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Nanospintronics with Molecular Magnets - Tunneling and Spin-Electric Coupling

Nossa Márquez, Javier Francisco LU (2013)
Abstract (Swedish)
Popular Abstract in English

In this thesis we investigate the manipulation of the magnetic properties of molecular magnets by means of external electric fields. This manipulation is mediated by either the spin-electric coupling or the magnetic anisotropy of the molecular magnet. In order to understand what this means, let us first explain some basic concepts about magnetism. We will start explaining what a molecular magnet is. Imagine you have a bunch of transition metal atoms, such as iron, cobalt, nickel or manganese, arranged in such a way that the interaction between them makes them stick together and provide magnetic features to the molecule. We will call this arrangement the {\it magnetic core} of the molecular... (More)
Popular Abstract in English

In this thesis we investigate the manipulation of the magnetic properties of molecular magnets by means of external electric fields. This manipulation is mediated by either the spin-electric coupling or the magnetic anisotropy of the molecular magnet. In order to understand what this means, let us first explain some basic concepts about magnetism. We will start explaining what a molecular magnet is. Imagine you have a bunch of transition metal atoms, such as iron, cobalt, nickel or manganese, arranged in such a way that the interaction between them makes them stick together and provide magnetic features to the molecule. We will call this arrangement the {\it magnetic core} of the molecular magnet. Now imagine this core to be surrounded by other atoms (inorganic ligands) that can be designed to ensure the molecule binds on surfaces or into junctions. We will call this shield {\it inorganic shell}.

But why a molecule can be called a molecular magnet? First of all, a molecule is a collection of atoms. Each atom has electrons. Electrons in the universe have internal magnetic properties, more precisely an intrinsic angular momentum that generates a magnetic moment. One could think that they are basically like little tiny bar magnets, one of those with north and south poles. This intrinsic property is called the {\it spin}. Although in reality the spin is purely a quantum mechanical object that comes from the solution of the relativistic Dirac’s equation in quantum mechanics, it is commonly represented by an arrow pointing either up or down. A representation of the spin orientation is shown in Fig. \ref{fig:spins} a). The up or down illustrates the orientation of the tiny little magnet (see Fig \ref{fig:spins} b)). When an electron is placed in a magnetic field, its spin lines up with that field. A familiar effect can be viewed when a compass needle lines up with the magnetic field of the earth (see Fig. \ref{fig:spins} c)).

From magnetic materials to molecular magnets one can follow this trend of thoughts. A magnetic material is created when the spins (intrinsic magnetic fields) of the electrons in the bulk of material are all aligned. The same happens in a finite system, a magnetic domain is created when the spins of a number of electrons in a collection of atoms become parallel. Now, down to the molecular size, when the spins of two or more electrons in the atoms of a molecule line up with each other, a magnetic molecule is created. It exhibits the classical properties of a magnet, but because of its little tiny size, it also exhibits quantum properties. Note that, so far, we have not used any external magnetic field to line up the spins of the molecule. This alignment has purely quantum mechanical origin. In a molecular magnet the orientation of this aligned spin along a particular direction is determined by the interaction of the electron spin and the electron orbital motion in the molecular structure. This property is called magnetic anisotropy and it depends on the complicated bonding of the magnetic atoms of the core with the non-magnetic atoms of the structure. Nowadays this bonding can be, to a certain extent, designed in the laboratory. It gives us the opportunity of create molecules with particular properties. The amount of parallel spins in a molecular magnet determines the robustness of its magnetic behavior: the larger the number of parallel spins, the more magnetic the molecule is.

So far, we have defined what molecular magnets are. Now, let us talk about how we can manipulate their magnetic properties. One could think a molecular magnet as a collection of parallel spins or as a giant spin representing all the spins at once. In the latter case, the magnetic behavior of a molecular magnet comes from its (giant) spin. One could control the magnetic properties of the molecular magnets by means of the manipulations of its spin. Traditionally the spin is manipulated by means of magnetic fields. This manipulation has, however, some challenges when it comes to the molecular size. The typical size of a molecular magnet is about few nanometers. A nanometer is one billion times smaller than one meter. Therefore, it is very difficult to apply magnetic fields locally at this nanoscale regime. Magnetic fields present slow switching. In addition, it is hard to obtain a very strong magnetic field. On the other hand, strong electric fields are easy to obtain and can readily be applied locally on the nanoscale. They can also be turned on and off very fast. Therefore, the manipulation of the magnetic properties of molecular magnets by means of an electric field is an interesting and promising field of study.

In this thesis we study two methods of manipulating the magnetic properties of molecular magnets by means of an external electric field. In the first method we investigate the coupling of the spin of a molecular magnet with the external electric field. We consider a special class of molecular magnet with interesting and particular properties of its ground state. The ground state tells us how the molecule is when it is in its lowest energetic state. Due to the special molecular magnet geometry, an electric field can couple with the spin of the system. Therefore, manipulating the orientation and strength of the electric field, one could manipulate the spin of the molecular magnet. In the second method, we manipulate the magnetic anisotropy of the molecular magnet. In this case we use another type of molecular magnet characterized for its large magnetic anisotropy energy, which is the energy that it takes to rotate the total spin of the molecule away from its preferential direction. By manipulating this energy barrier one could control the magnetic properties of the system. We investigate the control of the molecular magnet anisotropy by means of adding or subtracting an electron to the system. An external electric field is able to drive electrons in or out of the molecular magnet.

We consider relevant to underline the reasons we study the manipulation of the magnetic properties of molecular magnets. Today's technology needs to find more efficient ways to store and process digital information. This can be achieved using quantum computers instead of conventional computers. Quantum computers store and process data using quantum mechanical states called quantum bits or qubits that might increase massively computer power. Conventional computers are built from silicon chips, which contain millions of transistors. Each one of them represents a bit of information, which can either be zero or one (binary digits). A bit could be represented by a spin pointing up or down as shown in Fig. \ref{fig:spins} a) or as the hour hand at 12 and at 6 in a clock in Fig. \ref{fig:spins} b).

In order to convey a more clear meaning we take a glance at the basic difference between conventional and quantum computers. Imagine you are in front of a clock (see Fig. \ref{fig:spins} b)) and the hour hand points towards the 12. That is the {\it one} in digital information. Now imagine it pointing towards the 6. That is the {\it zero} of digital information. In a classical computer the hour hand can only point towards either 12 or 6. Conventional computers perform operations using classical bits. On the other hand, in a quantum computer the hour hand can point towards any other number. It could point towards the numbers 3, 5, 11 or any point between them. It can be in a superposition of both bits of information. A quantum computer performs operations using quantum bits or qubits. They can be magically {\it zero} and {\it one} at the same time. They are in a quantum superposition of states. This is what gives a quantum computer its superior computing power.

As a final remark, the spin of a molecular magnet is a quantum object that can be used as a qubit. It can be up ({\it one}), down ({\it zero}) or both at once. If a molecular magnet can function as a little tiny magnet, then one could use it to store information. One could think to have either one bit or qubit per molecule. One could think a molecular magnet as a switching device, just like a transistor: a molecular transistor, where electricity can either flow or stop. Since molecular magnets are about ten times smaller than the present smallest transistors, it could increase considerably the amount of transistors in a chip. Additionally, the two spin states in a molecular magnet can be used to encode a qubit. It has been said that every time a quantum bit is added to a quantum computer, it doubles its computational power. It has been predicted that by having a 300-qubit quantum computer it would be more powerful than all the world computers connected together. That is the power of quantum computation. Therefore, controlling the magnetic properties of molecular magnets electrically could take us to the next computer generation.



Popular Abstract in Swedish

I denna avhandling undersöker vi hur man med hjälp av externa elektriska fält kan manipulera de magnetiska egenskaper som finns hos molekylära magneter. Denna manipulation förmedlas av antingen spinn-elektrisk koppling eller den magnetiska anisotropin hos den molekylära magneten. För att förstå vad detta betyder så ska vi först förklara vissa grundläggande begrepp om magnetism. Vi kommer att börja med att förklara vad en molekylär magnet är. Tänk dig att du har ett antal atomer av övergångsmetaller, såsom järn, kobolt, nickel eller mangan, arrangerade på ett sådant sätt att samspelet mellan dem får dem att hålla ihop och ge magnetiska egenskaper till molekylen. Vi kommer att kalla detta arrangemang den magnetiska kärnan av den molekylära magneten. Tänk dig nu att denna kärna är omgiven av andra atomer (oorganiska ligander) som kan vara utformade

för att säkerställa att molekylen binder på ytor eller i knutpunkter. Vi kommer att kalla denna sköld det oorganiska skalet.



Men varför kan en molekyl kallas för molekylär magnet? Till att börja med är en molekyl en samling av atomer. Varje atom har elektroner. Elektroner i universum innehar magnetiska egenskaper, närmare bestämt en inneboende rörelsemängdsmoment som genererar ett magnetiskt moment. I stort sett skulle man kunna se dem som mycket

små stavmagneter, det vill säga att de har nord- och sydpoler. Denna inneboende egenskap kallas spinn. I verkligheten är spinn ett rent kvantmekaniskt objekt som kommer från losningen av den relativistiska Dirac ekvationen inom kvantmekaniken. Ofta

representeras det av en pil som pekar antingen upp eller ner vilket illustrerar riktningen på det magnetiska flätet (Fig. 1 a). Då en elektron är placerad i ett magnetfält, anpassas dess spinn till det magnetfältet. En välbekant effekt kan ses när en kompassnål faller in i linje med det magnetiska fältet på jorden (se Fig. 1. c)).



Detta tankesätt kan användas för att fröstå både magnetiska material och magnetiska molekyler. Ett magnetiskt material skapas när elektronernas spinn i huvuddelen av materialet är i linje med varandra. Samma effekt syns på molekyl¨r nivå d¨r magnetiska moment skapas genom att elektronernas spinn i en samling av atomer blir parallella. En magnetisk

molekyl egenskaperna likt en klassik magnet, men uppvisar även kvantmekaniska egenskaper

på grund av sin minimala storlek, uppvisar den också kvantmekaniska egenskaper.

Notera att så här långt har vi inte använt något yttre magnetfält för att ordna molekylens

spinn, denna uppställning har ett rent kvantmekaniskt ursprung. I en molekylär magnet

styrs spinnens riktning av interaktionen mellan elektronens spinn och elektronens omloppsbana

i den molekylära strukturen. Denna egenskap kallas magnetisk anisotropi och

det beror på den komplicerade bindning av de magnetiska atomerna i kärnan med de ickemagnetiska

atomerna i strukturen. Numera kan denna bindning till viss del vara utformad

i laboratoriet vilket ger oss möjlighet att skapa molekyler med specifika egenskaper.

Mängden parallella spinn i en molekylär magnet bestämmer hur robust det magnetiska

beteendet är: Ju fler parallella spinn, desto mer magnetisk är molekylen.

Hittills har vi definierat vad molekylära magneter är. Låt oss nu tala om hur vi kan manipulera

deras magnetiska egenskaper. Man skulle kunna se en molekylär magnet som en

samling parallella spinns eller som ett gigantiskt spinn som representerar alla spinn på en

gång. Det magnetiska beteendet hos en molekylär magnet styrs av detta gigantiska spinn.

Genom att manipulera molekylernas spinn kan man styra dess magnetiska egenskaper.

Traditionellt så manipuleras spinn med hjälp av externa magnetfält vilket emellertid är

problematiskt på molekylär nivå. Den typiska storleken på en molekylär magnet är några

nanometer, en nanometer är en miljard gånger mindre än en meter och det är därför mycket

svårt att tillämpa magnetfält lokalt på den nivån. Magnetfält ger långsam växling,

dessutom är det svårt att uppbåda ett tillräckligt kraftfullt magnetfält. Åandra sidan, starka

elektriska fält kan enkelt åstadkommas och kan utan vidare tillämpas lokalt på nanoskala.

De kan också slås på och av mycket snabbt. Därför är manipulation av de magnetiska

egenskaperna hos molekylära magneter med hjälp av ett elektriskt fält en intressant och

lovande tutveckling.

I denna avhandling studeras två metoder för hur man med hjälp av elektriska fält kan

manipulera magnetiska egenskaper hos molekylära magneter. I den första metoden undersöker

vi kopplingen av spinn hos en molekylär magnet med det externa elektriska fältet.

Vi beaktar en särskild klass av molekylär magnet med intressanta och specifika egenskaper

i sitt lägsta energitillstånd (grundtillstånd). På grund av den molekylära magnetens

speciella geometri, kan ett elektriskt fält kopplas ihop med spinnet i systemet. Genom att

manipulera riktningen och styrkan hos det elektriska fältet kan man därför manipulera

den molekylära magnetens spinn. I den andra metoden manipulerar vi den magnetiska anisotropin hos den molekylära magneten. I detta fall kan vi använda en annan typ av

molekylär magnet som kännetecknas av sin stora magnetiskt anisotropiska energi, vilket

är den energi det krävs för att ¨ndra molekylens spinns. Genom att manipulera denna energibarriär

kan man styra de magnetiska egenskaperna hos systemet. Vi undersöker den

molekylära magnets anisotropin genom att addera eller subtrahera en elektron till systemet.

Ett yttre elektriskt fält kan driva elektroner in eller ut ur den molekylära magneten.

Det är relevant att understryka varför att vi studerar manipulation av magnetiska egenskaperna

hos molekylära magneter: Dagens teknik måste hitta effektivare sätt att lagra och

bearbeta digital information. Detta kan uppnås genom att använda kvantdatorer istället för

konventionella datorer. Kvantdatorer skulle kunna lagra och bearbeta data med hjälp av

kvantmekaniska tillstånd som kallas kvantum bitar eller kvantbitar vilket i sin tur skulle

kunna öka beräkningskraften drastiskt. Konventionella datorer byggs av kiselkretsar, som

innehåller miljontals transistorer, där var och en av dem representerar en bit av informationen

som antingen kan vara noll eller ett (binära siffror). En bit skulle kunna representeras

av ett spinn som pekar uppåt eller nedåt så som visas i Fig. 1 a) eller som timvisaren på

kl 12 och kl 6 på en klocka i Fig. 1 b).

För att förmedla en tydligare innebörd tar vi en blick på den grundläggande skillnaden

mellan konventionella datorer och kvantdatorer. Tänk att du har en klocka framför dig (se

Fig. 1 b)) och timvisaren pekar mot tolvan, som i detta fall motsvarar ett i digital information.

Tänk dig nu att timvisaren pekar mot sexan, i detta fall motsvarar det noll i

digital information. I konventionella datorer kan timvisaren bara peka mot antingen 12

(ett) eller 6 (noll), det vill säga utföra operationer med klassiska bitar. Till skillnad från

detta kan timvisaren i en kvantdator peka mot ett annat nummer. Den skulle kunna peka

mot siffrorna 3, 5, 11 eller någon punkt mellan dem, på detta vis uppnås överlagring av

informationen. En kvantdator utför dessutom operationer som använder kvantum (kvantbitar),

som magiskt nog kan vara noll och ett samtidigt. De är i ett tillstånd av kvantum

superposition, detta är vad som ger en kvantdator dess överlägsna beräkningskraft.

En molekyls spinn är allts°5 ett kvantum objekt som kan användas som en kvantbit,

det kan vara upp (ett), nedåt (noll) eller båda på en gång. Om en molekylär magnet kan

fungera som en pytteliten magnet, kan man därför använda den för att lagra information.

Man skulle kunna föreställa sig att ha antingen en bit eller kvantbit per molekyl. Man

skulle också kunna föreställa sig en molekylär magnet som en strömbrytare, precis som en

transistor; en molekylär transistor, där elektricitet antingen kan vara av eller på. Eftersom

molekylära magneter är ungefär tio gånger mindre än de nuvarande minsta transistorerna, skulle det avsevärt öka mängden transistorer i en krets. Dessutom kan de två spinntillstånden

i en molekylär magnet användas för att koda en kvantbit. Det har sagts att varje

gång en kvantum bit sätts till en kvantdator, fördubblas datorns beräkningskraft. Man

har förutspått att en kvantdator på 300-kvantbitar skulle vara mer kraftfull än dagens alla

datorer sammantaget vilket illustrerar kraften i kvantmekaniska beräkningar. Elektrisk

kontroll av dessa magnetiska molekyler kan följaktligen vara ett steg mot utvecklandet av

en helt ny och mycket kraftfull typ av datorer. (Less)
Abstract
This dissertation investigates theoretically electric control of the magnetic properties of molecular magnets. Two classes of magnetic molecules are considered. The first class consists of molecules that are spin frustrated. As a consequence of the frustration, the ground-state manifold of these molecules is characterized by states of different spin chirality, which can be coupled by an external electric field. Electric control of these spin states can be used to encode and manipulate quantum information. The second class comprises molecules known as single-molecule magnets, which are characterized by a high spin and a large magnetic anisotropy. Here the main goal is to control and manipulate the magnetic properties, such as the anisotropy... (More)
This dissertation investigates theoretically electric control of the magnetic properties of molecular magnets. Two classes of magnetic molecules are considered. The first class consists of molecules that are spin frustrated. As a consequence of the frustration, the ground-state manifold of these molecules is characterized by states of different spin chirality, which can be coupled by an external electric field. Electric control of these spin states can be used to encode and manipulate quantum information. The second class comprises molecules known as single-molecule magnets, which are characterized by a high spin and a large magnetic anisotropy. Here the main goal is to control and manipulate the magnetic properties, such as the anisotropy barriers, by adding and subtracting individual electrons, as achieved in tunneling transport.

Papers I, II and III deal with spin-electric coupling in spin frustrated molecules. Spin density functional theory is used to evaluate the parameters that control the strength of this coupling. Paper I reports the electronic and magnetic properties of the triangular antiferromagnet Cu3. It is found that an external electric field couples to the spin chirality of the system. The strength of this coupling is large enough to allow efficient spin-electric manipulation with electric fields generated by a scanning tunneling microscope.

Paper II investigates the zero-field splitting in the ground-state manifold of the triangular Cu3 molecular magnet caused by the Dzyaloshinskii-Moriya (DM) interaction. It employs a Hubbard model approach to elucidate the connection between the spin-orbit and the DM interaction. It is shown that the DM interaction constant D can be expressed in terms of the microscopic Hubbard-model parameters, which are calculated by first principles methods.

Paper III investigates systematically the spin-electric coupling in several triangular molecular magnets, such as V3 and Cu3O, and its dependence on different types of magnetic atoms, distances between magnetic centers and exchange paths between magnetic atoms. A generalization of the spin-electric coupling for a V15 molecular magnet, comprising fifteen magnetic centers, is also reported in this paper.

In Paper IV first-principles methods are employed to study theoretically the properties of an individual Fe4 single-molecule magnet attached to metallic leads in a single-electron transistor geometry. It is demonstrated that an external electric potential, modeling a gate electrode, can be used to manipulate the magnetic properties of the system by adding or subtracting electrons to the molecule.

In Paper V quantum transport via a triangular molecular magnet such as Cu3 is investigated. It is proposed that Coulomb-blockade transport experiments can be used to determine the spin-electric coupling strength in triangular molecular magnets. The theoretical analysis, based on a Hubbard model, is supported by master-equation calculations of quantum transport in the cotunneling regime. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Sanvito, Stefano, School of Physics, Trinity College Dublin, Ireland
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Molecular magnets, spin exchange, spin-orbit interaction, magnetic anisotropy, spin frustration, spin chirality, spin-electric control, quantum transport, Coulomb blockade, density functional theory, quantum master equation.
pages
219 pages
defense location
Room NY227, Kalmar-Nyckel, Linnaeus University, Gröndalsvägen 19, Kalmar
defense date
2013-09-12 13:00
ISBN
978-91-7473-548-2 (pdf)
978-91-7473-547-5 (print)
language
English
LU publication?
yes
id
c0e59b92-0255-4f2a-a22a-613aa30aa083 (old id 3972091)
date added to LUP
2013-08-19 08:17:51
date last changed
2016-09-19 08:45:16
@misc{c0e59b92-0255-4f2a-a22a-613aa30aa083,
  abstract     = {This dissertation investigates theoretically electric control of the magnetic properties of molecular magnets. Two classes of magnetic molecules are considered. The first class consists of molecules that are spin frustrated. As a consequence of the frustration, the ground-state manifold of these molecules is characterized by states of different spin chirality, which can be coupled by an external electric field. Electric control of these spin states can be used to encode and manipulate quantum information. The second class comprises molecules known as single-molecule magnets, which are characterized by a high spin and a large magnetic anisotropy. Here the main goal is to control and manipulate the magnetic properties, such as the anisotropy barriers, by adding and subtracting individual electrons, as achieved in tunneling transport.<br/><br>
Papers I, II and III deal with spin-electric coupling in spin frustrated molecules. Spin density functional theory is used to evaluate the parameters that control the strength of this coupling. Paper I reports the electronic and magnetic properties of the triangular antiferromagnet Cu3. It is found that an external electric field couples to the spin chirality of the system. The strength of this coupling is large enough to allow efficient spin-electric manipulation with electric fields generated by a scanning tunneling microscope. <br/><br>
Paper II investigates the zero-field splitting in the ground-state manifold of the triangular Cu3 molecular magnet caused by the Dzyaloshinskii-Moriya (DM) interaction. It employs a Hubbard model approach to elucidate the connection between the spin-orbit and the DM interaction. It is shown that the DM interaction constant D can be expressed in terms of the microscopic Hubbard-model parameters, which are calculated by first principles methods.<br/><br>
Paper III investigates systematically the spin-electric coupling in several triangular molecular magnets, such as V3 and Cu3O, and its dependence on different types of magnetic atoms, distances between magnetic centers and exchange paths between magnetic atoms. A generalization of the spin-electric coupling for a V15 molecular magnet, comprising fifteen magnetic centers, is also reported in this paper.<br/><br>
In Paper IV first-principles methods are employed to study theoretically the properties of an individual Fe4 single-molecule magnet attached to metallic leads in a single-electron transistor geometry. It is demonstrated that an external electric potential, modeling a gate electrode, can be used to manipulate the magnetic properties of the system by adding or subtracting electrons to the molecule.<br/><br>
In Paper V quantum transport via a triangular molecular magnet such as Cu3 is investigated. It is proposed that Coulomb-blockade transport experiments can be used to determine the spin-electric coupling strength in triangular molecular magnets. The theoretical analysis, based on a Hubbard model, is supported by master-equation calculations of quantum transport in the cotunneling regime.},
  author       = {Nossa Márquez, Javier Francisco},
  isbn         = {978-91-7473-548-2 (pdf)},
  keyword      = {Molecular magnets,spin exchange,spin-orbit interaction,magnetic anisotropy,spin frustration,spin chirality,spin-electric control,quantum transport,Coulomb blockade,density functional theory,quantum master equation.},
  language     = {eng},
  pages        = {219},
  title        = {Nanospintronics with Molecular Magnets - Tunneling and Spin-Electric Coupling},
  year         = {2013},
}