Linear dichroism in angle-resolved core-level photoemission spectra reflecting 4f ground-state symmetry of strongly correlated cubic Pr compounds

TL;DR

This study demonstrates how linear dichroism in angle-resolved core-level photoemission spectra reveals the ground-state symmetry of 4f electrons in cubic Pr compounds, distinguishing between different crystalline-electric-field states.

Contribution

The paper provides experimental evidence and theoretical analysis linking linear dichroism to 4f ground-state symmetry in PrIr2Zn20 and PrB6, using spectral simulations and polarization-dependent measurements.

Findings

Linear dichroism differs between PrIr2Zn20 and PrB6 due to 4f charge distribution differences.

Spectral simulations confirm Gamma_3 ground state for PrIr2Zn20.

Spectral analysis indicates Gamma_5 ground state for PrB6.

Abstract

We report experimentally observed linear dichroism in angle-resolved core-level photoemission spectra of PrIr2Zn20 and PrB6 in cubic symmetry. The different anisotropic 4f charge distributions between the compounds due to the crystalline-electric-field splitting are responsible for the difference in the linear dichroism, which has been verified by spectral simulations with the full multiplet theory for a single-site Pr3+ ion in cubic symmetry. The observed linear dichroism and polarization-dependent spectra in two different photoelectron directions for PrIr2Zn20 are reproduced by theoretical analysis for the Gamma_3 ground state, whereas those of the Pr 3d and 4d core levels indicate the Gamma_5 ground state for PrB6.

Equations

$$H_{CEF}=B_{40}(O_{40}+5O_{44})+B_{60}(O_{60}-21O_{64}),$$

$$|{\Gamma }_1⟩=\sqrt{5/24}|+4⟩+\sqrt{7/12}|0⟩+\sqrt{5/24}|-4⟩,$$

$$\displaystyle|{\Gamma_{3}}\rangle=\left\{\begin{array}[]{l}\sqrt{7/24}|{+4}\rangle-\sqrt{5/12}|{0}\rangle+\sqrt{7/24}|{-4}\rangle\\ \sqrt{1/2}|{+2}\rangle+\sqrt{1/2}|{-2}\rangle\\ \end{array},\right.$$

$$\displaystyle|{\Gamma_{4}}\rangle=\left\{\begin{array}[]{l}\sqrt{1/8}|{\pm 3}\rangle+\sqrt{7/8}|{\mp 1}\rangle\\ \sqrt{1/2}|{+4}\rangle-\sqrt{1/2}|{-4}\rangle\\ \end{array},\right.$$

$$\displaystyle|{\Gamma_{5}}\rangle=\left\{\begin{array}[]{l}\sqrt{7/8}|{\pm 3}\rangle-\sqrt{1/8}|{\mp 1}\rangle\\ \sqrt{1/2}|{+2}\rangle-\sqrt{1/2}|{-2}\rangle\\ \end{array},\right.$$

Full text

††preprint: APS/123-QED

I Introduction

Rare earth compounds have been investigated for many years in relation to the physical properties of the strongly correlated electron systems, such as heavy fermion behavior, unconventional superconductivity, and multipole ordering. In these systems, the total angular momentum $J$ of the $4f$ electrons is the good quantum number due to the stronger Coulomb interactions between the $4f$ electrons and their spin-orbital coupling than the crystalline electric field (CEF). Therefore, the observable is not the orbital degrees of freedom but the quadrupoles which are described as second-order tensors of $J$. When the dipole magnetic moments are quenched but the quadrupoles remain active under CEF, which is possible in non-Kramers ions with an integer number of $J$ under cubic symmetry, the quadrupoles often play an important role in forming exotic electronic ground states such as the antiferroquadrupolar (AFQ) state with a staggered quadrupolar component,morin and a non-Fermi liquid (NFL) state attributed to the two-channel (quadrupole) Kondo effect.cox1 ; cox2 ; onimaru0 Furthermore, the feasibility of superconductivity mediated by quadrupolar fluctuations in the Pr-based superconductor PrOs4Sb12 with $T_{c}$ = 1.5 Kbauer has been pointed out by neutron scattering and NQR measurements.kuwahara ; yogi A well-known example of a $4f^{2}$ cubic system is PrPb3 which undergoes an AFQ transition at $T_{Q}$ = 0.4 K.tayama ; onimaru00

Here reported cubic PrIr2Zn20 undergoes an AFQ ordering at $T_{Q}$ = 0.11 K and a superconducting transition at $T_{c}$ = 0.05 K.onimaru1 ; onimaru2 Below 10 K, the increase in magnetic susceptibility for this compound tends to saturate, which implies the van Vleck susceptibility with nonmagnetic CEF ground states of the $\Gamma_{3}$ doublet.onimaru3 On the other hand, PrB6 with a cubic crystal structure show the incommensurate antiferromagnetic transition at 7 K and a commensurate antiferromagnetic ordering at 4.2 K.kobayashi These phenomena suggest the $\Gamma_{5}$ ground state for PrB6. However, direct or microscopic verifications of the proposed $4f$ ground-state symmetry are still lacking for these compounds. In this letter, we show spectroscopic signs for the $\Gamma_{3}$ symmetry of the Pr3+ sites in the ground state of PrIr2Zn20 and the $\Gamma_{5}$ ground state of PrB6 on the basis of linear dichroism in angle-resolved core-level photoemission from the Pr sites.

Experimentally, it is difficult to detect the anisotropic $4f$ charge distributions in cubic symmetry. Although inelastic neutron scattering is useful for revealing the CEF splittings, the symmetry itself cannot be directly probed by unpolarized neutrons. Linear dichroism (LD) in $3d$-$4f$ soft X-ray absorption spectroscopy (XAS) for single crystals is powerful for tetragonal Ce compoundshansman ; willers1 ; willers2 ; willers3 owing to the dipole selection rules, but it is no longer applicable for compounds with cubic crystal structure. On the other hand, the selection rules work also in the photoemission process. Furthermore, by virtue of the angle-resolved measurements with the acceptance angle of $\pm$several degrees, there is another measurement parameter as the photoelectron direction relative to the single-crystalline axis in addition to the excitation light polarization. Indeed, by using LD in $3d$ core-level hard X-ray photoemission (HAXPES) spectra, the Yb3+ $4f$ ground state has been determined for cubic YbB12.kanai LD in the core-level HAXPES for cubic Pr compounds is also expected to be observed, as discussed below.

The Pr ions are encapsulated in the highly symmetric Frank-Kasper cages formed by 16 zinc atoms in PrIr2Zn20, where the actual local point-group symmetry is $T_{d}$.nasch For PrB6, on the other hand, the Pr ions are in the $O_{h}$ symmetry.maccarthy Because of the even number of $4f$ electrons, the CEF electronic states are free from the Kramers theorem. The ninefold degenerated ground-state multiplets with $J$ = 4 ($L$ = 5, $S$ = 1) in the $4f^{2}$ configurations determined by the Hund’s rules is lifted by the CEF Hamiltonian for the $T_{d}$ or $O_{h}$ symmetry,

[TABLE]

where $O_{mn}$ and $B_{mn}$ denote the Stevens operator and the CEF parameter, respectively.stevens It has been reported that candidates of the CEF parameters ($B_{40}$, $B_{60}$) are ($-1.1\times 10^{-2}$ K, $-4.5\times 10^{-4}$ K)iwasa and ($1.5\times 10^{-1}$ K, $3.8\times 10^{-4}$ K)loewenhaupt for PrIr2Zn20 and PrB6, respectively. Then the ninefold $J$ = 4 states split generally into one singlet, one doublet, and two triplets as

[TABLE]

where the integers in the kets denote $J_{z}$. It is known that the $\Gamma_{4}$ states are ruled out from the candidates of the ground state because there is no solution of $B_{40}$ and $B_{60}$ to set them as the lowest state.llw Since their $4f$ charge distributions deviate from spherical symmetry owing to the CEF splitting even in the cubic symmetry, as shown in Fig. 1, it is natural to expect the observation of LD in core-level photoemission for cubic Pr compounds. Actually, we have performed ionic calculations including the full multiplet theorythole and the local CEF splitting using the XTLS 9.0 program,tanaka by which finite LDs as a function of the photoelectron direction have been predicted as discussed below. The atomic parameters such as the $3d$-$4f$ Coulomb and exchange interactions (Slater integrals) and the $3d$ and $4f$ spin-orbit couplings have been obtained using Cowan’s codecowan based on the Hartree-Fock method. The $4f$-$4f$ Slater integrals have been obtained using Cowan’s code and their relations.carnall The $3d$-$4f$ and $4f$-$4f$ Slater integrals ($3d$ and $4f$ spin-orbit couplings) are reduced to 80% and 60% (99% and 100%) to reproduce the Pr3+ $3d$ core-level photoemission spectra with final-state multiplet structures including Pr3+ $3d_{3/2}$ spectra, respectively.

II Experimental

We have observed LD in HAXPEShaxpes2 ; mori ; fujiwara at BL19LXU of SPring-8bl19lxu using a MBS A1-HE hemispherical photoelectron spectrometer. A Si(111) double-crystal monochromator selected linearly polarized 7.9 keV radiation within the horizontal plane, which was further monochromatized using a Si(620) channel-cut crystal. To switch the linear polarization of the excitation light from the horizontal to vertical directions, two single-crystalline (100) diamonds were used as a phase retarder placed downstream of the channel-cut crystal. The $P_{L}$ (degree of linear polarization) of the polarization-switched X-ray after the phase retarder was estimated as $-0.89$, corresponding to the vertically linear polarization component of 93.8%. Since the detection direction of photoelectrons was set in the horizontal plane with an angle to incident photons of 60∘, the experimental configuration at the vertically (horizontally) polarized light excitation corresponds to the s-polarization (p-polarization). To precisely detect LD in the Pr $3d$ core-level photoemission spectra, we optimized the photon flux so as to set comparable photoelectron count rates between the s- and p-polarization configurations. Single crystals of PrIr2Zn20 synthesized by the melt-growth methodonimaru2 ; saiga were fractured along the (110) plane in situ, where the base pressure was $1\times 10^{-7}$ Pa. The experimental geometry was controlled using our developed two-axis manipulator,fujiwara where the photoelectron detection along the [100] direction was set by polar rotation of 45∘ from the normal direction parallel to the [110] direction, and the [111] direction was set by polar rotation by $\sim$35∘ after azimuthal rotation. A single crystal of PrB6 synthesized by the floating zone method was fractured along the (100) plane in situ. The sample and surface qualities were examined on the basis of the absence of O and C $1s$ core-level spectral weights caused by possible impurities or surface oxidization. The energy resolution was set to 500 meV. The measuring temperature is 5 K (10 K) for PrIr2Zn20 (PrB6), which is sufficiently lower than the excited states.iwasa

III Results and Discussions

The polarization-dependent Pr3+ $3d_{5/2}$ HAXPES spectra in the [100] direction of PrIr2Zn20 are shown in Fig. 2. Caused by the relatively low density of the Pr ions as $<$5% determined by the composition, the intrinsic Pr $3d_{5/2}$ signals are much weaker than the background contributed by the photoelectrons from the other orbitals in the other elements. A broad peak at a binding energy of $\sim$934 eV, shoulder centered at 939 eV and another shoulder structure ranging from 925 to 930 eV exist in the spectra. The former peak and the shoulder at 939 eV are ascribed to the Pr3+ states ($|{3d^{9}4f^{2}}\rangle$ final states) with the atomic-like multiplets structure, and the shoulder structure at $925-930$ eV comes from the $|{3d^{9}4f^{3}}\rangle$ final states with hybridization between the $4f$ and valence/conduction electrons. The so-called Shirley-type backgrounds are also displayed in Fig. 2. We have optimized the backgrounds as follows: After the normalization of the background-subtracted spectra by the $3d_{5/2}$ spectral weight in the $931-940$ eV region corresponding to the $|3d^{9}4f^{2}\rangle$ final-state (ionic Pr3+) region, the intensities in the high binding energy region of $941-942$ eV become equivalent between the s- and p-polarization configurations. When we have normalized the spectra by the $3d_{5/2}$ spectral weight in the region included both the $|{3d^{9}4f^{2}}\rangle$ and $|{3d^{9}4f^{3}}\rangle$ final states, the LD is slightly suppressed but the sign of the LD is not changed. Therefore, we discuss below by the normalized spectra by only the spectral weight in the $|{3d^{9}4f^{2}}\rangle$ final states. The reference binding energy on the higher side for subtracting the background has been set to 940.8 eV corresponding to the local minimum of the raw spectral weight. As a result, there are finite spectral weights at $\sim$940 eV in the background-subtracted spectra. However, they should be intrinsic due to the overlap of the tails of the lifetime-broadened Pr3+ $3d_{5/2}$ main peaks and a plasmonic energy-loss structure at the higher binding energy.

Figure 3 shows comparisons of the polarization-dependent background-subtracted Pr3+ $3d_{5/2}$ HAXPES spectra of PrIr2Zn20 and their LD (defined as the difference in the spectral weight between the s- and p-polarization configurations) with the photoelectron directions of [100] and [111] with the simulated ones for the $\Gamma_{3}$ and $\Gamma_{1}$ states. Here, we have simulated the spectra for the $\Gamma_{3}$ state at 5 K using the CEF parameters for PrIr2Zn20 listed above, which gives the first excited CEF level of 20 K. For the experimental spectra and the simulated spectra for the $\Gamma_{3}$ state, the LDs are found to be finite but subtle. As shown in Fig. 3(c), the sign of the experimental LD at $\sim$934 eV is positive, whereas that in the $935-938$ eV region is negative along the [100] direction. These tendencies are consistent with the simulated LDs for the $\Gamma_{3}$ and $\Gamma_{1}$ states although the LD for the $\Gamma_{1}$ state is much stronger at $\sim 934$ eV than the experimentally observed LD. For the data in the [111] direction in Fig. 3(d), the LD in the $932-940$ eV region in the experiment is strongly suppressed compared with that in the [100] direction, being consistent with, at least not contradictory to, the simulation for the $\Gamma_{3}$ state. If the $4f$ ground state of PrIr2Zn20 were in the $\Gamma_{1}$ symmetry, a finite LD beyond the statistics would be seen with the negative sign at $\sim 934$ eV. The sign and amount of LD for the $\Gamma_{5}$ state are completely inconsistent with our experimental results in both directions. Therefore, we can conclude that our experimental results support the $\Gamma_{3}$ ground-state symmetry for PrIr2Zn20. The LDs are positive in the $|{3d^{9}4f^{3}}\rangle$ final-state region with the binding energies of 928-930 eV for both directions, for which the origin is not clear. The relatively smaller LDs in the [111] direction than in the [100] direction in both experiments and simulations originate from the larger number of the equivalent direction (e.g. [100], [010] and [001]) in the cubic unit cell (8 for [111] and 6 for [100]), where the simulated LD in the [110] direction (not shown here) is much smaller than that in the [100] and [111] directions. (Note that the LD cancels out for really angle-integrated spectra over 4$\pi$ steradian.)

Figure 4 shows the polarization-dependent background-subtracted Pr3+ $3d_{5/2}$ and $4d$ core-level HAXPES spectra and LDs of cubic PrB6 in the [100] direction. In the case of PrB6, the broad peak and the shoulder structures are seen in the Pr3+ $3d_{5/2}$ spectra. On the other hand, there are multiplets ranging from 114 to 127 eV and a shoulder structure ranging from 106 to 114 eV in the Pr3+ $4d$ spectra. The former multiplets is ascribed to the Pr3+ states ($|{4d^{9}4f^{2}}\rangle$ final states), and the latter shoulder structure comes from the $|{4d^{9}4f^{3}}\rangle$ final states with hybridization between the $4f$ and conduction electrons. These features are qualitatively consistent with the previous reported ones.suga The $3d_{5/2}$ main peak is broader for PrB6 than for PrIr2Zn20 in Fig. 3(c), of which the origin is unclear at present. It is difficult to distinguish clearly the structure of the $|{4d^{9}4f^{2}}\rangle$ final states from that of the $|{4d^{9}4f^{3}}\rangle$ final states in the Pr $4d$ spectra. Therefore, Pr $4d$ spectra have been normalized by spectral weight in the region included both the $|{4d^{9}4f^{2}}\rangle$ and $|{4d^{9}4f^{3}}\rangle$ final states.

The simulated polarization-dependent Pr3+ $3d_{5/2}$ ($4d$) HAXPES spectra for the $\Gamma_{5}$ state at 10 K with the CEF parameters for PrB6 listed above, which gives the first excited CEF level of 300 K, and LDs for the $\Gamma_{1}$, $\Gamma_{3}$, and $\Gamma_{5}$ states are also shown in Fig. 4. For obtaining the simulated Pr3+ $4d$ spectra, the $4d$-$4f$ Slater integrals ($4d$ spin-orbit coupling) are reduced to 80% (100%) to best reproduce the experimental Pr3+ $4d$ core-level photoemission spectra with respect to the multiplet splittings. To reproduce the spectra, the Lorentian width of 3.0 eV (full width of half maximum), which is larger than the value for PrIr2Zn20 of 1.8 eV as shown in Fig. 3(c), has been employed for PrB6. The peak at 934 eV is slightly stronger in the p-polarization configuration than in the s-polarization one in the experimental Pr3+ $3d_{5/2}$ spectra along the [100] direction, which is in contrast to the case of PrIr2Zn20. This tendency and LD are reproduced by the simulations for the $\Gamma_{5}$ states as shown in Fig. 4(a). In the case of the Pr3+ $4d$ spectra, the highest peak at a binding energy of $\sim$116 eV is slightly stronger in the p-polarization configuration than in the s-polarization one for both experimental and simulated spectra while the sign of LD is flipped in the binding energies of $120-125$ eV. As shown in Figs. 4(b) and 4(c), the observed LDs are qualitatively reproduced by the simulations for the $\Gamma_{5}$ state although LDs are somehow smaller in the experiment. Furthermore, the LD signs for the $\Gamma_{3}$ and $\Gamma_{1}$ states are completely opposite to those of the experimental data in all binding energy region. Thus, our results undoubtedly indicate the $\Gamma_{5}$ ground-state symmetry for PrB6, being consistent with the previous report.loewenhaupt The origin for the reduced LD in the experiment compared with the simulations for the Pr3+ ion in cubic symmetry is not clear at present, but we can speculate a couple of possible origins. One is the $c$-$f$ hybridization effects giving the $|3d^{9}4f^{3}\rangle$ final states. The other is a possible antiferromagnetic fluctuation at 10 K just above the transition temperature of 7 K (Ref. kobayashi ). Further detailed temperature and angular dependence of the LD could solve the problem in future. Note that the Pr $4d$ spectral weight has not unfortunately been detected for PrIr2Zn20 since it has been buried in the background from the other sites by the HAXPES at $h\nu$ = 7.9 keV.

IV Summary

In summary, we have performed the polarization-dependent core-level HAXPES of the Pr3+ sites in cubic PrIr2Zn20 and PrB6. Our results support the so far predicted their ground-state symmetry, showing the potential of LD in the core-level HAXPES for probing the partially-filled strongly correlated orbital symmetry of the Pr compounds in cubic symmetry, as established for the Yb systems.kanai ; mori

Acknowledgements.

We thank S. Kunii for providing the single crystals of PrB6 with excellent quality. We are grateful to K. Kuga, H. Aratani, Y. Aoyama, T. Hattori, M. Kawada, S. Takano, M. Murata, and C. Morimoto for supporting the experiments. AS thanks Y. Saitoh for fruitful discussions. K. T. Matsumoto, Y. Nakatani and Y. Kanai were supported by the JSPS Research Fellowships for Young Scientists. This work was financially supported by a Grant-in-Aid for Scientific Research of “J-Physics” (JP15H05886, JP16H01074) from MEXT, Japan and that for Scientific Research (JP16H04014) from JSPS, Japan.