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R. Schäfer

Publications and source records attributed to R. Schäfer.

At least 19 recordsLinked to original sources

Observation of Dipolar Spin-ice--like Correlations in the Quantum Spin Ice Candidate Ce$_2$Sn$_2$O$_7$

We report diffuse scattering measurements on the dipolar-octupolar pyrochlore, Ce$_2$Sn$_2$O$_7$, to elucidate its magnetic correlations within the correlated paramagnetic regime above its ordering temperature, $\mathrm{T_N}\sim 40~$mK. The magnetic transition at $\mathrm{T_N}$, observed in recent specific heat measurements, has been interpreted within the nearest-neighbor XYZ model as a transition into an all-in-all-out (AIAO) magnetic order. However, the observed diffuse scattering above $\mathrm{T_N}$ argues against an AIAO magnetic order by exhibiting $no$ short-range order at the AIAO wave-vectors, inconsistent with the nearest neighbor model. Instead, the observed diffuse scattering strongly resembles that observed in classical dipolar spin ice, Dy$_2$Ti$_2$O$_7$, and suggests the presence of short-range correlated structures such as chains, or clusters in the low energy manifold of Ce$_2$Sn$_2$O$_7$, favored by further neighbor interactions. We discuss how chain-like states qualitatively account for the observed H-T phase diagram under a [1,1,0]-field.

cond-mat.str-el↗

Zero-Field Long Range Order at $T \sim 40$ mK in the Proximate Quantum Spin Ice Ce$_2$Sn$_2$O$_7$ and Phase Diagram for Magnetic Fields Along [1,1,0]

The Ce$^{3+}$ pseudospin-1/2 degrees of freedom in the pyrochlore magnets Ce$_2$X$_2$O$_7$, with $X$ = Zr, Hf, or Sn, possess dipole-octupole character. The XYZ nearest-neighbor model Hamiltonians which have successfully described their properties make them attractive candidates for quantum spin ice ground states. We report new heat capacity measurements to very low temperatures on a high-quality single crystal of Ce$_2$Sn$_2$O$_7$ grown by hydrothermal techniques. Our zero-field measurements uncover a clear first order transition to long-ranged order at $T \sim 0.04$ K, well below the downturn in the broader Schottky-like anomaly that is a common feature in the zero-field heat capacity for cerium pyrochlores. This observation settles the debate as to whether Ce$_2$Sn$_2$O$_7$ possesses a QSI ground state in zero field - it does not. However, we also find compelling evidence suggesting that spin ice physics is nearby, and remains relevant to Ce$_2$Sn$_2$O$_7$. Application of a magnetic field along the $[1,1,0]$ direction leads to an evolution of this peak to a weak anomaly at higher temperature more characteristic of a continuous, mean field transition. At higher fields along $[1,1,0]$, the Schottky-like anomaly bifurcates similar to expectations for independent polarized $α$ and orthogonal $β$ chains in classical spin ice. These new experimental results demonstrate richness to the phase diagram for Ce-based pyrochlores.

cond-mat.str-el↗

Reflections on future problems in cluster science

This article is a collection of contributions from speakers at the 2025 DEAMN [Dynamics of Electrons in Atomic and Molecular Nanoclusters] workshop at the Majorana Centre in Erice. Not ordinary contributions to a conference proceeding, this gives a new and different perspective on the work done by the workshop participants.

physics.atm-clus↗

Two-Peak Heat Capacity Accounts for $R\ln(2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce$_2$Hf$_2$O$_7$

Magnetic heat capacity measurements of a high-quality single crystal of the dipole-octupole pyrochlore Ce$_2$Hf$_2$O$_7$ down to a temperature of $T = 0.02$ K are reported. These show a two-peaked structure, with a Schottky-like peak at $T_1 \sim 0.065$ K, similar to what is observed in its sister Ce-pyrochlores Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$. However, a second sharper peak is observed at $T_2 \sim 0.025$ K, signifying the entrance to the ground state. The ground state appears to have gapped excitations, as even the most abrupt extrapolation to $C_P=0$ at $T = 0$ K fully accounts for the $R\ln(2)$ entropy associated with the pseudospin-1/2 doublet for Ce$^{3+}$ in this environment. The ground state could be conventionally ordered, although theory predicts a much larger anomaly in $C_P$ at much higher temperatures than the measured $T_2$ for expectations from an all-in all-out ground state of the XYZ Hamiltonian for Ce$_2$Hf$_2$O$_7$. The sharp low-temperature peak could also signify a cross-over from a classical spin liquid to a quantum spin liquid (QSL). For both scenarios, comparison of the measured $C_P$ with NLC calculations suggests that weak interactions beyond the nearest-neighbor XYZ Hamiltonian become relevant below $T \sim 0.25$ K. The diffuse magnetic neutron scattering observed from Ce$_2$Hf$_2$O$_7$ at low temperatures between $T_2$ and $T_1$ resembles that observed from Ce$_2$Zr$_2$O$_7$, which is well established as a $π$-flux quantum spin ice (QSI). Together with the peak in the heat capacity at $T_2$, this diffuse scattering from Ce$_2$Hf$_2$O$_7$ is suggestive of a classical spin liquid regime above $T_2$ that is distinct from the zero-entropy quantum ground state below $T_2$.

cond-mat.str-el↗

Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce$_2$Zr$_2$O$_7$: No Apparent Octupolar Correlations Above $T = 0.05$ K

The insulating magnetic pyrochlore Ce$_2$Zr$_2$O$_7$ has gained attention as a quantum spin ice candidate with dipole-octupole character arising from the crystal electric field ground state doublet for the Ce$^{3+}$ ion. This permits both spin ice phases based on magnetic dipoles and those based on more-exotic octupoles. We report low-temperature neutron diffraction measurements on single crystal Ce$_2$Zr$_2$O$_7$ with $Q$-coverage both at low $Q$ where the magnetic form factor for dipoles is near maximal and at high $Q$ where the magnetic form factor for Ce$^{3+}$ octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, Ce$_2$Sn$_2$O$_7$ and Ce$_2$Hf$_2$O$_7$, which each showed temperature-dependent diffuse diffraction at high $Q$ that was interpreted as arising from octupolar correlations. Our measurements use an optimized single crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from Ce$_2$Zr$_2$O$_7$. The temperature-difference neutron diffraction reveals a low-$Q$ peak consistent with dipolar spin ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher $Q$. These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for Ce$_2$Zr$_2$O$_7$, Ce$_2$Sn$_2$O$_7$, and Ce$_2$Hf$_2$O$_7$. Importantly, neither the measured data nor any of the NLC calculations show evidence for increased scattering at high $Q$ resulting from octupolar correlations. We conclude that at the lowest attainable temperature for our measurements ($T = 0.05$ K), scattering from octupolar correlations in Ce$_2$Zr$_2$O$_7$ is not present in the neutron diffraction signal on the level of our observation threshold of ~ 0.1 % of the low-$Q$ dipole scattering.

cond-mat.str-el↗

Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce$_2$Sn$_2$O$_7$

The dipolar-octupolar (DO) pyrochlores, R$_2$M$_2$O$_7$ (R = Ce, Sm, Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of Ce$_2$Sn$_2$O$_7$, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in Ce$_2$Sn$_2$O$_7$ using the near-neighbor $XYZ$ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown Ce$_2$Sn$_2$O$_7$ samples, we place Ce$_2$Sn$_2$O$_7$'s ground state within the ordered dipolar all-in-all-out (AIAO) Néel phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown Ce$_2$Sn$_2$O$_7$ powders show a broad signal at low scattering wave vectors, reminiscent of a \textit{dipolar} spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic {\it octupoles} and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown Ce$_2$Sn$_2$O$_7$ samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO Néel order.

cond-mat.str-el↗

$μ$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce$_2$Zr$_2$O$_7$

The Ce$^{3+}$ pseudospin-1/2 degrees of freedom in Ce$_2$Zr$_2$O$_7$ possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. Here we report new muon spin relaxation and rotation ($μ$SR) measurements on single crystal samples of Ce$_2$Zr$_2$O$_7$ in zero magnetic field and in magnetic fields directed along the $[1,\bar{1},0]$ and $[1,1,1]$ crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field $μ$SR measurements on a powder sample of Ce$_2$Zr$_2$O$_7$, and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for Ce$_2$Zr$_2$O$_7$ in zero-field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation, and correspondingly, the high stoichiometry of our single crystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in Ce$_2$Zr$_2$O$_7$ remain dynamic at $T = 0.1$ $\mathrm{K}$. For both $[1,\bar{1},0]$ and $[1,1,1]$ magnetic fields, our $μ$SR Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbour exchange parameters of Ce$_2$Zr$_2$O$_7$.

cond-mat.str-el↗

Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce$_2$Zr$_2$O$_7$

We report new heat capacity measurements on single crystal Ce$_2$Zr$_2$O$_7$ down to $\sim$ 0.1 K in a magnetic field along the $[1,\bar{1}, 0]$ direction. These new measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two humps by the $[1,\bar{1}, 0]$ field at $\sim$ 2 T. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: one set of chains ($α$-chains) is polarized by the field while the other ($β$-chains) remains free. Our theoretical modelling suggests that the $β$-chains are close to a critical state, with nearly-gapless excitations. We also report new elastic and inelastic neutron scattering measurements on single crystal Ce$_2$Zr$_2$O$_7$ in $[1, \bar{1}, 0]$ and $[0, 0, 1]$ magnetic fields at temperatures down to 0.03 K. The elastic scattering behaves consistently with the formation of independent chains for a $[1, \bar{1}, 0]$ field, while the $[0, 0, 1]$ field produces a single field-induced magnetic Bragg peak at $(0, 2, 0)$ and equivalent wavevectors, indicating a polarized spin ice for fields above $\sim$ 3 T. For both $[1, \bar{1}, 0]$ and $[0, 0, 1]$ fields, our inelastic neutron scattering results show an approximately-dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modelling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in Ce$_2$Zr$_2$O$_7$ and the smallness of the parameter $θ$ which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters.

cond-mat.str-el↗

Reply to "Comment on: 'Case for a U(1)$_π$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore $\mathrm{Ce}_2\mathrm{Zr}_2\mathrm{O}_7$' "

In his comment [arXiv:2209.03235], S. W. Lovesey argues that our analysis of neutron scattering experiments performed on Ce$_2$Zr$_2$O$_7$ is invalid. Lovesey argues that we have not properly accounted for the higher-order multipolar contributions to the magnetic scattering and that our use of pseudospin-$1/2$ operators to describe the scattering is inappropriate. In this reply, we show that the multipolar corrections discussed by Lovesey only become significant at scattering wavevectors exceeding those accessed in our experiments. This in no way contradicts or undermines our work, which never claimed a direct observation of scattering from higher-order multipoles. We further show that Lovesey's objections to our use of pseudospins are unfounded, and that the pseudospin operators are able to describe all magnetic scattering processes at the energy scale of our experiments, far below the crystal field gap. Finally, we comment on certain assumptions in Lovesey's calculations of the scattering amplitude which are inconsistent with experiment.

cond-mat.str-el↗

The case for a U(1)$_π$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce$_2$Zr$_2$O$_7$

The Ce$^{3+}$ pseudospin-$\frac{1}{2}$ degrees of freedom in the pyrochlore magnet Ce$_2$Zr$_2$O$_7$ are known to possess dipole-octupole (DO) character, making it a candidate for novel quantum spin liquid (QSL) ground states at low temperatures. We report new polarized neutron diffraction at low temperatures, as well as heat capacity ($C_p$) measurements on single crystal Ce$_2$Zr$_2$O$_7$. The former bears both similarities and differences from that measured in the canonical dipolar spin ice compound Ho$_2$Ti$_2$O$_7$, while the latter rises sharply at low temperatures, initially plateauing near 0.08 K, before falling off towards a high temperature zero beyond 3 K. Above $\sim$0.5 K, the $C_p$ data set can be fit to the results of a quantum numerical linked cluster (NLC) calculation, carried out to 4$^{\mathrm{th}}$ order, that allows estimates for the terms in the near-neighbour XYZ Hamiltonian expected for such DO pyrochlore systems. Fits of the same theory to the temperature dependence of the magnetic susceptibility and unpolarized neutron scattering complement this analysis. A comparison between the resulting best fit NLC calculation and the polarized neutron diffraction shows both agreement and discrepancies, mostly in the form of zone-boundary diffuse scattering in the non-spin flip channel, which are attributed to interactions beyond near-neighbours. The lack of an observed thermodynamic anomaly and the constraints on the near-neighbour XYZ Hamiltonian suggest that Ce$_2$Zr$_2$O$_7$ realizes a U(1)$_π$ QSL state at low temperatures, and one that likely resides near the boundary between dipolar and octupolar character.

cond-mat.str-el↗

Analyser-free, intensity-based wide-field magneto-optical microscopy

In conventional Kerr- and Faraday microscopy the sample is illuminated with plane-polarised light and a magnetic domain contrast is generated by an analyser making use of the Kerr- or Faraday rotation. In this paper we demonstrate possibilities of analyser-free magneto-optical microscopy based on magnetisation-dependent intensity modulations of the light: (i) The transverse Kerr effect can be applied for in-plane magnetised material, demonstrated for an FeSi sheet. (ii) Illuminating the same sample with circularly polarised light leads to a domain contrast with a different symmetry as the conventional Kerr contrast. (iii) Circular polarisation can also be used for perpendicularly magnetised material, demonstrated for a garnet film and an ultrathin CoFeB film. (iv) Plane-polarised light at a specific angle can be employed for both, in-plane and perpendicular media. (v) Perpendicular light incidence leads to a domain contrast on in-plane materials that is quadratic in the magnetisation and to a domain boundary contrast. (vi) Domain contrast can even be obtained without polariser. In cases (ii) and (iii), the contrast is generated by MCD (Magnetic Circular Dichroism), while MLD (Magnetic Linear Dichroism) is responsible for the contrast in case (v). The domain boundary contrast is due to the magneto-optical gradient effect in metallic samples. A domain boundary contrast can also arise due to interference of phase-shifted magneto-optical amplitudes. An explanation of these contrast phenomena is provided in terms of Maxwell-Fresnel theory.

cond-mat.mtrl-sci↗

Tuning the superconducting transition of SrTiO$_3$-based 2DEGs with light

The resistivity of the two dimensional electron gas that forms at the interface of strontium titanate with various oxides is sensitive to irradiation with visible light. In this letter we present data on the interface between the band gap insulators LaAlO$_3$ (LAO) and SrTiO$_3$ (STO). We operate a light emitting diode at temperatures below 1 K and utilize it to irradiate the LAO/STO interface at ultra low temperatures. On irradiation the resistance of this system is lowered continuously by a factor of five and the resistance change is persistent at low temperatures as long as the sample is kept in the dark. This makes a characterization of transport properties in different resistive states over extended time periods possible. Our pristine sample gets superconducting below 265 mK. The transition temperature $T_c$ shifts downwards on the persistent photo-induced lowering of the resistance. The persistent photoconductance can be completely reverted by heating the structure above 10 K in which case $T_c$ as well takes on its original value. Thus very similar to field effect control of electron densities irradiation at low temperatures offers a versatile tuning knob for the superconducting state of STO-based interfaces which in addition has the advantage to be nonvolatile.

cond-mat.supr-con↗

Imaging Domains in a Zero-Moment Half Metal

We have a choice of methods for examining domains at the surface of a ferromagnet that depend on probing the stray field distribution, but these methods do not work in antiferromagnets or compensated ferrimagnets, which produce no stray field. The discovery of compensated ferrimagnetic half-metals allows for the local magnetization state to be observed directly with polarized light. The example considered here, Mn$_{2}$Ru$_{x}$Ga, has two inequivalent but oppositely-aligned Mn sublattices with equal and opposite moments, but only one of them contributes spin polarized conduction electrons at the Fermi energy. The material looks like an antiferromagnet from the outside, but from the point of view of electronic structure it resembles a spin-polarized ferromagnetic metal. The anisotropy axis is perpendicular to the film plane, which allows domains to be imaged directly by polar magneto-optic Kerr effect. The domain structure in a film with a composition of Mn$_{2}$Ru$_{0.4}$Ga has been imaged in a Kerr microscope and hysteresis loops traced. Domains have dimensions of order 20 μm with meandering domain walls and a fractal dimension D$_{f}$ = 1.85. Our results open new direct imaging possibilities for magnetically-ordered materials with no net moment.

cond-mat.mtrl-sci↗

Anisotropic electronic transport and Rashba effect of the two-dimensional electron system in (110) SrTiO$_3$-based heterostructures

The two-dimensional electron system in (110)Al$_2$O$_{3-δ}$/SrTiO$_3$ heterostructures displays anisotropic electronic transport. Largest and lowest conductivity and electron mobility $μ$ are observed along the $[001]$ and $[1\bar{1}0]$ direction, respectively. The anisotropy of the sheet resistance and $μ$ likewise leads to a distinct anisotropic normal magnetotransport (MR) for T < 30K. However, at temperatures T<5K and magnetic field B<2T MR is dominated by weak antilocalization.Despite the rather strong anisotropy of the Fermi surfaces, the in-plane anisotropic magnetoresistance (AMR) displays two-fold non-crystalline anisotropy. However, the AMR-amplitude is found to be anisotropic with respect to the current direction, leading to a 60% larger AMR amplitude for current I along the $[001]$ direction compared to I parallel to $[1\bar{1}0]$. Tight binding calulations evidence an anisotropic Rashba-induced band splitting with dominant linear k-dependence. In combination with semiclassical Boltzmann theory the non-crystalline AMR is well described, despite the anisotropic Fermi surface.

cond-mat.str-el↗

The complete micromagnetic characterization of asymmetrically sandwiched ferromagnetic films

The magnetic properties of ferromagnetic thin films down to the nanoscale are ruled by the exchange stiffness, anisotropies and the effects of magnetic fields. As surfaces break inversion symmetry, an additional effective chiral exchange is omnipresent in any magnetic nanostructure. These so-called Dzyaloshinskii-Moriya interactions (DMI) affect all inhomogeneous magnetic states either subtly or spectacularly. E.g., DMIs cause a chirality selection of the rotation sense and can fix the local rotation axis for the magnetization in domain walls (DW). But, they can stabilize also entirely different twisted magnetic structures. The chiral skyrmions a two-dimensional particle-like topological soliton is the ultimately smallest of these objects, which currently is targetted as a possible information carrier in novel spintronic devices. Observation and quantification of the chiral exchange effects provide for the salient point in understanding magnetic properties in ultrathin films and other nanostructures. An easy and reliable method to determine the DMI constant as materials parameter of asymmetric thin films is the crucial problem. Here, we put forth an experimental approach for the determination of the complete set of the micromagnetic parameters. Quasi-static Kerr microcopy observations of DW creep motion and equilibrium sizes of circular magnetic objects in combination with standard magnetometry are used to derive a consistent set of these materials parameters in polycrystalline ultrathin film systems, namely CrOx/Co/Pt stacks. The quantified micromagnetic model for these films identifies the circular magnetic objects, as seen by the optical microscopy, as ordinary bubble domains with homochiral walls. From micromagnetic calculations, the chiral skyrmions stabilized by the DMI in these films are shown to have diameters in the range 40-200nm, too small to be observed by optical microscopy.

cond-mat.mtrl-sci↗

Roughness-induced domain structure in perpendicular Co/Ni multilayers

We investigate the correlation between roughness, remanence and coercivity in Co/Ni films grown on Cu seed layers of varying thickness. Increasing the Cu seed layer thickness of Ta/Cu/8x[Co/Ni] thin films increases the roughness of the films. In-plane magnetization loops show that both the remanance and coercivity increase with increasing seed layer roughness. Polar Kerr microscopy and magnetic force microscopy reveal that the domain density also increases with roughness. Finite element micromagnetic simulations performed on structures with periodically modulated surfaces provide further insight. They confirm the connection between domain density and roughness, and identify the microsocpic structure of the domain walls as the source of the increased remanence in rough films. The simulations predict that the character of the domain walls changes from Bloch-like in smooth films to Néel-like for rougher films.

cond-mat.mtrl-sci↗

Anisotropic electronic transport of the two-dimensional electron system in Al2O3/SrTiO3 heterostructures

Transport measurements on the two dimensional electron system in Al2O3 SrTiO3 heterostructures indicate significant noncrystalline anisotropic behavior below T = 30 K. Lattice dislocations in SrTiO3 and interfacial steps are suggested to be the main sources for electronic anisotropy. Anisotropic defect scattering likewise alters magnetoresistance at low temperature remarkably and influences spin-orbit coupling significantly by the Elliot Yafet mechanism of spin relaxation resulting in anisotropic weak localization. Applying a magnetic field parallel to the interface results in an additional field induced anisotropy of the conductance, which can be attributed to Rashba spin orbit interaction. Compared to LaAlO3 SrTiO3, Rashba coupling seems to be reduced indicating a weaker polarity in Al2O3 SrTiO3 heterostructures.

cond-mat.str-el↗

Patterning of two-dimensional electron systems in SrTiO3 based heterostructures using a CeO2 template

Two-dimensional electron systems found at the interface of SrTiO3-based oxide heterostructures often display anisotropic electric transport whose origin is currently under debate. To characterize transport along specific crystallographic directions, we developed a hard-mask patterning routine based on an amorphous CeO2 template layer. The technique allows preparing well-defined microbridges by conventional ultraviolet photolithography which, in comparison to standard techniques such as ion- or wet-chemical etching, does not induce any degradation of interfacial conductance. The patterning scheme is described in details and the successful production of microbridges based on amorphous Al2O3-SrTiO3 heterostructures is demonstrated. Significant anisotropic transport is observed for T < 30 K which is mainly related to impurity/defect scattering of charge carriers in these heterostructures.

cond-mat.str-el↗