Thickness-Dependent Curie Temperatures of Ultrathin Magnetic Films: Effect of the Range of Spin-Spin Interactions

Zhang, Renjun; Willis, R. F.

doi:10.1103/physrevlett.86.2665

Cited by 247 publications

(221 citation statements)

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“…In the case of different dopants, trends for T c as a function of film thickness were reported by using different techniques. For comparison, we mention the results of Zhang and Willis based on measurements of bulk film magnetism through the magneto-optical Kerr effect (38), which were theoretically verified by Rausch and Nolting (41) in the molecular field approximation (Weiss mean-field theory) of the Heisenberg model. Furthermore, a recent ferromagnetic resonance study of Bi 2 Se 3 :Mn has revealed a stronger ferromagnetic order in the bulk than on the surface, which was attributed to the bulk layer being more homogeneously doped than the surface layer (34), in agreement with our observation.…”

Section: Resultsmentioning

confidence: 99%

Nanoscale β-nuclear magnetic resonance depth imaging of topological insulators

Koumoulis

Morris

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Considerable evidence suggests that variations in the properties of topological insulators (TIs) at the nanoscale and at interfaces can strongly affect the physics of topological materials. Therefore, a detailed understanding of surface states and interface coupling is crucial to the search for and applications of new topological phases of matter. Currently, no methods can provide depth profiling near surfaces or at interfaces of topologically inequivalent materials. Such a method could advance the study of interactions. Herein, we present a noninvasive depth-profiling technique based on β-detected NMR (β-NMR) spectroscopy of radioactive 8 Li + ions that can provide "one-dimensional imaging" in films of fixed thickness and generates nanoscale views of the electronic wavefunctions and magnetic order at topological surfaces and interfaces. By mapping the 8 Li nuclear resonance near the surface and 10-nm deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we provide signatures related to the TI properties and their topological nontrivial characteristics that affect the electronnuclear hyperfine field, the metallic shift, and magnetic order. These nanoscale variations in β-NMR parameters reflect the unconventional properties of the topological materials under study, and understanding the role of heterogeneities is expected to lead to the discovery of novel phenomena involving quantum materials.topological insulator | nuclear magnetic resonance | depth profiling | condensed matter physics | nanoscale physics T opological insulators (TIs) are narrow-gap semiconductor materials that are insulating in the bulk and conductive on their surface. The constituent atoms are typically heavy elements with large spin-orbit coupling (SOC). In time-reversal-invariant materials, the electronic structure of TIs is characterized by band inversions from strong SOC at an odd number of time-reversalinvariant momenta in the bulk Brillouin zone. Unlike metals or ordinary insulators (OIs), charge carriers in TIs evolve from metallic to insulating as a function of depth from the surface. The surface-state electrons are characterized by a suppression of backscattering and an intrinsic chirality of spin-momentum locking, making them of interest in spintronics. A number of theoretical predictions of experimental observations have been made including Majorana fermions, condensed-matter axions, and quantized Hall conductance (1, 2). Heterostructure engineering, where a crystal is formed consisting of a sequence of different building blocks (for example, alternating TI and OI layers), can trigger new physical phenomena such as TIs with enhanced bulk band gaps (3) or Weyl semimetals (4).Because topological materials are characterized by sharp changes in electronic properties at their surfaces and at interfaces with other materials, sensitive techniques are required to probe electronic and magnetic properties in a spatially resolved manner down to the atomic length scale. It has become clear that TI properties are spatially de...

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Section: Resultsmentioning

confidence: 99%

Nanoscale β-nuclear magnetic resonance depth imaging of topological insulators

Koumoulis

Morris

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…For Co and Fe, T C is much higher than Ni. The experimentally available data for the transition temperature and the corresponding reduction in T C are mainly in the linear region, as discussed in [18]. More experiments to determine ξ 0 and λ are still in need.…”

Section: Eq (3) It Indicates That T B Is Proportional To the Potentmentioning

confidence: 99%

“…In the expression, T C (∞) is the Curie temperature for the bulk and T C (d), for nanoparticles with diameter d, ξ 0 is the correlation length and λ = 1/ν with ν the critical exponent. In addition to the geometric confinement effect, T C will be further modified by the free surface effect as the particle size approaches the ultrafine limit smaller than N 0 , which is the effective range of spin-spin interaction according to the simple model proposed by R. J. Zhang et al [18]. In this region, T C varies linearly with the particle size.…”

Section: Eq (3) It Indicates That T B Is Proportional To the Potentmentioning

confidence: 99%

“…One is the geometric confinement on the correlation length near the critical regime. It becomes significant for nano-sized particles, causing a reduction in the ferromagnetic ordering temperature, T C , according to the power law, [18][19][20][21][22]. In the expression, T C (∞) is the Curie temperature for the bulk and T C (d), for nanoparticles with diameter d, ξ 0 is the correlation length and λ = 1/ν with ν the critical exponent.…”

Section: Eq (3) It Indicates That T B Is Proportional To the Potentmentioning

confidence: 99%

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Effect of temperature-dependent shape anisotropy on coercivity for aligned Stoner-Wohlfarth soft ferromagnets

Chen

2007

Phys. Rev. B

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The temperature variation effect of shape anisotropy on the coercivity, H C (T), for the aligned Stoner-Wohlfarth (SW) soft ferromagnets, such as fcc Ni, fcc Co and bcc Fe, are investigated within the framework of Néel-Brown (N-B) analysis. An extended, by introducing a single dimensionless correction function, the reduced magnetization,, in which τ = T/T C is the reduced temperature, M S (T) is the saturation magnetization, and T C is the Curie temperature. The factor, m(τ), accounts for the temperature-dependent effect of the shape anisotropy. The constants, H 0 and E 0 , are for the switching field at zero temperature and the potential barrier at zero field, respectively. According to this newly derived equation, the blocking temperature 2 above which the properties of superparamagnetism show up is described by the expression, T B = E 0 m 2 (τ Β )/[k B ln(t/t 0 )], with the extra correction factor m 2 (τ Β ). The possible effect on H C (T) and the blocking temperature, T B , attributed to the downshift of T C resulting from the finite size effect has been discussed also.3

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“…It is possible that the Curie temperature for the I ML Fe/W(l00) system is much lower than the corresponding Curie temperature of 282K for the I ML FeCW(i 10). It is known that Curie temperature is very sensitive to the film thickness, the coordination number, the capping and substrate layer thickness, and the interatomic distance [23][24][25][26][27]. Since exchange couplingJ decays as -I/R 3 [28], in which R is the interatomic distance, the Curie temperature will be dependent upon the crystallographic orientation of the thin film as demonstrated in [27].…”

Section: Uil Results and Discussionmentioning

confidence: 99%

Crystal-field Effect on Magnetic Moment and Exchange-Coupling for Fe/W(100) and Fe/W(110)

Qian

Hübner

2002

MRS Proc.

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The Full-potential Linearized Augmented Plane-wave (FP-LAPW) method was employed to investigate the magnetic properties of 1 monolayer (ML) Fe on W(100) and W(110) substrates. Magnetic moments of the Fe overlayer are found to be very different with ∼2.0 μB for Fe on W(100) and ∼2.56 μB for Fe on W(110). The exchange coupling between Fe film and W substrate are also found to be orientation-dependent. The electronic coupling in Fe/W(100) thin film is found to be more long-range, compared to the one in Fe/W(110). These differences could be explained by the differences of local atomic bonding and crystal-field splitting in these two orientations.

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Thickness-Dependent Curie Temperatures of Ultrathin Magnetic Films: Effect of the Range of Spin-Spin Interactions

Cited by 247 publications

References 23 publications

Nanoscale β-nuclear magnetic resonance depth imaging of topological insulators

Nanoscale β-nuclear magnetic resonance depth imaging of topological insulators

Effect of temperature-dependent shape anisotropy on coercivity for aligned Stoner-Wohlfarth soft ferromagnets

Crystal-field Effect on Magnetic Moment and Exchange-Coupling for Fe/W(100) and Fe/W(110)

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