Magnets and superconductors strange bedfellows of the quantum world

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					    Magnets and superconductors: strange
      bedfellows of the quantum world.

                      Patrick Lee


Supported by NSF and DOE over the years.

•What is condensed matter physics?
•Conventional superconductors.
• Conventional antiferromagnets (AF).
•Emergence of new phenomena at low energies, a theme
of modern condensed matter physics.
• Unconventional superconductors:
   High Tc superconductors, proximity to Mott insulator
• Search for unconventional AF, the quantum spin liquid.
Condensed matter physics: the study of
novel properties of materials.

              Material preparation

 experiment                          theory

Magnetism and superconductivity are two of the
most common and important properties. The
explanation of both relies on quantum mechanics.
     Ferromagnetism (FM): known for thousands of years, but
     explained only in 1930’s after the invention of quantum
   1. Electrons carry angular momentum called spin.
   2. Electrons are fermions and obey Pauli’s exclusion Principle, ie 2
      electrons with the same spin cannot be at the same place.

A third ingredient is that electrons repel each other by Coulomb repulsion.

  This is the main theme of my talk: electrons hate each other!

                                                  By having all spins up,
                                                  the electrons
                                                  automatically stay
                                                  away from each other
                                                  to lower the Coulomb
   metal               Ferromagnetic metal        repulsion.

FM is relatively rare: Fe, Ni, Co and some rare earths among the elements.
Superconductivity was discovered by
Kammerling Onnes
in 1911, when he cooled mercury to liquid
helium temperature and its resistivity vanishes!

Until 1986, the highest transition temperature
(Tc) was 23K. (room temperature is 300K.)
                                                   Nobel prize
Superconductors are commonplace,
but limited to low temperatures.
Microscopic theory given by Bardeen, Cooper and Schrieffer (BCS) in
1957. The theory takes 2 steps.
Step 1 : pairing of electrons to form “Cooper pairs,” a molecule of two

Electrons have an effective attraction due to coupling to lattice vibration.
But electrons hate each other! The attraction is short
range in space but retarded in time.
But electrons hate each other! The attraction is short
range in space but retarded in time.

   Trouble is that the attraction strength is very weak and
   superconductivity is limited to low temperatures.
   Step 2. Cooper pairs are bosons. They can “Bose-Einstein
   condense”, ie they behave like waves rather than particles.

    Superconductor is described by a
    “macroscopic wave-function” which is a
    complex number with a phase angle f.
    In short, we associate an angle with every
    point along a superconducting wire.

The resistance of a superconductor is
exactly zero (not just very small!) and
persistent current flows around a ring for
the life of the universe.
The explanation of this mystery has to
do with topology.
  Conventional Anti-ferromagnet (AF):
Louis Néel (theory 1933)                   Cliff Shull
   1970 Nobel Prize                     1994 Nobel Prize

                                 Anti-ferromagnetic insulators:
                            When repulsion is strong enough, the
                            electrons are localized on lattice sites and
                            form an insulator (called a Mott insulator.)
                            The spins are aligned opposite.
                           Common among transition metal oxides.
Note that superconductors and
magnets are mutually exclusive.
 Why are superconductors and magnets mutually exclusive?

1. The Cooper pair is formed by opposite spins whereas FM has parallel
spins. This explains why it cannot co-exists with FM.

2. Most AF are insulators. The spins are immobile and cannot
carry current. This is just the opposite to superconductor.
High Tc superconductivity began with the
discovery of Bednorz and Muller in 1986.
The highest Tc is now about 150K.

   J. G. Bednorz             K. A. Mueller

              Nobel prize 1987
                                 150                        HgBa2Ca2Cu3O8
Critical tem perature T c (K )

                                       LIQUID NITROGEN

                                  50                                                        Sm(O1-xFx)FeAs (March, 2008)
                                                             La2-xSrxCuO4           MgB2
                                                            V3Si                Cs2RbC60
                                          Hg                       Nb3Ge    Ba0.6K0.4BiO3
                                   1900    1920      1940     1960    1980      2000
                                                  Year of discovery
A key feature of superconductor is that it repels magnetic field.
(Meissner effect.)


  20 years later, large scale
  applications are beginning to appear.

American Superconductor 2G wires: YBCO
based, with Y2O3 nano particles for flux pinning.

                                                    Weight reduction of wind
                                                    10 MW generator will
                                                    weight 120 metric tons
                                                    instead of 300 using
                                                    conventional copper wires.
Basic features of High-Tc cuprates


                       Spins are immobile and form
                       an anti-ferromagnet. This is
                          called a Mott insulator.

How did they do it? Turn insulator into superconductors.
Doped Mott insulator: superconductor!


    CuO2 plane with
     doped holes:

   La3+  Sr2+: La2-
                       Physicist pair caught doping.

What is unconventional about high Tc superconductors?
  Superconductivity by doping a Mott insulator.

   This strongly suggest the origin of pairing comes from
   electronic repulsion.
   Its proximity to anti-ferromagnet indicates the energy scale
   is set by anti-ferromagnetism and is not necessarily a
   low temperature phenomenon.
In the intervening 20 years, we have discovered
many examples of unconventional SC’s.
•Organics (Tc=12K)
•Heavy fermion superconductors.
•Fe based superconductors. (Tc=55K)

  In all cases these SC’s are in close proximity to AF.

  A marriage of SC and AF?

 “Politics does not make strange bedfellows, marriage does,”
 Groucho Marx.
Why does doping a Mott insulator antiferromaget give
rise to a superconductor?
Qualitative picture given by Philip Anderson in 1987.
Anderson’s resonating valence bond (RVB) idea:
spin liquid and its doping.

Unconventional anti-ferromagnetism may be a partner to
unconventional superconductors!
       Competing visions of the antiferromagnet
“….To describe antiferromagnetism, Lev landau and
Cornelis Gorter suggested quantum fluctuations to mix
Neel’s solution with that obtained by reversal of
moments…..Using neutron diffraction, Shull confirmed
(in 1950) Neel’s model.
……Neel’s difficulties with antiferromagnetism and
inconclusive discussions in the Strasbourg international
meeting of 1939 fostered his skepticism about the
usefulness of quantum mechanics; this was one of the
few limitations of this superior mind.”
Jacques Friedel, Obituary of Louis Neel, Physics today,    Lev Landau

                                            |  | 
             Classical                           Quantum
                          In 1973 P. W. Anderson proposed a
                          resonating valence bond (RVB) state
                          (Instead of Neel state) for triangular lattice.
                          It is a linear superposition of singlet pairs.

                          With doping, vacancies becomes
                          mobile in the spin liquid background.

When the vacancies become phase coherent, we have superconductivity.
In high Tc superconductors , the physics of spin liquid
show up only at finite temperature. Difficult to make
precise statements and sharp experimental tests. It will
be very useful to have a spin liquid ground state which
we can study.

Requirements: insulator, one
  electron per unit cell,
  absence of AF order.
After 30 years physicists
   finally discovered several
   promising new candidate for
   spin liquid states, thus
   ending the drought.
      The kagome lattice.

The most frustrated 2 dimensional lattice.

        One of the few known examples is Iron jarosite, a rare mineral
        which was studied by Dan Nocera (chemist) and Young Lee
        (physicist) at MIT.
        KFe3(SO4)2OH)6      S=5/2.
On April 15,2004, in the outcropping, mission scientists found a hydrated iron
sulfate mineral called jarosite, an uncommon mineral on Earth, which forms in
dilute sulfuric acid in ground water. Jarosite was first discovered on Earth in 1852
in ravines in the mountainous coast of southeastern Spain.
Finally in 2007 Spin liquid was discovered in a S=1/2 Kagome system. (Dan
Nocera, Young Lee etc. MIT).
No spin order down to milli Kelvin.
                                                  Mineral discovered in
                                                  Chile in 1972 and
          Herbertsmithite : Spin ½ Kagome.        named after H. Smith.

     Many of us are excited by the discovery of a new state of matter with
     new emergent properties.

The hatred of electrons for each other and quantum
mechanics are the key ingredients which are responsible for
common phenomena such as magnetism and more exotic
phenomena such as high temperature superconductors.

These strange bedfellows have opened up new realms of
possibilities in condensed matter physics.

Let us see what more surprises Nature has in store for us.