Spin ice
Encyclopedia
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
. A spin ice has "spin"
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
degrees of freedom (i.e. it is a magnet), with frustrated interactions
Geometrical frustration
In condensed matter physics, the term geometrical frustration means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site.This may lead to highly...
which prevent it freezing. It shows low-temperature properties – in particular residual entropy
Residual entropy
Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero...
– closely related to those of crystalline water ice
Ice
Ice is water frozen into the solid state. Usually ice is the phase known as ice Ih, which is the most abundant of the varying solid phases on the Earth's surface. It can appear transparent or opaque bluish-white color, depending on the presence of impurities or air inclusions...
. The most prominent compounds
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...
with such properties are dysprosium titanate
Dysprosium titanate
Dysprosium titanate is an inorganic compound, a ceramic of the titanate family, with pyrochlore structure. Its CAS number is .Dysprosium titanate, like holmium titanate and holmium stannate, is a spin ice material...
and holmium titanate. The magnetic ordering of a spin ice resembles the positional ordering of hydrogen atoms in conventional water ice.
Recent experiments have shown strong evidence for the existence of deconfined
Deconfinement
In physics, deconfinement is the property of a phase in which certain particles are allowed to exist as free excitations, rather than only within bound states...
magnetic monopole
Magnetic monopole
A magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...
s in these materials, with analogous properties to the hypothetical magnetic monopoles postulated to exist in the vacuum.
Technical description
In 1935, Linus PaulingLinus Pauling
Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists of the 20th century...
noted that the structure of water ice exhibited degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
that would be expected to remain disordered even at absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
. That is, even upon cooling to zero temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, water ice is expected to have residual entropy
Residual entropy
Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero...
(i.e. intrinsic randomness). This is a result of the fact that the structure of ice contains oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s with four neighboring hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
atoms. For each oxygen atom, two of the neighboring hydrogen atoms are near (forming the traditional H2O molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
), and two are further away (being the hydrogen atoms of neighboring water molecules). Pauling noted that the number of configurations conforming to this "two-in two-out" rule grows exponentially
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
with the system size, and therefore that the zero-temperature entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of ice was expected to be extensive
Intensive and extensive properties
In the physical sciences, an intensive property , is a physical property of a system that does not depend on the system size or the amount of material in the system: it is scale invariant.By contrast, an extensive property In the physical sciences, an intensive property (also called a bulk...
. Pauling's findings were confirmed by specific-heat measurements, though pure crystals of water ice are particularly hard to create.
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
of ions, each of which has a non-zero spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
, which must satisfy some two-in, two-out rule analogous to water ice because of the interactions between neighbouring ions. Spin ice materials therefore exhibit the same residual entropy properties as water ice. However, depending on the material used in a spin ice, it is generally much easier to create large single crystals of spin ice materials than the corresponding water ice materials. Additionally, the interaction of a magnetic field with the spins in a spin ice material make spin ice materials much better materials for examining residual entropy than water ice.
While Philip Anderson
Philip Anderson
Philip Anderson may refer to:* Phil Anderson , cyclist* Philip Carr Anderson, , professor of medicine* Philip W. Anderson , film editor* Philip Warren Anderson , physicist-See also:...
had already noted in 1956 the connection between the problem of the frustrated Ising
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
antiferromagnet on a (pyrochlore
Pyrochlore
Pyrochlore 2Nb2O6 is a solid solution between the niobium end member , and the tantalum end member .-Occurrence:...
) lattice of corner-shared tetrahedra and Pauling's water ice problem, real spin ice materials were only discovered quite recently. The first materials identified as spin ices were the pyrochlore
Pyrochlore
Pyrochlore 2Nb2O6 is a solid solution between the niobium end member , and the tantalum end member .-Occurrence:...
s Dy2Ti2O7 (dysprosium titanate
Dysprosium titanate
Dysprosium titanate is an inorganic compound, a ceramic of the titanate family, with pyrochlore structure. Its CAS number is .Dysprosium titanate, like holmium titanate and holmium stannate, is a spin ice material...
), Ho2Ti2O7 (holmium titanate) and Ho2Sn2O7 (holmium stannate). Very recently, compelling evidence has been reported that Dy2Sn2O7 (dysprosium stannate) is also a spin ice.
Spin ice materials are characterized by disorder of magnetic ions even when said ions are at very low temperatures
Cryogenics
In physics, cryogenics is the study of the production of very low temperature and the behavior of materials at those temperatures. A person who studies elements under extremely cold temperature is called a cryogenicist. Rather than the relative temperature scales of Celsius and Fahrenheit,...
. AC magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...
measurements find evidence for a dynamical freezing of the magnetic moments as the temperature is lowered somewhat below the temperature at which the specific heat displays a maximum.
Spin ices and magnetic monopoles
Spin ices are geometrically frustratedGeometrical frustration
In condensed matter physics, the term geometrical frustration means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site.This may lead to highly...
magnetic systems. While frustration is usually associated with triangular or tetrahedral
Tetrahedral molecular geometry
In a tetrahedral molecular geometry a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1 ≈ 109.5° when all four substituents are the same, as in CH4. This molecular geometry is common throughout the first...
arrangements of magnetic moments coupled via antiferromagnetic exchange interactions, spin ices
are frustrated ferromagnets. It is the local nature of the strong crystal field forcing the magnetic moments to point either in or out of a tetrahedron that renders ferromagnetic interactions frustrated in spin ices. Interestingly, it is the long range magnetic dipolar interaction and not the nearest-neighbor exchange coupling that causes the frustration and the consequential "two-in two-out" spin orientations and which leads to the spin ice phenomenology.
In a paper published in Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
in September 2009, researchers Jonathan Morris and Alan Tennant from the Helmholtz-Zentrum Berlin für Materialien und Energie
Helmholtz-Zentrum Berlin
The Helmholtz-Zentrum Berlin for Materials and Energy is a research centre and part of the Helmholtz Association of German Research Centres. The institute carries out research into the structure and dynamics of novel materials and also investigates solar cell technology.Several large scale...
(HZB) along with Santiago Grigera from Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB, CONICET) and other colleagues from Dresden University of Technology
Dresden University of Technology
The Technische Universität Dresden is the largest institute of higher education in the city of Dresden, the largest university in Saxony and one of the 10 largest universities in Germany with 36,066 students...
, University of St. Andrews and Oxford University described the observation of quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
s resembling monopoles. A single crystal of dysprosium titanate
Dysprosium titanate
Dysprosium titanate is an inorganic compound, a ceramic of the titanate family, with pyrochlore structure. Its CAS number is .Dysprosium titanate, like holmium titanate and holmium stannate, is a spin ice material...
in a highly frustrated pyrochlore lattice
Pyrochlore
Pyrochlore 2Nb2O6 is a solid solution between the niobium end member , and the tantalum end member .-Occurrence:...
(F d -3 m) was cooled to 0.6 to 2 K. Using neutron scattering
Neutron scattering
Neutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
, the magnetic moments were shown to align in the spin ice into interwoven tube-like bundles resembling Dirac string
Dirac string
In physics, a Dirac string is a fictitious one-dimensional curve in space, conceived of by the physicist Paul Dirac, stretching between two Dirac magnetic monopoles with opposite magnetic charges, or from one magnetic monopole out to infinity. The gauge potential cannot be defined on the Dirac...
s. At the defect
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
of the system from an effective gas of these quasiparticles is also described.
The effective charge of a magnetic monopole in a spin-ice has been measured as (Bohr magnetons per angstrom
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
)
. The elementary constituents of spin ice are magnetic dipoles, so the emergence of monopoles is an example of the phenomenon of fractionalization
Fractionalization
In physics, fractionalization is the phenomenon whereby the quasiparticles of a system cannot be constructed as combinations of its elementary constituents...
.
See also
- Geometrical frustrationGeometrical frustrationIn condensed matter physics, the term geometrical frustration means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site.This may lead to highly...
- Spin glassSpin glassA spin glass is a magnet with frustrated interactions, augmented by stochastic disorder, where usually ferromagnetic and antiferromagnetic bonds are randomly distributed...
- Magnetic monopoleMagnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...
- Magnetricity