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| {{technical|date=May 2011}}
| | Got nothing to write about myself I think.<br>I enjoy of finally being a part of wmflabs.org.<br>I really hope I'm useful in one way .<br><br>Also visit my web site; [http://safedietsthatwork.bravesites.com/ diet plans] |
| [[File:Diagram of Ferromagnetic Magnetic Moments.png|thumb|240px|right| '''Figure 1''' Below the Curie temperature, neighbouring magnetic spins align in a ferromagnet in the absence of an applied [[magnetic field]].]]
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| [[File:Diagram of Paramagnetic Magnetic Moments.png|thumb|240px|right|'''Figure 2''' Above the Curie temperature, the magnetic spins are randomly aligned in a paramagnet unless a magnetic field is applied.]]
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| In [[physics]] and [[materials science]], the '''Curie temperature''' ({{math|''T''<sub>c</sub>}}), or '''Curie point''', is the temperature where a material's permanent [[magnetism]] changes to induced magnetism. The force of magnetism is determined by [[magnetic moments]].
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| The Curie Temperature is the critical point where a material's intrinsic magnetic moments change direction. Magnetic moments are permanent [[Magnetic dipole moment|dipole moments]] within the atom which originate from electrons' [[angular momentum]] and [[spin (physics)|spin]].
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| Materials have different structures of intrinsic magnetic moments that depend on temperature. At a material's Curie Temperature those intrinsic magnetic moments change direction.
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| Permanent magnetism is caused by the alignment of magnetic moments and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field.
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| For example, the ordered magnetic moments ([[ferromagnetism|ferromagnetic]], figure 1) change and become disordered ([[paramagnetism|paramagnetic]], figure 2) at the Curie Temperature.
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| Higher temperatures make magnets weaker as spontaneous magnetism only occurs below the Curie Temperature. [[Magnetic susceptibility]] only occurs above the Curie Temperature and can be calculated from the [[Curie-Weiss Law]] which is derived from [[Curie's Law]].
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| In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the temperature where a material's spontaneous electric [[Dipolar polarization|polarisation]] changes to induced electric polarisation or the reverse upon reduction of the temperature below the Curie temperature.
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| The Curie temperature is named after [[Pierre Curie]] who showed that magnetism was lost at a critical temperature.<ref>{{cite web |title=Pierre Curie - Biography |url=http://www.nobelprize.org/nobel_prizes/physics/laureates/1903/pierre-curie-bio.html |work=Nobelprize.org |publisher=The Nobel Foundation 1903 |accessdate=2013-03-14}}</ref>
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| {| class="wikitable sortable" style="float:right;margin:0 0 1em 1em;"
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| |+ style="font-size: 80%"|Curie Temperature of materials
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| <ref>{{harvnb|Buschow|2001|loc=p5021, table 1}}</ref><ref name="table 3.1">{{harvnb|Jullien|1989|p=155}}</ref><ref name=Kitteltable>{{harvnb|Kittel|1986|pp=}}</ref>
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| |-
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| ! Material
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| ! Curie <br/>temperature (K)
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| |-
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| |[[Iron]] (Fe) ||1043
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| |-
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| |[[Cobalt]] (Co) ||1400
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| |-
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| |[[Nickel]] (Ni) ||631
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| |-
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| |[[Gadolinium]] (Gd) ||292
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| |-
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| | [[Dysprosium]] (Dy)
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| || 88
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| |-
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| | [[Manganese|Mn]][[Bismuth|Bi]]
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| || 630
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| |-
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| | Mn[[Antimony|Sb]]
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| || 587
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| |-
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| | [[Chromium(IV) oxide|CrO<sub>2</sub>]]
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| || 386
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| |-
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| | Mn[[Arsenic|As]]
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| || 318
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| |-
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| | [[Europium|Eu]]O
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| || 69
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| |-
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| |Iron(III) oxide (Fe<sub>2</sub>O<sub>3</sub>) ||948
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| |-
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| | [[Iron(II,III) oxide]] (FeOFe<sub>2</sub>O<sub>3</sub>)
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| || 858
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| |-
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| | NiOFe<sub>2</sub>O<sub>3</sub>
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| || 858
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| |-
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| | [[Copper|Cu]]OFe<sub>2</sub>O<sub>3</sub>
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| || 728
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| |-
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| | MgOFe<sub>2</sub>O<sub>3</sub>
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| || 713
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| |-
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| | MnOFe<sub>2</sub>O<sub>3</sub>
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| || 573
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| |-
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| | [[Yttrium iron garnet|Y<sub>3</sub>Fe<sub>5</sub>O<sub>12</sub>]]
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| || 560
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| |}
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| ==Magnetic moments==
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| Magnetic moments are permanent [[Magnetic dipole moment|dipole moments]] within the atom which are made up from electrons angular momentum and spin.<ref name=Hall>{{harvnb|Hall|1994|p=200}}</ref>
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| Electrons inside atoms contribute magnetic moments from their own [[angular momentum]] and from their orbital momentum around the nucleus. Magnetic moments from the nucleus are insignificant in contrast to magnetic moments from electrons.<ref name=Jullien136>{{harvnb|Jullien|1989|pp=136–138}}</ref> Thermal contribution will result in higher energy electrons causing disruption to their order and alignment between dipoles to be destroyed.
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| [[ferromagnetism|Ferromagnetic]], [[paramagnetism|paramagnetic]], [[ferrimagnetism|ferrimagnetic]] and [[Antiferromagnetism|antiferromagnetic]] materials have different structures of intrinsic magnetic moments. It is at a material's specific Curie Temperature where they change properties.
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| The transition from antiferromagnetic to paramagnetic (or vice versa) occurs at the [[Néel Temperature]] which is analogous to Curie Temperature.
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| {|
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| ! Below {{math|''T''<sub>c</sub>}} !! Above {{math|''T''<sub>c</sub>}}
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| | Ferromagnetic ||↔ Paramagnetic
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| | Ferrimagnetic ||↔ Paramagnetic
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| | Antiferromagnetic ||↔ Paramagnetic
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| |}
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| <gallery caption="Orientations of magnetic moments in materials" widths="180px" heights="120px" perrow="4">
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| File:Diagram of Ferromagnetic Magnetic Moments.png|'''[[Ferromagnetism]]''' The magnetic moments in a ferromagnetic material. The moments are ordered and of the same magnitude in the absence of an applied magnetic field.
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| File:Diagram of Paramagnetic Magnetic Moments.png|'''[[Paramagnetism]]''' The magnetic moments in a paramagnetic material. The moments are disordered in the absence of an applied magnetic field and ordered in the presence of an applied magnetic field.
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| File:Diagram of Ferrimagnetic Magnetic Moments.png|'''[[Ferrimagnetism]]''' The magnetic moments in a ferrimagnetic material. The moments are aligned oppositely and have different magnitudes due to being made up of two different ions. This is in the absence of an applied magnetic field.
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| File:Diagram of Antiferromagnetic Magnetic Moments.png|'''[[Antiferromagnetism]]''' The magnetic moments in an antiferromagnetic material. The moments are aligned oppositely and have the same magnitudes. This is in the absence of an applied magnetic field.
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| </gallery>
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| ==Materials with magnetic moments that change properties at the Curie temperature==
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| Ferromagnetic, paramagnetic, ferrimagnetic and antiferromagnetic structures are made up of intrinsic magnetic moments. If all electrons within the structure are paired, these moments cancel out due to having opposite spins and angular momentum. Thus even with an applied magnetic field will have different properties and no Curie Temperature.<ref name="Lüth 2009"/><ref name=Levy>{{harvnb|Levy|1968|pp=236–239}}</ref>
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| ===Paramagnetic===
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| {{main|Paramagnetism}}
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| A material is paramagnetic only above its Curie Temperature.
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| Paramagnetic materials are non-magnetic when a [[magnetic field]] is absent and magnetic when a magnetic field is applied.
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| When the magnetic field is absent the material has disordered magnetic moments; that is, the atoms are unsymmetrical and not aligned.
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| When the magnetic field is present the magnetic moments are temporarily realigned parallel to the applied field;<ref name=Dekker1>{{harvnb|Dekker|1958|pp=217–220}}</ref><ref name=Levy4>{{harvnb|Levy|1968|pp=}}</ref> the atoms are symmetrical and aligned.<ref name=Fan>{{harvnb|Fan|1987|pp=164–165}}</ref> The magnetic moment in the same direction is what causes an induced magnetic field.<ref name=Fan/><ref name=Dekker>{{harvnb|Dekker|1958|pp=454–455}}</ref>
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| For paramagnetism this response to an applied magnetic field is positive and known as [[magnetic susceptibility]].<ref name="Lüth 2009">{{cite book|last=Lüth|first=Harald Ibach, Hans|title=Solid-state physics : an introduction to principles of materials science|year=2009|publisher=Springer|location=Berlin|isbn=978-3-540-93803-3|edition=4th extensively updated and enlarged ed.}}</ref> The magnetic susceptibility only applies above the Curie Temperature for disordered states.<ref name=Mendelssohn3>{{harvnb|Mendelssohn|1977|p=162}}</ref>
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| '''Sources of Paramagnetism (Materials which have Curie Temperatures)''';<ref name=Levy1>{{harvnb|Levy|1968|pp=198–202}}</ref>
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| * All atoms which have unpaired electrons;
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| * Atoms where inner shells are incomplete in electrons;
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| * [[Free radicals]];
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| * Metals
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| Above the Curie Temperature the atoms are excited, the spin orientation becomes randomised,<ref name=Levy/> but can be realigned in an applied field and the material paramagnetic. Below the Curie Temperature the intrinsic structure has under gone a [[phase transition]],<ref name=Cusack>{{harvnb|Cusack|1958|p=269}}</ref> the atoms are ordered and the material is ferromagnetic.<ref name=Fan/> The paramagnetic materials induced magnetic fields are very weak in comparison to ferromagnetic materials magnetic fields.<ref name=Cusack/>
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| ===Ferromagnetic===
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| {{main|Ferromagnetism}}
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| Materials are only ferromagnetic below their corresponding Curie temperatures.
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| Ferromagnetic materials are magnetic in the absence of an applied magnetic field.
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| When a magnetic field is absent the material has [[spontaneous magnetization]] which is a result of the ordered magnetic moments; that is, for ferromagnetism, the atoms are symmetrical and aligned in the same direction creating a permanent magnetic field.
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| The magnetic interactions are held together by [[exchange interactions]]; otherwise thermal disorder would overcome the weak interactions of magnetic moments. The exchange interaction has a zero probability of parallel electrons occupying the same point in time, implying a preferred parallel alignment in the material.<ref name=Hall1>{{harvnb|Hall|1994|pp=220–221}}</ref> The Boltzmann factor contributes heavily as it prefers interacting particles to be aligned in the same direction.<ref name=Palmer>{{harvnb|Palmer|2007|pp=}}</ref> This causes [[ferromagnets]] to have strong magnetic fields and high Curie temperatures of around 1000K.<ref name=Hall3>{{harvnb|Hall|1994|p=220}}</ref>
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| Below the Curie temperature, the atoms are aligned and parallel, causing spontaneous magnetism; the material is ferromagnetic. Above the Curie temperature the material is paramagnetic, as the atoms lose their ordered magnetic moments when the material undergoes a phase transition.<ref name=Cusack/>
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| ===Ferrimagnetic===
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| {{main|Ferrimagnetism}}
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| Not to be confused with ferromagnetic.
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| Materials are only ferrimagnetic below their materials corresponding Curie Temperature.
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| Ferrimagnetic materials are magnetic in the absence of an applied magnetic field and are made up of two different [[ions]].<ref name=Jullien158/>
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| When a magnetic field is absent the material has a spontaneous magnetism which is the result of ordered magnetic moments; that is, for ferrimagnetism one ion's magnetic moments are aligned facing in one direction with certain magnitude and the other ion's magnetic moments are aligned facing in the opposite direction with a different magnitude. As the magnetic moments are of different magnitudes in opposite directions there is still a spontaneous magnetism and a magnetic field is present.<ref name=Jullien158>{{harvnb|Jullien|1989|pp=158–159}}</ref>
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| Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions. The orientations of moments however are anti-parallel which results in a net momentum by subtracting their momentum from one another.<ref name=Jullien158/>
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| Below the Curie Temperature the atoms of each ion are aligned anti-parallel with different momentums causing a spontaneous magnetism; the material is ferrimagnetic. Above the Curie Temperature the material is paramagnetic as the atoms lose their ordered magnetic moments as the material undergoes a phase transition.<ref name=Jullien158/>
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| ===Antiferromagnetic and the Néel temperature===
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| {{main|Antiferromagnetism}}
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| Materials are only antiferromagetic below their corresponding [[Néel Temperature]]. This is similar to the Curie Temperature as above the Néel Temperature the material undergoes a [[phase transition]] and becomes paramagnetic.
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| The material has equal magnetic moments aligned in opposite directions resulting in a zero magnetic moment and a net magnetism of zero at all temperatures below the Néel Temperature. Antiferromagnetic materials are weakly magnetic in the absence or presence of an applied magnetic field.
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| Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions preventing thermal disorder from overcoming the weak interactions of magnetic moments.<ref name=Hall1/><ref name=Jullien10/> When disorder occurs it is at the Néel Temperature.<ref name=Jullien10>{{harvnb|Jullien|1989|pp=156–157}}</ref>
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| ==Curie-Weiss law==
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| The [[Curie-Weiss law]] is an adapted version of [[Curie's law]].
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| The Curie-Weiss law is a simple model derived from a [[mean field theory|mean-field]] approximation, this means it works well for the materials temperature,T, much greater than their corresponding Curie Temperature,{{math|T<sub>c</sub>}}, i.e. ''T'' >> {{math|''T''<sub>c</sub>}}; however fails to describe the [[magnetic susceptibility]], {{math|χ}}, in the immediate vicinity of the Curie point because of local fluctuations between atoms.<ref name=Jullien153>{{harvnb|Jullien|1989|pp=153}}</ref>
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| Both Curie's law and the Curie-Weiss law do not hold for ''T''< {{math|''T''<sub>c</sub>}}.
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| Curie's law for a paramagnetic material;<ref name=Hall205>{{harvnb|Hall|1994|pp=205–206}}</ref>
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| :<math>\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T} </math>
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| {|
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| ! Definition !!
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| | {{math|χ}} ||the magnetic susceptibility; the influence of an applied [[magnetic field]] on a material
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| | ''M'' ||the [[magnetic moments]] per unit volume
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| |-
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| | ''H'' || the macroscopic magnetic field
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| | ''B'' ||the magnetic field
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| | ''C''||the material-specific [[Curie constant]]
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| |}
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| :<math>C = \frac{\mu_0 \mu_B^2}{3 k_B}N g^2 J(J+1)</math><ref name=Levy201>{{harvnb|Levy|1968|pp=201–202}}</ref>
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| {|
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| ! !!
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| | µ<sub>0</sub> || the [[permeability of free space]]. Note - in [[CGS]] units is taken to equal one.<ref name=Kittel1996>{{harvnb|Kittel|1996|pp=444}}</ref>
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| |-
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| | g || the [[Landé g-factor]]
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| |-
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| | J(J+1) || the eigenvalue for eigenstate J<sup>2</sup> for the stationary states within the incomplete atoms shells (electrons unpaired)
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| | µ<sub>B</sub> || the [[Bohr Magneton]]
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| |-
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| | k<sub>B</sub> || [[Boltzmann's constant]]
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| |-
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| | total magnetism || is N number of magnetic moments per unit volume
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| |}
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| The Curie-Weiss law is then derived from Curie's law to be
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| :<math>\chi = \frac{C}{T-T_c}</math>
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| where
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| :<math>T_C = \frac{C \lambda }{\mu_0}</math>
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| λ is the Weiss molecular field constant.<ref name=Levy201/><ref name=Myers>{{harvnb|Myers|1997|pp=334–345}}</ref>
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| For full derivation see [[Curie-Weiss law]]
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| ==Physics of Curie temperature==
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| ===Approaching Curie temperature from above===
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| As the Curie-Weiss Law is an approximation a more accurate model is needed when the temperature,T, approaches the materials Curie Temperature,T<sub>C</sub>.
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| Magnetic susceptibility occurs above the Curie Temperature.
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| An accurate model of critical behaviour for magnetic susceptibility with [[critical exponent]] {{math| <var>γ</var>}};
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| :<math>\chi \sim \frac{1}{(T - T_{c})^\gamma}</math>
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| The critical exponent differs between materials and for the [[mean field theory|mean-field]] model is taken as {{math| <var>γ</var>}}=1.<ref name=Hall227>{{harvnb|Hall|1994|pp=227–228}}</ref>
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| As temperature is inversely proportional to magnetic susceptibility when T approaches T<sub>C</sub> the denominator tends to zero and the magnetic susceptibility approaches [[infinity]] allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials.<ref name=Kittel>{{harvnb|Kittel|1986|pp=424–426}}</ref><ref>{{harvnb|Spaldin|2010|pp=52–54}}</ref>
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| ===Approaching Curie temperature from below===
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| Magnetism depends on temperature and spontaneous magnetism occurs below the Curie Temperature.
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| An accurate model of critical behaviour for spontaneous magnetism with critical exponent β;
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| :<math>M \sim (T - T_C)^\beta</math>
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| The critical exponent differs between materials and for the mean-field model as taken as β=0.5 where ''T''<<''T''<sub>C</sub>.<ref name=Hall227/>
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| The spontaneous magnetism approaches zero as the temperature increases towards the materials Curie Temperature.
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| ===Approaching absolute zero (0 [[Kelvin]])===
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| The spontaneous magnetism, occurring in ferromagnetic, ferrimagnetic and antiferromagnetic materials, approaches zero as the temperature increases towards the material's Curie Temperature. Spontaneous magnetism is at its maximum as the temperature approaches 0K.<ref name=Hall4>{{harvnb|Hall|1994|pp=225}}</ref> That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to no thermal disturbance.
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| In paramagnetic materials temperature is sufficient to overcome the ordered alignments. As the temperature approaches 0K the [[entropy]] decreases to zero, that is, the disorder decreases and becomes ordered. This occurs without the presence of an applied magnetic field and obeys the [[third law of thermodynamics]].<ref name=Hall1/>
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| Both Curie's Law and the Curie-Weiss law fail as the temperature approaches 0K. This is because they depend on the magnetic susceptibility which only applies when the state is disordered.<ref name=Mendelssohn1>{{harvnb|Mendelssohn|1977|pp=180–181}}</ref>
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| Gadolinium Sulphate continues to satisfy Curie's law at 1K. Between 0-1K the law fails to hold and a sudden change in the intrinsic structure occurs at the Curie Temperature.<ref name=Mendelssohn2>{{harvnb|Mendelssohn|1977|p=167}}</ref>
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| ===Ising model of phase transitions===
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| The [[Ising model]] is mathematically based and can analyse the critical points of [[phase transitions]] in ferromagnetic order due to spins of electrons having magnitudes of either +/- ½. The spins interact with their neighbouring [[dipole]] electrons in the structure and here the Ising model can predict their behaviour with each other.<ref name=Bertoldi>{{harvnb|Bertoldi|2012}}</ref><ref name=Brout>{{harvnb|Brout|1965|pp=6–7}}</ref>
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| This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie Temperature. As a result many different dependencies that effect the Curie Temperature can be analysed.
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| For example the surface and bulk properties depend on the alignment and magnitude of spins and the Ising model can determine the effects of magnetism in this system.
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| ===Weiss domains and surface and bulk Curie temperatures===
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| [[File:Weiss domains in a ferromagnetic material.png|thumb|right|'''Figure 3''' The Weiss domains in a ferromagnetic material; the magnetic moments are aligned in domains.]]
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| Materials structures consist of intrinsic magnetic moments which are separated into domains called [[Weiss domains]].<ref name=Jullien160>{{harvnb|Jullien|1989|p=161}}</ref> This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out.<ref name=Jullien160/>
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| The position of particles can therefore have different orientations around the surface than the main part (bulk) of the material. This property directly affects the Curie Temperature as there can be a bulk Curie Temperature T<sub>B</sub> and a different surface Curie Temperature T<sub>S</sub> for a material.<ref name=Rau>{{harvnb|Rau|1988|pp=}}</ref>
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| This allows for the surface Curie Temperature to be ferromagnetic above the bulk Curie Temperature when the main state is disordered, i.e. Ordered and disordered states occur simultaneously.<ref name=Bertoldi/>
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| The surface and bulk properties can be predicted by the Ising model and electron capture spectroscopy can be used to detect the electron spins and hence the [[magnetic moments]] on the surface of the material. An average total magnetism is taken from the bulk and surface temperatures to calculate the Curie Temperature from the material, noting the bulk contributes more.<ref name=Bertoldi/><ref name=Skomski>{{harvnb|Skomski|2000|pp=}}</ref>
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| The [[angular momentum]] of an electron is either +ħ/2 or - ħ/2 due to it having a spin of ½, which gives a specific size of magnetic moment to the electron; the [[Bohr Magneton]].<ref name=Jullien138>{{harvnb|Jullien|1989|pp=138}}</ref> Electrons orbiting around the nucleus in a current loop create a magnetic field which depends on the Bohr Magneton and [[magnetic quantum number]].<ref name=Jullien138/> Therefore the magnetic moments are related between angular and orbital momentum and affect each other. Angular momentum contributes twice as much to magnetic moments than orbital.<ref name=Hall1994>{{harvnb|Hall|1994|pp=}}</ref>
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| For [[terbium]] which is a [[rare earth metal]] and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high [[anisotropy]] on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie Temperature while its bulk becomes ferrimagnetic and then at higher temperatures its surface remains ferrimagnetic above its bulk Néel Temperature before becoming completely disordered and paramagnetic with increasing temperature. The anisotropy in the bulk is different from its surface anisotropy just above these phase changes as the magnetic moments will be ordered differently or ordered in paramagnetic materials.<ref name=Rau/>
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| ===Changing a material's Curie temperature ===
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| ====Composite materials====
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| [[Composite materials]], that is, materials composed from other materials with different properties, can change the Curie Temperature. For example a composite which has [[silver]] in can create spaces for oxygen molecules in bonding which decreases the Curie Temperature<ref name=Hwang>{{harvnb|Hwang|1998|pp=}}</ref> as the crystal lattice will not be as compact.
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| The alignment of magnetic moments in the composite material affects the Curie Temperature. If the materials moments are parallel with each other the Curie Temperature will increase and if perpendicular the Curie Temperature will decrease<ref name=Hwang/> as either more or less thermal energy will be needed to destroy the alignments.
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| Preparing composite materials through different temperatures can result in different final compositions which will have different Curie Temperatures.<ref name=Jones>{{harvnb|Jones|2003|pp=}}</ref> [[Doping (semiconductor)|Doping]] a material can also affect its Curie Temperature.<ref name=Jones/>
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| The density of nanocomposite materials changes the Curie Temperature.
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| [[Nanocomposites]] are compact structures on a nano-scale. The structure is built up of high and low bulk Curie Temperatures, however will only have one mean-field Curie Temperature. A higher density of lower bulk temperatures results in a lower mean-field Curie Temperature and a higher density of higher bulk temperature significantly increases the mean-field Curie Temperature. In more than one dimension the Curie Temperature begins to increase as the magnetic moments will need more thermal energy to overcome the ordered structure.<ref name=Skomski/>
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| ====Particle size====
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| The size of particles in a material's crystal lattice changes the Curie Temperature.
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| Due to the small size of particles (nanoparticles) the fluctuations of electron spins become more prominent, this results in the Curie Temperature drastically decreasing when the size of particles decrease as the fluctuations cause disorder. The size of a particle also affects the [[anisotropy]] causing alignment to become less stable and thus lead to disorder in magnetic moments.<ref name=Bertoldi/><ref name=Lopez-Dominguez>{{harvnb|Lopez-Dominguez|2012|pp=}}</ref>
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| The extreme of this is [[superparamagnetism]] which only occurs in small ferromagnetic particles and is where fluctuations are very influential causing magnetic moments to change direction randomly and thus create disorder.
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| The Curie Temperature of nanoparticles are also affected by the [[crystal lattice]] structure, [[body-centred cubic]] (bcc), [[face-centred cubic]] (fcc) and a [[hexagonal]] structure (hcp) all have different Curie Temperatures due to magnetic moments reacting to their neighbouring electron spins. fcc and hcp have tighter structures and as a results have higher Curie Temperatures than bcc as the magnetic moments have stronger effects when closer together.<ref name=Bertoldi/>
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| This is known as the [[coordination number]] which is the number of nearest neighbouring particles in a structure. This indicates a lower coordination number at the surface of a material than the bulk which leads to the surface becoming less significant when the temperature is approaching the Curie Temperature. In smaller systems the coordination number for the surface is more significant and the magnetic moments have a stronger affect on the system.<ref name=Bertoldi/>
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| Although fluctuations in particles can be minuscule, they are heavily dependent on the structure of crystal lattices as they react with their nearest neighbouring particles. Fluctuations are also affected by the exchange interaction<ref name=Lopez-Dominguez/> as parallel facing magnetic moments are favoured and therefore have less disturbance and disorder, therefore a tighter structure influences a stronger magnetism and therefore a higher Curie Temperature.
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| ====Pressure====
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| Pressure changes a material's Curie Temperature.
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| Increasing [[pressure]] on the [[crystal lattice]] decreases the volume of the system. Pressure directly affects the [[kinetic energy]] in particles as movement increases causing the vibrations to disrupt the order of magnetic moments. This is similar to temperature as it also increases the kinetic energy of particles and destroys the order of magnetic moments and magnetism.<ref name=Bose>{{harvnb|Bose|2011|pp=}}</ref>
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| Pressure also affects the [[density of states]] (DOS).<ref name=Bose/> Here the DOS decreases causing the number of electrons available to the system to decrease. This leads to the number of magnetic moments decreasing as they depend on electron spins. It would be expected because of this that the Curie Temperature would decrease however it increases. This is the result of the [[exchange interaction]]. The exchange interaction favours the aligned parallel magnetic moments due to electrons being unable to occupy the same space in time<ref name=Hall1/> and as this is increased due to the volume decreasing the Curie Temperature increases with pressure. The Curie Temperature is made up of a combination of dependencies on kinetic energy and the DOS.<ref name=Bose/>
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| It is interesting to note that the concentration of particles also affects the Curie Temperature when pressure is being applied and can result in a decrease in Curie Temperature when the concentration is above a certain percent.<ref name=Bose/>
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| ====Orbital ordering====
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| [[Atomic orbital|Orbital ordering]] changes the Curie Temperature of a material.
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| Orbital ordering can be controlled through applied [[Strains]]{{Disambiguation needed|date=March 2013}}.<ref name=Sadoc>{{harvnb|Sadoc|2010|pp=}}</ref> This is a function that determines the wave of a single electron or paired electrons inside the material. Having control over the [[probability]] of where the electron will be allows the Curie Temperature to be altered. For example the [[delocalised]] electrons can be moved onto the same [[lattice plane|plane]] by applied strains within the crystal lattice.<ref name=Sadoc/>
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| The Curie Temperature is seen to increase greatly due to electrons being packed together in the same plane, they are forced to align due to the [[exchange interaction]] and thus increases the strength of the magnetic moments which prevents thermal disorder at lower temperatures.
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| ==Curie temperature in ferroelectric and piezoelectric materials==
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| In analogy to ferromagnetic and paramagnetic materials, the Curie Temperature can also used to describe the temperature where a material's spontaneous electric [[Dipolar polarization|polarisation]] changes to induced electric polarisation, or vice versa.<ref name=Myers404>{{harvnb|Myers|1997|pp=404–405}}</ref>
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| Electric polarisation is a result of aligned electric [[dipoles]]. Aligned electric dipoles are composites of positive and negative charges where all the dipoles are facing in one direction. The charges are separated from their stable placement in the particles and can occur spontaneously, from pressure or an applied [[electric field]].<ref name=Jullien58>{{harvnb|Jullien|1989|pp=56–59}}</ref>
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| [[Ferroelectric]], [[dielectric]] (paraelectric) and [[piezoelectric]] materials have electric polarisation. In ferroelectric materials there is a spontaneous electric polarisation in the absence of an applied electric field.<ref name=Myers404/> In dielectric materials there is electric polarisation aligned only when an electric field is applied.<ref name=Jullien58/> Piezoelectric materials have electric polarisation due to applied [[mechanical stress]] distorting the structure from pressure.<ref name=Hall75>{{harvnb|Hall|1994|p=275}}</ref>
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| T<sub>0</sub> is the temperature where ferroelectric materials lose their spontaneous polarisation as a first or second order phase change occurs, that is the internal structure changes or the internal symmetry changes.<ref name=Myers404/>
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| In certain cases T<sub>0</sub> is equal to the Curie Temperature however the Curie Temperature can be 10 kelvin lower than T<sub>0</sub>.<ref name=Webster>{{harvnb|Webster|1999|pp=}}</ref>
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| [[File:Ferroelectric polarisation.svg|thumb|150px|right|'''Figure 4''' (Below T<sub>0</sub>) Ferroelectric polarisation '''P''' in an applied electric field '''E'''.]]
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| [[File:Paraelectric polarisation.svg|thumb|150px|right|'''Figure 5''' (Above T<sub>0</sub>) Dielectric polarisation '''P''' in an applied electric field '''E'''.]]
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| {|
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| |-
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| ! Below {{math|''T''<sub>0</sub>}} !! Above {{math|''T''<sub>0</sub>}}<ref name=Kovetz>{{harvnb|Kovetz|1990|p=116}}</ref>
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| |-
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| | Ferroelectric ||↔ Dielectric
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| |}
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|
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| All ferroelectric materials are piezoelectric.<ref name=Myers404/>
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| '''Piezoelectric'''
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| An external force applies pressure on particles inside the material which affects the structure of the crystal lattice. Particles in a unit cell become unsymmetrical which allows a net polarisation from each particle. Symmetry would cancel the opposing charges out and there would be no net polarisation.<ref name=Pascoe>{{harvnb|Pascoe|1973|pp=186–187}}</ref> Below the transition temperature T<sub>0</sub> displacement of electric charges causes polarisation. Above the transition temperature T<sub>0</sub> the structure is cubic and symmetric, causing the material to become dielectric. Electric charges are also agitated and disordered causing the material to have no electric polarisation in the absence of an applied electric field.
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| '''Ferroelectric and Dielectric'''
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| Materials are only ferroelectric below their corresponding transition temperature T<sub>0</sub>.<ref name=Myers404/>
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| Ferroelectric materials are all piezoelectric and therefore have a spontaneous electric polarisation as the structures are unsymmetrical.
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| Materials are only dielectric above their corresponding transition temperature T<sub>0</sub>.<ref name=Hummel>{{harvnb|Hummel|2001|pp=189}}</ref> Dielectric materials have no electric polarisation in the absence of an applied electric field. The electric dipoles are unaligned and have no net polarisation. In analogy to magnetic susceptibility, electric susceptibility only occurs above T<sub>0</sub>.
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| Ferroelectric materials when polarised are influenced under [[hysteresis]] (Figure 4); that is they are dependent on their past state as well as their current state. As an electric field is applied the dipoles are forced to align and polarisation is created, when the electric field is removed polarisation remains. The hysteresis loop depends on temperature and as a result as the temperature is increased and reaches T<sub>0</sub> the two curves become one curve as shown in the dielectric polarisation (Figure 5).<ref name=Pascoe1>{{harvnb|Pascoe|1973|pp=190–191}}</ref>
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| '''Relative Permittivity'''
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| A modified version of the Curie Weiss law applies to the dielectric constant, also known as the [[relative permittivity]]:<ref name=Webster/><ref>{{cite book|last=Webster|first=John G.|title=The measurement, instrumentation, and sensors handbook|year=1999|publisher=CRC Press published in cooperation with IEEE Press|location=Boca Raton, Fla.|isbn=9780849383472|pages=6.55–6.56|edition=[Online-Ausg.]}}</ref>
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| :<math>\epsilon = \epsilon_0 + \frac{C}{T-T_c}.</math>
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| ==Applications==
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| A heat-induced ferromagnetic-paramagnetic transition is used in [[magneto-optical]] storage media, for erasing and writing of new data. Famous examples include the [[Sony]] [[Minidisc]] format, as well as the now-obsolete [[CD-RW#CD-MO|CD-MO]] format. Other uses include temperature control in [[soldering iron]]s, and stabilizing the magnetic field of [[tachometer]] generators against temperature variation.<ref>{{harvnb|Pallàs-Areny|Webster|2001|pp=262–263}}</ref>
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| ==See also==
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| * [[Ferroelectric effect]]
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| * [[Curie's law]]
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| == Notes ==
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| {{Reflist|colwidth=30em}}
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| *{{cite journal|last=Jones|first=Paulsen, Jason A. Lo, Chester C H; Snyder, John E.; Ring, A. P.; Jones, L. L.; Jiles, David C.|title=Study of the Curie temperature of cobalt ferrite based composites for stress sensor applications|date=Sept. 2003|year=2003|volume=39 , Issue: 5|pages=3316–3318|accessdate=12/03/2013}}
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| *{{cite journal|last=Hwang|first=Hae Jin|coauthors=Nagai, Toru; Ohji, Tatsuki; Sando, Mutsuo; Toriyama, Motohiro; Niihara, Koichi|title=Curie Temperature Anomaly in Lead Zirconate Titanate/Silver Composites|journal=Journal of the American Ceramic Society|date=21 January 2005|volume=81|issue=3|pages=709–712|doi=10.1111/j.1151-2916.1998.tb02394.x|accessdate=12/03/2013}}
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| *{{cite journal|last=Sadoc|first=Aymeric|coauthors=Mercey, Bernard; Simon, Charles; Grebille, Dominique; Prellier, Wilfrid; Lepetit, Marie-Bernadette|title=Large Increase of the Curie Temperature by Orbital Ordering Control|journal=Physical Review Letters|date=1 January 2010|volume=104|issue=4|doi=10.1103/PhysRevLett.104.046804|accessdate=2013-02-19|arxiv = 0910.3393 |bibcode = 2010PhRvL.104d6804S }}
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| *{{cite web|title=Pierre Curie - Biography|url=http://www.nobelprize.org/nobel_prizes/physics/laureates/1903/pierre-curie-bio.html|work=Nobelprize.org, From Nobel Lectures, Physics 1901-1921, Elsevier Publishing Company, Amsterdam, 1967|publisher=The Nobel Foundation 1903|accessdate=2013-03-14}}
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| *{{cite journal|authors=Martin Kochmański, Tadeusz Paszkiewicz, Sławomir Wolski |title=Curie-Weiss magnet: a simple model of phase transition |journal=European Journal of Physics |volume=34 |year=2013 |pages=1555–1573|doi=10.1088/0143-0807/34/6/1555}}
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| {{Refend}}
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| == External links ==
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| * [http://es.youtube.com/watch?v=X8ZHQQUusGo Ferromagnetic Curie Point]. Video by [[Walter Lewin]], [[M.I.T.]]
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| [[Category:Phase transitions]]
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| [[Category:Critical phenomena]]
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| [[Category:Temperature]]
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