecimien os (Spanish eade s)
En p ime luga me gus a ía ag adece a mi di ec o , el P o .
M. A u o López Quin ela, po da me la opo unidad de abaja en su
g upo y con ia en mí du an e odo es e iempo. De su pa e siemp e
he ecibido buenas ideas, consejos, libe ad y oda la di ección que
he necesi ado.
Mi más since o ag adecimien o ambién pa a mi co-di ec o el
P o . F ancisco Ri adulla. Lo que a con inuación pod éis lee es el
esul ado de un e o que ambos nos p opusimos hace ya unos años,
y que él enía en su cabeza. De él des aco y ag adezco su
p o esionalidad, su me odología, su dedicación, y esas cha las de
ca é en las que consigue eno a u mo i ación e ilusión, an as
eces decaídas. Con él comencé a amilia iza me con el mundo del
es ado sólido, y sin duda que el u u o con i ma á que hab á sido el
mejo maes o posible. Mis disculpas si no he es ado a la al u a y no
he ap endido más. Pe o además de un buen je e es un mejo amigo,
siemp e accesible y dispues o a ayuda cuando se le necesi a, an o
en lo p o esional como en lo pe sonal; se me ocu en muchas cosas
que ag adece e, pe o bueno…mejo es que siga con es o. G acias
F an.
G acias ambién a mi co-di ec o el P o . Ca los Vázquez, con
el que empecé a abaja en un labo a o io sin e izando
nanopa ículas de óxidos de c omo, y más a de, lo que se puso po
delan e. Con él ap endí a ija me en los de alles y no da nada po
pe dido en el lab. G acias Ca los po es a siemp e disponible pa a
echa esa mano que an as eces hizo al a. Un g an amigo.
G acias ambién al P o . José Ri as, que siemp e que lo he
necesi ado me ha dado su iempo y nunca me ha esca imado medios
pa a a anza y segui adelan e. Y po pe mi i me el plu iempleo!, e i
e minando es a esc i u a al iempo que abajamos en la hipe e mia
magné ica de ma e iales híb idos y mul i uncionales.
Mi más since o ag adecimien o pa a el P o . J. B.
Goodenough, po acep a me en su g upo pa a una es ancia ealizada
en el Texas Ma e ials Ins i u e de la Uni e sidad de Texas en Aus in.
Una ejempla combinación de lucidez, esponsabilidad y espe o. Su
pue a siemp e es u o abie a pa a ecibi me y esponde mis
p egun as, segu amen e absu das. Aunque ha sido poco iempo, la
expe iencia de abaja en su g upo y habe lo conocido ha sido
inol idable, y un hono . G acias ambién a Román Caudillo, po su
ecibimien o y su colabo ación en el es udio del NaxCoO2. Y al D .
Huang, po enseña me a ab ica ba e ías!
Aquí de nue o…G acias a los X-men (y a la X-woman) de la
unidad de di acción de ayos-X de la USC, especialmen e al D .
B uno Dacuña, a quién ecu ía cuando algún ajus e se podía
mejo a o cuando que ía echa me unas isas.
Y llega el u no del FEDER…hay una la ga lis a de amigos ahí
den o, ellos son los esponsables de ese g an ambien e que
consigue que uno abaje agus o. Sois muchos, así que g acias a
odos. Pe o pe mi idme que des aque a los componen es del
labo a o io de es ado sólido, que han sido los e dade os
compañe os de ba alla: a los que es án, Bea (de ines imable ayuda
en su e apa en Física, ¿cuán os ans e s hab emos hecho?), Camilo
(el p incipal esponsable del diseño de es a po ada y de la sín esis
indus ial del C N en el lab); y a los que ya no es án, Ma a, San i,
Pabli o Bo a…con quiénes solucionaba los p oblemas que su gían
en el día a día. Y a Suelih, mi con abandis a de pape s en B asil!
G acias ambién a Al onso Fondado, que an as eces u o que
a egla el apa a o de pode e moeléc ico po mi culpa. Pe o, sob e
odo, g acias a mis compis de despacho: Yolanda (la Mamma, los
galones, cuan os consejos me hab á dado!), Ana (la mejo ges o a
del iempo que conozco, la que siemp e es á pa a una caña (ejem…),
la que poco a poco es á descub iendo el pe eccionismo,
jeje…ánimo!), Camilo o a ez (un e udi o de las ciencias y las a es,
espe uoso del o den y las p opo ciones y iel seguido de Diógenes,
jeje), C is ina Hoppe (la bohemia ma pla ense que nos isi a en
cuan o puede)…Ellos son los que han su ido más de ce ca aquellos
días en que uno se le an aba con mejo o peo pie, los que
escuchaban las a en u as y des en u as co ididanas, las isas, los
p oblemas, el silencio a eces, y los más dispues os a a ima el
homb o cuando hacía al a. Sois ya amigos de una época, g acias!.
G acias ambién a odos los co-au o es que han pa icipado
de una u o a o ma en las publicaciones en las que apa ece mi
nomb e, po su abajo.
G acias aho a a los amigos que hacen que el iempo de ocio
sea, p ecisamen e, eso, especialmen e a los de la “aldea Gala”, a
Jena o en pa icula po esa capacidad de saca GB lib es de un
disco du o eple o, cuán as eces me hab á sal ado la ida...Mención
especial pa a My iam, que ha seguido de ce ca es a esis y a la que
engo mucho que ag adece , en e o as cosas su con ianza y sus
palab as de ánimo.
A A nold, el ilóso o-psicólogo de la ida de enso de la
ag icul u a o gánica y aho a ambién de las ce ezas de iple
e men ación, jeje. Y a Ma , po esas cañas con acen o inglés!
Y a los colegas emig ados, que a pesa de los kilóme os de
dis ancia siemp e hacen lo que sea po euni se, Juan Ca los (un
llane o soli a io en el Saha a que con ie e la a ena en cemen o;
como e echo de menos, ío), Da id de Li es (un pe cebei o da Cos a
da Mo e econ e ido a “Texan d ille enginee ” en el Gol o de
México) y Juli o (un “bilingual eache ” que iene la “ ecnología pa a
hace lo”).
Y a Da id Abeal, un amigo de siemp e que lo ela i iza odo, y
eso ayuda.
G acias ambién a la inanciación, pa e c ucial en es as
labo es. A la Xun a de Galicia y al Minis e io de Educación y Ciencia
(en aquella época), po la es abilidad que me p opo ciona on en mis
inicios y en esos cua o años de FPU, espec i amen e.
Cla o, GRACIAS a C is iana, po su sosiego, po deci
siemp e lo que uno necesi a oí en los momen os di íciles y po
ayuda me a encon a un inal eliz pa a es a his o ia.
Y el úl imo luga lo ese o pa a quién más se lo me ece, mi
amilia. GRACIAS. Especialmen e a mis pad es, a mi mad ina
( ambién abuela) y a mi pad ino ( ambién abuelo, ambién Manolo),
de quiénes nunca se deja de ap ende . Vues a comp ensión y
ues o sac i icio ha sido undamen al pa a llega has a aquí, de o a
o ma no hab ía sido posible. G acias po compa i ues a ilusión y
po no cansa os nunca de p egun a “¿como a esa esis?” Aho a os
espondo: “Aquí es á”. Es ambién ues a.
Table o Con en s
P ologue (Spanish eade s)………………………………………………...1
P ologue (English eade s)……………………………………………....... 13
Chap e 1: Syn hesis, chemical and s uc u al cha ac e iza ion
o NaxCoO2……………………………………………………. 25
1.1 Polyc ys alline Samples…………………………………………............ 25
1.1.1. Pa en Compound: Na0.7CoO2………………………........... 25
1.1.2. NaxCoO2, 0.3x0.7........................................................... 31
1.1.2.1. Na+ dein e cala ion............................................. 31
1.1.2.2. Na+ in e cala ion................................................. 44
1.1.3. NaxCoO2, x>0.7…………………………….......................... 49
1.2 Single-c ys al Samples....................................................................... 52
Chap e 2: Magne ic and anspo p ope ies o NaxCoO2………. 55
2.1. NaxCoO2 (0.30x0.7) ……………………………………………… 57
2.2. NaxCoO2 (x>0.7)……………………………………………………...75
Chap e 3: P oximi y o a Quan um Phase T ansi ion……………… 83
Chap e 4: The ole o wa e in he de elopmen o
Supe conduc i i y…………………………………………… 107
Chap e 5: The special case o hal -doping: Na0.5CoO2……………. 125

Chap e 6: Topo ac ic Ca ion exchange in NaxCoO2
Li+, S 2+, Ca2+………………………………………………… 145
6.1 Mono alen ca ion exchange……………………………………………. 147
6.1.1 LixCoO2………………………………………………………… 147
6.2 Di alen ca ion exchange…………………………………………………161
6.2.1 S xCoO2………………………………………………………… 161
6.2.2 CaxCoO2……………………………………………………….. 171
Conclusions………………………………………………………………… 185
Appendix A: Syn hesis and Magne ic p ope ies o Co3O4……….. 187
A.1. Syn hesis o Co3O4 nanopa icles……………………………………… 188
A.2. Magne ic p ope ies o Co3O4 powde ………………………………….190
Pos -g adua e Publica ions......................................................... 194
Chemical, magne ic and elec onic
p ope ies o NaxCoO2 and ela ed
compounds.
1
P ologue (Spanish eade s)
En el momen o de esc ibi es a esis ace ca de las p opiedades
químicas y ísicas del NaxCoO2, mi ambición p incipal ue la de
p esen á sela al lec o de una o ma sencilla y amena. Con el obje i o de
o ece una lec u a comp ensible, lige a y dinámica, es a esis ue
con eccionada como un ensamblaje de his o ias indi iduales en las que, a
menudo, esul ados, in e p e aciones y e e encias se in e calan casi sin
pausa, más al es ilo de un lib o especializado en un sis ema en pa icula
que al de una esis.
Teniendo es o en cuen a, es a p esen ación se di ide en seis
capí ulos, conclusiones y un apéndice. La común in oducción eó ica
gene al u ilizada no malmen e en las dise aciones doc o ales, ha sido
sus i uida aquí po una b e e in oducción especí ica al p incipio de cada
capí ulo. Po lo an o, el lec o dispond á de una isión gene al del es ado
del a e de la ma e ia que se desa olla en cada capí ulo en pa icula y
ap ecia á mucho mejo la con ibución de es e abajo a la comp ensión de
las p opiedades químicas y ísicas del sis ema.
Sin emba go, una in oducción gene al a la enomenología básica
del sis ema, así como la desc ipción de la mo i ación que nos ha lle ado a
la ealización de es a esis, sigue siendo necesa ia, y se á, po an o,
b e emen e p opo cionada en las páginas siguien es.
P ologue
2
El NaxCoO2 no es un ma e ial nue o; ue p ime amen e
sin e izado en la década de 19701 y ha sido es udiado ampliamen e desde
en onces2,3,4. Sin emba go, el descub imien o de nue as p opiedades y su
posible elación con enómenos simila es en o os ma e iales, ha impulsado
un eno ado in e és en es e sis ema. Si se hace una búsqueda bibliog á ica
en un explo ado cien í ico (Sci inde , po ejemplo) po la palab a cla e
"NaxCoO2", y se ep esen an los esul ados siguiendo un o den c onológico,
podemos obse a el g an núme o de a ículos publicados en la úl ima
década ace ca de es e sis ema (Figu a P.1).
70's 80's 90's 00's
0
50
100
150
200
250 x0.25
NaxCoO2
Publica ed a icles numbe
Decade
Figu e P.1: E olución del núme o de a ículos cien í icos publicados cada
año du an e la úl ima década en el sis ema NaxCoO2, de acue do con el buscado
Sci inde . La lecha en cian indica c onológicamen e el pun o inicial de es a esis.
1 C. Fouassie , G. Ma ejka, J.-M. Reau and P. Hagenmulle . J. Solid S a e Chem. 6, 532
(1973).
2 R. Be helo , D. Ca lie and C. Delmas. Na u e Ma e ials 10, 74 (2011).
3 S. Hébe and A. Maignan. The moelec ic Oxides, in Func ional Oxides (eds D. W. B uce,
D. O'Ha e and R. I. Wal on), John Wiley & Sons, L d, Chiches e , UK. ISBN:
9780470997505 (2010).
4 Y. Iha a, K. Ishida, H. Saku ai and E. Takayama-Mu omachi. Phase diag am o
Nax(H3O)zCoO2yH2O, in New esea ch on Supe conduc i i y (ed. B. P. Ma ins), No a
Science Publishe s, Inc, New Yo k, USA. ISBN: 978-1-59454-197-1 (2007).

& Mo i a ion
3
El NaxCoO2 es excepcional en es e sen ido, ya que ha conseguido
el in e és de la comunidad cien í ica du an e las úl imas es décadas po
di e en es azones. Así, en los años 80 se in es igó debido a sus
p opiedades elec oquímicas (al a mo ilidad iónica, al a conduc i idad
eléc ica) 5,6,7,8,9 y su po encial aplicación como cá odo en ba e ías alcalinas
e e sibles, al igual que su análogo LixCoO2.10 En los 90, sus p opiedades
e moeléc icas ue on las que despe a on el in e és de es e ma e ial pa a
la cap ación de ene gía a al a empe a u a y la e ige ación11. El
endimien o e moeléc ico de un sis ema pa icula se cuan i ica a pa i del
alo p opo cionado po la igu a de mé i o e moeléc ica (ecuación [P.1]),
k
S
Z

.
 eq. [P.1]
donde S,

and

son el pode e moeléc ico, la esis i idad eléc ica y la
conduc i idad é mica, espec i amen e. El pode e moeléc ico ep esen a
el ol aje c eado po un g adien e é mico en e dos pun os de la mues a.
La abla P.1 mues a los alo es del pode e moeléc ico
exp esados a pa i de la igu a de mé i o de la ecuación [P.1] a di e en es
empe a u as pa a monoc is ales y polic is ales de NaxCoO2, en
compa ación con un ma e ial e moeléc ico con encional ipo-p.
Pe o la e dade a e olución cien í ica o iginada po es e ma e ial
llega ía en 2005, después de que Takada e a12l epo a an
supe conduc i idad (SC) a empe a u as po debajo de 5 K en una ase de
bajo con enido de Na+ después de que moléculas de agua se in e calasen
en su es uc u a, Na0.3CoO2•1.3H2O (Figu a P.2). Después de es a
5 C. Delmas, J. J. B aconnie , C. Fouassie and P. Hagenmulle . Solid S a e Ionics 3-4, 165
(1981).
6 J. Molenda, C. Delmas and P. Hagenmulle . Solid S a e Ionics 9-10, 431 (1983).
7 S. Kikkawa, S. Miyazaki and M. Koizumi. J. o Powe Sou ces, 14, 231 (1985).
8 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Solid S a e Chem. 62, 35 (1986).
9 J. Molenda, C. Delmas, P. Do do . Solid S a e Ionics 12, 473 (1989).
10 K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough. Ma e . Res. Bull. 15, 6,
783 (1980).
11 I. Te asaki, Y.Sasago, K.Uchinoku a. Phys. Re . B 56, 12685 (1997).
12 K. Takada, H. Saku ai, E. Takayama-Mu omachi, F. Izumi, R. A. Dilanian and T. Sasaki.
Na u e 422, 53 (2003).
P ologue
4
publicación, las simili udes en e el NaxCoO2 y los cup a os
supe conduc o es su gie on de o ma inminen e. Pa icula men e, la
p oximidad a una ase aislan e de Mo en x=0.5 inc emen ó las
especulaciones de que la supe conduc i idad en los óxidos de cobal o y de
cob e pod ía es a gobe nada po mecanismos simila es.
Table P.1: Valo es de la igu a de mé i o adimensional, ZT, pa a
monoc is ales y polic is ales de NaxCoO2 en compa ación con un ma e ial
e moeléc ico con encional.
Figu e P.2: Suscep ibilidad magné ica en unción de la empe a u a en
NaxCoO2

H
2O epo ada po Takada e al (Re . 12) mos ando el es ado SC po
debajo de 5 K.
0.570.160.310.081.20.03ZT --
800K300K800K300K800K300K
Si
0.95
Ge
0.05
ypical p- ype
Na
x
CoO
2-δ
polyc ys al
Na
x
CoO
2-δ
single c ys al
0.570.160.310.081.20.03ZT --
800K300K800K300K800K300K
Si
0.95
Ge
0.05
ypical p- ype
Na
x
CoO
2-δ
polyc ys al
Na
x
CoO
2-δ
single c ys al
& Mo i a ion
5
Sin emba go, muchos pun os undamen ales en la química y ísica
de es e sis ema pe manecen sin se cla i icados pa a el en endimien o de la
supe conduc i idad en NaxCoO2. El más impo an e es el cuál es el papel
que eje ce el agua en la apa ición de la supe conduc i idad en el sis ema.
Pe o ambién la elación exis en e en e el con enido de Na+ y la
concen ación de po ado es en los planos de CoO2, o el e ec o de la
dimensionalidad es uc u al y elec ónica son aspec os cla e que no han
sido explicados oda ía.
Con el obje i o de comp ende un poco mejo las p opiedades
químicas y ísicas de es e sis ema, es esencial desc ibi b e emen e los
aspec os es uc u ales y elec ónicos del NaxCoO2.
La es uc u a c is alina de es e óxido consis e en capas
bidimensionales de oc aed os CoO6 que compa a en a is as y que se
encuen an sepa adas en e sí po capas de iones Na+ (see Figu e P.3). En
es a es ucu u a, los á omos de Co o man una ed hexagonal con enlaces
iangula es M-M.
CoO6
Na+
CoO6
Figu e P.3: Izquie da: Rep esen ación 3D de la es uc u a bidimensional de
NaxCoO2. Las bolas g ises ( ojas) [na anjas] ep esen an los á omos de cobal o
(oxígeno) [sodium]. De echa: (a iba) Disposición de los oc aed os CoO6 a lo la go
de las capas de CoO2 pe pendicula es al eje c (abajo) De alle de la coo dinación
al ededo de un á omo de Co.
P ologue
6
Los iones Na+ ocupan dos posiciones c is alog á icas di e en es en
la es uc u a del NaxCoO2: oc aéd ica (O) o igonal p ismá ica (P), ambas
si uadas en el mismo plano y a la mi ad de la dis ancia que sepa a las capas
de CoO2. La celda unidad de NaxCoO2 es á de e minada po la o ien ación
ela i a de los planos de CoO2 y la geome ía de los si ios de Na+ (Figu e
P.4). 13
Figu e P.4: Rep esen ación de las di e en es celdas unidad pa a NaxCoO2:
O3, P2 and P3. La le a indica la geome ía del si io de Na+, oc aéd ica (O) o igonal
p ismá ica (P). El núme o 2 o 3 indica el núme o de capas de CoO2 p esen es en la
celda unidad (Re . 13).
De es a o ma, ases y es uc u as di e en es pueden apa ece en
unción del con enido de Na+ (Table P.2) 1432:
13 B. L. Cushing and J. B. Wiley. J. Solid S a e Chem. 141, 385 (1998).
14 L. Viciu, J. W. G. Bos, H. W. Zandbe gen, Q. Huang, M. L. Foo, S. Ishiwa a, A. P.
Rami ez, M. Lee, N. P. Ong and R. J. Ca a. Phys. Re . B 73, 174104 (2006).
13
P ologue (English eade s)
A he ime o w i ing his hesis, my main conce n was o p esen
he chemical and physical p ope ies o NaxCoO2 in an amenable way o he
eade . In o de o o e an unde s able, ligh e and dynamic eading o his
hesis, he whole disse a ion can be conside ed as an assembly o
indi idual “s o ies”, whe e esul s, in e p e a ions and e e ences a e
in e cala ed con inuously in an almos “non-s op” way, mo e in he s yle o a
book o a scien i ic pape abou a pa icula sys em, han in a hesis.
Taking his in o accoun , his p esen a ion is di ided in o se en
chap e s and wo appendixes. The common gene al heo e ical in oduc ion
no mally used in he PhD disse a ions, has been eplaced by a b ie speci ic
in oduc ion a he beginning o each chap e . The e o e, he eade will ha e
a speci ic o e iew o he s a e o he a in he opic de eloped in each
pa icula chap e and will app ecia e much be e he con ibu ion o his
wo k o he unde s anding o he chemical and physical p ope ies o he
sys em.
Howe e , some gene al in oduc ion o he basic phenomenology o
he sys em, as well as o he mo i a ion o he hesis is s ill needed, and
p o ided in he ollowing pages.

Chap e 1
14
NaxCoO2 is no a no el ma e ial; i was i s syn he ized in he
1970’s20 and i has been ex ensi ely s udied since hen21,22,23. Howe e , he
disco e y o no el p ope ies and hei possible ela ionship wi h simila
phenomena ound in o he ma e ials, boos ed a enewed in e es in his
sys em. I we make a bibliog aphic sea ch in a scien i ic b owse (i. e.
Sci inde ) by he key_wo d “NaxCoO2”, and plo he esul s ollowing a
c onological o de , we can obse e he la ge numbe o a icles published in
he las decade (Figu e P.1).
70's 80's 90's 00's
0
50
100
150
200
250 x0.25
NaxCoO2
Publica ed a icles numbe
Decade
Figu e P.1: E olu ion o he numbe o scien i ic a icles published each
yea in he sys em NaxCoO2, acco ding o he Sci inde . The cian a ow ma ks he
s a ing poin o his hesis.
20 C. Fouassie , G. Ma ejka, J.-M. Reau and P. Hagenmulle . J. Solid S a e Chem. 6, 532
(1973).
21 R. Be helo , D. Ca lie and C. Delmas. Na u e Ma e ials 10, 74 (2011).
22 S. Hébe and A. Maignan. The moelec ic Oxides, in Func ional Oxides (eds D. W.
B uce, D. O'Ha e and R. I. Wal on), John Wiley & Sons, L d, Chiches e , UK. ISBN:
9780470997505 (2010).
23 Y. Iha a, K. Ishida, H. Saku ai and E. Takayama-Mu omachi. Phase diag am o
Nax(H3O)zCoO2yH2O, in New esea ch on Supe conduc i i y (ed. B. P. Ma ins), No a
Science Publishe s, Inc, New Yo k, USA. ISBN: 978-1-59454-197-1 (2007).
& Mo i a ion
15
NaxCoO2 is excepcional in his sense, as i aised he in e es o he
communi y by di e en easons du ing he las h ee decades. In he 80´s, i
was in es iga ed due o i s elec ochemical p ope ies (high ionic mobili y,
high elec ical conduc ion)24,25,26,27,28 and es ed as a ca hod in e e sible
alkaline cells, as i s analogous LixCoO229. In he 90’s, i s he moelec ic
p ope ies aised he in e es o his ma e ial o ene gy ha es ing a high
empe a u e and e ige a ion30. The he moelec ic pe o mance o a
pa icula sys em is quan i ied by he he moelec ic igu e o me i (equa ion
[P.1]),
k
S
Z

.
 eq. [P.1]
whe e S,

and

a e he he moelec ic powe , elec ical esis i i y and
he mal conduc i i y, espec i ely. The he moelec ic powe ep esen s he
ol age c ea ed by a he mal g adien be ween wo poin s o he sample.
Table P.1 shows he alues o he he moelec ic pe o mance
exp eseed by he igu e o me i (equa ion [P.1]) a di e en empe a u es o
NaxCoO2 single- and polyc ys als in compa ison wi h a con en ional p- ype
he moelec ic ma e ial.
Bu he b eak h ough come in 2005, a e Takada e al31 epo ed
supe conduc i i y (SC) below 5 K a e wa e in e cala ion in a phase wi h
low Na+ con en , Na0.3CoO21.3H2O (Figu e P.2). Inmedia ely a e his
epo he simila i ies o NaxCoO2 wi h he supe conduc ing cup a es we e
aised. Pa icula y, he p oximi y o a Mo insula ing phase a x=0.5 uelled
24 C. Delmas, J. J. B aconnie , C. Fouassie and P. Hagenmulle . Solid S a e Ionics 3-4, 165
(1981).
25 J. Molenda, C. Delmas and P. Hagenmulle . Solid S a e Ionics 9-10, 431 (1983).
26 S. Kikkawa, S. Miyazaki and M. Koizumi. J. o Powe Sou ces, 14, 231 (1985).
27 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Solid S a e Chem. 62, 35 (1986).
28 J. Molenda, C. Delmas, P. Do do . Solid S a e Ionics 12, 473 (1989).
29 K. Mizushima, P.C. Jones, P.J. Wiseman and J.B. Goodenough. Ma e . Res. Bull. 15, 6,
783 (1980).
30 I. Te asaki, Y.Sasago, K.Uchinoku a. Phys. Re . B 56, 12685 (1997).
31 K. Takada, H. Saku ai, E. Takayama-Mu omachi, F. Izumi, R. A. Dilanian and T. Sasaki.
Na u e 422, 53 (2003).
Chap e 1
16
specula ion ha supe conduc i i y in he cobal and coppe oxides could be
go e ned by simila mechanisms.
Table P.1: Values o he dimensionless igu e o me i , ZT, o NaxCoO2
single- and polyc ys als in compa ison wi h a con en ional he moelec ic ma e ial.
Figu e P.2: Tempe a u e dependence o he magne ic suscep ibili y in
NaxCoO2

H2O by Takada e al (Re . 12) showing he SC s a e below 5K.
Howe e , many undamen al issues emain o be cla i ied o he
unde s anding o SC in NaxCoO2. The mo e impo an is he ole ha wa e
plays in he occu ence o supe conduc i i y. Also he di ec ela ionship
be ween he Na+ con en and he concen a ion o cha ge ca ie s in he
0.570.160.310.081.20.03ZT --
800K300K800K300K800K300K
Si
0.95
Ge
0.05
ypical p- ype
Na
x
CoO
2-δ
polyc ys al
Na
x
CoO
2-δ
single c ys al
0.570.160.310.081.20.03ZT --
800K300K800K300K800K300K
Si
0.95
Ge
0.05
ypical p- ype
Na
x
CoO
2-δ
polyc ys al
Na
x
CoO
2-δ
single c ys al
& Mo i a ion
17
CoO2 planes, o he e ec o s uc u al/elec onic dimensionali y a e key
aspec s ha ha e no been explained ye .
In o de o unde s and a li le be e he chemical and physical
p ope ies o his sys em, i is essen ial o desc ibe sho ly he basic
s uc u al and elec onic aspec s o NaxCoO2.
The c ys al s uc u e o his oxide consis s o wo dimensional laye s
o edge-sha ing CoO6 oc ahed a sepa a ed by Na+ laye s (see Figu e P.3).
Co-a oms o m an hexagonal la ice wi h iangula M-M bonding.
CoO6
Na+
CoO6
Figu e P.3: Le : 3D- ep esen a ion o he laye ed s uc u e o NaxCoO2.
The g ey ( ed) [o ange] balls ep esen he cobal (oxygen) [sodium] a oms. Righ :
(uppe ) A angemen o he CoO6 oc ahed a in he CoO2 laye s pe pendicula o he
c-axis. (lowe ) De ail o he coo dina ion a ound a Co a om.
Chap e 1
18
In NaxCoO2, Na+ ions can occupy wo di e en c ys allog aphic
posi ions in he s uc u e, oc ahed ic (O) o igonal p isma ic (P), bo h o
hem in he same plane and a hal way be ween he CoO2 laye s. The uni
cell o NaxCoO2 is de e mined by he ela i e o ien a ion o he CoO2 planes
and he geome y o he Na+ si es (Figu e P.4).32
Figu e P.4: Rep esen a ion o di e en uni cells o NaxCoO2: O3, P2 and
P3. The le e indica es he geome y o he Na si e, oc ahed al (O) o igonal
p isma ic (P). The numbe 2 o 3 indica es he numbe o CoO2 laye s in he uni cell
(Re . 13).
In his way, di e en phases and s uc u es can be dis inguished
depending on he Na+ con en (Table P.2)3332:
32 B. L. Cushing and J. B. Wiley. J. Solid S a e Chem. 141, 385 (1998).
33 L. Viciu, J. W. G. Bos, H. W. Zandbe gen, Q. Huang, M. L. Foo, S. Ishiwa a, A. P.
Rami ez, M. Lee, N. P. Ong and R. J. Ca a. Phys. Re . B 73, 174104 (2006).

& Mo i a ion
19
Table P.2: Symme y o he uni cell o NaxCoO2 compounds (0.3<x<1)
depending on he Na+ coo dina ion and he numbe o laye s pe uni cell (Re . 14).
In he case o he supe conduc ing phase, wa e in e cala es
be ween he Na+ and CoO2 laye s o Na0.3CoO21.3H2O, inc easing
d ama ically he c-axis la ice pa ame e om ~11.1 Å o ~19.5 Å, Figu e P.5.
I has been sugges ed ha he in luence o wa e in educing dimensionali y
o he s uc u e is essen ial o supe conduc i i y (Re . 10). This is suppo ed
by he obse a ion o he absence o SC in Na0.3CoO20.6H2O wi h he same
Chap e 1
20
oxida ion s a e bu subs an ially less sepa a ion be ween he CoO2 laye s
han he SC samples.34
Figu e P.5: Schema ic ep esen a ion o he inc ease o he uni cell o
NaxCoO2 in he c-di ec ion as wa e is in e cala ed in o he s uc u e ( om Re . 9).
Once wa e in e cala es in o he la ice, new s uc u al de ails a ise
ha should be analyzed. Sol ing he c ys al s uc u e o he supe conduc ing
phase has been one o he mos impo an asks o he las yea s. I
cons i u es a c ucial poin o he unde s anding o he pai ing mechanism
ha o igina es supe conduc i i y in his sys em. Howe e , di e en s uc u al
models o wa e -in e cala ed NaxCoO2yH2O ha e been p oposed and no
ag eemen has been eached be ween hem o da e. Wha is clea is ha
many composi ions wi h di e en amoun s o in e cala ed H2O coexis in
hyd a ed samples, complica ing he analysis e en u he .
Now, le ´s look close a he elec onic s uc u e o he Co a oms in
NaxCoO2. Fo x=0, simply CoO2, each Co a om is in he Co4+ alence s a e
and 5 elec ons occupy he 3d o bi als (assuming a pu ely ionic pic u e). In a
low-spin con igu a ion, only one elec on is unpai ed and Co4+ has a spin ½.
As Na+ ions a e added o he s uc u e, each con ibu es one elec on,
he eby changing Co4+ o a diamagne ic Co3+ s a e. A x=1, NaCoO2, all he
34 M. L. Foo, R. E. Schaak, V. L. Mille , T. Klimczuk, N. S. Rogado, Y. Wang, G. C. Lau, C.
C aley, H. W. Zandbe gen, N. P. Ong and R. J. Ca a. Solid S a e Comm. 127, 33 (2003).
& Mo i a ion
21
Co a oms would be in he Co3+ alence s a e, ende ing a diamagne ic
sys em. The ene gy le els o hese wo limi ing spin con igu a ions a e
ep esen ed in he diag am o Figu e P.6.
x=0 Co4+ (d5) x=1 Co3+ (d6)
Figu e P.6: Schema ic ep esen a ion o he ene gy le els and spin
con igu a ions o NaxCoO2 x=1 and x=0.
The possibili y o mixed alence, along wi h he esul ing spin
con igu a ions and he s ong Co-3d:O-2p hyb idiza ion, a e esponsible o
he ichness o he phase diag am o NaxCoO2.
A he beggining o his hesis, he accep ed phase diag am o his
sys em was ha one epo ed by Shaak e al35, which shows a wide a ie y
o magne ic and elec ic phases wi h doping and empe a u e (Figu e P.7). A
numbe o di e en magne ic phases like Pauli pa amagne ism (PM), Cu ie-
Weiss empe a u e dependence (CW), an i e omagne ic o de (AFM), spin
densi y wa es (SDW) a e ound as a unc ion o Na+. All o hese ha e a
me al-like beha iou , excep a x=0.5, whe e he sys em goes h ough a
“me al-insula o ” ansi ion due o a ce ain ype o cha ge o de 36. A
1/4x1/3 supe conduc ing s a e appea s below 5 K as wa e is in e cala ed
in o he s uc u e.
35 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Ca a. Na u e, 424, 527 (2003).
36 M. L. Foo, Y. Wang, S. Wa auchi, H. W. Zandbe gen, T. He, R. J. Ca a and N. P. Ong.
Phys. Re . Le . 92, 247001 (2004).
Low-S
p
in 6-x Low-S
p
in 6-x
Chap e 1
22
Figu e P.7: Magne ic/elec ic phase diag am o NaxCoO2 p opposed by
Schaak e al in Re . 16.
In his na ow ange o Na+ composi ions in which supe conduc i i y
is achie ed, he dependence o supe conduc ing empe a u e ansi ion (Tc)
as a unc ion o Na+ doping emains s ill unclea . Ini ially, a s ongly
co ela ion be ween Tc and he Na+ con en o he samples was es ablished,
and an op imal chemical doping le el o supe conduc i i y wi h Tc ≈ 4.5 K a
x0.3 was epo ed35. This “dome-like” dependence o Tc wi h doping shows
he same kind o end ha cup a es. Fo his eason, i has been hough
ha his ma e ial would be a good candida e o shed a ligh on he
supe conduc i i y mechanism in hese compounds. Howe e , a g ea
con o e sy was gene a ed when subsequen epo s obse ed an almos
independen alue o Tc wi h x.37,38
37 D. P. Chen, H. C. Chen, A. Maljuk, A. Kulako , H. Zhang, P. Lemmens, and C. T. Lin.
Phys. Re . B 70, 024506 (2004).
T (K)
0.28 0.37 0.50 0.750 0.70
10
30
50
40
20 SC
(H2O in e caled)
PM
me al
CW
me al
SDW
me al
Insula o CO
x,Na
Syn hesis, cha ac e iza ion…
29
calcula ed om Rie eld analysis o his phase, a=2.8355(1) Å and
c=10.8987(4) Å a e close o he alues epo ed by Fouassie e al,47
a=2.833 Å and c=10.88 Å.
10 20 30 40 50 60 70 80
-5000
0
5000
10000
15000
20000
Na0.67CoO2 293 K
Coun s
2
Figu e 1.3: X- ay di ac ion pa e n (+) and Rie eld e inmen ( ed line) o
Na0.67CoO2 a oom empe a u e. Ve ical blue lines ma k he expec ed posi ion o
he e lexions o he space g oup P63/mmc. The g een line is he di e ence be ween
he expe imen al and calcula ed in ensi ies. Rwp=9.92%.
We also ied o syn hesize o he samples wi h a di e en Na+
con en , in he ange 0.5<x<1, om he di ec solid s a e eac ion o he
co esponding s ochiome ic mix u e o eac an s. Howe e , in all he cases,
he p oduc ob ained inally p esen ed a simila Na+ con en o x0.7.
The e o e, i is impo an o ema k ha he Na+ con en o he inal cobal
oxides ob ained di ec ly om his con en ional solid-s a e eac ion does no
depend on he ini ial Na/Co a io. The mos s able phase o NaxCoO2
sys em ob ained di ec ly om he syn hesis co esponds o x0.7. So, his
obse a ion should be conside ed in he case o he olde pape s whe e
NaxCoO2 samples wi h x≠0.7 we e epo ed om di ec , solid s a e
eac ions48,49.
47 C. Fouassie , G. Ma ejka, J. M. Reau and Hagenmulle . J. Solid S a e Chem. 6, 532 (1973).
48 V. M. Jansen and R. Hoppe. Z. ano g. Allg. Chem. 408, 104 (1974).

Chap e 1
30
Scanning elec on mic oscopy (SEM) images om polyc ys alline
samples we e aken o some ep esen a i e Na+ composi ions in he
NaxCoO2 sys em o s udy he mo phology o his compound. Mic og aphs
we e aken in a LEO-435VP scanning elec onic mic oscope wo king a
20 kV wi h a maximum esolu ion o 6 nm (unde P~10 Pa).
Figu e 1.4 shows SEM and op ical pho og aphs o polyc ys alline
samples o NaxCoO2 wi h x=0.67. Pic u es we e aken o e he su ace o
cold-p essed pelle s o ~5 mm, which we e p essed mechanically a
12-13 Ton/cm2. In he case o he non-hyd a ed sample (a), as i would be
deduced by Ene gy Dispe si e X- ay (EDAX) analyses la e , we can isually
e i y by SEM ha he su ace o he pelle is ac ually homogeneous in
composi ion. I can also be obse ed he p esence o se e al po ous along
he whole su ace. This ac is a gene al cha ac e is ic o he NaxCoO2
sys em in a wide ange o x. This po osi y complica es in insic esis i i y and
he mal conduc i i y measu emen s in polyc ys alline samples o hese
compunds. In pic u e (b), an op ical pho og aph o exac ly he same pelle
a e being exposed o ambien condi ions o one week is shown. These
compounds a e highly hyg oscopic. Thei ageing unde ambien condi ions
leads o he o ma ion o small whi e c ys als app eciable o e he whole
su ace o he pelle . They esul ed o be NaOH c ys als as de e mined by
EDAX analyses and X- ay di ac ion. They a e o med because o he
eac ion o Na+ ions a he su ace and he wa e p esen in he a mosphe e
a no mal condi ions o p essu e and empe a u e.
I is impo an o ealize ha his spon aneous eac ion o o ma ion
o NaOH will lea e behind a su ace o he sample wi h a Na+ con en lowe
han inside he pelle , so he Co4+ concen a ion will be highe in he su ace
han in he inne egions. I is indica i e o an inhomogeneous composi ion,
esul ing in a di e en dis ibu ion o cha ge ca ie s h ough he sample.
This is some hing no no mally conside ed in he li e a u e, al hough i could
de e mine he beha iou o he sys em o a la ge ex en , e en in single
c ys als.
49 T. Valla, P. D. Johnson, Z. Yuso , B. Wells, Q. Li, S. M. Lou ei o, R. J. Ca a, M. Mikami,
Y. Mo i, M. Yoshimu a and T. Sasaki. Na u e 417, 627 (2002).
Syn hesis, cha ac e iza ion…
31
(a) (b)
Figu e 1.4: (a) SEM and (b) op ical pho og aphs om he su ace o a (a)
esh sample o Na0.67CoO2 and (b) he same sample a e being exposed o ambien
o one week. The e is a Cu wi e (20

m) a ached wi h sil e epoxy esin o he
su ace o he sample in (b).
1.1.2. NaxCoO2 se ies, 0.3<x<0.7
In o de o ob ain samples wi h di e en alues o Na+,
in e cala ion/dein e cala ion p ocesses we e done by using chemical
me hods o oxida ion/ educ ion o he Co4+/Co3+ edox pai .
1.1.2.1. Na+ dein e cala ion
The e a e di e en me hods in he li e a u e ha can achie e an
e icien Na+ dein e cala ion om Na0.7CoO2. They can be g ouped in wo
ypes: chemical and elec ochemical me hods. In he i s g oup
a e included hose p ocedu es in ol ing a chemical oxida ion o he
ansi ion me al edox pai . Among hem, B 2/CH3CN4, I2/CH3CN3,50,
50 X. Z. Chen, Z. A. Xu, G. H. Cao, J. Q. Shen, L. M. Qiu and Z. H. Gan. a Xi :cond-
ma /0412299 (unpublished).
Na0.67CoO2
Chap e 1
32
KMnO4/H2O51, Na2S2O8/H2O52 o NaClO3/H2O53 oxidizing solu ions a e
employed. On he o he hand, using KMnO4 as oxidizing agen can esul in
subs i u ions a he Na and Co si es, being eplaced by K and Mn,
espec i ely, e en a oom empe a u e. Howe e , he oxidizing
dein e cala ion wi h B 2 in non-aqueous medium4 is he me hod mo e
ex ensi ely used o educe he sodium con en be ween he CoO6 shee s in
laye cobal oxides. I s simplici y and speed make i a e y use ul me hod o
Na+ dein e cala ion. Fu he mo e, i is possible o each low Na+ con en s
x~0.3. Using I2 ins ead o B 2 allows a mo e accu a e con ol o e he
expe imen al Na/Co a io due o he so e oxida ion s engh . The use o a
non-aqueous medium is also s ongly ecommended o a oid he wa e
in e cala ion be ween he CoO2 laye s54.
The dependence o he edox po en ial o he Co4+/Co3+ pai in
NaxCoO2 upon x epo ed in he li e a u e sugges s ha he minimum x alue
which can be ob ained using B 2 as he oxidizing agen is x=0.4-0.5 ( he
po en ial o he Co3+/Co4+ edox pai inc eases as Na+ con en dec eases).
Howe e , i is usual o ind x alues lowe han x=0.40 in he bibliog aphy,
and also ou esul s show a minimum Na+ con en o x=0.31.
Chou e al55 used an elec ochemical echnique o dein e cala ing
Na+ om Na0.7CoO2 as an al e na i e o chemical dein e cala ion. They
highligh ed he p ecise con ol o e he inal Na+ con en and he educ ion o
he en i onmen al haza ds de i a ed o he use o high concen a ions o B 2
as he main ad an ages o hei p ocedu e.
In his hesis, samples o NaxCoO2 wi h sodium con en s be ween
0.25<x<0.67 we e ob ained by Na+ dein e cala ion om polyc ys alline
Na0.67CoO2 by s i ing he powde in a B 2/CH3CN oxidizing solu ion o 5
days a oom empe a u e56. B omine oxidizes he Co3+ o Co4+, a o ing he
mo ion o he Na+ ions ou om he in e laye space o keep he cha ge
elec oneu ali y in he compound.
51 (a) C.-J. Liu, C.-Y Liao, L.-C. Huang, C.-H. Su, S. Neeleshwa and Y.-Y. Chen. Chin. J.
Phys. 43, 547 (2005) (b) C.-J. Liu, W.-C. Hung, J.-S. Wang and C.-J. C. Liu. J. Ame . Chem.
Soc. 127, 830 (2005). (c) C.-J. Liu, C.-Y Liao, L.-C. Huang, C.-H. Su, S. Neeleshwa , Y.-Y.
Chen and C.-J.C. Liu. Physica C 416, 43 (2003).
52 S. Pa k, Y. Lee, A. Moodenbaugh and T. Vog . Phys. Re . B 68, 180505(R) (2003).
53 M. L. Foo, Y. Wang, S. Wa auchi, H. W. Zandbe gen, T. He, R. J. Ca a and N. P. Ong.
Phys. Re . Le . 92, 247001 (2004).
54 K.Takada, K. Fakuda, M. Osada, I. Nakai, F. Izumi, A. R. Dilanian, K. Ka o, M. Taka a, H.
Saku ai, E. Takayama-Mu omachi, E. J. Sasaki. J. Ma e . Chem. 14, 1448 (2004).
55 F. C. Chou, E. T. Abel, J. H. Cho and Y. S. Lee. J. Phys. Chem. Solid 66, 155 (2005).
56 K. Takada, H. Saku ai, E. Takayama-Mu omachi, F. Izumi, R. A. Dilanian and T. Sasaki.
Na u e 422, 53 (2003).
Syn hesis, cha ac e iza ion…
33
By adjus ing he B 2 concen a ion o he solu ion, a ious phases
wi h di e en x can be ob ained.53,57 B omine concen a ions ep esen ing
subs oichiome ic (0.5), s ochiome ic (1) and mola excess (5, 10, 50,
100) ela i e o he amoun ha would be needed o emo e all o he Na+
om Na0.67CoO2 we e employed, acco ding o he ollowing eac ion:
  








B yNaysCoONalB
y
sCoONa yxx 222 2
A e his ime, he samples we e il e ed, washed wi h gene ous
amoun s o CH3CN and ace one, d ied in an o en a low empe a u e
(60-70 ºC) and s o ed in a desica o unde acuum. In his way, samples
wi h a wide ange o sodium composi ions we e ob ained. All he samples,
independen ly o hei sodium con en , a e highly hyg oscopic. Fo his
eason, hei manipula ion was ca ied ou minizing as much as possible any
exposu e o ambien mois u e.
The Na and Co con en s we e de e mined in he NaxCoO2 phases by
induc i ely coupled plasma op ical emission spec oscopy (ICP-OES). To
dissol e he samples, an exac ly weigh ed amoun o he d ied powde was
added o a wa e dilu ed HCl solu ion (1:1) unde s i ing and hea ed in an
au ocla e a low empe a u e o 12 hou s. Na and Co olume ic s anda s
p o ided by Ald ich we e used in he de e mina ion o hese ions in he
samples. The Na/Co a ios ob ained a e shown in Table 1.2 o each
concen a ion o B 2.
57 R. E. Shaak, T. Klimczuk, M. L. Foo and R. J. Ca a. Na u e 2003, 424, 527.
Chap e 1
34
Table 1.2: Resul s o he ICP-OES o NaxCoO2
B 2
excess
Na/Co
Ra io
P ecu so 0.673(7)
1 0.450(4)
5 0.429(6)
10 0.402(5)
20 0.381(6)
30 0.369(5)
40 0.362(4)
50 0.322(4)
100 0.310(3)
The analysis con i ms ha he amoun o Na+ dec eases
sys ema ically as he excess o B 2 inc eases. The Na+ con en d ops e y
as o x~0.45, e en o he lowes amoun o B 2. Then, inc easing he
amoun o he oxidan educes x down o ~0.30.
The s uc u al da a o NaxCoO2 samples ha e been de e mined om
a lebail e inmen o he X- ay powde di ac ion pa e ns (XRD) using he
p og am Rie ica58. The Na+ dein e cala ed sample using a s ochiome ic
amoun o B 2 (1) was single phase, and can be indexed wi hin he space
g oup P63/mmc, like he o iginal Na0.7CoO2. Fo he sodium dein e cala ed
samples wi h B 2 excesses abo e he s ochiome ic amoun (5, 10,
20…100) new addi ional e lec ions we e ound. These new e lec ions
we e indexed a e conside ing wo mino i y phases wi h hexagonal
symme y, P63/m and P6/m, wi h la ice pa ame e s a=5.3443(4),
c=19.525(3) and a=5.4027(7), c=20.466(2), espec i ely. Figu e 1.5 shows
all he X- ay pa e ns o he NaxCoO2 se ies. So a mix u e o 3 phases is
p esen om x~0.43 down o x~0.3.
58 Rie ica: B. A. Hun e and C. J. Howa d. Aus alian Nuclea Science and Technology
O ganiza ion. Lucas Heigh s Resea ch Labo a o ies, 1998.

Syn hesis, cha ac e iza ion…
35
10 20 30 40 50 60
‡
*
‡
*
**
****
*
B x100
B x10
B x20
B x30
B x40
B x50
B x5
B x1
pa en phase
(x=0.67)
In ensi y (a. u.)
2
Figu e 1.5: X- ay di ac ion pa e ns o NaxCoO2 dein e cala ed samples.
Re lec ions belonging o hexagonal space g oups P63/mmc, P63/m (*) and P6/m (‡)
a e shown.
As indica ed be o e, he e is no p ecise con ol o e he s ochiome y
o he pa en compounds ha a e ob ained di ec ly om solid s a e eac ion,
al hough mos o hem co espond o sodium con en abou x0.7. In
addi ion, he Na+ dein e cala ion wi h B 2 is a p ocess con olled by he
di usion o he Na+ ions h ough he ma e ial, om bulk o su ace. As a
consequence, he p esence o inhomogenei ies in se e al zones o he
ma e ial is expec ed and se e al c ys allog aphic phases can esul in he
same sample due o sligh a ia ion o Na+ con en . Fo his eason, he
appea ance o se e al phases wi h di e en symme y is expec ed, al hough
he a io among hem unp edic able. The e a e se e al epo s in he
li e a u e o samples wi h an equal Na+ con en ha belong o di e en space
g oups44,45,47,48. In my oppinion, his is mos p obably a consequence o an
inhomogeneous dis ibu ion o Na+ along he sample and/o possible Na+
o de ing53. So, disc epancies be ween esul s ob ained by di e en g oups
could esul om small a ia ions in he empe a u e o syn hesis, numbe o
hea ea men s, B 2 concen a ion used in he Na+ dein e cala ion p ocess o
he ime employed in each one o hese expe imen al s eps.
Chap e 1
36
Ano he impo an ac o o ake in o accoun is he ime ha he
samples a e kep in an open a mosphe e be o e being measu ed, due o
hei high hyg oscopic cha ac e . Mo eo e , his hyg oscopic cha ac e
inc eases as Na+ con en dec eases; so dein e cala ed samples wi h highe
B 2 excess will be mo e easily hyd a ed. The wa e abso p ion in be ween
he CoO6 laye s p o okes impo an s uc u al changes cha ac e ized by he
appea ance o new e lec ions, especially a low angles59 ( o be discussed
la e ).These can be e onously indexed as a new phase o he “d y” sample.
A signi ican displacemen o he (002) e lec ion o lowe (2θ) angles
is clea ly obse ed a e Na+ dein e cala ion a he P63/mmc phase
(Figu e 1.6). This e lec ion is indica i e o he sepa a ion be ween adjacen
CoO6 planes, indica ing an app eciable expansion o he la ice in he
di ec ion pe pendicula o hem a e Na+ emo al.
Figu e 1.6: Displacemen o he (002) e lec ion o he majo i y phase
P63/mmc a e Na+ dein e cala ion in NaxCoO2.
The la ice pa ame e s calcula ed o he majo i y P63/mmc phase
we e ob eained o each sample, by i ing all he e lec ions o he X- ay
59 J. D. Jo gensen, M. A dee , D. G. Hinks, J. C. Bu ley and S. Sho . Phys Re . B 68,
214517 (2003).
14 15 16 17 18
x=0.31
x=0.32
x=0.36
x=0.37
x=0.38
x=0.40
x=0.43
x=0.45
x=0.67
In ensi y (a. u.)
2
Syn hesis, cha ac e iza ion…
37
pa e n wi h Rie ica. The esul s a e shown in he Table 1.3. A signi ican
inc ease o he c-axis la ice pa ame e is obse ed wi h dec easing Na+
con en while he a-axis pa ame e dec eases sligh ly, bu con inuously o e
all he sodium con en ange. This app eciable expansion o he uni cell
along he c-axis is signaling a dec ease in bonding s eng h be ween he
CoO2 laye s as Na+ is emo ed. This has been ypically associa ed o he
inc ease o he Coulomb epulsion be ween he CoO6 shee s as he
Co4+/Co3+ a io inc eases. Su p isingly, he expansion o he c-axis
pa ame e is less ma ked below x=0.40, leading o an app oxima ely
cons an c/a a io down o x=0.30. I he explana ion o he Coulomb
epulsion is co ec , his ac could be signaling he impossibili y o u he
cha ging he CoO2 planes upon doping beyond x0.4.
Figu es 1.7 and 1.8 show di e en plo s o he la ice pa ame e s as
a unc ion o he Na+ con en in he NaxCoO2 samples.
Table 1.3: La ice pa ame e s o NaxCoO2 ( o he majo i y phase
P63/mmc). The hexagonal symme y o he space g oup P63/mmc implies ha a=b.
x a=b c
0.673(7) 2.8355(1) 10.8987(4)
0.642(6) 2.8295(1) 10.9287(6)
0.450(4) 2.8145(1) 11.1207(2)
0.429(6) 2.8132(5) 11.114(2)
0.420(6) 2.8152(1) 11.1324(2)
0.402(5) 2.8125(7) 11.169(2)
0.381(6) 2.8129(6) 11.128(3)
0.380(6) 2.8149(1) 11.1761(2)
0.369(5) 2.8097(1) 11.162(1)
0.362(4) 2.8108(1) 11.177(2)
0.322(4) 2.8113(4) 11.163(1)
0.310(3) 2.8074(3) 11.146(2)
Chap e 1
38
0.3 0.4 0.5 0.6 0.7
2.80
2.81
2.82
2.83
10.8
10.9
11.0
11.1
11.2
11.3
c (Å)
a (Å)
x, Na con en
Figu e 1.7: La ice pa ame e s o NaxCoO2 as a unc ion o he Na+ con en .
Line is a guide o he eye.
0.3 0.4 0.5 0.6 0.7
3.84
3.86
3.88
3.90
3.92
3.94
3.96
3.98
c / a
x, Na con en
Figu e 1.8: E olu ion o he c/a a io in NaxCoO2 o he majo i y phase
P63/mmc. Line is a guide o he eye.
Syn hesis, cha ac e iza ion…
45
Na0.32CoO2 was spli ed in se e al pa s (0.200 g each one) and added in o
NaI/ace oni ile mix u es (25 mL) p esen ing di e en amoun s o NaI
(0.0075-1.5 g). The ime o he eac ion was also a pa ame e o con ol,
a ying om 23 h o 140 h o a gi en NaI concen a ion. A he end o he
eac ion all he samples we e il e ed and washed se e al imes wi h
ace oni ile in o de o a oid possible es s o NaI.
All he samples we e cha ac e ized s uc u ally by X- ay di ac ion.
All he di ac ion pa e ns esul ed o be single phase and hey we e indexed
o he hexagonal P63/mmc space g oup. Figu e 1.10 shows he e olu ion o
he (002) e lexion peak o some ep esen a i e Na+ in e cala ed samples.
La ge amoun s o NaI, and longe imes led o phases wi h he highes Na+
con en . The con inuous displacemen o he (002) e lexion o highe angles
indica es ha he Na+ con en in he samples is inc easing, educing he
in e laye dis ance. On he o he hand, he wid h o he peaks emains
cons an a e he in e cala ion p ocess, which suppo s an homogeneous
dis ibu ion o Na+ h ough he sample.
I is impo an o ema k ha wi h his echnique he highes Na+
con en achie ed was x~0.63, only sligh ly lowe han he Na+ composi ion o
he ini ial p ecu so ob ained di ec ly h ough solid s a e eac ion, x=0.67.
Howe e , we we e able o ob ain a wide ange o composi ions in he ange
o 0.5<x<0.7.
Figu e 1.10: E olu ion o he (002) e lexion peak as Na+ is in e cala ed in o
Na0.32CoO2.
15.8 16.0 16.2
0.0
0.4
0.8
x=0.32
x=0.49
x=0.53
x=0.54
x=0.55
x=0.56
x=0.58
x=0.63
x=0.67
In ensi y no malized
2

Chap e 1
46
All he di ac ion pa e ns we e i ed wi h Rie ica in o de o
calcula e he cell pa ame e s o he di e en phases. Figu e 1.11 shows he
e olu ion o he he cell pa ame e s o he Na+ in e cala ed/dein e cala ed
se ies.
0.3 0.4 0.5 0.6 0.7
2.80
2.81
2.82
2.83
10.8
10.9
11.0
11.1
11.2
c (Å)
a (Å)
x, in NaxCoO2
Figu e 1.11: La ice pa ame e s o Na+ dein e cala ed (open symbols) and
Na+ in e cala ed (closed symbols) NaxCoO2 se ies, as a unc ion o he Na+ con en .
Lines a e guides o he eye.
The magne ic and anspo p ope ies o hese samples will be
discussed in he ollowing chap e s, paying special a en ion o he
compa ison o samples wi h he same x bu ob ained a e
dein e cala ion/in e cala ion om a highe /lowe x.
Combining he dein e cala ion and in e cala ion app oaches, i is
possible o co e a b oad ange o composi ions be ween 0.3x0.7.
Syn hesis, cha ac e iza ion…
47
I is impo an o men ion he e ha Na+ dein e cala ion/in e cala ion
p ocesses can be also pe o med elec ochemically, in which a NaxCoO2
hos would ac as a ca hode. Mo eo e , phase ansi ions in in e cala ion
ma e ials can be iden i ied elec ochemically by s udying he open ci cui
ol age (o.c. .) o a ba e y as a unc ion o he amoun o in e cala ed ion
p esen in he hos s uc u e. In a ba e y con igu a ion he anode po en ial is
cons an , he ne concen a ion o Li+ ions in he elec oly e is also cons an
and he a ia ions in he o.c. . wi h dein e cala ion/in e cala ion a e he
ela i e o he elec ochemical po en ial o elec ons in he ca hode ma e ial.
The e o e, he shape o he o.c. .-composi ion cu e depends on he
elec onic s uc u e o he ca hod ma e ial and he ela ed a ia ion o hei
Fe mi le el. The o.c. .-composi ion cu e73 o NaxCoO2 shows a
discon inuous po en ial change wi h se e al cha ac e is ic pla eaus ha a e
associa ed o di e en phase ansi ions along x. These s uc u al phase
ansi ions a e ela ed o he al e a ion o sodium coo dina ion om
oc ahed al o igonal p isma ic. In ac , he coexis ence o wo di e en
s uc u al phases (O3 and P3) has been obse ed o Na+ composi ions
0.65x0.8.
Figu e 1.12: Open ci cui ol age da a o a NaxCoO2 cell. (Plo aken om
Re . 35). Blue c osses co espond o he o.c. . measu ed o h ee di e en NaxCoO2
cells.
73 S. Kikkawa, S. Miyazaki and M. Koizumi. J. Powe Sou ces 14, 231 (1985).
2-PHASES
x
x
x
2-PHASES2-PHASES
x
x
x
Chap e 1
48
Th ee NaxCoO2 ba e ies wi h di e en x we e pe o med in o de o
measu e hei o.c. . and compa e i wi h ha one ob ained in Re . 35. The
Na+ composi ion es ima ed om he o.c. . cu e is simila o ha de e mined
by ICP-OES.
On he o he hand, sodium cobal a es a e highly hig oscopic.
Howe e , he amoun o wa e abso bed and he chemical s abili y depends
s ongly on he sodium con en o he samples. As a gene al ule, as sodium
con en dec eases, he hyg oscopic cha ac e inc eases no ably. Figu e 1.13
shows he he mog a ime ic analysis (TGA) up o 360 ºC o he pa en
compound (x0.7) and o a Na+ dein e cala ed sample (x0.4) a e being
syn he ized and kep o one day in a desica o wi h a 40% o humidi y. The
x=0.4 sample shows a d as ic weigh loss o abou 3% below 100 ºC, while
he mass o he x0.7 sample emains almos in a ian in he whole ange o
empe a u e. This weigh loss is ela ed o he humidi y p esen in he
powde . Abo e 100 ºC, he x0.4 sample shows a con inuous weigh loss
wi h empe a u e up o he highes empe a u e measu ed, which mus be
due o in e cala ed wa e .
100 200 300
93
94
95
96
97
98
99
100
x=0.4
x=0.7
weigh loss (%)
Tempe a u e (K)
Figu e 1.13: TGA analysis o he x

0.7 and x

0.4 samples wi h empe a u e
up o 360 ºC a 10 ºC/min unde N2 lowing.
Figu e 1.14 shows SEM images o a Na+ dein e cala ed sample wi h
x0.5, be o e and a e hyd a ion. Thei laye ed s c u e is clea ly e idenced
in bo h o hem by he s acking o he CoO2 shee s. The mic og aph a he
Syn hesis, cha ac e iza ion…
49
igh co esponds o he hyd a ed sample and a la ge ex olia ion be ween
he s acked laye s can be obse ed.
Figu e 1.13: SEM mic og aphs o he non-hyd a ed (le ) and hyd a ed
( igh ) x

0.5 sample.
1.1.3. NaxCoO2, x>0.70
The achie emen o NaxCoO2 phases wi h x>0.7 is no i ial. The
di ec syn hesis by solid s a e eac ion om he mos common s a ing
ma e ials, Na2CO3 and Co3O4, leads always o he mo e s able phase,
Na~0.7CoO2. The p epa a ion o phases wi h a low Na+ con en (x<0.7), is
ela i ely easy h ough Na+ dein e cala ion. Taking his in o accoun , o he
me hods o syn hesis in ol ing di e en expe imen al p ocedu es we e
ca ied ou in o de o ob ain di e en NaxCoO2 composi ions wi h x>0.7.
Among he mos popula , we can dis inguish hose based on he di ec
syn hesis be ween Na2O2 and Co3O474,75, Co me al and NaOH o ob ain he
NaCoO2 (O3) phase76 o Na2CO3 and Co3O4 o gi e, a e se e al
annealings a high empe a u e, x>0.8 samples77. Also an o iginal chemical
me hod whe e he pa en compound Na0.7CoO2 eac s wi h Na me al was
74 G. Lang, J. Bob o , H. Alloul, P. Mendels, N. Blancha d and G. Collin. Phys. Re . B, 74,
094404 (2005).
75 Q. Huang, M. L. Foo, R. A. Pascal, J ., J. W. Lynn, B. H. Toby, Tao He, H. W. Zandbe gen
and R. J. Ca a. Phys. Re . B, 70, 184110 (2004).
76 B. L. Cushing and J. B. Wiley. Syn h. Reac . Ino g. Me .-O g. Chem, 29(7), 1199 (1999).
77 H. Saku ai, S. Takenouchi, N. Tsujii and E. Takayama-Mu omachi. J. Phys. Soc. Jpn. 73,
2081 (2004).
Chap e 1
50
used o ob ain x>0.8 samples78. Howe e , in spi e o he exis ence o se e al
me hods o syn hesis, in many cases he sodium composi ion o he
esul an p oduc s epo ed in he li e a u e is e y ambiguous and unce ain,
and ac ually no well in e cala ed be ween he CoO2 laye s.
In o de o ob ain a sample o NaxCoO2 wi h x>0.7 sample, we ha e
checked he e icence o some o hese me hods. A e an exhaus i e
analysis o he inal p oduc o de e mine unambiguously he ac ual sodium
composi ion o he sample, we ob ained he bes esul s wi h he me hods
epo ed in he e e ences 39 and 40. Below, we will desc ibe he
expe imen al p ocedu es ca ied ou ollowing hese me hods o ou speci ic
case o NaxCoO2 (x>0.7) syn hesis:
1) Solid s a e eac ion77.
In o de o ob ain a inal p oduc wi h x=0.82, s ochiome ic amoun s
o Na2CO3 and Co3O4 (p e iously d ied a 300ºC o e nigh ) we e well mixing
and pes le unde mechanical cold p essu e a ~15 ons/cm2. The eac ion
ha akes place is exac ly he same ha one p e iously desc ibed in he
syn hesis o he pa en compound Na0.7CoO2. All he pelle s we e placed in a
ubula u nace unde O2 low gas and h ee hea ea men s we e pe o med
a di e en empe a u es: 800ºC, 850ºC and 900ºC espec i ely. Each
he mal annealing ook 6h and he samples we e eg inding and p essed
be o e each new annealing. A mo e de ailed desc ip ion abou he
expe imen al condi ions o he annealings pe o med in he samples is ound
in e e ence 38.
2) Chemical syn hesis78.
Fo he syn hesis o samples wi h x>0.75, sodium me al (0.3g) and
e ahyd o u an (40 ml) we e placed in a 25mm x 150mm Py ex sc ew-
capped ube, and we e hea ed by placing he lowe 25mm in an silicon ba h
main ained a 95 °C. A e 1 h, benzophenone (2g) was added. A e hea ing
ano he hou , powde ed Na0.7CoO2 p ecu so (1.5g) was added, and he
mix u e was hea ed, wi h agi a ion by a magne ic s i ing ba , o 48 h. As he
mix u e was cooled down o oom empe a u e, e hanol (20 ml) was added
o des oy he benzophenone ke yl adical anion and any un eac ed sodium
me al. A e 20 min, he mix u e was cen i uged o 3 min a 2000 pm in a
78 Q. Huang, M. L. Foo, R. A. Pascal, J ., J. W. Lynn, B. H. Toby, Tao He, H. W. Zandbe gen
and R. J. Ca a. Phys. Re . B, 70, 184110 (2004).

Syn hesis, cha ac e iza ion…
51
s ainless-s eel cen i uge ube. The o ganic supe na an was decan ed, he
solid was esuspended in dichlo ome hane (20ml), he mix u e was
cen i uged, and he o ganic supe na an was again decan ed. Two mo e
dichlo ome hane washes we e pe o med in he same way, and hen he
inal black pelle was b oken up and ai d ied o e nigh . This p ocess led in
di e en syn heses o sodium-en iched ma e ials wi h 0.80<x<0.90. This
di e ence may be associa ed o he p esence o a wo-phase egion in he
phase diag am a hese composi ions, o possibly due o unce ain ies in he
empe a u e o any o he a iable o he eac ion.
The sodium con en o he samples was de e mined by he ICP-OES
me hod. The s ochiome y o he esul an samples was Na0.82CoO2. Also he
inc ease in he Na+ con en o he samples was con i med h ough s uc u al
e inemen s o he XRD pa e ns. Figu e 1.14 shows he X- ay di ac ion
pa e n o Na0.69CoO2 as well as o he samples wi h a high Na+ con en
ob ained by solid s a e eac ion and chemical syn hesis, espec i ely. Bo h o
hem a e single phase and we e indexed wi h he hexagonal space g oup
P63/mmc, main aining he P3 symme y. This is opposi e o o he wo ks
whe e a change om P3 o O3 s uc u e was epo ed o samples wi h
s ochiome y x=0.75 and 0.9279. Only he pa e n o he sample ob ained by
chemical syn hesis p esen a couple o small e lexions ma ked wi h s a s
which ha e no been iden i ied, p obably due o pa ially hyd a ed phases.
The displacemen obse ed o he (002) e lexion peak o highe angles
indica es ha he in e laye dis ance is sho e han in he case o he pa en
compound Na0.69CoO2. This is consis en wi h a highe numbe o si es being
ocupped by Na+ ions.
79 L. Viciu, J. W. G. Bos, H. W. Zandbe gen, Q. Huang, M. L. Foo, S. Ishiwa a, A. P.
Rami ez, M. Lee and N. P. Ong. Phys. Re . B, 73, 174104 (2006).
Chap e 1
52
10 20 30 40 50 60 70 80
15.5 16.0 16.5 17.0
*
**
Na0.67CoO2 p ecu so
solid s a e eac ion ( e 4)
chemical syn hesis ( e 5)
(002)
In ensi y ( u. a. )
2
(002)
Figu e 1.14: XRD pa e ns o he pa en compound Na0.67CoO2 and he
samples wi h a highe Na+ con en ob ained by solid s a e eac ion and chemical
syn hesis, espec i ely. The inse shows he posi ion o he (002) e lexion o all
hese samples, indica ing a shi o highe angles in he case o he samples
p esen ing a highe Na+ con en . The s a s (*) indica e e lec ions belonging o
impu i ies which ha e no been iden i ied.
1.2. Syn hesis o Na0.7CoO2 single-c ys al.
The e a e basically wo syn he ic ou es in he li e a u e o ob ain
single c ys als o NaxCoO2: he lux me hod and g ow h by he op ical
loa ing-zone (FZ) echnique. Single c ys als ob ained om he la e can be
se e al cen ime es long and wid h, so hey a e easily o ien able and hei
anspo and magne ic p ope ies can be measu ed as a unc ion o a
pa icula c ys allog aphic di ec ion.
In his wo k, due o he lack o a FZ u nace, single c ys als o
Na0.7CoO2 ha e been syn hesized by he lux me hod om Co(NO3)3.5H2O
and NaOH ollowing a sligh modi ica ion o he me hod by Shi akuma a e
Syn hesis, cha ac e iza ion…
53
al80. The eac an s we e weigh ed in he a io 1:10 (Co(NO3)3.5H2O:NaOH),
g ounded and mixed unde A a mosphe e in a d y box o a oid wa e
abso p ion. Then, hey we e placed in an Al2O3 c ucible and hea ed a
400 ºC in ai o 12 hou s. The hea ing a e was 3 ºC/min while he cooling
a e was 0.5 ºC/h om 400 ºC o 200 ºC, and 3 ºC/min om 200 ºC o oom
empe a u e.
The size o he c ys als ob ained using he lux me hod is o he
o de o a ew ens o m. Some o he mic og aphs ob ained o Na0.7CoO2
single c ys als a e shown in Figu e 1.15. In all o hem, he hexagonal
s uc u e can be clea ly app ecia ed. I is also dis inguishable he s acking o
laye s along he c-axis, sligh ly ex olia ed.
Figu e 1.15: SEM mic og aphs o Na

0.7CoO2 single c ys als.
80 C. Shi akuma a and M. S. Hegde. P oc. Indian Acad. Sci (Chem. Sci.) 115, 447 (2003).
Chap e 1
54
Single c ys als o KxCoO2 we e also syn he ized by his echnique.
The echniques desc ibed p e iously o dein e cala e sodium om
polyc ys alline samples, a e equally applicable o NaxCoO2 single c ys als.
Howe e , i is impo an o ema k ha chemical dein e cala ion om single
c ys als esul s in an inhomogeneous dis ibu ion o Na+ along he sample.
This is due o he smalle e ec i e su ace a ea o he single c ys al
compa ed o he powde . This makes he esul s in dein e cala ed single
c ys als e y much sample-dependen . This, along wi h he di icul y o
ob ain la ge enough c ys als o make eliable anspo expe imen s, d o e
us o ocus on he polyc ys alline samples.
Magne ic and anspo p ope ies…
61
phase. Figu e 2.5 shows he TEP o he new NaxCoO2 se ies wi h h ee
ep esen a i e samples e y close o x=0.5.
Figu e 2.4: E olu ion o he empe a u e dependence o he he mopowe
wi h Na+ con en . Below x~0.42, he he mopowe does no show a dependence on
he Na/Co a io due o he in a iance o doping a he CoO2 planes in his ange o x.
Dash cu e shows a DSC analysis wi h empe a u e o a x

0.4 sample pe o med a
10 ºC/min.
100 200 300 400
-20
0
20
40
60
0.52(1)
0.51(1)
0.48(1)
S ( V / K )
T
(
K
)
Figu e 2.5: The moelec ic powe o a Na+ dein e cala ed NaxCoO2 se ies.
100 200 300 400
0
20
40
60
80
100
0
5
10
x = 0.69(1)
x = 0.450(4)
x = 0.429(6)
x = 0.402(5)
x = 0.381(6)
x = 0.369(5)
x = 0.362(4)
S (V/K)
Tempe a u e (K)
dH/dT (mW)

Chap e 2
62
Now, we a e in a posi ion o es ablish gene al ends ela ed o he
Na+ con en , which can be summa ized in:
(a) A la ge x (0.5<x<0.7) he TEP is always la ge and posi i e, and
inc eases almos linea ly o e he whole empe a u e ange.
(b) In he samples e y close o x0.5 (0.47<x0.5) S(T) also
inc eases con inuously o e he whole empe a u e ange, al hough a
cha ac e is ic c osso e o nega i e alues is clea ly obse ed below 150K.
(c) Fo x<0.5 he posi i e sign o he TEP is eco e ed in he whole
empe a u e ange.
(d) As x dec eases below x<0.5 he he mopowe shows a
empe a u e independen pla eau which is p ac ically insensi i e o a ia ions
in he Na+ con en . The linea T-dependence is eco e ed abo e ~375 ºC, in
ag eemen wi h he exo he mic peak obse ed in DSC calo ime y. I could
be p esumibly associa ed o Na+ ion mobili y.
The in a iance o he he mopowe in he lowes doping egion
co obo a es he ine iciency o Na+ emo al o in oduce cha ge ca ie s in
he CoO2 laye s. The same TEP beha iou wi h empe a u e was con i med
o a NaxCoO2 se ies in which Na+ was p og esi ely in e cala ed om x=0.47
(Figu e 2.6).
Figu e 2.6: Tempe a u e dependence o he he mopowe o a Na+
in e cala ed NaxCoO2 se ies om a sample wi h x=0.47.
100 150 200 250 300 350 400 450
-20
0
20
40
60
80
0.63(1)
0.57(1)
0.56(1)
0.55(1)
0.54(1)
0.53(1)
0.52(1)
0.50(1)
0.47(1)
S (V / K)
T ( K )
Magne ic and anspo p ope ies…
63
These measu emen s we e ex ended down o ~10 K o h ee
ep esen a i e samples o hese doping anges (Figu e 2.7).
0 100 200 300 400
-20
0
20
40
60
80
Na0.50
S (V/K)
Na0.36
Na0.70
Tempe a u e ( K )
Figu e 2.7: Tempe a u e dependence o he he moelec ic powe o
ep esen a i e Na+ composi ions in NaxCoO2 (x= 0.70, 0.50 and 0.36).The low-T
(open) and high-T ( illed) da a we e measu ed in di e en equipmen s.
I is highly imp obable ha exac ly he same Na+ a angemen is
eached a e chemical emo al/inse ion o Na+. So, hese esul s
demons a e ha only he Na+/Co3+/IV a io is impo an in de e mining he
S(T) o NaxCoO2.
An impo an in o ma ion abou he band s uc u e o NaxCoO2 could
be ob ained om he analysis o hese da a. O special in e es he e a e he
inc ease o he slope wi h inc easing Na+ con en a low-T and he c osso e
o nega i e alues a T~190 K in he x0.5 sample. A his speci ic
composi ion, x0.5, he Seebeck coe icien is nega i e a low empe a u es
and c osses o posi i e alues be ween 100-150 K, depending on he exac
composi ion.
Chap e 2
64
Kau a e al99 showed simila esul s al hough he nega i e cuad an
and he minimum Seebeck we e obse ed a T~85 K and T~50 K,
espec i ely. Based on p e ious neu on sca e ing, suscep ibili y, magne ic
esonance and anspo esul s in Na0.5CoO284,100,101, he au ho s associa ed
his c osso e o he cha ge and an i e omagne ic o de s. The di e ence o
hese cha ac e is ic empe a u es wi h ou da a o he same Na+
composi ion could lie in e y small di e ences in he Na+ con en .
Such a change in he sign o S(T) and he b oad peak obse ed a
low empe a u e indica es ha he elec onic s uc u e o his sample mus
be undamen ally di e en o he neighbo ing composi ons. Howe e , o an
AFM phase wi h an associa ed con en ional cha ge-ode ing below ~40 K,
he e should be a subs an ial inc ease o he absolu e alue o h e
he mopowe and a he mal ac i a ed conduc ion; none o hese a e
obse ed.
On he o he hand, he combina ion o an elec ical esis i i y as low
as ha o a me al, wi h a he moelec ic powe ha is ypically an o de o
magni ude la ge han expec ed on he basis o his, is no easily unde s ood
wi hin he amewo k o con en ional band heo y o me als. So, he
ques ion being asked he e is…wha is he o igin o his enhancemen o he
he moelec ic powe ?
The magni ude o he linea empe a u e dependence o he
Seebeck coe icien in an i ine an -elec on sys em is de e mined by he
band s uc u e a ound he Fe mi ene gy, acco ding o Mo ’s equa ion102:



F
E
B
dE
Nd
e
Tk
TS 








ln
3
22
eq. [3.1]
which ep esen s he solu ion o he Bol zman anspo equa ion94 in he low
empe a u e limi (KBT<W, whe e W is he bandwid h) and whe e B
k is he
99 N. Kau a , K. K. Wu, Y. K. Kuo, G. J. Shu and F. C. Chou. Phys. Re . B 79, 075105
(2009).
100 G. Gaspa o ic, R. A. O , J-H. Cho, F. C. Chou, Y. Chu, J. W. Lynn and Y. S. Lee. Phys.
Re . Le . 96, 046403 (2006).
101 F. L. Ning, S. M. Golin, K. Ahilan, T. Imai, G. J. Shu and F. C. Chou. Phys. Re . Le .
100, 086405 (2008).
102 N. F. Mo and H. Jones. “The heo y o he p ope ies o me als and alloys”. Ed. By
Do e , NY 1958.
Magne ic and anspo p ope ies…
65
Bol zman cons an ,
T
is he empe a u e, e is he cha ge o he elec on and


N is he densi y o elec onic s a es a he Fe mi le el. Rapidly a ying


N, cha ac e is ic o many s ongly co ela ed sys ems, esul in la ge
alues o S(T), h ough he inc ese o he de i a i e pa o equa ion [3.1]
The complex band s uc u e de i ed om he igonal- ield spli ing o he
Co3+/CoIV
2g mani old, could in p inciple jus i y he la ge slope o S(T).
Chemical doping wi h di e en ca ions could help es ing his hypo hesis, as
we will discuss la e .
On o he hand, Bol zmann anspo equa ion ends o a
empe a u e-independen solu ion a he high empe a u e limi (KBT>W),
esul ing in he so-called Heikes o mula







 x
x
e
k
Sb
1
ln eq. [3.2]
whe e x is he concen a ion o mobile holes (CoIV) in he Co3+ la ice. So, on
he basis o con en ional Bol zmann anspo heo y, he gene al beha io
ha can be expec ed o a co ela ed (no so la ge W) sys em is
schema ically pic u ed in Figu e 2.8.
Chap e 2
66
Figu e 2.8: Gene al beha iou o S(T) expec ed o a co ela ed sys em in
basis o Bol zman anspo heo y.
The ansi ion be ween he Mo and Heikes limi s will be de e mined
by he band wid h and i s s uc u e a ound EF o each pa icula ma e ial.
In he las ew yea s some al e na i e explana ions ha e been gi en
o he empe a u e dependence o S(T) in laye ed cobal i es.103 Te asaki e
al104 specula ed ha he high he moelec ic powe in NaxCoO2 could a ise
om spin luc ua ions, as in he case o hea y e mions and/o alence-
luc ua ion sys ems105. Pa icula y, Koshibae e al96,97 p oposed a
gene aliza ion o he Heikes o mula106 o include he spin en opy
con ibu ion om Co3+ and CoIV. In hei heo y, he compe i ion be ween he
c ys alline ield and Hund coupling leads o la ge degene acy in he cobal
3d s a es, whe e he elec ons would be a he localized. They ook in o
acoun hese conside a ions in a new e m ha includes he di e en
possible spin con igu a ions (LS, IS and HS) in addi ion o he Heikes
o mula,
103 J. O. Hae e , M. R. Pe e son and B. S. Shas y. Phys. Re . Le . 97, 226402 (2006)
104 I. Te asaki, Y. Sasago and K. Uchinoku a. Phys. Re . B 56, 685 (1997).
105 C. S. Ga de and J. Ray. Phys. Re . B 51, 2960 (1995).
106 P. M. Chaikin and G. Beni. Phys. Re . B 13, 647 (1976).
S
T
Heikes
~W
Mo

Magne ic and anspo p ope ies…
67









 x
x
g
g
e
k
Sb
1
ln
4
3 eq. [3.3]
whe e 3
gand 4
g ep esen he degene acy o he spin sa e o he Co3+ and
CoIV ions. Ini ial suppo o his in e p e a ion came om he s ong
supp ession o he he mopowe unde a magne ic ield107,108. Howe e , i
has been demons a ed ecen ly109 ha he supp ession o S(T) by a
magne ic ield can be explained by he ield-induced spin pola iza ion, in he
con ex o Bol zman anspo heo y110. In ac , he applicabili y o equa ion
[3.3] o sys ems like NaxCoO2 is doub ul. Fi s o all, i p edic s a
empe a u e independen he moelec ic powe , no obse ed in NaxCoO2 a
la ge doping (see Figu e 2.4). Since his equa ion is s ic ly applicable only in
he limi whe e incohe en cha ge exci a ions domina e he elec onic
anspo (kBT > W), he empe a u e dependence o S(T) in me allic
NaxCoO2 (x≈0.7) demons a e ha his limi is s ill no eached a oom
empe a u e.
On he o he hand, o x=0.35 and x=0.5 he e is a empe a u e-
independen pla eau in which he applicabili y o Heikes o mula can be
es ed.
I is impo an o emembe a his poin ha in NaxCoO2 he amoun
o holes is no exac ly de e mined by he Na+ con en 111,112,113,114. Fo x≈0.7
he a e age alence is ≈3.2+ ins ead o 3.3+, and a cons an cha ge o
3.57(3)+ is eached o x<0.45. Fo a compa ison be ween he esul s om
equa ion [3.3] and he expe imen , a p ecise de e mina ion o he ac ual
concen a ion o holes in he sys em is c ucial. Using he expe imen al
alues o Co3+/CoIV, he alues o S(x=0.35, x=0.5) a he pla eau a e well
107 Y. Wang, N. S. Rogado, R. J. Ca a and N. P. Ong. Na u e 423, 425 (2003).
108 P. Limele e, S. Hébe , V. Ha dy, R. F ésa d, Ch. Simon, and A. Maignan. Phys. Re .
Le . 97, 046601 (2006).
109 H. J. Xiang and D. J. Singh. Phys. Re . B 76, 195111 (2007).
110 T. Takeuchi, T. Kondo, T. Takami, H. Takahashi, H. Iku a, U. Mizu ani, K. Soda, R.
Funahashi, M. Shikano, M. Mikami, S. Tsuda, T. Yokoya, S. Shin and T. Mu o. Phys Re . B
69, 125410 (2004).
111 M. Ka ppinen, I. Asako, T. Mo ohashi and H. Yamauchi. Chem. Ma e . 16, 1693 (2004).
112 H. Saku ai, S. Takenouchi, N. Tsujii and E. Takayama-Mu omachi. J. Phys. Soc. Jpn. 73,
2081 (2004).
113 M. Bañob e-López, F. Ri adulla, R. Caudillo, M. A. López-Quin ela, J. Ri as and J. B.
Goodenough. Chem. Ma e ., 17, 1965 (2005).
114 C. A. Ma iane i, G. Ko lia and G. Cede . Phys. Re . Le . 92, 196405 (2004).
Chap e 2
68
ep oduced by he Heikes equa ion wi hou he need o include he spin
degene acy e m.
On he o he hand, he Heikes limi seems o be eached also a
highe doping (Na0.84CoO2) and in mis i Ca3Co4O9 (also sha ing a iangula
Co-la ice), as can be seen in Figu e 2.9.
Fo Na0.84CoO2 using equa ion [3.3] wi h a LS con igu a ion
(g3/g4=1/6) will equi e an unphysical numbe o holes o jus i y he pla eau a
S(kBT > W)≈ 105 μVK-1. Howe e , he con en ional Heikes o mula (g3/g4=1)
p edic s he co ec expe imen al alue o a concen a ion o holes o 0.23,
oughly consis en wi h he chemical o mula.
The same end is obse ed o Ca3Co4O9. In his ma e ial
pho oemission spec oscopy expe imen s measu ed a concen a ion o holes
[Co4+]≈0.23, consis en wi h a LS con igu a ion in he 3+/4+ ionic species.
Using equa ion [3.3] would p edic a S(kBT > W)≈ 258 μVK-1, while he
con en ional Heikes equa ion esul s in S(kBT > W)≈ 105 μVK-1. The la e
alue is e y close o he expe imen al one (see Figu e 2.9).
So, he conclusion wi h espec o x=0.7 is ha he Heikes limi is no
eached and, he e o e, ou expe imen al da a only show he p og esi e S(T)
e olu ion om a dominan Mo o Heikes s a e.
To econcile his wi h he la ge slope o he he mopowe a low
empe a u es is only possible i a complex band s uc u e wi h con ibu ions
om a na ow a1 and a b oad e band a EF is conside ed.115
An impo an poin ha emains o be explained is he apid inc ease
o he TEP wi h empe a u e abo e 350 K, pa icula ly e iden a low x. The
o ma ion o la ge pola ons and/o a dynamic spin ansi ion om LS o IS o
HS spin con igu a ions wi h empe a u e would explain his beha io om he
eno malized s a is ics (numbe o holes s a ailable si es) ha mus be
conside ed in he Heikes o mula.
115 F. Ri adulla, J.-S. Zhou and J. B. Goodenough. Phys. Re . B 68, 07510 (2003).
Magne ic and anspo p ope ies…
69
0 100 200 300 400
0
25
50
75
100
125
Na0.84CoO2
Na0.7CoO2
Ca3Co4O9
S (V/K)
Tempe a u e (K)
Figu e 2.9: Tempe a u e dependence o he he moelec ic powe o wo
composi ions o NaxCoO2 (da a o x=0.84 aken om Re .20, and Ca3Co4O9. No e
ha in Na0.70CoO2 he linea beha iou p edic ed by eq. [4] is no obeyed in he whole
empe a u e ange. Ins ead S(T) shows a change o slope abou 150 K, al hough i
does no each sa u a ion. We ha e aken he low empe a u e pa o i he da a o
equa ion [3.1].
So, he ag eemen be ween he esul s o equa ion [3.3] wi h he
expe imen is mos p obably based on an e oneous es ima ion o he
concen a ion o holes. Con en ional Heikes o mula p edic s he co ec
alue o he high empe a u e limi o he he mopowe in laye ed cobal i es,
once he co ec numbe o cha ge ca ie s is conside ed.
Magne ic measu emen s pe o med in NaxCoO2 a e p esen ed
below. I is impo an o men ion again ha no u he he mal annealings o
he samples we e pe o med a e syn hesis and special a en ion has been
paid in hei s o age du ing he ime passed be ween he elec ical,
he moelec ic and magne ic measu emen s in o de o p ese e hei
in insic chemical and physical p ope ies, and o make hese measu emen s
ully compa able among hem. The ime be ween he anspo and magne ic
measu emen s o each speci ic Na+ composi ion did no exceed mo e han
one day in any case.
Figu e 2.10 shows he e olu ion o he ze o ield and ield cooled
(ZFC-FC) magne iza ion cu es wi h x in he NaxCoO2 se ies. In gene al, an
almos empe a u e independen magne iza ion egion o e a la ge ange o
Chap e 2
70
empe a u e (abo e ~100 K) is app ecia ed. Howe e , a ca e ul analysis o
he esul s shows a sligh and con inuous inc ease o he magne iza ion om
~140 K up o 300 K o Na+ con en s be ween 0.52x0.40 (see inse o Fig.
2.10).
Figu e 2.10: ZFC-FC cu es as a unc ion o empe a u e in NaxCoO2 a an
applied magne ic ield o H=100 Oe. Inse : Zoom in he empe a u e egion T>100 K
o show he he mically ac i a ed e m o he magne iza ion.
This obse a ion has been al eady epo ed by o he au ho s84,116
and i could be a ibu ed o a con inuous exci a ion abo e a spin gap whose
o igin is unknown.
Below T~140K,

(T) inc eases in all he samples wi h dec easing
empe a u e. The magne iza ion is no i ed by a Cu ie-Weiss law, so i
should be sepa a ed in wo di e en magne ic beha iou s: di e gen
suscep ibili y a low empe a u e and Pauli suscep ibili y abo e a ce ain
empe a u e (i is no as empe a u e independen as expec ed because o
he spin gap ansi ion, which p o okes a sligh inc ease o he
magne iza ion a ha empe a u e ange.
116 G. Lang, J. Bo o , H. Alloul, G. Collin and N. Blancha d. Phys. Re . B 78, 155116
(2008).
0 100 200 300
0.0
3.0x10-3
6.0x10-3
9.0x10-3
150 200 250 300
2.0x10-4
3.0x10-4
4.0x10-4
5.0x10-4
H=100 Oe
x=0.70 (p ecu so )
x=0.52
x=0.50
x=0.48
x=0.43
x=0.40
x=0.37
x=0.32
x=0.31
M ( emu.g-1 )
Tempe a u e ( K )
T ( K )
M ( emu / g )
Magne ic and anspo p ope ies…
77
Figu e 2.16: Diamond an il cell used in he measu emen s o X- ay wi h
p essu e, and scheme o he cell assembly.
A small uby mixed wi h he sample was used o moni o he in e nal
p essu e h ough he p essu e dependence o i s luo escence peak. The
luo escence lines exhibi a p onounced ed-shi wi h applied p essu e, as
shown in Figu e 2.17. A 4:1 e hanol-me hanol mix u e was used as he
hyd os a ic p essu e- ansmi ing medium. Da a o each pa e n we e
collec ed o 10 minu es.
A s anda d o Silicon was e ined o ob ain he ins umen al
pa ame e s ha we need o e ine ou measu emen s by he Rie eld
me hod.
690 692 694 696 698
0,0
0,2
0,4
0,6
0,8
1,0
Ruby
P=0 kba
P=3.0 kba
P=5.7 kba
P=11.3 kba
P=25.6 kba
P=33.6 kba
P=59.0 kba
In ensi y (a.u.)

(nm)
Figu e 2.17: Example o he ed-shi o he luo escence lines o uby wi h
p essu e.
o ce
gascke
ub
y
sample
diamond

Chap e 2
78
In Figu e 2.18 we show all he x- ay di ac ion pa e ns ob ained o
polyc ys alline Na0.82CoO2 as p essu e is inc eased. The inse shows a de ail
o he e olu ion o he main peak o he XRD pa e ns wi h p essu e.
5 10152025
10.3 10.4 10.5 10.6
0.3 GPa
0.6 "
0.7 "
1 "
1.6 "
2 "
2.3 "
2.8 "
4 "
4.9 "
5.6 "
In ensi y ( u. a. )
2

P
Figu e 2.18: E olu ion o he XRD wi h p essu e a oom empe a u e o
Na0.82CoO2. The inse shows he e olu ion o he main peak o highe angles as
p essu e inc eases. The wa e leng h o he beam line used was

=0.44397 Å.
Th ough Lebail i ings wi h Rie ica o all he di ac ion pa e ns a
di e en p essu es, we ha e de i ed he e olu ion o he olume wi h he
p essu e, and i ed he olume-p essu e da a o he Bi ch-Mu naghan
equa ion, o ob ain he bulk modulus, K0, o he ma e ial127.





 EEE K KP )4'(
2
3
1)21(3 2/5
0 (Eq. A1)
127 R. J. Angel, in “High-Tempe a u e and High-P essu e C ys al Chemis y”, Re iews in
Mine alogy and Geochemis y, Vol. 41, Mine alogical Socie y o Ame ica, Vi ginia (2000).
Magne ic and anspo p ope ies…
79
whe e K0 is he ze o p essu e bulk modulus, K’=

K0/

P, and














1
2
13/2
0
V
V
E is he Eule ian s ain.
Figu e 2.19 shows he esul s ob ained conside ing he i s o de o
he Bi ch-Mu nagan equa ion, k’=4. The i ing o he P(V0/V) da a o he
Bi ch Mu nagham equa ion, le us o es ima e an expe imen al alue o K0 o
he o de o 120(3) kba .
1.00 1.01 1.02 1.03 1.04
0
1
2
3
4
5
6
Na0.82CoO2
P ( GPa )
Vo/V
Figu e 2.19: Fi ing o he expe imen al P(V0/V) da a o he Bi ch-
Mu naghan equa ion, unca ed a second o de , k’=4.
In o de o analyze he e ec o he p essu e sepa a ely on he c and
ab-di ec ions, we plo ed in he Figu e 2.20 he e olu ion o he c and a-
la ice pa ame e s wi h inc easing p essu e and i ed he da a o he same
Bi ch-Mu naghan equa ion desc ibed abo e.
Chap e 2
80
1.000 1.005 1.010
0
1
2
3
4
5
6
1.000 1.005 1.010 1.015 1.020 1.025
0
1
2
3
4
5
6
P (GPa)
a0/a
P (GPa)
c0/c
Figu e 2.21: Fi ing o he P(a0/a) (uppe ) and P(c0/c) (lowe ) da a o he
Bi ch-Mu naghan equa ion, unca ed a second o de , k’=4.
The pseudo Bulk modulus es ima ed we e 537(14) GPa in he ab-
plane and 232(9) GPa in he c-axis. This indica es ha he sys em is mo e
comp esible in he c-di ec ion, as i is expec ed om he laye ed s uc u e.
The comp essibili y o he uni cell along he c-di ec ion wi h
p essu e is s ongly ela ed o he p essu e dependence o he AFM o de ing
empe a u e obse ed by Woold idge e al 128 in x>0.7 single-c ys als,
inc easing om 21.5 K o 25.5 K a 10 Gpa. This p essu e dependence o Tm
is simila o dTm/dP = 4.4(3) K/GPa es ima ed in x=0.8.126
These esul s indica e he exis ence o a di ec e ec o he in e laye
dis ance on he AFM exchange in e ac ion, which is s abilized as he CoO2-
128 J. Woold idge, D. McK. Paul, G. Balak ishnan and M. R. Lees. Condens. Ma e . J. Phys.:
Condens. Ma e 18, 4731 (2006).
Magne ic and anspo p ope ies…
81
CoO2 sepa a ion is educed. The e o e, hey sugges ha no only he CoO2
planes domina e he physical p ope ies o he sys em a x>0.7, he 3D
dimensionali y plays an ac i e ole ha should be conside ed. We will ake
his in o acoun and will be discussed in nex chap e s.
To suma ize, we epo ed a de ailed analysis o he magne ic
suscep ibili y, , and he moelec ic powe , S, o me allic NaxCoO2 and
Ca3Co4O9, as ep esen a i e examples o laye ed cobal oxides wi h a
iangula Co la ice. We ha e shown ha he magne ic and anspo
p ope ies a e mos ly de e mined by CoO2 planes in he ange 0.3<x<0.7.
This ac explains he simila phenomenology ound in di e en 2D cobal
oxides based on hexagonal Co a angmen s, pa icula y he puzzling
empe a u e dependen

(T) and la ge he moelec ic powe combined wi h
a me allic esis i i y.
We ha e demons a ed ha he empe a u e dependence o he
magne ic suscep ibili y in iangula la ice Co-oxides canno be jus i ied
assuming a spin localized model. We sugges ha he o igin o he
empe a u e dependence o he magne iza ion is due o he empe a u e
dependence o he spin luc ua ions o i ine an elec ons.
We ha e also shown ha he unusually la ge he mopowe is ela ed
o a band-s uc u e e ec unde s andable wi hin he amewo k o Bol zmann
anspo heo y, wi hou h he need o conside an ex a spin-en opy
con ibu ion. In he high empe a u e limi he Heikes o mula p edic s
co ec ly he sign and magni ude o he empe a u e independen
he mopowe in hese sys ems, when a co ec es ima ion o he cha ge
ca ie densi y is a ailable.
In he special case a ound x0.5, ou da a e idence he di e en ia e
na u e o he elec onic p ope ies.
Finally, we ha e shown ha he AFM exchange in e ac ion is
s ongly in luenced by he 3D cha ac e o he s ucu u e o x>0.7, ha plays
a mo e han expec ed ac i e ole.

3
3.
.
P oximi y o a quan um
phase ansi ion
In his chap e we ca y ou an exhaus i e s udy o he magne ic
p ope ies o me allic NaxCoO2, bo h abo e and below x=0.5. We will ocus
on he wo ep esen a i e compounds x≈0.69 and x≈0.36. These
expe imen s p o ide a good e idence o he p oximi y o his ma e ial o a
magne ic phase ansi ion a e y low empe a u e. Ou da a show ha he
ac ual empe a u e o his ansi ion is well below 1.8 K and p obably a ze o
Kel in (quan um phase ansi ion, QPT). The possible ole o magne ic
luc ua ions in he supe conduc i i y is discussed o he ligh o he obse ed
(H, T) scaling o he magne iza ion. The new elec onic phases iden i ied
lead us o p oposs a new (T, H) phase diag am o hese wo dis inguishable
me allic s a es.
Chap e 3
84
I is commonly belie ed ha he mic oscopic explana ion o high
empe a u e supe conduc i i y can be cons ained by de e mining he
in e play be ween band- illing, magne ic in e ac ions and dimensionali y. In
his sense, he epo 129 o supe conduc i i y in NaxCoO2•yH2O gene a ed an
in ense deba e abou he na u e o he pai ing in e ac ion in his ma e ial,
which is becoming a es g ound o he heo ies o supe conduc i i y.
Al hough he laye ed s uc u e, he mixed alence cha ac e , and he
p oximi y o he supe conduc i e composi ions o a localized cha ge-o de ed
phase130 makes i e y emp ing o make a s aigh o wa d compa ison wi h
he cup a es, he me allic p ecu so o he supe conduc ing phase shows i s
own peculia i ies: an elec onically ac i e iangula cobal la ice is supposed
o be esponsible o he s ong empe a u e dependence o he me allic
suscep ibili y (so called “Cu ie-Weiss me al” beha iou a high x)131, he
anomalous empe a u e dependence o he esis i i y132, o he su p isingly
la ge he mopowe 133. Mo eo e , local densi y app oxima ion (LDA)
calcula ions134,135 p edic ed a e omagne ic (FM) g ound s a e in he me allic
p ecu so , al hough he ma e ial ne e o de s down o he lowes
empe a u e p obed. The disc epancy be ween heo y and expe imen was
en a i ely a ibu ed o he p oximi y o a quan um phase ansi ion (QPT)135,
which would imply he exis ence o s ong FM luc ua ions in he me al. This
opens he possibili y o a magne ically media ed supe conduc ing s a e due
o exchange o FM spin luc ua ions, like i was p oposed o S 2RuO4 136 and
high-p essu e UGe2137. Ac ually, 59Co NMR and 23Na NQR expe imen s138
129 K. Takada, H. Saku ai, W. T. Mu omachi, F. Izumi, R. A. Dilanian and T.
Sasaki. Na u e 422, 53 (2003).
130 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Ca a. Na u e. 424, 527 (2003)
131 M. L. Foo, Y. Wang, S. Wa auchi, H. W. Zandbe gen, T. He, R. J. Ca a and N.
P. Ong. Phys. Re . Le . 92, 247001 (2004).
132 F. Ri adulla, J.-S. Zhou and J. B. Goodenough. Phys. Re . B 68, 75108 (2003).
133 Y. Wang, N. S. Rogado, R. J. Ca a and N. P. Ong. Na u e 423, 425 (2003)
134 D. J. Singh. Phys. Re . B 61, 13397 (2000).
135 D. J. Singh. Phys. Re . B 68, 20503 (2003).
136 I. I. Mazin and D. J. Singh. Phys. Re . Le . 79, 733 (1997).
137 S. S. Saxena, P. Aga wal, K. Ahilan, F. M. G osche, R. K. W. Haselwimme , M.
J. S eine , E. Pugh, I. R. Walke , S. R. Julian, P. Mon houx, G. G. Lonza ich, A.
Huxley, I. Sheikin, D. B ai hwai e and J. Flouque . Na u e 406, 587 (2000).
138 K. Ishida, Y. Iha a, Y. Maeno, C. Michioka, M. Ka o, K. Yoshimu a, K. Takada,
T. Sasaki, H. Saku ai and E. Takayama-Mu omachi, J. Phys. Soc. Japan 72, 3041
(2003); Y. Iha a, K. Ishida, C. Michioka, M. Ka o, K. Yoshimu a, H. Saku ai and E.
Takayama-Mu omachi. J. Phys. Soc. Japan 73, 2963 (2004).
P oximi y o a QPT
85
e ealed an uncon en ional o m o a supe conduc ing spin- iple phase in
NaxCoO2•yH2O, as well as he exis ence o s ong FM spin luc ua ions in he
me allic coun e pa , con i med by inelas ic neu on sca e ing139,140.
Howe e , a solid e idence o any pa icula pai ing s a e emains lacking in
NaxCoO2•yH2O, al hough mos o he p oposals ound in he li e a u e ha e
been excluded a e es ing hem agains he well es ablished p ope ies o
he compound.141
Ha ing in mind ha unde s anding supe conduc i i y equi es a deep
knowledge o he elec onic p ecu so om which i o ms, we ha e
pe o med a de ailed magne ic s udy o he wa e - ee me allic p ecu so s a
ep esen a i e composi ions o he NaxCoO2 se ies. Fo high Na+ con en
(x0.69, when supe conduc i i y is ne e achie ed unde hyd a ion) we ha e
ound ha he empe a u e independen magne ic suscep ibili y, (T,H), in he
Fe mi liquid (FL) s a e is eno malized a low empe a u e. This beha io is
consis en wi h p e ious esis i i y142 and speci ic hea 143,144 esul s, which
suppo he exis ence o a s ongly co ela ed s a e a high Na+ con en , wi h
m* s ongly ield dependen . On he o he hand, a x0.36, nea he op imum
alue o supe conduc i i y, s ong magne ic luc ua ions in oduce a new
phase wi h non-FL beha io and spin-glass elaxa ion. A de ailed scaling
analysis o he low empe a u e (T, H) sugges s ha hese e ec s a e due
o he p oximi y o me allic NaxCoO2 o a magne ic QPT.
Samples wi h composi ions NaxCoO2, x0.69 and x0.36 we e
syn hesized as desc ibed in Chap e 1. All he esul s discussed he e
co espond o single-phase ma e ials, whe e long- ime X- ay scans e ealed
he comple e absence o any seconda y phase; we paid special a en ion o
a oid any ace o Co3O4. The peaks a e e y na ow, which ensu es a good
c ys allini y, and he la ice pa ame e s a e in acco dance wi h he
li e a u e145.
139 A. T. Boo h oyd, R. Coldea, D. A. Tennan , D. P abhaka an, L. M. Helme and C.
D. F os . Phys. Re . Le . 92, 197201 (2004).
140 L. M. Helme, A. T. Boo h oyd, R. Coldea, D. P abhaka an, D. A. Tennan , A.
Hiess and J. Kulda. Phys. Re . Le . 94, 157206 (2005).
141 I. I. Mazin and M. D. Johannes. Na u e Physics 1, 91 (2005).
142 S. Y. Li, L. Taille e , D. G. Haw ho n, M. A. Tana a , J. Paglione, M. Su he land,
R. W. Hill, C. H. Wang and X. H. Chen. Phys. Re . Le . 93, 56401 (2004).
143 M. B ühwile , B. Ba logg, S. M. Kazako and J. Ka pinski. Cond-ma /0309311.
144 F. C. Chou, J. H. Cho, P. A. Lee, E. T. Abel, K. Ma an and Y. S. Lee. Phys. Re .
Le . 92, 157004 (2004).
145 C. Fouassie , G. Ma ejka, J. M. Reau and P. Hagenmulle . J. Solid S a e Chem. 6, 532
(1973).
Chap e 3
86
10 20 30 40 50 60 70 80
0
5000
10000
15000
20000
10 20 30 40 50 60 70 80
15.0 15.5 16.0 16.5 17.0
x=0.69
I (a.u.)
2
x=0.36
I (a.u.)
2º
x=0.69
x=0.36
2º
Figu e 1: X- ay di ac ion pa e ns o wo samples wi h x=0.36 and x=0.69.
Main panel: Expe imen al do s a e ma ked by c osses and he ed line is a lebail
i ing wi h he p og am Rie ica, using he space g oup P63/mmc. In bo h Na+-
composi ions, all he peaks belong o his phase. The e ical blue lines ma k he
posi ions o he e lec ions expec ed on he basis o a P63/mmc space g oup. The le
inse shows he e olu ion o he (002) e lec ion a e Na+-dein e cala ion, which
indica es he expec ed inc ease in he in e laye dis ance.
I is impo an o ema k ha he ollowing esul s p esen ed he e o
x0.36 co espond o samples ha we ha e e i ied o become
supe conduc i e a e wa e inse ion. Supe conduc ing samples we e
ob ained by s i ing NaxCoO2, x0.36, in wa e o wo days a oom
empe a u e. Only hose ha showed he non-FL phase a low empe a u e
ha will be discussed in he ollowing pages became supe conduc i e a e
wa e imme sion. He e is an example in Figu e 2.
P oximi y o a QPT
93
The mos p obable scena io is ha he spin pola iza ion achie ed
wi h an applied magne ic ield a enua es he ampli ude o he magne ic
luc ua ions and es o es p og essi ely he no mal FL beha io . F om he
minimum in he de i a i e o

(T) we can de e mine he exis ence o an
in lexion poin in he suscep ibili y cu e. This would ma k he la ening o
he cu e and hence would poin o he eco e y o cons an FL beha iou .
Figu e 7 shows he de i a i e o he empe a u e-dependen suscep ibili y
below 20 K a di e en applied magne ic ields. This esul is consis en wi h
he obse a ion o an anomalously la ge AT2 coe icien in he elec ical
esis i i y142 o a sublinea empe a u e a ia ion o he speci ic hea 143,144,
s ongly ield dependen .
Figu e 7: De i a i e o he

s. T cu es a di e en applied magne ic ields
(H=1, 3 and 5T) in he x=0.69 sample.
In Figu e 8,

(T) is shown o x=0.36 a wo di e en ields. The
beha iou is comple ely di e en o he sample wi h high Na+ con en . A clea
i e e sibili y be ween he ze o- ield and ield cooling (ZFC-FC)
magne iza ion cu es shows up below Ti 12 K, which is supp essed a
10
-0.2
-0.1
0.0
Na0.69CoO2
H= 1 T
H= 3 T
H= 5 T
dM/dT
Tempe a u e (K)

Chap e 3
94
mode a ely la ge ields. Figu e 9 shows he disappea eance o his
i e e sibili y in he ZFC magne iza ion cu e as H inc eases om 0.05 T o
0.1 T. The exis ence o he i e e sibili y, i s ield dependence, and he
loga i hmic a ia ion o he elaxa ion a e below Ti (Figu e 10) would
sugges he eme gence o a new phase wi h spin-glass (SG) like dynamics
a low empe a u es, and o low alues o x. This has been obse ed in
o he samples and is ep esen a i e o composi ions a ound x~0.3-0.4. In he
SG phase,

(T) emains s ongly empe a u e-dependen down o he lowes
empe a u e p obed (1.8 K), no eco e ing he cons an beha io . The
deg ee o diso de o us a ion in he sys em mus be absolu ely
compa able be ween samples wi h di e en doping le els, so we hink ha
he SG phase a x=0.36 is an e ec o he unde lying mechanism ha
in oduces s ong quasipa icle co ela ions. One possibili y o he
b eakdown o he FL desc ip ion in i ine an pa amagne s is he p oximi y o
a QPT. In some cases, he p oximi y o he QPT only eno malizes he
sca e ing a e o he e ec i e mass o he quasipa icles, bu he desc ip ion
in e ms o a FL model is s ill applicable, as i happens a x=0.69.
Figu e 8: ZFC magne ic suscep ibili y o x=0.36 a wo di e en magne ic
ields. The do ed line is he Pauli suscep ibili y calcula ed om high empe a u e
M(H) iso he ms. Uppe inse : De ail o he ZFC-FC i e e sibili y isible a low ields
below

12 K.
0 5 10 15 20
3.0x10-3
6.0x10-3
9.0x10-3
0 100 200 300
0.0
2.0x10-3
4.0x10-3
6.0x10-3 FC
ZFC
H=0.05 T
 (emu.mol-1.Oe-1)
Tempe a u e (K)
Na0.36CoO2
H=1 T
H=0.05 T
Pauli
 (emu.mol-1.Oe-1)
Tempe a u e (K)
P oximi y o a QPT
95
0 5 10 15 20
1
2
3H =0.1T
H =0.05T
M (emu.mol-1)
Tempe a u e (K)
Figu e 9: ZFC magne iza ion cu e o x=0.36 a low empe a u e a wo
di e en magne ic ields, H=0.05 and 0.1 T.
Figu e 10: Relaxa ion a e o he no malized magne iza ion o x=0.36.
Abo e Ti , he elaxa ion depa s om he slow loga i hmic beha io obse ed a low
empe a u es.
102103104
1
4 K
17 K
13 K
M/M( =0)
ime (s)
Chap e 3
96
The expe imen al signa u es o he p oximi y o a second-o de
phase ansi ion a e he di e gen cha ac e o he suscep ibili y, and o e
all, i s scaling. In Figu e 11 we show he di e gence o

(T) as T0 K, and
he p og essi e eco e y o he cons an beha io as H inc eases. Below
5 K, he low empe a u e suscep ibili y shows a powe -law empe a u e
dependence o he o m



T eq. [1]
wi h  s ongly ield dependen . The alues o  go om ~0.30 a low ields
o close o ze o a high ields (Figu e 12), which indica es he eco e y o he
FL s a e a low empe a u es, due o he ield supp ession o spin
luc ua ions.
Figu e 11: The di e gen cha ac e o he low ield (T

0) i s o equa ion
[1] below

5 K (ma ked by he a ow) o x=0.36. A high ields he suscep ibili y
eco e s FL beha iou , wi h a dec easing cons an alue o (T

0) as H inc eases.
01234
5
5
1.38 10-3
9.17 10-3
10
2
Tempe a u e (K)
0.01 T
H (T)
5 T

(emu.mol-1.Oe-1)
P oximi y o a QPT
97
012345
0.0
0.1
0.2
0.3

H ( T )
Figu e 12: Values o

ob ained om i ings o he M(T) cu es o equa ion
[1] below ≈5 K a di e en applied magne ic ields om 0.01 T o 5 T. (Dashed line is
a guide o he eye). The alue o

goes asim o ically o ze o a high ield.
Ano he indi ec e idence o he p oximi y o Na0.36CoO2 o a
magne ic phase ansi ion comes om he beha iou o he 3; a he icini y
o a phase ansi ion non-linea magne iza ion becomes ele an and he
highe o de e ms o he magne iza ion mus be e ained in he equa ion o
s a e. In he pa amagne ic ange M is an odd unc ion o H, so
M = 1H + 3 H3 + 5 H5 +… eq. [2]
whe e he hi d-o de suscep ibili y, 3, is no mally quo ed as he nonlinea
suscep ibili y. In a mean ield app oxima ion we can ge some in o ma ion
Chap e 3
98
abou he beha io o he linea and cubic e ms o he suscep ibili y when
he c i ical empe a u e is app oached om abo e153
4
3
1
1
1
1
1



















C
C
T
T
T
T


eq. [3]
Equa ion [3] gi es a posi i e di e gence o 1 and a nega i e
di e gence o 3 abo e he Cu ie poin . A simila ea men gi es a posi i e
di e gence o 3 as T→TC om below. This p o ides an accu a e me hod o
de e mine he ansi ion empe a u e o a e omagne ic-pa amagne ic
ansi ion. Howe e , and in spi e o he c i ical beha io o 3 is commonly
used o cha ac e ize he spin-glass ansi ion154, i has been a ely applied
o he cha ac e iza ion o con en ional second o de FM-PM phase
ansi ions.153
We ha e i ed he M(H) cu es o se e al composi ions o NaxCoO2
in he in e al 0.33≤x≤0.69 e e y deg ee below 25 K down o 1.8 K o ex ac

3(T), and he esul s a e plo ed in Figu e 13 o wo ep esen a i e
composi ions. The e is a clea depa u e om he high empe a u e alue
(3→0) and a nega i e di e gence o 3 below 15 K. The nonlinea
suscep ibili y shows he ypical signa u es o a sys em jus abo e he
ansi ion empe a u e om a magne ically o de ed s a e.
We should emind he e ha he possibili y o a sa u a ing
pa amagne ic impu i y as he sou ce o he non-linea suscep ibili y has been
disca ded be o e.
An impo an poin is whe he his magne ic ansi ion occu s a ze o
kel in o i i akes place a low bu ini e empe a u e. Al hough ou
expe imen s canno eassu e he absence o he ansi ion below 1.8 K, 3
does no show any sign o ounding s ill a his empe a u e, which indica es
ha we a e s ill a om he c i ical poin .
153 S. Nai and A. Bane jee. Phys. Re . B 68, 94408 (2003).
154 Spin Glasses and Random Fields. Ed. by A. P. Young, Wo ld Scien i ic (1998).

P oximi y o a QPT
99
Figu e 13: Tempe a u e dependence o he nonlinea suscep ibili y as
T→0 K o x

0.69 (open ci cles) and x

0.36 (solid ci cles). Simila beha iou was
obse ed in he whole ange o x checked (be ween 0.3 and 0.69).
In he con en ional heo y o me als close o a magne ic QCP, long-
wa eleng h luc ua ions (q0) o he o de pa ame e (pa amagnons) a e
he ele an low-ene gy magne ic exci a ions. Fo 2D magne ic sys ems
close o a QPT Si e al155 p edic ed he p esence o spa ially localized
magne ic luc ua ions (q) coexis ing wi h he spa ially ex ended ones
(q0). In his scena io close o a second o de QPT, hype scaling
ela ionships ensu e ha he ollowing scaling law mus be obeyed by he
singula pa o he suscep ibili y, once he educed empe a u e has been
eplaced by T o accoun o he 0 K ansi ion empe a u e,156,157
155 Q. Si, S. Rabello, K. Inge sen e and J. L. Smi h. Na u e 413, 804 (2001).
156 N. Golden eld in “Lec u es on phase ansi ions and he eno maliza ion g oup”, F on ie s
in Physics Vol 85, Addison-Wesley, NY 1992.
157 G. R. S ewa . Re . Mod. Phys. 73, 797 (2001).
0 5 10 15 20 25
-4
-3
-2
-1
0
x=0.69
x=0.36
3 (a.u.)
Tempe a u e (K)
Chap e 3
100









T
H
T
H
M eq. [4]
The esul o he scaling is shown in Figu e 14. The bes i ings we e
ob ained wi h he alues

=0.31(1) and

=1.12(3). The alue o

is
consis en wi h he i ing o he low- ield suscep ibili y o equa ion [1], and
bo h

and

a e in e nally consis en (1+

/2=

) wi hin he e o . Fo a ue
FL, no such scaling beha io should be obse able as i s me e p esence
shows ha he e is an ene gy scale o he han Fe mi ene gy ha domina es
i s he modynamic p ope ies.
100 1000
1.8x10-6
3.2x10-6
1.8 K
2.0 K
2.2 K
2.5 K
3.0 K
3.5 K
5.0 K
7.0 K

= 0.31 (1)

= 1.12 (3)
(M/H)T-
(H/T)
Figu e 14: Scaling o he di e gen low empe a u e suscep ibili y o
x=0.36. The da a depa s om he low empe a u e scaling abo e

4 K, i.e. as he
limi o he di e gen beha io in

(T

0) is app oached om below (see Fig. 11). The
5 K and 7 K cu es a e shown as an example o de ia ion o he scaling a highe
empe a u es.
P oximi y o a QPT
101
To disca d comple ely he p oximi y o a magne ic phase ansi ion a
e y low empe a u e bu abo e ze o, measu emen s a he milikel in ange
a e desi able.
As discussed be o e, Li e al.142 ela ed he anomalously high alue
o he Kadowaki-Woods a io in Na0.7CoO2 (and i s supp ession by a
magne ic ield) o he p oximi y o a magne ic QPT. This scena io is now
suppo ed by he i ing o he da a o equa ions [1] and [4] shown in Figu es
11 and 14.
A undamen al issue ha has o be explo ed is he o igin o he SG
phase and he na u e o he magne ic luc ua ions a low empe a u e, as
well as i s ela ionship wi h he appea ance o supe conduc i i y. NaxCoO2 is
an i ine an pa amagne no mally conside ed as a us a ed an i e omagne
due o he iangula a angemen o he Co a oms in he close-packed CoO2
planes158. Howe e , acco ding o Goodenough,159 a simple ex ension o he
ca ion-ca ion supe exchange spin co ela ions o localized elec ons o he
low-spin oc ahed al-si e Co- 2g i ine an elec ons would p edic he exis ence
o an i ine an FM g ound s a e o his ma e ial. E en pa ial spli ing o he
h ee old-degene a e 2g o bi als in o an a1T and wo old-degene a e eT
o bi als by he igonal ield, will keep he same p edic ion. The O:2p-Co:eg
ehyb idiza ion p ocess p oposed by Ma iane i e al,160 would in oduce he
possibili y o a Zene -like double exchange mechanism, also esul ing in a
e omagne ic, me allic g ound s a e like in S CoO3 o S 2CoO4.161,162 The
con ac ion o he a-axis on Na+ emo al, as well as he almos cons an
cobal alence,163 ensu es ha ehyb idiza ion is indeed playing a ole in he
ma e ial. These a gumen s a e in clea ag eemen wi h NMR138 and neu on
sca e ing140 expe imen s which demons a e he exis ence o s ong FM
luc ua ions. Fluc ua ions can be he sou ce o a sho - ange pa ial o de ing
o he conduc ion elec ons, as i was obse ed in he high-p essu e non-FL
phase o MnSi.164 The coexis ence o pa ially o de ed egions (supe -spins),
was p oposed o be esponsible o he non-FL and SG cha ac e is ics o
158 N. P. Ong and R. J. Ca a. Science 305, 52, (2004).
159 J. B. Goodenough, in Magne ism and he Chemical Bond, John Willey & Sons, New Yo k
(1963).
160 C. A. Ma iane i, G. Ko lia and G. Cede . Phys. Re . Le . 92, 196405 (2004).
161 R. H. Po ze, G. A. Sawa zky and M. Abba e. Phys. Re . B 51, 11501 (1995).
162 J. Ma suno, Y. Okimo o, Z. Fang, X. Z. Yu, Y. Ma sui, N. Nagaosa, M. Kawasaki and Y.
Toku a. Phys. Re . Le . 93, 167202 (2004).
163 M. Bañob e-López, F. Ri adulla, R. Caudillo, M. A. López-Quin ela, J. Ri as and J. B.
Goodenough. Chem. Ma e , 17, 1965 (2005).
164 C. P leide e , D. Reznik, L. Pin scho ius, H. . Löhneysen, M. Ga s and A. Rosch.
Na u e 427, 227 (2004).
Chap e 3
102
many hea y- e mions,147 in which a di e gence o he ype

(T)  C(T)/T 
T-1+

was p edic ed.165 This elec onically inhomogeneous s a e is
cha ac e ized by an exponen <1, and is equi alen o he G i i hs phase o
dilu e magne ic sys ems.166 Reanalysis o ou da a ollowing his a gumen
leads o 0.7 om he i ing o he di e gen low- empe a u e suscep ibili y
a low applied magne ic ields (Figu e 15).
012345
0.6
0.7
0.8
0.9
1.0

H ( T )
Figu e 15: Values o

ob ained om i ings o he

(T)cu es o he ela ion

(T)

C(T)/T

T-1+

below ≈5 K a di e en applied magne ic ields om 0.01 T o
5 T. (Dashed line is a guide o he eye).
The esul s o he elec onic hea capaci y,

C(T)/T, a e shown in
Figu e 16. To ob ain he elec onic pa , a la ice con ibu ion was i ed o

3T3+

5T5, and sub ac ed om he o al speci ic hea . F om ou speci ic hea
measu emen s, 0.4(2). This alue is e y much in luenced by he
empe a u e ange aken o i he la ice con ibu ion (

3 and

5 change
conside ably wi h he ange i ed, be ween 0.15-0.30 mJ.mol-1.K-4 and
210-3-710-4 mJ.mol-1.K-6, espec i ely). Ve y impo an is ha he elec onic
componen is supp essed by a magne ic ield below ~5 K, which is
app oxima ely he same empe a u e below which he low ield

(T) di e ges
165 A. H. Cas o Ne o, G. Cas illa and B. A. Jones. Phys. Re . Le . 81, 3531 (1998).
166 R. B. G i i hs. Phys. Re . Le . 23, 17 (1969).
Role o wa e in SC
he con igu a ion o he elec onic p ope ies o his sys em170. Also, i is no
clea whe he H2O, H3O+ o bo h a e playing he decissi e ole o he
appea ance o supe conduc i i y in hyd a ed NaxCoO2.
On o he hand, s ong magne ic luc ua ions could be impo an in
such geome y and play a ole in he occu ence o supe conduc i i y171,172
In es iga ions o cla i y i he supe conduc ing s a e o Na+ is con en ional
(BCS) o no , ha e been ca ied ou om bo h heo e ical and expe imen al
sides. Al hough a de ini i e conclusion has no been eached ye , mos
au ho s op ed o an uncon en ional mechanism o supe conduc i i y, in
which he magne ic luc ua ions o igina ed in he adjacen magne ic o de ed
phase (x~0.5) would be in ense enough o d i e he sys em SC.
Howe e , om ou poin o iew, o he basic poin s ha e no been
s ill elucida ed, and could play a ole in he ocu ence o supe conduc i i y in
NaxCoO2. Mainly, we can lis he ollowing open ques ions:
1. Wha is he ole o in e cala ed wa e in he achie emen o
supe conduc i i y in his sys em?
2. I is eally impo an he cha ge o de ed phase a x=0.5, e y
close in composi ion o he supe conduc ing hos ?
3. Can NaxCoO2 s ill be conside ed as a 2D sys em a e wa e
in e cala ion? Does i beha e like a 2D sys em om he
elec onic poin o iew?
Ob iously, in e cala ed wa e in o he galle ies be ween CoO6 shee s
leads o a subs an ial inc ease o he in e laye dis ance, inc easing he 2D
cha ac e o he sys em (a leas s uc u ally), which is belie ed o play an
impo an ole in induc ing supe conduc i i y. The supe conduc i e hyd a ed
phase co esponds o ha one wi h an amoun o wa e o y=1.3 molecules
pe uni o mula H2O molecules coo dina e o he Na+ ions and o m wo
wa e laye s in he galle y sandwiching he Na+ plane, ans o ming he
pa en oxide in o a bilaye -hyd a e (BLH). On he o he hand, he mos
common pa ially hyd a ed phases con ain a ound y=0.6 wa e molecules
170 M. Roge , D. J. P. Mo is, D. A. Tennan , M. J. Gu mann, J. P. Go , J.-U. Ho mann, R.
Feye he m, E. Dudzik, D. P abhaka an, A. T. Boo h oyd, N. Shannon, B. Lake and P. P.
Deen. Na u e 445, 631 (2007).
171 N. D. Ma hu , F. M. G osche, S. R. Julian, I. R. Walke , D. M. F eye, R. K. W.
Haselwimme and G. G. Lonza ich. Na u e 394, 39 (1998).
172 P. Mon houx, D. Pines and G. G. Lonza ich. Na u e 450, 1177 (2007).

Chap e 4
110
pe uni o mula, in which H2O molecules occupy posi ions in he same laye
o Na+ ions, o ming a monolaye -hyd a e (MLH)173.
H2O
Na
-H2O N Na/H2O
+H2O
BLH-NaxCoO2 MLH-NaxCoO2
Figu e 4.2: S uc u al d awings o (le ) BLH-NaxCoO2 and ( igh ) MLH-
NaxCoO2. (F om Re . 6).
Also o he pa ially hyd a ed and no supe conduc i e phases wi h
smalle wa e con en , such as y=0.3 and y=0.1, ha e been
epo ed174,175,176,177. Al hough di ec wa e con en is e y di icul o be
measu ed, i is ansla ed in di e en in e laye dis ances178,179,180,181. I
173 K. Takada, H. Saku ai, E. Takayama-Mu omachi, F. Izumi, R. A. Dilanian and T. Sasaki.
J.Solid S a e Chem. 177, 372 (2004).
174 D. P. Chen, H. C. Chen, A. Maljuk, A. Kulako , H. Zhang, P. Lemmens and C. T. Lin.
Phys. Re . B 70, 024506 (2004).
175 M. L. Foo, R. E. Schaak, V. L. Mille , T. Klimczuk, N. S. Rogado, Y. Wang, G. C. Lau,C.
C aley, H. W. Zandbe gen, N. P. O g and R. J. Ca a. Solid S a e Commun. 127, 33 (2003).
176 J. Cmaidalka, A. Baikalo , Y. Y. Xue, R. L. Meng and C. W. Chu. Physica C 403, 125
(2004).
177 C. T. Lin, D. P. Chen, P. Lemmens, X. N. Zhang, A. Maljuk and P. X. Zhang. Jou nal o
C ys al G ow h 275, 606 (2005).
178 K. Takada, H. Saku ai, E. Takayama-Mu omachi, F. Izumi, R. A. Dilanian, and T. Sasaki,
Phys. C 14, 412 (2004).
Role o wa e in SC
sugges s ha he sepa a ion be ween CoO2 laye s appea s o be c i ical in
ob aining supe conduc i i y, since i is only achie ed o a hyd a ed phase
wi h c~19.8 Å, while in e media e hyd a ed phases wi h c~12 Å and
anhyd ous phases wi h e en smalle CoO2-CoO2 in e laye spacing a e no
supe conduc ing173,175. The impo ance o a educed in e laye coupling o
s abilizing he supe conduc ing g ound s a e in his compound is e idenced
by he hyd os a ic p essu e dependence o Tc, whe e a supp ession o he
supe conduc ing s a e akes place a high p essu e as a consequence o a
signi ican educ ion o he c- axis182 (Figu e 4.3). In ac , synch o on
measu emen s wi h p essu e in Na~0.8CoO2 e idenced ha he
comp essibili y in he c-di ec ion is much highe han in he a-di ec ion (see
Chap e 2).
Figu e 4.3: Supe conduc ing ansi ion empe a u e (Tc) dependence o he
applied hyd os a ic p essu e (p). Tc was es ima ed om he onse o he diamagne ic
signal. Fill squa e ep esen s he eco e y o he ini ial supe conduc ing p ope ies as
highes p essu e is eleased. (F om Re . 15).
179 K. Ishida, Y. Iha a, H. Takeya, C. Michioca, K. Yoshimu a, K. Takada, T. Sasaki, H.
Saku ai and E. Takayama-Mu omachi. Phys. C 460-462, 192 (2007).
180 H. Saku ai, K. Takada, F. Izumi, R. A. Dilanian, T. Sasaki and E. Takayama-Mu omachi.
Phys. C 412-414, 182 (2004).
181 C. J. Milne, D. N. A gy iou, A. Chemseddine, N. Aliouane, J. Vei a, S. Landsgesell and
D. Albe . Phys. Re . Le . 93, 247007 (2004).
182 B. Lo enz, J. Cmaidalka, R. L. Meng and C. W. Chu. Phys. Re . B 68, 132504 (2003).
Chap e 4
112
Al hough he in e laye dis ance inc eases as sodium con en
dec eases and s ill mo e a e wa e in e cala ion, does i beha e like a 2D
sys em also om an elec onic poin o iew? Elec ical esis ance
measu emen s in single c ys als om Wang e al183 show a dimensional
c osso e om 2D o 3D wi h dec easing concen a ion o Na+, opposi e o
wha we expec ed o an inc ease o he in e laye dis ance be ween he
CoO6 shee s because o a lowe sodium con en . In his sense, he
beha iou is e y simila o wha happens in in e cala ed g aphi e184, in which
2D o 3D ansi ion has been ob ained a e in e cala ion. Reco e y o he 2D
cha ac e akes place as wa e is in e cala ed in o he s uc ue a e
hyd a ion p ocess. So, he ac ha he ca ie densi y in he CoO6 is kep
unchanged in bo h BLH and MLH phases s ongly sugges s ha only an
op imum le el o ca ie doping in o he CoO6 laye s is no enough o
inducing he supe conduc i i y, and also ha an op imum in e laye
sepa a ion be ween he CoO6 laye s is indispensable o he
supe conduc i i y.
Bu he mos impo an and maybe he mos con o e sial ques ion is
he dependence o Tc wi h Na+ doping. I is well know he exis ence o a
ce ain ange o Na+ composi ion whe e he supe conduc i i y occu s in his
ma e ial (0.3x0.45), bu he dependence o Tc as a unc ion o Na+ doping
inside his in e al emains s ill unclea . The i s supe conduc ing phase
diag am o he hyd a ed supe conduc o Na0.3CoO2•1.3H2O has been
p oposed by Schaak e al185 (Figu e 4.4).
183 C. H. Wang, X. H. Chen, J. L. Luo, G. T. Liu, X. X. Lu, H. T. Zhang, G. Y. Wang, X. G.
Luo and N. L. Wang. Phys. Re . B 71, 224515 (2005).
184 T. E. Welle , M. Elle by, S. S. Saxena, R. P. Smi h and N. T. Skippe . Na u e Physics 1,
39 (2005).
185 R. E. Schaak, T. Klimczuk, M. L. Foo and R. J. Ca a. Na u e 424, 527 (2003).
Role o wa e in SC
Figu e 4.4: Supe conduc ing phase diag am o NaxCoO2•1.3H2O. Main
panel: Tc as a unc ion o x as de e mined om he AC suscep ibili y measu emen s.
(F om Re . 18).
These expe imen al esul s show a s ong co ela ion be ween Tc
and he Na+ con en o he samples. Bulk supe conduc i i y wi h Tc>2 K has
been epo ed o exis o e a e y na ow ange o Na+ composi ions,
app oxima ely 1/4x1/3, whe e i is es ablished an op imal chemical doping
le el o supe conduc i i y wi h Tc≈4.5 K a ound x=0.3. And Tc dec eases o
bo h unde doped and o e doped ma e ials. This “dome-like” dependence o
supe conduc ing ansi ion empe a u e wi h doping shows he same end
as in cup a e supe conduc o s. Fo his eason, i has been hough ha he
o igin o SC in his ma e ial could ha e some poin s in common wi h he
supe conduc i i y in cup a es.
To explain his dependence Baska an e al186 p esen ed a heo y
based on he idea ha his compound would gi e di e en o de ed phases a
he Na+ composi ions o x=1/4 and x=1/3 espec i ely. They a gued ha
cha ge o de ing a hese doping le els in he CoO2 laye s would be a
compe i o o supe conduc i i y leading o a s ong dec ease in Tc.
The e o e, he highes Tc would be achie ed be ween hese speci ic
composi ions.
Howe e , expe imen al esul s om Chen e al174 disag ee wi h he
supe conduc ing “dome” o Tc(x) by Shaak e al185:
186 G. Baska an. Phys. Re . Le . 91, 097003 (2003).
Chap e 4
114
1. No a ia ion in Tc as a unc ion o sodium con en in he ange
0.22<x<0.47 is ound (Figu e 4.5). Ou o his doping le el
in e al no supe conduc ing ansi ion has been de ec ed.
2. The supe conduc ing phase app oaches o he phase line whe e
he non-hyd a ed Na0.5CoO2 shows a me al-insula o
ansi ion187. We will see om ou esul s in he nex chap e ha
his ac could be mo e impo an han p e iously hough .
Figu e 4.5: Supe conduc ing ansi ion empe a u e, Tc, as a unc ion o
sodium doping, x, in NaxCoO2•1.3 H2O. The dashed line is a guide o he eye. The
dashed ba ma ks he me al-insula o ansi ion obse ed in non-hyd a ed Na0.5CoO2.
(F om Re . 20)
Also Milne e al181 ha e ound ha Tc does no change signi ican ly
wi h x o e he egion 0.28<x<0.37. In he supe conduc ing phase diag am
de e mined om hei measu emen s, Figu e 4.6 (a), Tc di e s om 4.3 K o
4.8 K in ha Na+ composi ion ange, which is e y close o he op imum
alue epo ed by Shaak e al o his ma e ial185.
All pape s ha ha e appea ed a e he epo o Schaak e al185 on
physical p ope ies and heo e ical calcula ions ha e been based on he Co
oxida ion s a e o ca. 3.7+, which is deduced di ec ly om he Na+ con en
187 Q. Huang, M. L. Foo, J. W. Lynn, H. W. Zandbe gen, G Lawes, YayuWang, B. H. Toby,
A. P. Rami ez, N. P. Ong and R J Ca a. J. Phys.: Condens. Ma e 16, 5803 (2004).

Role o wa e in SC
(x~0.3). Bu , as we ha e al eady shown in Chap e 1 and also om o he
wo ks, he Co alence s a e does no a y no ably in he sodium composi ion
ange whe e SC is ob ained, he elec onic band illing is he esul o a
complex Co( 2g):O(2p) hib idiza ion plus he 2g spli ing. Tha makes ha
ep esen a ion o Tc as a unc ion o he sodium con en no o ally co ec ,
since he oxida ion s a e o Co is lowe ha he expec ed only om Na+
con en 174,181,188,189 (see Figu e 1.9 in Chap e 1).
On he o he hand, Milne e al181 epo ed a signi ican disc epancy
be ween he expec ed alence o Co based on Na+ con en and he alues
ob ained om edox i a ion, d awing a mo e co ec ep esen a ion whe e
Tc is plo ed agains Co o mal alence and no as a unc ion o Na+ con en .
Figu e 4.6 (b) shows his ep esen a ion in compa ison wi h ha one
ob ained om he da a o Schaak e al185.
Figu e 4.6: (a) Tc as a unc ion o Na+ con en , x, in NaxCoO2•1.3 H2O. (b)
Tc as a unc ion o he Co alence s a e ( igh ) ob ained om edox i a ion in
compa ison wi h (le ) plo de i ed om Shaak’s da a185. (F om Re . 14).
In his supe conduc ing phase diag am hey ind ha op imal Tc is
eached o e he egion o cobal alence 3.24-3.35 ( ha will co espond o
an x~0.6), while Tc dec eases o alues o <3 K o Co alence s a es
>3.35+. They also demons a ed ha he occu ence o supe conduc i i y is
s ongly linked o he dimensionali y o he s uc u e. They obse ed ha he
c/a a io inc eases as Co oxida ion s a e is uned in o he op imal Tc egion.
188 M. Ka ppinen, I. Asako, T. Mo ohashi and I. Yamauchi. Phys. Re . B 71, 092105 (2005).
189 H. Saku ai, S. Takenouchi, N. Tsujii and E. Takayama-Mu omachi. J. Phys. Soc. Jpn. 73,
2081 (2004).
Chap e 4
116
S uc u al cha ac e iza ion o he hyd a ed supe conduc ing cobal
oxide phase has been ca ied ou by se e al g oups169,190,191,192. Bu mos o
hem conside ed jus he Na+ ions and H2O molecules as he gues species.
Tha means ha he o ma ion p ocess o he supe conduc ing phase was
hough o in ol e jus he oxida i e ex ac ion o Na+ ions and he opo ac ic
inse ion o H2O molecules. Howe e , he ac ual achi emen o
supe conduc i i y in his sys em is mo e complica ed and o he chemical
species and mo e complex eac ions ake place. In ac , he s ochiome y o
his supe conduc o has been again e ised by Takada e al190 and mo e
ecen ly Saku ai e al193. They concluded ha H3O+ ions a e necessa ily
inse ed subs i u ing pa ially he Na+ ions be ween wo CoO2 laye s o
compensa e he cha ge, in addi ion o wa e molecules. This opo ac ic ion-
exchange o Na+ ions by H3O+ mechanism main ains a cons an Co alence
and is s ongly suppo ed by hei s uc u al s udies based on Raman
spec oscopy and X- ay powde di ac ion, which also sugges ed ha he
oxonium ions occupy he same c ys allog aphic si es as Na+ ions. Tha
means ha gues species in he new s uc u e model a e no only Na+ ions
and H2O molecules bu also H3O+ ions, gi ing a composi ion o he
supe conduc ing phase o Na0.337(H3O)0.234CoO2•yH2O ins ead o he
p e ious Na0.3CoO2•yH2O. A e wa ds, ha was also con i med by Milne e
al181, indica ing ha Na+ subs oichiome y alone does no con ol he
elec onic doping o hese ma e ials, H3O+ playing an impo an ole also.
Howe e , none o hese ecen wo ks conside ed he possibili y o a
p esence o oxygen acancies in he chemical composi ion o he
supe conduc ing phase (al eady p opposed by Molenda e al 194 in 1989).
P e iously, Ri adulla e al195 discussed ha possibili y in he
supe conduc ing hyd a ed phase and hey p opossed a model whe e, i
exis ing, hey would be e illed by he O2- heads o he in e cala ed wa e
molecules, leading o a c ea ion o H+ p o ons in o he s uc u e. La e , ou
esul s and hose ones om o he au ho s196,197,198 con i med he p esence o
190 K. Takada, K. Fukuda, M. Osada, I. Nakai, F. Izumi, R. A. Dilanian, K. Ka o, M. Taka a,
H. Saku ai, E. Takayama-Mu omachi and T. Sasaki. J. Ma e . Chem. 14, 1448 (2004).
191 J. W. Lynn, Q. Huang, C. M. B own, V. L. Mille , M. L. Foo, R. E. Schaak, C. Y. Jones,
E. A. Mackey and R. J. Ca a. Phys. Re . B 68, 214516 (2003).
192 J. D. Jo gensen, M. A dee , D. G. Hinks, J. C. Bu ley and S. Sho . Phys. Re . B 68,
214517 (2003).
193 H. Saku ai, M. Osada and E. Takayama-Mu omachi. Chem. Ma e . 19, 6073 (2007).
194 J. Molenda, C. Delmas, P. Do do and A. S oklosa. Solid S a e Ionics 12, 473 (1989).
195 F. Ri adulla, J.-S. Zhou and J. B. Goodenough. Phys. Re . B 68, 75108 (2003).
196 M. Ka ppinen, I. Asako, T. Mo ohashi and H. Yamauchi. Chem. Ma e . 16, 1693 (2004).
197 Mo i a e al. J. Solid S a e Chem. 177, 3150 (2004).
Role o wa e in SC
oxygen acancies in he sys em below x<0.7, which inc ease as Na+ con en
dec eases. Bu , e en hough a lowe han expec ed Co alence s a e was
also ound by o he au ho s in bo h non-supe conduc ing and
supe conduc ing phases, in he case o he supe conduc ing phase hey
could no dis inguish which e ec ook place o aise he cha ge balance: i
oxygen acancies o o ma ion o ex a H3O+.
Figu e 4.7 shows he X- ay di ac ion pa e ns o he unhyd a ed
Na+ dein e cala ed p ecu so and he supe conduc ing phase a e hyd a ion.
Bo h o hem we e single phase wi hou he p esence o any impu i y.
Howe e , he pa e n co esponding o he hyd a ed sample shows a
complex mix u e cons i u ed by bo h unhyd a ed and hyd a ed phases wi h
di e en amoun s o H2O pe o mule uni , as epo ed by o he au ho s174.
This ac leads o an o e lapping o he e lexions om di e en phases and
made di icul hei indexing. Fo his eason he e inmen o he s uc u e
could no be ca ied ou in he hyd a ed and supe conduc i e phase. On he
o he hand, i can be obse ed, looking a he e lexion indexed as (002),
ha he CoO2 in e laye dis ance inc eases as wa e is in oduced in o he
s uc u e.
20 40 60 80 100
In ensi y ( a. u. )
2
Figu e 4.7: X- ay di ac ion pa e ns o ( ed) Na0.36CoO2 and (g een)
Na0.36CoO2•yH2O.
198 F. C. Chou, E. T. Abel, J. H. Cho and Y. S. Lee. J. Phys. Chem. Solids 66, 155 (2005).
Chap e 4
118
The de e mina ion o he ac ual con en o wa e o di e en hyd a ed
samples by a di ec me hod is highly inaccu a e. The mog a ime ic analysis
o supe conduc ing phases can be ound in he li e a u e.175,177 Howe e , he
con inuous and as dec ease o he mass in he whole empe a u e ange
makes di icul a ce ain de e mina ion o he wa e con en o each s able
hyd a ed phase. The e o e, i is impo an o ake in o accoun ha he
s ochiome y o he wa e con en o he ully and pa ially hyd a ed phases
appea ing in he li e a u e could be a ec ed by simila inaccu acies.
Figu e 4.8 shows he ZFC-FC o he sample be o e hyd a ion. Once
he sample has been hyd a ed by s i ing in des illed wa e o wo days, a
diamagne ic esponse, cha ac e is ic o he supe conduc ing s a e, shows up
a T<4 K.
0 50 100 150
1.0x10-3
2.0x10-3
3.0x10-3
4.0x10-3
5.0x10-3
Na0.36CoO2
 (emu.mol-1.Oe-1)
Tempe a u e (K)
Figu e 4.8:

(T) cu es o Na0.36CoO2 in ZFC-FC condi ions a a magne ic
applied ield o H=100 Oe.
Figu e 4.9 shows he supe conduc ing beha iou o
Na0.36CoO2•1.3H2O a di e en magne ic applied ields. I is impo an o
ema k ha he magne ic ansi ion a T~30 K in he ZFC cu e o he non-
hyd a ed sample dissapea s comple ely once he sample became
supe conduc i e. Tha ein o ces ou heo y abou i s in insic magne ic
cha ac e , no due o impu i ies.
125
5
5.
.
The especial case o hal
doping: Na0.5CoO2
A e ou sys ema ic explo a ion o he magne ic and
he moelec ic p ope ies o NaxCoO2, we conside ed in e es ing o ocus on
he hal -doped sample (x=0.5) because o i s pa icula /o iginal physical
p ope ies, i.e. i is he only membe o he se ies a x0.7 ha shows some
kind o magne ic o de ing, i unde goes a me al- o-semiconduc o ansi ion
associa ed o a CO ansi ion and i displays a c osso e o a nega i e
Seebeck coe icien wi h empe a u e. The e o e, a e a b ie in oduc ion
abou his speci ic phase, we will show a mo e de ailed s udy abou he
cha ac e is ic physical p ope ies o he Na0.5CoO2 phase and he decisi e
ole ha we hink his phase plays in he appea ance o supe conduc i i y in
NaxCoO2•yH2O.

Chap e 5
126
The supe conduc ing phase in hyd a ed NaxCoO2 is conside ed o
condense om a Fe mi liquid (FL) wi h AFM co ela ions a low alues o x,
ypically a ound x0.35202. A high doping, x0.7, he coupling o i ine an
ca ie s o localized S=1/2 spins is no mally conside ed as he o igin o he
non-FL beha iou , es ablishing a candida e quan um spin-liquid s a e a low
empe a u e203. These wo he modynamically dis inguishable me als a e
sepa a ed a ze o Kel in by an AFM cha ge o de ed s a e a hal doping,
x=0.5204. The o igin o his s a e is no absolu ely cla i ied, al hough i has
been en a i ely ela ed o he in luence o an o de ed pa e n o Na+ ions
be ween he CoO2 laye s, which dis u bs he po en ial o e he Co3+/4+
shee s and o ces he sys em o a ce ain ype o cha ge o de ing205,206,207.
Se e al supe es uc u es ha e been obse ed expe imen ally om elec on
di ac ion s udies in a wide composi ion ange205 and i was sugges ed ha
he low empe a u e CO is a spin densi y wa e (SDW) s a e d i en by a
nes ing o he Fe mi su ace cha ac e is ic o he o de ed Na+ pa e n a
x=0.5 208,209. In an al e na i e possibili y, he SDW could esul om he
s ong nes ing endencies o a hexagonal Fe mi su ace in which six small
hole pocke s de i ed om he eg’ bands a e symme ically placed a ound he
 poin 210.
Polyc ys alline γ-Na0.7CoO2 was ob ained by con en ional solid s a e
eac ion wi h a inal i ing a 900 ºC as desc ibed p e iously in Chap e 1.
The XRD pa e n shows a single phase consis en wi h a hexagonal uni cell,
202 G. Lang, J. Bo o , H. Alloul, G. Collin and N. Blancha d. Phys. Re . B 78, 155116
(2008).
203 L. Balicas, Y. J. Jo, G. J. Shu, F. C. Chou and P. A. Lee. Phys. Re . Le . 100, 126405
(2008).
204 M. L. Foo, Y. Wang, S. Wa auchi, H. W. Zandbe gen, T. He, R. J. Ca a and N. P. Ong.
Phys. Re . Le . 92, 247001 (2004).
205 H. W. Zandbe gen, M. Foo, Q. Xu, V. Kuma , and R. J. Ca a. Phys. Re . B 70, 024101
(2004).
206 D. N. A gy iou, O. P okhnenko, K. Kie e and C. J. Milne. Phys. Re . B 76, 134506
(2007).
207 T. P. Choy, D. Galanakis and P. Phillips. Phys. Re . B 75, 073103 (2007).
208 J. Bob o , G. Lang, H. Alloul, N. Blancha d and G. Collin. Phys. Re . Le . 96, 107201
(2006).
209 N. L. Wang, Dong Wu, G. Li, X. H. Chen, C. H. Wang and X. G. Luo Phys. Re . Le . 93,
147403 (2004).
210 M. D. Johannes, I. I. Mazin, D. J. Singh and D. A. Papacons an opoulos. Phys. Re . Le .
93, 097005 (2004).
Hal doped: Na0.5CoO2
127
space g oup P63/mmc, and la ice pa ame e s a=2.8328(1) Å and
c=10.8511(6) Å. To ob ain Na0.5CoO2, Na+ was emo ed wi h B 2/ace oni ile
The Na/Co a io was con i med by ICP-OES o be 0.51(1). Re lexions om
Co3O4 o o he mino i y phases a e comple ely absen (see Figu e 5.1).
10 20 30 40 50 60
In ensi y (a.u.)
Na0.51CoO2
Na0.70CoO2
2
Figu e 5.1: X- ay di ac ion pa e n o NaxCoO2 (x=0.70 and x=0.51). The
e ical blue lines show he expec ed e lec ions o he space g oup P63/mmc. The
Na/Co a io was measu ed by ICP-OES.
Figu e 5.2 shows he empe a u e dependence o he absolu e
elec ical esis ance and he ZFC-FC magne iza ion cu es in Na0.51CoO2.
The esul s a e simila o hose epo ed by Shu e al211 o elec ochemically
dein e cala ed c ys als. We wan o emphasize ha we ha e no pe o med
any addi ional annealing o he samples a e Na+ ex ac ion and be o e he
anspo /magne ic expe imen s. This was done so in o de o p e en any
possible ea angemen o Na+, oxygen loss, e c. a e he syn hesis, and o
211 G. J. Shu, A. P odi, S. Y. Chu, Y. S. Lee, H. S. Sheu and F. C. Chou. Phys. Re . B 76,
184115 (2007).
Chap e 5
128
make he esul s as much compa able o he p ocess ollowed in single
c ys als as we can. Then, only he ela i e changes in he esis ance should
be conside ed and no i s absolu e alue.
Figu e 5.2: ZFC-FC magne iza ion cu es a H=100 Oe, and elec ic
esis ance o Na0.51CoO2. The a ows indica e he di ec ion ollowed du ing he
measu emen .
We ha e ound an inc ease in he esis ance eminiscen o a CO
e ec below 45 K, simila o he epo ed in single c ys als204, al hough i is
e y modes compa ed wi h ha in single c ys als. This e ec is ela ed o
he o ma ion o a SDW212 and hence does no esul in such an e ec i e
localiza ion as i does he CO s a e in mangani es o nickela es o
example213, in which he s ep in esis ance in ol es se e al o de s o
magni ude.
212 J. Bob o , G. Lang, H. Alloul, N. Blancha d and G. Collin. Phys. Re . Le . 96, 107201
(2006).
213 “Colossal Magne o esis ance, Cha ge O de ing and Rela ed P ope ies o Manganese
Oxides”, C. N. R. Rao, B. Ra eau, Eds. Wo ld Scien i ic, Singapo e (1998).
0 20406080100
0.0
1.0x10-3
2.0x10-3
3.0x10-3
4.0x10-3
5.0x10-3
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
R (  )
M (emu.g-1)
Tempe a u e ( K )
Hal doped: Na0.5CoO2
129
On he o he hand, in insic anspo p ope ies can be p o ed
h ough he Seebeck coe icien , a magni ude ha is no sensi i e o
in e g ain sca e ing as now cu en lows h ough he sample. Figu e 5.3
shows he empe a u e dependence o he he mopowe o wo
ep esen a i e Na+ composi ions. As i was discussed in he p e ious
chap e , S(T) shows a c osso e owa ds nega i e alues in he x=0.5 phase
which is absen a la ge and lowe concen a ions o Na+. This is consis en
wi h a local change in he cu a u e o he N(εF) close o x=0.5, due o a
pa ial gaping o he densi y o s a es, ha de elops g adually as
empe a u e is educed (no like a con en ional phase ansi ion).
Scheme 5.1: Rep esen a ion o he densi y o s a es p oposed o
Na0.5CoO2. The sign o S depends on he posi ion o he Fe mi le el (do lines) a a
speci ic empe a u e, which de elops as indica ed wi h empe a u e (a ow).
Recen 23Na NMR esul s ound a c osso e a T*200 K ha
changes he na u e o he spin co ela ion in x=0.5 om AFM a low
empe a u es o FM a high empe a u es202. On he o he hand, e idences
o a pseudogap a low doping we e ob ained om pho oemission
S<0
S=0
S>0

N(

)
T
Chap e 5
130
spec oscopy214. All hese esul s a e consis en wi h a pa ial gaping o he
Fe mi su ace by a SDW ins abili y occu ing below ~200 K, whe e we ha e
obse ed he change o sign o S(T) in x0.5.
0 100 200 300 400 500
-20
0
20
40
60
80 NaxCoO2
x=0.51
x=0.7
S (V.K-1)
Tempe a u e (K)
Figu e 5.3: Tempe a u e dependence o he Seebeck coe icien a di e en
x. A x

0.5 he mopowe goes nega i e below T

200 K.
The inc ease in he elec onic esis ance is accompanied by a
magne ic ansi ion, indica ing a pa ial spin pola iza ion. Two addi ional
magne ic ansi ions a e obse ed a 18 K and 86 K ( he la e no isible
on he scale o Figu e 5.2 bu in Figu e 5.4), consis en wi h p e ious epo s,
which epo ed up o h ee magne ic ansi ions o he hal -doped phase a
~20 K, ~50 K and ~90 K215,216,217. The magne ic ansi ion a ~90 K has been
associa ed o a long ange AFM o de ing.202 The small empe a u e
214 T. Shimojima, T. Yokoya, T. Kiss, A. Chainani, S. Shin, T. Togashi, S. Wa anabe, C.
Zhang, C. T. Chen, K. Takada, T. Sasaki, H. Saku ai and E. Takayama-Mu omachi. Phys.
Re . B 71, 020505(R) (2005).
215 Q. Huang, M. L. Foo, J. W. Lynn, H. W. Zandbe gen, G. Lawes, Y. Wang, B. H. Toby, A.
P. R. N. P. Ong, and R. J. Ca a. J. Phys.: Condens. Ma e 16, 5803 (2004).
216 G. Gaspa o ic, R. A. O , J.-H. Cho, F. C. Chou, Y. Chu, J. W. Lynn and Y. S. Lee. Phys.
Re . Le . 96, 046403 (2006).
217 C. H. Wang, X. H. Chen T. Wu, X. G. Luo, G. Y. Wang and J. L. Luo. Phys. Re . Le . 96,
216401 (2006).

Hal doped: Na0.5CoO2
131
di e ences wi h espec o ou da a could be due o small di e ences in he
composi ion o Na+ be ween he samples.
Also, as men ioned in Chap e 2, we ha e obse ed (as many
au ho s epo ed be o e)202,204 he exis ence o a he mally ac i a ed e m in
(T) o x≤0.5, indica i e o some kind o spin gap. Figu e 5.4 shows a mo e
de ailed scale o he magne iza ion da a o se e al ep esen a i e Na+
composi ions, whe e a dec ease o he magne ic suscep ibili y wi h
empe a u e in he ange abo e he magne ic phase ansi ion and up o
oom empe a u e is obse ed. In ac , he slope o he cu es changes om
nega i e o posi i e a a ound x=0.5 (see Figu e 5.5), u he suppo ing he
singula na u e o his poin .
100 150 200 250 300
4.0x10-4
5.0x10-4
6.0x10-4
x=0.40
x=0.51
x=0.7
M (emu.g-1)
Tempe a u e (K)
Figu e 5.4: Tempe a u e dependence o he magne iza ion o di e en x.
Chap e 5
132
0.40.50.60.7
-8
-4
0
4
dM/dT (10-7.emu.g-1.K-1)
x in NaxCoO2
Figu e 5.5: Change o slope om posi i e (x≤0.5) o nega i e (x>0.5). The
alues a e calcula ed om he i ing o he high empe a u e da a o a s aigh line,
and hence a e only indica i e o he gene al beha io .
Fo a mo e de ailed cha ac e iza ion o he magne ic p ope ies o
he hal doped phase, he s abili y o he magne ic phases wi h he applied
magne ic ield was also s udied. Figu e 5.6 shows he magne ic cu es a
di e en applied magne ic ields be ween 2.510-3 T and 1 T. Thei posi ion
a 17 K and 40 K emains unchanged un il H=0.1 T, bu hey a e sligh ly
shi ed a H=1 T. Howe e , he i e e si ili y be ween he ZFC-FC cu es is
educed as he applied magne ic ield inc eases abo e 10-2 T. In o de o
ca y ou a comple e magne ic cha ac e iza ion and de e mine which is he
magne ic na u e o he magne ic phases eme ging a x=0.50, he hys e isis
magne ic loops we e pe o med a di e en ep esen a i e empe a u es
below and abo e he magne ic ansi ions in ZFC condi ions. Figu e 5.7
shows he hys e isis cycles a T=5 K, 28 K and 80 K.
Hal doped: Na0.5CoO2
133
10 100
1E-4
1E-3
0.01
0.1 1 T
0.1 T
10-2 T
2.5.10-3 T
M (emu.g-1)
Tempe a u e ( K )
Figu e 5.6: Magne iza ion cu es as a unc ion o he applied magne ic ield
(H=2.5

10-3, 10-2, 0.1, 1 T) in a log-log scale.
-1.0 -0.5 0.0 0.5 1.0
-0.10
-0.05
0.00
0.05
0.10
5K
28K
80K
M (emu.g-1)
H
(
T
)
Figu e 5.7: ZFC magne iza ion loops a se e al empe a u es (T=5 K, 28 K
and 80 K) o he x=0.50 phase, up o an applied magne ic ield o 1 T.
Chap e 5
134
A T=80 K he magne iza ion is in he almos empe a u e
independen egime (Pauli PM-like), wha is also e idenced by he linea
con ibu ion o he magne iza ion wi h he applied magne ic ield and he no
p esence o cohe ci i e ield (Hc). As he empe a u e dec eases, T=28 K, an
impo an FM con ibu ion wi h Hc4.210-2 T and highe absolu alues o
he magne iza ion a e obse ed, al hough i is no sa u a ed a he maximum
applied magne ic ield (H=1 T). The same e ec is e en mo e p onunced a
T=5 K, whe e he Hc om he FM con ibu ion is o ~0.052 T. So, om hese
esul s we hink ha an inhomogeneous AFM s a e (wi h a esul ing ne FM
momen ) de elops a low empe a u e om a PM s a e a high empe a u e.
So, in o de o con i m he s abili y o he magne ic phases and i s
ela ionship wi h a pa icula Na+ a angemen , we ha e s udied hei
e olu ion wi h ime, doping, as quenching o low empe a u es, hyd a ion
and opo ac ic exchange wi h di alen -ca ions. Fi s o all we ha e obse ed
ha all he magne ic and elec onic ansi ions discussed in his pape a e
obus agains bo h ela i ely long ime aging (Figu e 5.8) and as quenching
o he sample om oom empe a u e o liquid He. The cooling a e does no
a ec o hei appea eance, and hence i seems o be o elec onic ins ead o
ionic o de ing o igin. This mos p obably disca ds any link be ween hem and
a pa icula Na+ a angemen , as i was discussed o o he magne ic
ansi ions a high doping218. Howe e , i also ue ha i any Na+
a angemen is pa icula ly s able a x=0.5 al eady a oom empe a u e, as
quenching is no expec ed o ha e any in luence on i .
218 T. F. Schulze, P. S. Hä lige , Ch. Niede maye , K. Ma enbe ge , S. Bubenho e and B.
Ba logg. Phys. Re . Le . 100, 026407 (2008).