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| '''Single domain''', in [[magnetism]], refers to the state of a [[ferromagnet]]<ref>in the broader meaning of the term that includes [[ferrimagnetism]].</ref> in which the [[magnetization]] does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a '''single domain particle''' (but other definitions are possible; see below).<ref>[[Superparamagnetic]] particles are often called single-domain as well because they behave like a [[paramagnet]] with a single large spin.</ref> Such particles are very small (generally below a [[micrometre]] in diameter). They are also very important in a lot of applications because they have a high [[coercivity]]. They are the main source of hardness in [[hard magnet]]s, the carriers of [[magnetic memory]] in [[tape drives]], and the best recorders of the ancient [[Earth's magnetic field]] (see [[paleomagnetism]]). | | My name's Gretchen Sikora but everybody calls me Gretchen. I'm from Poland. I'm studying at the college (2nd year) and I play the Pedal Steel Guitar for 8 years. Usually I choose music from my famous films :D. <br>I have two brothers. I like Vintage Books, [http://www.adobe.com/cfusion/search/index.cfm?term=&watching+movies&loc=en_us&siteSection=home watching movies] and Judo.<br><br>Feel free to visit my web page [http://aussiesolarenergy.wordpress.com/2014/10/06/what-facts-to-consider-while-hiring-solar-power-company/ solar panel australia] |
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| == History ==
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| Early theories of [[magnetization]] in [[ferromagnets]] assumed that ferromagnets are divided into [[magnetic domains]] and that the magnetization changed by the movement of [[Domain wall (magnetism)|domain wall]]s. However, as early as 1930, Frenkel and Dorfman predicted that sufficiently small particles could only hold one domain, although they greatly overestimated the upper size limit for such particles.<ref name=Brown>{{Harvnb|Brown, Jr.|1978}}</ref> The possibility of single domain particles received little attention until two developments in the late 1940s: (1) Improved calculations of the upper size limit by Kittel and Néel, and (2) a calculation of the magnetization curves for systems of single-domain particles by Stoner and Wohlfarth.<ref>{{Harvnb|Wohlfarth|1959}}</ref><ref name=SW>{{Harvnb|Stoner|Wohlfarth|1948}}</ref> The [[Stoner–Wohlfarth model]] has been enormously influential in subsequent work and is still frequently cited.
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| == Definitions of a single-domain particle ==
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| Early investigators pointed out that a ''single-domain particle'' could be defined in more than one way.<ref name=Brown1958>{{Harvnb|Brown, Jr.|1958}}</ref> Perhaps most commonly, it is implicitly defined as a particle that is in a single-domain state throughout the hysteresis cycle, including during the transition between two such states. This is the type of particle that is modeled by the [[Stoner–Wohlfarth model]]. However, it might be in a single-domain state except during reversal. Often particles are considered single-domain if their saturation [[remanence]] is consistent with the single-domain state. More recently it was realized that a particle's state could be single-domain for some range of magnetic fields and then change continuously into a non-uniform state.<ref name=Newell>{{Harvnb|Newell|Merrill|1998}}</ref>
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| Another common definition of ''single-domain particle'' is one in which the single-domain state has the lowest energy of all possible states (see below).
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| == Single domain hysteresis ==
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| If a particle is in the single-domain state, all of its internal [[magnetization]] is pointed in the same direction. It therefore has the largest possible [[magnetic moment]] for a particle of that size and composition. The magnitude of this moment is <math>\mu = V M_s</math>, where <math>V</math> is the volume of the particle and <math>M_s</math> is the [[saturation magnetization]].
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| The magnetization at any point in a ferromagnet can only change by rotation. If there is more than one [[magnetic domain]], the transition between one domain and its neighbor involves a rotation of the magnetization to form a [[Domain wall (magnetism)|domain wall]]. Domain walls move easily within the magnet and have a low [[coercivity]]. By contrast, a particle that is single-domain in all magnetic fields changes its state by rotation of all the magnetization as a unit. This results in a much larger [[coercivity]].
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| The most widely used theory for hysteresis in single-domain particle is the [[Stoner–Wohlfarth model]]. This applies to a particle with uniaxial [[magnetocrystalline anisotropy]].
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| == Limits on the single-domain size == | |
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| Experimentally, it is observed that though the magnitude of the magnetization is uniform throughout a homogeneous specimen at uniform temperature, the direction of the magnetization is in general not uniform, but varies from one region to another, on a scale corresponding to visual observations with a microscope. Uniform of direction is attained only by applying a field, or by choosing as a specimen, a body which is itself of microscopic dimensions (a ''fine particle'').<ref name=Brown1958/> The size range for which a ferromagnet become single-domain is generally quite narrow and a first quantitative results in this direction are due to [[William Fuller Brown, Jr.]] who, in his fundamental paper,<ref>{{cite journal|last=Brown|first=William Fuller|title=The Fundamental Theorem of Fine-Ferromagnetic-Particle Theory|journal=Journal of Applied Physics|date=1 January 1968|volume=39|issue=2|pages=993|doi=10.1063/1.1656363|bibcode = 1968JAP....39..993F }}</ref> rigorously proved (in the framework of [[Micromagnetics]]), though in the special case of a homogeneous sphere of radius <math>r\,\!</math>, what nowadays is known as ''Brown’s fundamental theorem of the theory of fine ferromagnetic particles''. This theorem states the existence of a critical radius <math>r_c\,\!</math> such that the state of lowest free energy is one of uniform magnetization if <math> r < r_c\,\!</math> (i.e. the existence of a critical size under which spherical ferromagnetic particles stay uniformly magnetized in zero applied field). A lower bound for <math>r_c\,\!</math> can then be computed. In 1988, [[Amikam Aharoni|Amikam A. Aharoni]],<ref>{{cite journal|last=Aharoni|first=Amikam|title=Elongated single-domain ferromagnetic particles|journal=Journal of Applied Physics|date=1 January 1988|volume=63|issue=12|pages=5879|doi=10.1063/1.340280|bibcode = 1988JAP....63.5879A }}</ref> by using the same mathematical reasoning as Brown, was able to extend the Fundamental Theorem to the case of a [[prolate spheroid]]. Recently,<ref>{{cite journal|last=Di Fratta|first=G.|coauthors=et Al.|title=A generalization of the fundamental theorem of Brown for fine ferromagnetic particles|journal=Physica B: Condensed Matter|date=30 April 2012|volume=407|issue=9|pages=1368–1371|doi=10.1016/j.physb.2011.10.010|bibcode = 2012PhyB..407.1368D }}</ref> Brown’s fundamental theorem on fine ferromagnetic particles has been rigorously extended to the case of a [[Ellipsoid|general ellipsoid]], and an estimate for the critical diameter (under which the ellipsoidal particle become single domain) has been given in terms of the [[Demagnetizing field|demagnetizing factors]] of the general ellipsoid.<ref>{{cite journal|last=Osborn|first=J.|title=Demagnetizing Factors of the General Ellipsoid|journal=Physical Review|date=31 May 1945|volume=67|issue=11-12|pages=351–357|doi=10.1103/PhysRev.67.351|bibcode = 1945PhRv...67..351O }}</ref>
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| Although pure single-domain particles (mathematically) exist for some special geometries only, for most ferromagnets a state of quasi-uniformity of magnetization is achieved when the diameter of the particle is in between about <math>10</math> nanometers and <math>100</math> nanometers {{citation needed|date=August 2013}}(Chris Binns, ''Introduction to Nanoscience and Technology'', page 31, Wiley). The size range is bounded below by the transition to [[superparamagnetism]] and above by the formation of multiple [[magnetic domains]].
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| === Lower limit: superparamagnetism ===
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| {{Main|Superparamagnetism}}
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| [[Thermal fluctuations]] cause the [[magnetization]] to dance around in a random manner. In the single-domain state, the moment rarely strays far from the local stable state. Energy barriers (see also [[activation energy]]) prevent the magnetization from jumping from one state to another. However, if the energy barrier gets small enough, the moment can jump from state to state frequently enough to make the particle [[superparamagnetic]]. The frequency of jumps has a strong exponential dependence on the energy barrier, and the energy barrier is proportional to the volume, so there is a critical volume at which the transition occurs. This volume can be thought of as the volume at which the ''[[Néel relaxation theory#Blocking temperature|blocking temperature]]'' is at room temperature.
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| === Upper limit: transition to multiple domains ===
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| As size of a ferromagnet increases, the single-domain state incurs an increasing energy cost because of the [[demagnetizing field]]. This field tends to rotate the magnetization in a way that reduces the total moment of the magnet, and in larger magnets the magnetization is organized in [[magnetic domains]]. The demagnetizing energy is balanced by the energy of the [[exchange interaction]], which tends to keep spins aligned. There is a critical size at which the balance tips in favor of the demagnetizing field and the [[magnetic domains|multidomain]] state is favored. Most calculations of the upper size limit for the single-domain state identify it with this critical size.<ref>{{Harvnb|Morrish|Yu|1955}}</ref><ref>{{Harvnb|Butler|Banerjee|1975}}</ref><ref>{{Harvnb|Aharoni|2001}}</ref>
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| == Notes ==
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| {{Reflist|2}}
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| == References ==
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| {{Refbegin}}
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| *{{cite journal
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| |doi = 10.1063/1.1407313
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| |last = Aharoni
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| |first = Amikam
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| |title = Brown's "fundamental theorem" revisited
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| |journal = [[Journal of Applied Physics]]
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| |volume = 90
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| |issue = 9
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| |pages = 4645–4650
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| |year = 2001
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| |bibcode = 2001JAP....90.4645A
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| |ref=harv}}
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| *{{cite journal
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| |doi = 10.1063/1.1723183
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| |last = Brown, Jr.
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| |first = William Fuller
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| |author-link = William Fuller Brown, Jr.
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| |title = Rigorous approach to the theory of ferromagnetic microstructure
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| |journal = [[Journal of Applied Physics]]
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| |volume = 29
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| |issue = 3
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| |pages = 470–471
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| |year = 1958
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| |bibcode = 1958JAP....29..470F
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| |ref=harv}}
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| *{{cite book
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| |last = Brown, Jr.
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| |first = William Fuller
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| |title = Micromagnetics
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| |author-link = William Fuller Brown, Jr.
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| |publisher = Robert E. Krieger Publishing Co.
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| |year = 1978
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| |origyear = Originally published in 1963
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| |isbn = 0-88275-665-6
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| |ref=harv
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| }}
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| *{{cite journal
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| |last1 = Butler
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| |first1 = Robert F.
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| |last2 = Banerjee
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| |first2 = S. K.
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| |title = Theoretical single-domain grain size range in magnetite and titanomagnetite
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| |journal = [[Journal of Geophysical Research]]
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| |volume = 84
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| |pages = 4394–4402
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| |year = 1975
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| |doi = 10.1029/JB080i029p04049
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| |bibcode = 1975JGR....80.4049B
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| |ref=harv}}
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| *{{cite journal
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| |doi = 10.1063/1.1722134
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| |last1 = Morrish
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| |first1 = A. H.
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| |last2 = Yu
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| |first2 = S. P.
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| |title = Dependence of the coercive force on the density of some iron oxide powders
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| |journal = [[Journal of Applied Physics]]
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| |volume = 26
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| |issue = 8
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| |pages = 1049–1055
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| |year = 1955
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| |bibcode = 1955JAP....26.1049M
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| |ref=harv}}
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| *{{cite journal
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| |doi = 10.1063/1.368661
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| |last1 = Newell
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| |first1 = A. J.
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| |last2 = Merrill
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| |first2 = R. T.
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| |title = The curling nucleation mode in a ferromagnetic cube
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| |journal = [[Journal of Applied Physics]]
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| |volume = 84
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| |issue = 8
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| |pages = 4394–4402
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| |year = 1998
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| |bibcode = 1998JAP....84.4394N
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| |ref=harv}}
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| *{{cite journal
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| |last1 = Stoner
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| |first1 = E. C.
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| |last2 = Wohlfarth
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| |first2 = E. P.
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| |title = A mechanism of magnetic hysteresis in heterogeneous alloys
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| |journal = [[Philosophical Transactions of the Royal Society A: Physical, Mathematical and Engineering Sciences]]
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| |volume = 240
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| |issue = 826
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| |pages = 599–642
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| |year = 1948
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| |doi = 10.1098/rsta.1948.0007
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| |bibcode = 1948RSPTA.240..599S
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| |ref=harv}}
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| *{{cite journal
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| |last = Wohlfarth
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| |first = E. P.
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| |title = Hard magnetic materials
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| |journal = [[Advances in Physics]]
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| |volume = 8
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| |issue = 30
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| |pages = 87–224
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| |year = 1959
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| |doi = 10.1080/00018735900101178
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| |bibcode = 1959AdPhy...8...87W
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| |ref=harv}}
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| {{Refend}}
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| [[Category:Rock magnetism]]
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| [[Category:Magnetic ordering]]
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My name's Gretchen Sikora but everybody calls me Gretchen. I'm from Poland. I'm studying at the college (2nd year) and I play the Pedal Steel Guitar for 8 years. Usually I choose music from my famous films :D.
I have two brothers. I like Vintage Books, watching movies and Judo.
Feel free to visit my web page solar panel australia