Magnetism on the verge of breakdown

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Magnetism on the verge of breakdown

H. Aourag

Laboratory for Study and Prediction of Materials

URMER; University of Tlemcen



What is magnetism?



Examples of collective behaviour



Itinerant magnetism



Disappearance of magnetism



Quantum critical points



Metamagnetism

A brief history of magnetism

Lodestone or magnetite Fe
3
O
4

known
since 500
-
800 BC by the Greeks and
Chinese


585 BC

Thales of Miletus theorises that lodestone attracts iron because


it has a soul

~100 AD

First compass in China

1200 AD

Pierre de Maricourt shows magnets have two poles

1600 AD

William Gilbert argues Earth is a giant magnet

1820
-
1888

Electricity



Magnetism


Light


Classical electromagnetism

1905
-
1930

Development of quantum mechanics and relativity: permanent



magnets explained

Magnetism in
pop culture

Collective behaviour:
the whole is greater than the sum of its parts

Each neuron has a binary
response: to fire or not. How
could we predict that 10
billion neurons working
together would do so much?

A bee colony consists of one
queen and hundreds of drones
and workers. How do they
organise themselves?

Correlated electrons

How do we calculate a system of 10
23

interacting electrons?



3 particles already a challenge to many
-
body theory!

Treat system as 10
23

non
interacting electrons!

Landau quasiparticle picture

consider e
-

(or horse!) plus cloud



same charge



different mass and velocity



interactions accounted for



Landau Fermi liquid theory



Extreme case: heavy fermions

4
f

and 5
f

electron compounds like UBe
13
, CeAl
3
, CeCu
2
Si
2
can
have electron masses up to 1000 times that of a bare electron

Elements with magnetic order

3
d
-

metals: Cr, Mn, Fe, Co, Ni

4
f
-

metals: Ce, Nd, Sm, Eu, Gd, Th, Dy, Ho, Er, Tm

Microscopic magnetism

-
conduction electrons participate in magnetism

-
narrow, dispersionless bands (like 3
d
): high density of states


D
(
e
F
) and so may fulfill Stoner criterion





B
2
D
(
e
F
)
1

UD
(
e
F
)
i.e. 1 ≈
UD
(
e
F
)

-
simple ferromagnet:




-
simple antiferromagnet:



Itinerant electron ferromagnetism

Tuning out magnetism

Chemical doping:
substitution of larger or smaller ions increase
or decrease lattice spacing and therefore change interactions

Pressure:
clean, continuous tuning; each pressure point
equivalent to one doping level without introduction of impurities
or defects

Basic hydrostatic pressure cell:
piston and cylinder design





nonmagnetic (BeCu, Russian submarine steel)




isotropic medium (mixture of two fluids)




electrical leads (feedthrough with 20 wires)




low friction (Teflon)




hard piston material (tungsten carbide)




maximum theoretical pressure ≈ 50 kbar or 5 GPa

Schematic design of hydrostatic cell

UGe
2
: first ferromagnetic

superconductor

Phase diagram

S.S. Saxena et al,
Nature

(2000)

P. Coleman,
Nature

(2000)



magnetisation shows


typical hysteresis loop



inverse susceptibility


marks
T
C

more sharply



smooth
T
C



0 with pressure



coexisting ferromagnetism


and bulk superconductivity



FM necessary for SC?

Quantum critical point

Instead of well
-
behaved low temperature Fermi liquid properties




constant specific heat
c/T




constant magnetic susceptibility





constant scattering cross
-
section
Dr
/
T
2

the above quantities
diverge

as
T


0 due to
critical
fluctuations

quantum


敲漠瑥t灥牡畲e

critical


捲楴楣慬i灨敮潭敮愯灨慳攠瑲慮獩t楯湳


point


獥sf
-
數灬慮慴潲礡

Nature avoids high degeneracy


system
will find

an escape!!!

Superconductivity

often the escape route

Magnetically mediated superconductivity



瑹灥
-
䥉I獵灥s捯湤畣瑩癩v礠


Consider
magnetic

glue for Cooper pairs. Parallel spin triplet state


rather than singlet state


as described by the BCS model





unconventional

superconductivity

UGe
2

and ZrZn
2

representatives of universal class of itinerant
-
electron ferromagnets close to ferromagnetic QCP? Require




-
low Curie temperature (below ~50 K)


-
long mean free paths (above 100

m)


-
low temperature probes (below 1 K)



CePd
2
Si
2
:
heavy fermion
compound with anti
-

ferromagnetic ground state

N.D. Mathur et al, Nature (1998)

Pressure
-
tuning to edge of
magnetic order


within
narrow range of critical
densities where magnetic
excitations dominate



long
-
range order allows
superconductivity to exist

NB: inset shows resistivity
with power
T
1.2

…high
-
T
c

phase diagram comes to mind!

Superconducting elements

Phenomenological model
(Landau theory of phase transitions)

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
F

aM
2

bM
4

dM
6


M
2

B

M
b
< 0

B
= 0

b
< 0

B


0

1
st

order transition: discontinuity or jump in order parameter
M

2
nd

order transition: continuously broken symmetry, LRO

Magnetic phase diagram

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Metamagnetism

Between paramagnetism and ferromagnetism

CaB
6

pure
(paramagnetic)

and
self
-
doped with vacancies
(ferromagnetic with T
C

above
600 K)

Sr
3
Ru
2
O
7

shows
metamagnetic
behaviour for T < 16 K

P. Vonlanthen
et al
, PRB (2000)

R. Perry
et al
, PRL (2001)

Sr
3
Ru
2
O
7



bilayer perovskite



Sr
2
RuO
4
2D

unconventional


superconductor T
c

1.5 K



SrRuO
3

3D

itinerant electron


ferromagnet T
C

160 K



Sr
3
Ru
2
O
7

on border of


superconductivity and


ferromagnetism

Park and Snyder, J Amer Ceramic Soc (1995)

Ground state:



Fermi liquid below 10 K



paramagnetic, ie
nonmagnetic



strongly enhanced, ie close to ferromagnetism (uniaxial stress)

Investigate interplay of superconductivity and magnetism by
application of hydrostatic pressure to Sr
3
Ru
2
O
7

Resistance reveals diverging scattering cross
-
section
(~effective mass) at metamagnetic field!

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T
1.25



捲c瑩捡氠獰楮⁦汵捴畡瑩潮猠慳⁩渠煵慮瑵洠捲c瑩c慬a浥瑡ts

r

=
r
0

+ AT
2

What about pressure?

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hydrostatic pressure appears


to push the system
away


from the magnetic instability




all peaks originate from one


single point at pc ~
-
14 kbar

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Relate to generic phase diagram

Quantum critical end
-
point




similar to tri
-
critical point in H
2
O phase diagram



second order end
-
point to first order line of transitions



no additional symmetry breaking since already in symmetry
-


breaking field; can go around continuously



possibility of
new state of matter
? quantum lifeforms???



metamagnetism dome defined by lines of first order transitions



we are probing positive pressure side of ferromagnetism bubble



how to get to negative pressure side?



how close to superconductivity? 100
-
200 kbar from Sr
2
RuO
4



what is located at (
p
m
,B
m
)?

Puzzle: scaling behaviour

Scaling
not compatible

with standard spin fluctuation theory



major assumption

that pressure mainly affects bandwidth


(DOS) not entirely correct



rotation and distortion of octehedra important

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Possible explanation:


neutron scattering suggests pressure predominantly affects
rotation angle of octehedra



mainly metamagnetic field affected but not critical fluctuations


(probably from Fermi surface fluctuations)

Future

require magnetic probe such as a.c. susceptibility under pressure



study rotation of applied field


higher purity samples in order to study Fermi surface changes
through metamagnetic transition


theoretical modelling must include rotation of octehedra and
differentiate between a classic quantum critical point and a
quantum critical end
-
point