Ferromagnetic ordering along the hard axis in the Kondo lattice YbIr3Ge7

TL;DR

This paper reports the discovery of a new ferromagnetic Kondo lattice compound, YbIr3Ge7, which uniquely orders ferromagnetically along its hard axis despite strong anisotropy, suggesting a fluctuation-driven mechanism.

Contribution

It introduces YbIr3Ge7 as the first rhombohedral ferromagnetic Kondo lattice with hard axis ordering and no inversion symmetry at the magnetic site.

Findings

YbIr3Ge7 has TK = 14 K and TC = 2.4 K.

Ferromagnetic order occurs along the hard CEF axis.

The ordering mechanism is likely fluctuation-induced.

Abstract

Ferromagnetic Kondo lattice compounds are far less common than their antiferromagnetic analogs. In this work, we report the discovery of a new ferromagnetic Kondo lattice compound, YbIr3Ge7. Like almost all ferromagnetic Kondo lattice systems, YbIr3Ge7 shows magnetic order with moments aligned orthogonal to the crystal electric field (CEF) easy axis. YbIr3Ge7 is unique in that it is the only member of this class of compounds that crystallizes in a rhombohedral structure with a trigonal point symmetry of the magnetic site, and it lacks broken inversion symmetry at the local moment site. AC magnetic susceptibility, magnetization, and specific heat measurements show that YbIr3Ge7 has a Kondo temperature TK = 14 K and a Curie temperature TC = 2.4 K. Ferromagnetic order occurs along the crystallographic [100] hard CEF axis despite the large CEF anisotropy of the ground state Kramers doublet with a saturation moment along [001] almost four times larger than the one along [100]. This implies that a mechanism which considers the anisotropy in the exchange interaction to explain the hard axis ordering is unlikely. On the other hand, the broad second-order phase transition at TC favors a fluctuation-induced mechanism.

Tables

Table 1. Table S1: Crystallographic parameters of YbIr 3 Ge 7 single crystals at T 𝑇 T = 299 K ( R ​ 3 ¯ ​ c 𝑅 ¯ 3 𝑐 R\bar{3}c )

$a$ (Å)	7.8062(10)
$c$ (Å)	20.621(5)
$V$ (Å3)	1088.2(4)
crystal dimensions (mm3)	0.02 x 0.04 x 0.06
$\theta$ range (∘)	3.6 - 30.4
extinction coefficient	0.000107(13)
absorption coefficient (mm-1)	94.87
measured reflections	7380
independent reflections	374
Rint	0.046
goodness-of-fit on F2	1.20
$R_1\left(F\right)$ for $F_{}^2{}_o{}^{}>2\sigma {\left(F_{}^2{}_o{}^{}\right)}^a$	0.017
$w{R}_2{\left(F_{}^2{}_o{}^{}\right)}^b$	0.033

Table 2. Table S2: Atomic positions, U e ​ q subscript 𝑈 𝑒 𝑞 U_{eq} values, and occupancies for single crystals of YbIr 3 Ge 7

Atom	x	y	z	$U_{eq}$ (Å2)a	Occupancy
Yb	0	0	0	0.00652(14)	1
Ir	0.31885(3)	0	$\frac{1}{4}$	0.00321(11)	1
Ge1	0.54369(8)	0.68054(8)	0.03056(2)	0.0050(2)	0.970(3)
Ge2	0	0	$\frac{1}{4}$	0.0048(4)	0.911(6)

Full text

Various competing ground states in Kondo lattice (KL) systems, governed by the delicate balance between the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction and on-site Kondo effect, have gained great interest for over three decades Doniach (1977); Stewart (2001); Löhneysen et al. (2007). These two interactions usually result in antiferromagnetic (AFM) order with a dense KL metallic ground state. The balance between Kondo and RKKY interactions can be tuned by applying non-thermal parameters such as pressure, magnetic field, or chemical doping, resulting in non-Fermi liquid behavior near a quantum critical point (QCP) where the AFM transition temperature is suppressed to absolute zero, or other quantum collective phenomena emerge including unconventional superconductivity Gegenwart et al. (2007); Paglione et al. (2007); Keimer and Moore (2017).

Among known KLs, the number of compounds that shows AFM order greatly surpasses that of the ferromagnetically ordered compounds Brando et al. (2016); Ahamed et al. (2018); Hafner et al. (2018). Thus, in stark contrast to the AFM counterpart, in-depth theoretical work to describe ferromagnetic (FM) KL compounds is largely missing Yamamoto and Si (2010); Krüger et al. (2014). Recently Ahamed et al. Ahamed et al. (2018) suggested that broken inversion symmetry at the local moment site could promote FM order in KLs. While this scenario is possible for most of the Ce- and Yb-based FM KL compounds, including CeTiGe3 Fritsch et al. (2015), YbNiSn Bonville et al. (1992), YbPtGe Katoh et al. (2009), YbRhSb Muro et al. (2004), YbPdSi Tsujii et al. (2016), and the most heavily studied FM KLs CeAgSb2 Myers et al. (1999); André et al. (2000); Sidorov et al. (2003); Araki et al. (2003); Takeuchi et al. (2003), CeRuPO Krellner and Geibel (2008); Krellner et al. (2007, 2008) and YbNi4P2 Krellner (2011), it does not apply to systems with inversion symmetry like Yb(Rh0.73Co0.27)2Si2 Klingner et al. (2011); Lausberg et al. (2013) and YbCu2Si2 Shimizu et al. (1987); Tateiwa et al. (2014). Moreover, it has been theoretically and experimentally found that the FM phase is inherently unstable, either towards a first-order phase transition Belitz et al. (1999) or towards inhomogeneous magnetic phases Kotegawa et al. (2013). Thus, the FM QCP either does not exist or is masked by other phases. Only in the case of YbNi4P2, FM order occurs via a second-order phase transition upon chemical substitution in YbNi4(P1-xAsx)2 Steppke et al. (2013). The presence of a FM QCP in this system has been attributed to its quasi-1D structure Krellner (2011); Steppke et al. (2013). Thus, in order to develop the theory surrounding FM KL systems in general, and experimentally realize new FM QCPs in particular, new FM KL compounds are called for.

In compounds with strong crystal electric field (CEF) effects, the CEF-induced anisotropy determines the direction of easy and hard magnetization axes in the paramagnetic (PM) state. Interestingly, in all of the FM KL compounds mentioned above, with the exception of CeTiGe3 and YbCu2Si2, this CEF anisotropy competes with the RKKY interaction and results in magnetic ordering along the axis orthogonal to the CEF easy axis Myers et al. (1999); Krellner and Geibel (2008); Krellner (2011); Krellner and Geibel (2012); Lausberg et al. (2013); Steppke et al. (2013). Even more astonishing is the fact that the FM hard axis ordering appears to be a general trait of FM KL systems, as of yet unexplained. Hafner et al. (2018).

In this paper, we report the discovery of a new FM KL compound YbIr3Ge7 with $T_{\rm C}$ = 2.4 K. In line with the above empirical observation, spontaneous magnetization occurs along the hard CEF axis. However, YbIr3Ge7 is unique among FM KLs because it is the only such compound crystallizing in a rhombohedral lattice, and it does not show broken inversion symmetry at the local moment site. Recently, we discovered a series of Ce- and Yb-based compounds in this 1-3-7 structural family, including YbRh3Si7 Rai et al. (2018a), CeIr3Ge7 Rai et al. (2018b); Banda et al. (2018), and YbIr3Si7 Stavinoha et al. . Among these compounds, YbRh3Si7 and YbIr3Si7 are KL compounds with the former proposed to order antiferromagnetically below 7.5 K based on neutron scattering, and the latter showing ferromagnetic correlations below 4 K, with the moments ordered along the hard CEF axis in both. In contrast, CeIr3Ge7 shows AFM order along the easy CEF axis at a remarkably low temperature $T_{\rm N}$ = 0.63 K, in the absence of Kondo screening or frustration. Although chemically and structurally similar, the balance between CEF effects, Kondo screening, and RKKY interactions in these systems differ drastically. Thus, this family of compounds presents an opportunity to study the delicate competition among these interactions and the resulting ground states.

Single crystals of YbIr3Ge7 were grown using Ge self-flux, as described in earlier publications Remeika (1980); Rai et al. (2015). The purity and crystal structure were identified by single crystal and powder x-ray diffraction analysis (Tables S1 and S2 and Fig. S1 in the Appendix). YbIr3Ge7 crystallizes in the ScRh3Si7 structure type Chabot et al. (1981); Lorenz and Jung (2006) with lattice parameters $a=7.8062(10)$ Å and $c=20.621(5)$ Å. The stoichiometry determined by free variable refinement of the occupancies is YbIr3Ge7-δ where $\delta$ = 0.3. The crystals were oriented along the [100] and [001] hexagonal axes using a back-scattering Laue camera. Room temperature powder x-ray diffraction data were collected using a Bruker D8 diffractometer with Cu K$\alpha$ radiation, with additional room temperature single crystal x-ray diffraction performed using a Bruker D8 Quest Kappa single crystal x-ray diffractometer equipped with an I$\mu$S microfocus source, a HELIOS optics monochromator, and a CMOS detector. The anisotropic DC magnetic susceptibility $M/H$ and magnetization data were measured using a Quantum Design (QD) Magnetic Property Measurement System (MPMS) with an applied magnetic field up to 7 T. AC susceptibility was measured with a QD MPMS with a modulation field amplitude $\mu_{0}H_{\rm{ac}}=1$ mT at a frequency of 113.7 Hz. AC susceptibility measurements at 20 mK were performed using an Oxford Instruments dilution refrigerator. Specific heat and electrical transport measurements were performed in a QD Physical Property Measurement System.

In YbIr3Ge7, the Yb atom occupies a trigonal point symmetry ($\bar{3}$), and the $J=7/2$ energy levels are split by the CEF in four Kramers doublets. While the CEF energy levels for the Ce isostructural compound were determined from magnetic susceptibility measurements and calculations Rai et al. (2018b); Banda et al. (2018), the larger angular momentum of the Yb leads to a corresponding Hamiltonian with six parameters in YbIr3Ge7, which can not be fully solved with the data at hand. However, large CEF anisotropy in YbIr3Ge7 is evidenced by the linear high-temperature inverse susceptibility $H/(M-M_{0})$ shown in Fig. 1a, measured for field $H\parallel[001]$ (blue symbols) and $H\parallel[100]$ (red symbols). The Curie-Weiss fit (solid line) of the average inverse susceptibility (purple) between 400 and 600 K yields the experimental effective moment $\mu_{\mathrm{eff}}=4.42\,\mu_{\mathrm{B}}$/Yb, close to the calculated value $4.54\,\mu_{\mathrm{B}}$/Yb for Yb3+. The paramagnetic Weiss temperatures along [100] and [001] are both negative, $\theta_{\rm W}^{[100]}=-400$ K and $\theta_{\rm W}^{[001]}=-70$ K, and yield a first CEF parameter $B_{2}^{0}=-1.6$ meV Bowden et al. (1971), which is a measure of the strength of the CEF anisotropy. Deviations from linearity below 300 K indicate that CEF splitting exceeds this temperature range, similar to the large splitting observed in the Ce analog Rai et al. (2018b); Banda et al. (2018).

Further insight into the low-temperature magnetic properties of YbIr3Ge7 comes from the magnetic AC susceptibility shown in Fig. 1b. AC susceptibility measurements reveal spontaneous magnetization below $T_{\mathrm{C}}=$ 2.4 K for H$\parallel$ [100], indicative of ferromagnetic order. This is indeed consistent with the transition moving up in temperature (vertical arrows, Fig. 1b) with increasing applied field. At zero field the susceptibilities measured with $H_{\mathrm{ac}}\parallel[100]$ and $H_{\mathrm{ac}}\parallel[001]$ cross each other at a temperature just above $T_{\mathrm{C}}$. This behavior is similar to that of the heavy fermion ferromagnet YbNi4P2 and of all other KL ferromagnets which order along the hard direction Steppke et al. (2013); Hafner et al. (2018).

The temperature-dependent electrical resistivity in YbIr3Ge7 is typical of dense KL systems, as shown in Fig. 2. Metallic behavior with a positive resistivity coefficient (d$\rho$/d$T>$ 0) is observed between 300 K and 40 K. On further cooling, the resistivity shows a local minimum around 35 K, followed by a $-$ln$T$ increase (dashed line) down to a coherence maximum around 6 K for $H$ = 0 (red open symbols, Fig. 2), reflecting the incoherent Kondo scattering behavior. A drop in resistivity is seen as the temperature is further lowered through a magnetic phase transition around 2.4 K, as shown more clearly in a derivative plot in Fig. S2. The resistivity in applied magnetic field $\mu_{0}H$ = 9 T (full symbols, Fig. 2) shows the partial suppression of the Kondo effect and the FM fluctuations as the logarithmic increase disappears and the local maximum moves up in temperature.

A closer look at the ordered state with $T$ = 1.8 K magnetization isotherms (Fig. 3) confirms the $H\parallel[100]$ ferromagnetic ordering (red closed circles), while the magnetization shows crossing around $\mu_{0}H~{}=0.1$ T when H$\parallel$[001] (blue, open symbols) and H$\parallel$[100] (red, full symbols): small spontaneous magnetization (left inset) is observed for $H\parallel[100]$, while the $H\parallel[001]$ $M(H)$ is nearly linear at low H. A small magnetization hysteresis with a coercive field $\approx$ 6 mT is revealed at 20 mK in AC susceptibility measurements with $H~{}\parallel$ [100], best illustrated in the $\chi^{\prime}(H)$ plot (right inset). These features indicate that the FM ordering occurs with moments along the CEF hard direction [100]. The field along the CEF easy direction [001] rotates the moments to saturation without increasing much above 5 T, suggesting the absence of a relevant Van Vleck contribution Lausberg et al. (2013). The saturation magnetization of the ground state Kramers doublet for $H\parallel[100]$ is reached at very small fields with $M^{\mathrm{sat}}_{[100]}\approx 0.41\,\mu_{B}$ whereas for $H\parallel[001]$ is reached at fields larger than 4 T with $M^{\mathrm{sat}}_{[001]}\approx 1.55\mu_{B}$. This yields a relatively large anisotropy factor of about 4. Therefore, assuming anisotropic exchange interaction to explain the FM ordering with moments along the CEF hard axis Andrade and Vojta (2014) seems unlikely in the case of YbIr3Ge7, because this would necessitate an extremely large anisotropy for the exchange interaction Hamann et al. (2018).

Further evidence of the FM order in YbIr3Ge7 is shown by the specific heat (Fig. 4), marked by the peak at $T_{\mathrm{C}}~{}=2.4$ K, consistent with the magnetization and resistivity derivatives (Fig. S2). As $T\rightarrow 0$, an enhanced electronic specific heat coefficient $\gamma_{0}~{}\sim~{}\frac{C_{p}}{T}~{}\approx 300$ mJ/mol$\cdot$K2 is observed in YbIr3Ge7 (red), while the corresponding $\gamma_{0}$ for the non-magnetic analog LuIr3Ge7 (black line) is, as expected, $<$ 5 mJ/mol K2. The mass renormalization and the small magnetic entropy release at $T_{\rm C}$, $S_{mag}~{}\sim~{}17\%$ (Fig. 4(b)), suggest Kondo lattice formation in YbIr3Ge7, with a Kondo temperature $T_{\rm K}\sim 14$ K estimated from $S_{mag}(0.5\,T_{\mathrm{K}})=0.5~{}\mathrm{R}\,\mathrm{ln}2$. This $T_{\rm K}$ estimate is in line with the temperature region where the resistivity exhibits Kondo resonance. YbIr3Ge7 thus appears to be a rare Yb-based KL ferromagnet with hard axis moment ordering, and the first such compound crystallizing in a rhombohedral lattice.

In Yb-based KLs, the development of FM order away from the CEF easy axis has been revealed in several compounds with different structures, and a wide range of $T_{\rm C}$, from 0.15 K in YbNi4P2 Krellner (2011) to 15 K in CeRuPO Krellner and Geibel (2008), while $T_{\rm K}$ ranges from 7 K in CeRuPO Krellner and Geibel (2008) up to 30 K in YbRhSb Muro et al. (2004). While YbIr3Ge7 has a three-dimensional crystal structure, YbNi4P2 is quasi-one-dimensional. This implies that the dimensionality of magnetic interactions and the relative magnitude of the magnetic and Kondo energy scales, i.e., the position in the Doniach phase diagram Doniach (1977), have little to no effect on the FM order along the hard axis in these Kondo ferromagnets.

Krüger et al. Krüger et al. (2014) proposed a theoretical model to account for the hard axis ferromagnetic order: they suggested that magnetic order along the hard axis can maximize the phase space for spin fluctuations in the easy plane, leading to a minimum in free energy. This is supported by the broadness of the specific heat peak (Fig. 4), hinting at the presence of fluctuations, but is brought into question by the nature of the magnetic anisotropy in YbIr3Ge7: The presence of an easy axis along $c$ rather than an easy plane does not fit well into this picture. In fact, in the case of CeTiGe3 Fritsch et al. (2015), which has a much stronger easy axis anisotropy, the moments do order along the easy axis. Furthermore, a comparison of YbIr3Ge7 with the other isostructural Yb compounds is called for: YbIr3Si7Stavinoha et al. and YbRh3Si7 Rai et al. (2018a) are both recently discovered highly anisotropic Kondo lattice systems, with hard axis ferromagnetic correlations in the former, and antiferromagnetic ground state in the latter as suggested by neutron scattering, with a small remanent magnetization of about 0.15 $\mu_{\mathrm{B}}/$Yb along the [100] direction. Beyond the KLs showing hard axis ordering, several other strongly correlated FMs Hafner et al. (2018) reveal that magnetic order away from the CEF easy axis is not an exception, but rather a frequent enough occurrence to warrant a thorough theoretical investigation. The ”1-3-7” compounds (YbIr3Ge7 with ferromagnetic order and YbIr3Si7 with ferromagnetic correlations Stavinoha et al. , together with the antiferromagnet YbRh3Si7Rai et al. (2018a)) have the Yb ions in the lowest point symmetry (trigonal) of all these KL compounds. With CEF effects inherently tied to the point symmetry of the magnetic moment, the observation of magnetic order away from the easy axis in different point symmetry cases underlines the difficulty of a generalized theory, which is left to a separate thorough theoretical study.

In conclusion, we report the discovery of a KL compound YbIr3Ge7 that shows FM ordering at $T_{\rm C}$ = 2.4 K, with the moment lying along the CEF hard direction. With a rhombohedral crystal lattice, this material expands this class of systems to include a new crystal structure. With relatively small $T_{\rm C}$ and $T_{\rm K}$, YbIr3Ge7 is an ideal candidate to study FM QCP by chemical substitution, and to further develop existing theories to explain FM KL compounds.

BKR, MS, CLH, and EM acknowledge support from the Gordon and Betty Moore Foundation EPiQS Initiative through grant GBMF 4417. E.M. acknowledges travel support to Max Planck Institute in Dresden, Germany from the Alexander von Humboldt Foundation Fellowship for Experienced Researchers. This research is funded in part by a QuanEmX grant from ICAM and the Gordon and Betty Moore Foundation through Grant GBMF 5305 to Binod K. Rai. We thank the DFG for financial support from project BR 4110/1-1. JYC acknowledges support from NSF: DMR-1700030.

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