Questions tagged [exchange-interaction]

An effective, but not actual, force used for effective description of geometric effects between identical particles, such as the apparent repulsion between fermions due to the Pauli principle.

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Why Hund's first rule neglect one of the spin triplet states?

For two electrons, the spin triplet states allow their spacial wavefunction to be antisymmetric with respect to the exchange of particles, and can minimize the coulomb repulsion energy because larger ...
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Why Does Exchange Symmetry Stabilize Quantum Systems?

When trying to solve Schrödinger equation approximately, we usually represent wavefunction of the system as the Slater determinant of some set of spin orbitals to take into account that fermions (...
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Exchange interaction between low spin $\rm Fe^{2+}$ and $\rm Fe^{3+}$

When people talk about superexchange and double exchange, they often use $Fe$ as an example. In the case of a double exchange, the high spin state of $Fe^{2+}$ and $Fe^{3+}$ are expected to have the ...
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Spin-orbit coupling in a Mott insulator with $J=1/2$

It seems that spin-orbit coupling in a Mott insulator with $J=1/2$ can have bond-dependent hamiltonians, as discussed in G. Jackeli 2009 PRL. But I don't understand the proof in this paper about the ...
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Spin Hamiltonian for 2 electron system

I am currently studying exchange interaction and came across the spin operator in Ashcroft and Mermin Chapter 32 page 680 which states that the spin hamiltonian can be defined as: ...
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What is the value of the exchange field in the 3d ferromagnets ($\rm Ni, Fe, Co$)?

I have been trying to find the values of the exchange field for Ni, Co and Fe. This website mentions, "Exchange forces are very large, equivalent to a field on the order of 1000 Tesla" https:...
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How can the exchange interaction make electron spins parallel?

Electrons repel by Coulomb interaction. When they get too close, Pauli exclusion principle ("Exchange interaction") becomes important. If their spins are parallel, they are further "...
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Question About Exchange

Is the Exchange term, for example in a set of Hartree-Fock equations for a solid, to be interpreted as arising from electrons actually, physically, exchanging positions constantly? So, for a metal, I ...
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Mathematical expression of the coordinate exchange operator

So I know that the total exchange operator is the product of the coordinate, spin and isospin exchange operators, as, \begin{equation} P_{12} = P_{12}^r P_{12}^\sigma P_{12}^\tau \end{equation} The ...
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Effect of Exchange Interaction on Magnetism

My physics book says that the magnetic properties of ferromagnetic substances are a resultant of a process called exchange coupling in atoms, but unfortunately does not explain any why or how it does ...
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What is the “exchange energy of electrons”?

First, do not try to give me the perplexing explanations involving higher QM. I am new to QM, so please give a gentle explanation. Now, my textbook see page 36 states that electrons of degenerate ...
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Finding general information about the Dzyaloshinskii-Moriya interaction (DMI)

I have to do an assignment on the Dzyaloshinskii-Moriya interaction for a magnetism (in condensed matter) course that I am following. My teacher said that this topic is rather popular, but I cannot ...
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Time evolution of spin with Anti-symmetric (Dzyaloshinkii-Moriya) interaction

I am trying to simulate the time evolution of a spin in spin chain interacting via Dzyaloshinkii-Moriya interaction. The Hamiltonian is of the form $$H_{A}=J_{A}\sum_{i}(S^{x}_{i}S_{i+1}^{y}-S^{x}_{i+...
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Sign of exchange integral in GKA (superexchange) rules

I was reading about the super-exchange mechanism that leads to magnetic order (Antiferromagnetic or Ferromagnetic) in insulating solids here. Kanamori breaks down the mechanisms in several specific ...
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Different types of magnetic exchange

I am a bit confused about the mechanisms of different types of exchange. Mainly, I am trying to understand mechanisms that lead to magnetic ordering and I came across several different types of ...
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Are combined fermion wavefunctions still antisymmetric after wavefunction collapse?

If we have two electrons in a state $|\psi\rangle=\frac{1}{\sqrt2}[|\uparrow\downarrow\rangle+|\downarrow\uparrow\rangle]$ and we measure the spin of the first electron to be up, does the wavefunction ...
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Can a photon's angular momentum couple to an electron spin, to cause a spin-flip (thus allowing intersystem crossings)?

Been reading up on intersystem crossing and have gotten rather confused by: a photon possesses an angular momentum of $h/2\pi$ so it can couple to an electron spin and in principle induce any ...
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Could the Fermi statistic be a force?

I'm aware that, according to the Pauli principle, identical fermions obey the Fermi-Dirac statistics, so they don't occupy the same state because they just can't, it's simply how they behave. I'm ...
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The Hund's J - Why can this be quantified?

I was reading on the the implementation of Hubbard 'U' in Density Functional Theory. The Hubbard 'U' can be thought of as a parameter that accounts for the on-site electron-electron interactions in ...
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Coupling of two spin half particles

If there are two electrons coupled by interaction having hamiltonian H=A*S1*S2 where S1 and S2 are spin angular momentum operators of two electrons, we know we have four possible eigenstates for the ...
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Does the (non-)collision of two fermion wave packets demonstrate that there is no exchange "force"?

In the paper "Quantum statistics: Is there an effective fermion repulsion or boson attraction?" by Mulling and Blaylock (2003), it is claimed that We can demonstrate there is no real force due to ...
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Exchange has closed form also in DFT?

I have heard from my lecturer that in the context of DFT, the exact exchange energy has a known closed form, even though it is not a functional of the density. I have been trying to figure out what ...
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DFT: When would one use a LDA over a GGA method?

Computationally using Density Functional Theory (DFT), is there any examples where Local Density Approximation (LDA) would be preferred over using Gradient Generalized Approximation (GGA) methods for ...
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Why don't all elements with unpaired electrons become ferromagnetic?

As a necessary condition, ferromagnetism in elements requires the existence of unpaired electrons. However, all elements with unpaired electrons are not ferromagnetic, e.g., metals such as aluminium ...
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Which mechanism causes ferromagnetism in iron?

There are at least three different mechanisms which can give rise to ferromagnetic order in iron. First is due to the band electrons called band magnetism or itinerant magnetism which is an exchange ...
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Why an insufficient overlap cause vanishing exchange interaction?

Why should the exchange interaction vanish if the atoms do not have sufficient overlap in their overfunctions? For exchange interaction not to vanish, the only requirement seems to be that the ...
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Symmetry in Fock-space 2-body interaction

The simplest two body interaction term for fermions is $$H = \sum_{ijkl} U_{ijkl} a_i^\dagger a_j^\dagger a_k a_l$$ and I'm trying to determine the symmetries on $U$. Unfortunately I keep getting ...
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To get short-range interaction from long-range interaction

Interactions in Condensed matter systems are almost exclusively the electromagnetic interactions which are long-range. But it often gives rise to short-range interactions in systems e.g., exchange ...
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Exchange Interaction Time Evolution

This is a hypothetical based on a result in Griffiths (which is my level of QM understanding). In it, he derives an "exchange force" - two particles states A and B, a two-particle state composed of ...
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Exchange stiffness for HCP

I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian: $\hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}}$ In the framework of constant ...
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Triplet states and the Hund's rule in identifying the ground state configuration (open shell)

I referred to some of the questions about Hund's rule on StackExchange, such as this for example, but still wasn't able to have my question resolved. (the wikiepdia page has $E_{ex} = C - \frac{1}{2}...
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Heisenberg exchange term in phenomenological nuclear potentials

In phenomenological nucleon-nucleon potentials there are three exchange forces terms: $V_M=V_M(r) P_{x}$ : Majorana exchange (exchange of position coordinates, $P_{x}$ is the operator of exchange of ...
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magnetic and electric interactions in atomic level

From what I understand Van der Waals (VDW) forces are the primary source of inter-molecular interaction. There are three different possible origins for van der Waals forces: permanent dipole-permanent ...
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particle exchange versus spin

Before us are two half-integer-spin particles. Their spin directions are parallel, aligned with the line connecting their locations. They are indistinguishable but for the fact we have affixed the ...
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Attractive exchange energy and correlation energy of different spin in DFT

In DFT, why do most texts ignore/don't mention the attractive exchange "force" between two antiparallel spins electrons? The repulsive "exchange" force of two same spins electrons are always ...
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Why does exchange lower energy with increasing electron density in Hartree-Fock

The Hartree-Fock equations include a term for the exchange interaction, which is usually explained as a repulsive force due to the Pauli exclusion principle. (It says so right in the description for ...
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Precise definition of exchange

I was wondering about how could one define the exchange interaction in the most general way. I am aware of the definition of exchange for the Coulomb interaction, which looks basically like $\int \...
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Understanding interatomic potential between hydrogen

Interatomic potential is usually described as consisting of two parts: one attractive and one repulsive, where the repulsive one prevails at short distances. The repulsive part is typically ...
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Defining the exchange operator $P_{12}$ without reference to dummy variables

Let $\Psi \in \mathcal{L}^{2}(\mathbb{R}^{6}; \mathbb{C}^{2}\otimes\mathbb{C}^{2})$ so that $\Psi$ represents the state of two interacting fermions. Traditionally, we define the exchange operator $P_{...
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Is there an exchange of electrons between two Cooper pairs in the BCS state?

The BCS state is $$\left|\psi\right>=\prod_k \left(u_k +v_k c_{k\uparrow}^\dagger c_{-k\downarrow}^\dagger\right)\left|0\right>$$ which pairs all the electrons into Cooper pairs. The ...
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Conduction electrons in ferromagnetic materials

As I understand it, in a ferromagnetic material unpaired electrons on the atomic sites interact (exchange interaction) with nearest neighbours, aligning the moments and producing the magnetisation ...
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Can the average temperature increase in a closed adiabatic (isolated) system?

Assume a closed and adiabatic (isolated) system (no energy or mass transfer at the boundaries) then is it possible for the average temperature to change (increase or decrease)? Corollary: 1. If yes ...
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Why does the weak interaction not conserve the flavour quantum number? [duplicate]

The weak interaction, in contrast to the strong and electromagnetic, is the mediator of the decay of the strange quark, purely because the weak interaction is 'allowed' to break conservation of ...
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Could someone explain how antisymmetric position states and symmetric spin states work in an atom?

I'm reading Griffiths QM 2nd ed and he talks about how all fermions are antisymmetric in nature. Later he talks about how exchange forces with identical particles. He states that because fermions are ...
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Is Blatt-Weisskopf's treatment of nuclear forces still relevant today?

As in the title, is the treatment of nuclear forces by Blatt and Weisskopf, as in Chapter III of "Theoretical Nuclear Physics", still relevant today, especially with regard to the role of exchange ...
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many body wavefunction and exchange correlation

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference ...
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Mathematical form of the de facto repulsive "force" associated with the Pauli Exclusion Principle [duplicate]

One of the principles of General Relativity is that test objects follow a geodesic unless otherwise acted upon by a force. From this perspective, it is clear that physicists, consciously or ...
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Can both types of W boson be responsible for a neutron-neutrino interaction?

My textbooks lists the exchange particle for a neutron-neutrino interaction as being the W- boson. Is this the only option, or can it also be a W+ boson? Nothing jumps out at me that would suggest it ...
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Outside of string theory, can exchange particles be understood as being one-dimensional?

I'm pretty new to quantum, without any formal education therein, so forgive my general layman ignorance when I ask how it is that point-like exchange particles can be modeled in Feynman diagrams as ...
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spin conservation in exchange polarization process

Exchange polarization is the process by which spin is transferred between an electron beam and a system of polarized atoms (with a single valence spin). The process occurs as a result of the Pauli ...
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