Session T29: Correlated Electron Magnetism II

Onset of ferromagnetism in EuB$_6$

We assess the magnetic experimental signatures of precursor magnetic polarons and characterize the ferromagnetic ordering transition in EuB$_6$. The results of bulk magnetometry and neutron scattering measurements will be discussed.   

High-pressure magnetotransport measurements of the semimetallic ferromagnet EuB$_{6}$

Hall effect measurements on EuB$_{6}$ have revealed manifestations of the microscopic electronic phase separation and resulting percolative phase transition in a macroscopic magnetotransport property of this semimetallic ferromagnet [1]: the Hall resistivity as a function of applied field in the paramagnetic phase exhibits two distinct linear regions with a transition point at a single critical magnetization in a broad temperature range, which was interpreted as the percolation point for the more conducting phase. To further understand this phenomenon, magnetotransport measurements were performed on EuB$_{6}$ under high pressure. Hydrostatic pressure is known to substantially modify the magnetic state of EuB$_{6}$ [2]. EuB$_{6}$ single crystals were inserted in a high-pressure cell filled with silicone oil and measurements were taken at different pressures up to 1.8 GPa. Increasing hydrostatic pressure caused a decrease in resistivity and an increase in T$_{\theta}$, while the ferromagnetic ordering temperature stayed approximately constant. The Hall resistivity in the paramagnetic phase developed an intermediate region between the two previously observed regions. The transition fields between the low-field and intermediate regions depend linearly on temperature and their intercepts increase with pressure similar to the variation of T$_{\theta}$ indicated by the resistivity peak.\\[4pt] [1] X. H. Zhang et al, Phys. Rev. Lett. 103, 106602 (2009).\\[0pt] [2] J.C. Cooley et al, Phys. Rev. B 56, 14541 (1997).   

Interplay of many-body and single-particle interactions in iridates and rhodates

Motivated by recent experiments exploring the spin-orbit-coupled magnetism in $4d$- and $5d$-band transition metal oxides, we study magnetic interactions in Ir- and Rh-based compounds. In these systems, the comparable strength of spin-orbit coupling (SOC), crystal field splitting (CF) and Coulomb and Hund's coupling leads to a rich variety of magnetic exchange interactions, leading to new types of ground states. Using a strong coupling approach, we derive effective low-energy super-exchange Hamiltonians from the multi-orbital Hubbard model by taking full account of the Coulomb and Hund's interactions in the intermediate states. We find that in the presence of strong SOC and lattice distortions the super-exchange Hamiltonian contains various kinds of magnetic anisotropies. Here we are primarily interested in the magnetic properties of Sr$_2$IrO$_4$ and Sr$_2$Ir$_{1-x}$Rh$_x$O$_4$ compounds. We perform a systematic study of how magnetic interactions in these systems depend on the microscopic parameters and provide a thorough analysis of the resulting magnetic phase diagram. Comparison of our results with experimental data shows good agreement.   

Impact of spin-orbit coupling on the magnetism of Sr$_{3}$MIrO$_{6}$ (M $=$ Ni, Co)

Recently, Iridates have recently drawn considerable attention due to their significant spin-orbit coupling (SOC) effect and possibly exotic properties [1]. In this work, we demonstrate, using density functional calculations, that the SOC of Ir$^{4+}$ ions plays an essential role in determining the antiferromagnetism of hexagonal spin-chain materials Sr$_{3}$MIrO$_{6}$ (M$=$Ni, Co) by tuning the crystal-field level sequence and altering the Ir-M inter-orbital interactions. Owing to the SOC effect, the single t$_{\mathrm{2g}}$ hole of the Ir$^{4+}$ ion resides on the e'$_{\mathrm{g}}$ upper branch and gives rise to the Ir$^{4+}$-M$^{2+}$ antiferromagnetic coupling. In absence of the SOC, however, the single t$_{\mathrm{2g}}$ hole would occupy the crystal-field a$_{\mathrm{1g}}$ singlet instead, which would mediate an unreal ferromagnetic exchange This work clarifies the nature and the origin of the intra-chain Ising antiferromagnetism of Sr$_{3}$MIrO$_{6}$(M $=$ Ni, Co) [2].\\[4pt] [1] B. J. Kim, et al., Phys. Rev. Lett. 101, 076402 (2008)\\[0pt] [2] X. Ou and H. Wu, Sci. Rep. 4, 4609 (2014); Phys. Rev. B 89, 035138 (2014).   

LDA+DMFT Approach to Magnetocrystalline Anisotropy of Strong Magnets

The new challenges posed by the need of finding strong rare-earth-free magnets demand methods that can predict magnetization and magnetocrystalline anisotropy energy (MAE). We argue that correlated electron effects, which are normally underestimated in band structure calculations, play a crucial role in the development of the orbital component of the magnetic moments. Because magnetic anisotropy arises from this orbital component, the ability to include correlation effects has profound consequences on our predictive power of the MAE of strong magnets. Here we show [1] that incorporating the local effects of electronic correlations with dynamical mean-field theory provides reliable estimates of the orbital moment, the mass enhancement and the MAE of YCo$_5$.\\[4pt] [1] J.-X. Zhu \em{et al.}, Phys. Rev. X {\bf 4}, 021027 (2014).   

Quantum Indian Rope Tricks: Fluctuation driven magnetic hard-axis ordering in metallic ferromagnets

We demonstrate that the interplay between soft electronic particle-hole fluctuations and magnetic anisotropies can drive ferromagnetic moments to point along a magnetic hard axis. As a proof of concept, we show this behavior explicitly for a generic two-band model with local Coulomb and Hund's interactions, and a spin-orbit-induced easy plane anisotropy. The phase diagram is calculated within the fermionic quantum order-by-disorder approach, which is based on a self consistent free-energy expansion around a magnetically ordered state with unspecified orientation. Quantum fluctuations render the transition of the easy-plane ferromagnet first-order below a tricritical point. At even lower temperatures, directionally dependent transverse fluctuations dominate the magnetic anisotropy and the moments flip to lie along the magnetic hard axis. We discuss our findings in the context of recent experiments that show this unusual ordering along the magnetic hard direction. \newline F. Kr\"uger, C.~J. Pedder, and A.~G. Green, Phys. Rev. Lett. {\bf 113}, 147001 (2014)   

New mechanism of kinetic exchange interaction induced by strong magnetic anisotropy

It is well known that the kinetic exchange interaction between single-occupied magnetic orbitals (s-s) is always antiferromagnetic, of the order $-t^2/U$, where $t$ is the transfer parameter and $U$ is the electron promotion energy. At the same time the exchange interaction between single- and double-occupied orbitals, s-d, is always ferromagnetic, of the order $t^2/U \cdot J/U$, where $J$ is the Hund's rule coupling parameter ($J/U \simeq 0.1$). Here we show that the exchange interaction between ground doublet states of lanthanide or actinide ions is characterized by equal in magnitude s-s and s-d kinetic exchange interactions, both scaling as $\sim t^2/U$ [1]. Moreover, the s-d kinetic mechanism prevails in many situations, contributing to antiferromagnetic coupling in the case of collinear magnetic ions. In the non-collinear case the s-d kinetic mechanism can cause an overall ferromagnetic exchange interaction of the order of $t^2/U$, already for the angle $\sim \pi/4$ between the main magnetic axes on sites, which appears quite counter-intuitive. This new s-d kinetic mechanism is not operative in the case of exchange interaction between strongly anisotropic magnetic doublets and an isotropic spin.\\[4pt] [1] N. Iwahara and L. F. Chibotaru, submitted to Phys. Rev. Lett.   

First-Order Magnetostructural Phase Transition in AlFe$_{2}$B$_{2}$

Understanding correlations between composition and crystal structure is key to tailoring the response of functional magnetic materials. In particular, the ferromagnetic AlFe$_2$B$_2$ compound with the layered AlMn$_2$B$_2$-type structure is reported to exhibit a magnetic transition of relevance for magnetocaloric cooling, with a reported entropy change $\Delta S \sim$ 4J/kg-K at an applied magnetic field of 2 T1.\footnote{X. Tan et al., J. Am. Chem. Soc., 135(2012) 9553.} New results derived from magnetic, structural and calorimetric probes confirm a thermodynamically first-order magnetic phase change in AlFe$_2$B$_2$ in the vicinity of the Curie temperature of $\sim$300 K. The transformation from the ferromagnetic to the paramagnetic state is accompanied by a non-uniform 1\% unit cell volume expansion upon heating, signifying that application of magnetic field is anticipated to have a similar effect (stabilizing the ferromagnetic phase) as the application of chemical or hydrostatic pressure. Relevant barocaloric effects are expected in this compound.   

Pressure tuning of itinerant magnetism in Mo$_{3}$Sb$_{7}$

Mo$_{3}$Sb$_{7}$ is a recently discovered itinerant antiferromagnet with a magnetic phase formed by spin dimerization at 53 K and ambient pressure, followed by a 2.3 K superconducting phase. In concert with the dimer pairing of S$=$1/2 Mo ions, a contraction of the crystalline lattice breaks the cubic symmetry. Here we use both high pressure x-ray single crystal diffraction and electrical transport techniques to investigate the magnetic behavior and map out the P-T phase diagram of Mo$_{3}$Sb$_{7}$. Our results demonstrate that the magnetic phase is eventually suppressed by high pressure, where the lattice structure returns to cubic. The disappearance of the antiferromagnetic phase in Mo$_{3}$Sb$_{7}$ could influence the evolution of the superconducting state.   

Possible Correlation-Enhanced Magnetic Ordering at Anomalously High Temperatures in Dy under Extreme Compression

Most lanthanides order magnetically at temperatures $T_{\mathrm{o}}$ well below ambient, the highest being 292 K for Gd. The highly localized magnetic state of the heavy lanthanides should become unstable at sufficiently high pressure, leading to a competition between the RKKY interaction and Kondo physics. Most lanthanides undergo a volume collapse at a critical pressure $P_{\mathrm{vc}}$, the largest being 16{\%} in Ce at only 0.7 GPa but 6{\%} in Dy at 73 GPa, possibly a sign that the magnetic state has become unstable. Recent electrical resistivity measurements on Dy reveal a highly non-monotonic dependence of $T_{\mathrm{o}}$ on pressure. Immediately above $P_{\mathrm{vc}}$, $T_{\mathrm{o}}(P)$ in Dy shows a dramatic increase, extrapolating to values near 400 K at 160 GPa (1.6 Mbar). Interestingly, the pressure dependence of the magnetic spin-disorder resistivity $\rho _{\mathrm{sd}}(P)$ tracks that of $T_{\mathrm{o}}(P)$. The results of parallel experiments on Gd and further heavy lanthanides will also be presented.   

Evidence for Highly Correlated Electron Behavior in Dy under Extreme Compression Resulting in Strongly Enhanced Magnet Interactions

Most lanthanide metals have stable, highly localized 4$f$ magnetic moments, the magnetic ordering temperature $T_{\mathrm{o}}$ following standard de Gennes scaling. Under extreme pressure, however, the 4$f $state of some lanthanides appears to become unstable, as evidenced by: (i) a volume collapse at a critical pressure $P_{\mathrm{vc}}$, usually accompanied by a structural transition from high to low symmetry, (ii) strong deviations from de Gennes scaling in the pressure dependence of $T_{\mathrm{o}}$, in particular, for Dy a dramatic increase in $T_{\mathrm{o}}$ above $P_{\mathrm{vc}}$, (iii) very strong magnetic pair breaking by lanthanide impurities in a superconducting host. Here we discuss possible origins for these anomalous findings in light of our recent electrical resistivity and synchrotron spectroscopy experiments on selected lanthanides and their dilute magnetic alloys in a superconducting Y host.   

CF excitations of CeCu$_2$Si$_2$: Revisited employing a single crystal and triple-axis spectrometers

CeCu$_2$Si$_2$ is the famous heavy-fermion system showing unconventional superconductivity mediated by low-energy magnetic excitations of the CF ground-state doublet. From the point symmetry of the Ce$^{3+}$ ions in the tetragonal crystal lattice a CF splitting into 3 doublets is expected for the (J=5/2) multiplet. First INS measurements on polycrystalline samples of CeCu$_2$Si$_2$ employing a time-of-flight technique revealed a CF level scheme of 0-12-30 meV but were disputed by more advanced INS data in subsequent years. Finally it was accepted that the CF excitations of CeCu$_2$Si$_2$ consist of only one very broad transition with 30 meV from the ground-state doublet to both of the more or less degenerated excited CF states, the so called ``quasi-quartet.'' Employing a large single crystal of CeCu$_2$Si$_2$ and the thermal neutron triple-axis spectrometers PUMA at FRM II and TAIPAN at OPAL we revisited the CF-transitions to verify or falsify this interpretation. We performed TAS measurements for different crystallographic directions. From our results we infer that the quasi-quartet actually consists of two doublets situated at 30 and 35 meV exhibiting a strong directional dependence of their transition matrix elements to the ground state doublet.   

Magnetism and magnetic ordering in \textit{Ln}CuGa$_{3}$ (\textit{Ln} $=$ lanthanide)

We report structural characterization and magnetization and transport measurements on \textit{Ln}CuGa$_{3}$ (\textit{Ln} $=$ La, Ce, Pr, Nd, Sm, Eu, and Gd) intermetallics. Magnetization in fixed field was measured for high quality polycrystalline samples at temperatures between 1.8 and 300 K, along with the isothermal variation of magnetization with field, while the temperature dependent resistivity was measured down to $T = $ 0.3 K. All members of this family, except for the PrCuGa$_{3}$ and non-magnetic LaCuGa$_{3}$ compounds, exhibit magnetic ordering above 1.8 K at temperatures ranging from 2 K (CeCuGa$_{3})$ to 75 K (EuCuGa$_{3})$. The Eu and Sm based compounds exhibit multiple magnetic transitions. SmCuGa$_{3}$ appears to be ferromagnetic, whereas the other compounds order antiferromagnetically. Preliminary studies on single crystals of SmCuGa$_{3}$ indicate that the ordered moments lie parallel to the $c$-axis in the low temperature magnetically ordered phase of this tetragonal system.   

Magnetic spiral induced by strong correlations in MnAu$_2$

The compound MnAu\(_2\) is one of the oldest known spin-spiral materials, yet the nature of the spiral state is still not clear. The spiral cannot be explained via relativistic effects due to the short pitch of the spiral and the weakness of the spin-orbit interaction in Mn, and another common mechanism, nesting, is ruled out as direct calculations show no features at the relevant wave vector. We propose that the spiral state is induced by a competition between the short-range antiferromagnetic exchange and a long-range interaction induced by the polarization of Au bands, similar to double exchange. We find that, contrary to earlier reports, the ground state in standard density functional theory is ferromagnetic, \emph{i.e.}, the latter interaction dominates. However, an accounting for Coulomb correlations via a Hubbard \(U\) suppresses the Schrieffer-Wolff type \(s-d\) magnetic interaction between Mn and Au faster than the superexchange interaction, favoring a spin-spiral state. For realistic values of \(U\) the resulting spiral wave vector is in close agreement with experiment.