Spin polarized quantum systems

An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagnetic-to-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density ( $n$ ) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field ( $B$ ), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\ensuremath{\sim}{n}^{p}$. For $p<{p}_{c}$ , with ${p}_{c}=1(2/3)$ in $2(3)\mathrm{D}$ , the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for $p>{p}_{c}$ , the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagnetic-to-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density ($n$) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field ($B$), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\ensuremath{\sim}{n}^{p}$. For $p<{p}_{c}$, with ${p}_{c}=1(2/3)$ in $2(3)\mathrm{D}$, the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for $p>{p}_{c}$, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.

arXiv:2106.02038Physical review. B./Physical review. BSep 8, 20211 citation

Phase Separation in ν=2/3 Fractional Quantum Hall Systems

Naokazu Shibata, Kentaro Nomura

We study the domain formation in the v=2/3 fractional quantum Hall systems basing on the density matrix renormalization group (DMRG) analysis. The ground-state energy and the pair correlation functions are calculated for various spin polarizations. The results confirm the domain formation in partially spin polarized states, but the presence of the domain wall increases the energy of partially spin polarized states and the ground state is either spin unpolarized state or fully spin polarized state depending on the Zeeman energy. We expect coupling with external degrees of freedom such as nuclear spins is important to reduce the energy of partially spin polarized state.We study the domain formation in the v=2/3 fractional quantum Hall systems basing on the density matrix renormalization group (DMRG) analysis. The ground-state energy and the pair correlation functions are calculated for various spin polarizations. The results confirm the domain formation in partially spin polarized states, but the presence of the domain wall increases the energy of partially spin polarized states and the ground state is either spin unpolarized state or fully spin polarized state depending on the Zeeman energy. We expect coupling with external degrees of freedom such as nuclear spins is important to reduce the energy of partially spin polarized state.

arXiv:0707.1840Journal of the Physical Society of JapanOct 10, 200714 citations

Spin-Polarized Atoms

Galina A. Nemova

SPIE eBooksNov 6, 20190 citations

n

) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field (

B

), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\ensuremath{\sim}{n}^{p}$. For

p<{p}_{c}

, with

{p}_{c}=1(2/3)

2(3)\mathrm{D}

, the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for

p>{p}_{c}

, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.