Dynamical coupling of dilute magnetic impurities with quantum spin liquid state in the S = 3/2 dimer compound Ba3ZnRu2O9
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Dynamical coupling of dilute magnetic impurities withquantum spin liquid state in the S = ZnRu O Takafumi D. Yamamoto, Hiroki Taniguchi, and Ichiro Terasaki
Department of Physics, Nagoya University, Nagoya 464-8602, JapanE-mail: [email protected]
Abstract.
We have investigated the dilute magnetic impurity effect on the magneticproperties of a quantum spin liquid candidate Ba ZnRu O and a spin gapped compoundBa CaRu O . The magnetic ground state of each compound stands against 2% substitutionof magnetic impurities for Zn or Ca. We have found that the magnetic response of theseimpurities, which behave as paramagnetic spins, depends on the host materials and thedifference of the two manifests itself in the Weiss temperature, which can hardly be explainedby the dilute magnetic impurities alone in the case of Ba ZnRu O . We consider a contributionfrom the Ru ions which would appear only in the substituted Ba ZnRu O and discuss apossible physical meaning of the observed Weiss temperature. Keywords: quantum spin liquid, magnetic oxide, impurity effects, magnetic susceptibility
Submitted to:
J. Phys.: Condens. Matter ynamical coupling of dilute magnetic impurities with quantum spin liquid state
1. Introduction
The impurity effect on quantum spin systems have attracted much interest because it has oftenprovided us the opportunity to discover novel physical phenomena. For example, in variousspin gapped (SG) systems such as the Haldane compound [1–4], the dilute non-magneticimpurities induce an exotic long-range antiferromagnetic order which coexists with the non-magnetic gapped state. In this context, one of intriguing targets is a quantum spin liquid(QSL) material, in which the interacting spins fluctuate down to the absolute zero temperaturedue to competing magnetic interactions and quantum fluctuations [5].Recent intensive studies have found out many candidates for a QSL state in realorganic/inorganic materials with geometrical frustration of antiferromagnetic spins [6–10].On the other hand, a new route to find QSL materials has been opened since Kitaev proposeda quantum spin model on a honeycomb lattice, which hosts a novel QSL state [11]. Suchso-called Kitaev spin liquid has been suggested to realize in strongly spin-orbit coupledMott insulators [12], and the experimental explorations on 4d and 5d transition-metal-basedcompounds actually have revealed several spin-orbit-driven spin liquid candidates [13–19].Nowadays the understanding of the physical properties of the QSL materials is one of thecentral issues in condensed matter physics. However, despite large amounts of theoretical andexperimental works, the effect of intentional impurity doping on the systems has not beenmuch explored except for several cases [8, 20–24].In this study, we will focus on a 6H hexagonal perovskite ruthenate Ba ZnRu O , whichis a QSL candidate that we have recently discovered [25]. This material is a member ofthe compounds with the general formula Ba M Ru O , which is composed of the three-dimensional network of two face-shared RuO octahedra (Ru O dimers) interconnected bythe M O octahedra with corner sharing, as shown in figure 1(a). The M site can accommodatevarious divalent ions, and the formal valence of Ru is pentavalent in this case. Then the Ru ion (4 d ) is responsible for the magnetism of the system as a localized moment of S = M Ru O depends on the species of M . For M = Co,Ni, and Cu [26–28], an antiferromagnetic ordering is observed below T N ∼
100 K. When the M sites are occupied by Ca, Sr, and Mg [26, 29], paired spins in the Ru O dimer form a spinsinglet, and then the system is in a non-magnetic SG ground state. In the case of the M = Znsample, we have found neither a long-range magnetic order nor a spin glass transition downto 37 mK [25], despite the magnetic interaction has been evaluated to be an energy scale ofaround 200 K in this family [29–31]. The magnetic susceptibility at low temperatures exhibitsa nearly temperature-independent value of about 10 − emu/mol, and the specific heat shows atemperature-linear contribution. These features suggest the presence of a QSL state. We haveproposed that the competition between intra- and inter-dimer interactions play important rolein stabilizing this QSL state. The exchange coupling pathways are shown in figure 1(b).We underline several advantages of Ba ZnRu O in investigating the impurity effectson the magnetism, compared with other QSL candidates. One is that this compound is freefrom an intermixture of cations as reported for Ba CuSb O [32] and ZnCu (OH) Cl [33],and thus one can introduce an impurity into a specific site in a controlled way. Another ynamical coupling of dilute magnetic impurities with quantum spin liquid state Figure 1. (Color Online) (a)Crystal structure of Ba M Ru O with the space group of P / mmc , drawn using VESTA [35]. (b) a honeycomb dimer lattice of Ru ions in the ab plane layer with the intra- ( J intra ) and inter-dimer ( J inter ) exchange coupling. is that a Curie tail is hardly visible at low temperatures in the title compound unlikeBaCu V O (OH) [10] and Cu V O (OH) · O [34], in which a substantial contribution ofunwanted impurities obscures the intrinsic physical properties in macroscopic measurements.Here we report the dilute magnetic impurity effect on the magnetic properties ofBa ZnRu O in comparison with Ba CaRu O . We have found that the magnetic groundstate of each compound stands against 2% substitution of magnetic impurities of Cu, Ni, andCo for Zn or Ca, and these impurities behave as paramagnetic spins. We have further foundthat the magnetic response of the paramagnetic spins depends on the host materials, whichappears in the difference of the Weiss temperature, which can be hardly explained by thesimple impurity-impurity interaction alone in the case of the substituted QSL candidate. Wediscuss a possible origin in terms of a coupling of the magnetic impurities with the Ru ions,which would be present only in the substituted Ba ZnRu O .
2. Experimental
Polycrystalline samples of Ba M Ru O and Ba M . A . Ru O ( M = Zn and Ca; A = Co,Ni, and Cu) were prepared by solid state reaction using high-purity reagents of BaCO (4N),RuO (3N), ZnO (4N), CaCO (4N), Co O (3N), NiO (3N), and CuO (4N). Stoichiometricmixtures of the oxides were ground, pressed into pellets, and pre-sintered in air at 1000 ◦ Cfor 12 h. The pre-sintered samples were then re-pelletized after regrinding and sinteredin air at 1200 ◦ C for 72 h. Powder X-ray diffraction measurements (Cu K α radiation) atroom temperature showed that all the prepared samples have the hexagonal structure withoutany trace of a secondary phase and the lattice parameters were unchanged by substitution.The magnetization measurements were conducted by a Quantum Design superconductingquantum interference device magnetometer. The magnetic susceptibility ( χ ) was measuredbetween 2 and 300 K in an external magnetic field ( H ) of 10 kOe. The magnetization ( M )data were collected at 2, 3, and 5 K in the magnetic field range from 0 to 70 kOe. ynamical coupling of dilute magnetic impurities with quantum spin liquid state Figure 2. (Color online) Temperature dependence of the magnetic susceptibility measuredin 10 kOe for (a) Ba ZnRu O and Ba Zn . A . Ru O , and (b) Ba CaRu O andBa Ca . A . Ru O ( A = Co, Ni, and Cu). The broken curve in (b) depicts the fit usingthe Curie-Weiss law (see text).
3. Results and discussion
Figures 2(a) and 2(b) show the temperature dependence of the magnetic susceptibility ofBa M Ru O and Ba M . A . Ru O ( M = Zn and Ca; A = Co, Ni, and Cu) on a logarithmicscale. The susceptibility of Ba ZnRu O smoothly decreases with decreasing temperatureand becomes almost constant below 50 K. The value of χ at 2 K is equal to about 1.12 × − emu/mol, which is comparable to those observed in other inorganic spin liquid candidates[10, 34]. Note that no Curie tail is found down to 2 K as reported in our previous study [25].In contrast, χ does show the Curie tail, i.e., it exhibits a rapid increase below 50 K inBa CaRu O , which would be due to unwanted magnetic impurities. We fit this term between2 and 20 K by assuming the Curie-Weiss law with a temperature-independent term χ givenby χ = C/ ( T + θ W ) + χ , where C is the Curie constant, θ W is the Weiss temperature. Thecalculated curve reproduces the experimental data when C = × − emu K/mol, θ W = χ = × − emu/mol (figure 2(b)). The obtained value of C correspondsto 0.1% of unpaired Ru ions out of the total Ru ions. χ is of the order of the VanVleck paramagnetic susceptibility, which is consistent with the spin gapped dimer state ofBa CaRu O [29].In all the impurity-substituted samples, the magnetic susceptibility at around 300 K is ynamical coupling of dilute magnetic impurities with quantum spin liquid state Table 1.
Results of a fit of χ = C imp / ( T + θ imp ) + χ Ru to the magnetic susceptibility χ below 20 K of Ba M . A . Ru O ( M = Zn and Ca; A = Co, Ni, and Cu). χ Ru is fixed to aspecific value for each of the M = Zn and M = Ca series and x imp represents the concentrationof substituted magnetic impurities estimated from C imp (see text).Material C imp (emu K/mol) θ imp (K) x imp ( M , A ) = (Zn, Cu) 8.37 × − M , A ) = (Zn, Ni) 4.96 × − M , A ) = (Zn, Co) 5.51 × − M , A ) = (Ca, Cu) 6.37 × − M , A ) = (Ca, Ni) 3.07 × − M , A ) = (Ca, Co) 4.77 × − almost the same as that of the corresponding parent compound, implying that the spin stateof the Ru ions is little affected by substitution. On the other hand, χ increases significantlybelow 50 K as the spin value of the substituent ions increases in order of Cu ( S imp = ( S imp = ( S imp = ions are still responsible for the ground state of each parent compound,and the substituted magnetic impurities behave as paramagnetic spins. Note that the impuritysubstitution for the M sites does not directly disrupt the network of the Ru O dimers.Let us evaluate the low-temerature susceptibility in the substituted samples. We assumethat this can be divided into two terms, a contribution from the magnetic impurities andthe Ru ions, i.e., χ = χ imp + χ Ru . The former may follow the Curie-Weiss law as χ imp = C imp / ( T + θ imp ) . We note here that not only the substituted impurities but alsounwanted impurities can contribute to this term, and it is difficult to distinguish them in thesusceptibility data. Namely, C imp may include both contributions and θ imp may reflect theinteraction between all these impurities. At sufficiently low temperatures below 50 K, thelatter term may be regarded as the temperature-independent term in the corresponding parentcompound. Accordingly, we fit the data with a constant χ Ru of 1.12 × − emu/mol forBa Zn . A . Ru O and 2.5 × − emu/mol for Ba Ca . A . Ru O , respectively.The results of the fit are summarized in Table 1, together with x imp = C imp /C . Here C is the Curie constant expected for a mole of magnetic impurities with S imp and g = 2 . Thusideally, x imp means the concentration of the substituted magnetic impurities per formula unit,and equals 0.02 in the nominal compositions. One finds that x imp ∼ M , A ) = (Zn, Ni). The reason of the exception of the sample is to be explored at this stage, but itmay reflect that a magnetic transition is about to occur at lower temperatures, as anticipatedfrom the saturation of χ . Besides, we notice that the contribution from unwanted magneticimpurities observed in Ba CaRu O may not be ignored for ( M , A ) = (Ca, Cu). If one simplysubtracts the contribution from C imp , the corrected value is obtained to be 3.05 × − emuK/mol, which corresponds to x imp ∼ x imp = ynamical coupling of dilute magnetic impurities with quantum spin liquid state Figure 3. (Color online) Temperature dependence of 1/( χ − χ Ru ) below 30 K for (a)Ba Zn . A . Ru O and (b) Ba Ca . A . Ru O ( A = Cu and Co). The broken linesdepict the calculation using the Curie-Weiss law (see text). χ − χ Ru ) ≃ χ imp below 30 Kof (a) Ba Zn . A . Ru O and (b) Ba Ca . A . Ru O ( A = Cu and Co). The inversesusceptibility goes to nearly zero in the limit of T = χ imp takes a finite value in the samelimit for the Zn-based materials, clearly indicating a substantial contribution of the magneticinteraction. Thus, the magnetic response of the impurity spins seems to depend on the hostmaterials. The difference between them can also be seen from the Curie-Weiss fitting, asdepicted in figure 3 with the broken lines. In Ba Ca . A . Ru O , θ imp is estimated to beabout 1 or 2 K independently of the magnetic ion in the A site, whereas it increases in themagnitude with increasing S imp in Ba Zn . A . Ru O , from about 3 K for the A = Cusample to about 10 K for the A = Co sample. These estimated values of θ imp is anomalouslylarge, considering that the magnetic interaction between a few percent of magnetic impuritiesis usually found to be of the order of 1 K in various spin gapped systems and QSL candidates[1, 10, 36, 37]. Note that the positive θ imp implies an antiferromagnetic coupling.To further investigate the difference of the magnetic response, we measure the fielddependence of the magnetization at several temperatures. For the free spins, the magnetization ynamical coupling of dilute magnetic impurities with quantum spin liquid state Figure 4. (Color online) Magnetization plotted as a function of µ B H/k B T at severaltemperatures in (a) Ba Zn . Co . Ru O and (b) Ba Zn . Co . Ru O . Each insetrepresents M versus µ B H/k B ( T + θ W ) with a certain value of θ W for the same temperatures. saturates for µ B H ≫ k B T , and follows the Brillouin function as a function of µ B H/k B T .Here µ B is the Bohr magneton and k B is the Boltzmann constant. Figures 4(a) and 4(b) showthe magnetization at 2, 3, and 5 K plotted against µ B H/k B T for Ba Zn . Co . Ru O andBa Ca . Co . Ru O , respectively. We find the distinct differences between the two. In theformer sample, the magnetization curves at each temperature deviate from each other withincreasing magnetic field. Moreover, M is unlikely to saturate even at 2 K in 70 kOe. Incontrast, all the experimental data are about to fall into a single curve with a sign of saturationin the latter sample.The slight deviation observed in Ba Ca . Co . Ru O can be explained by consideringthe impurity-impurity interaction. When the paramagnetic spins weakly interact with eachother, the Brillouin function is modified, and then M scales to µ B H/k B ( T + θ W ) [36, 37],which means the reduction of the field effect. As shown in the inset of figure 4(b), a goodscaling is indeed established with a small θ W , which is adopted the same value as θ imp . Thisfact allows us to attribute θ imp in Ba Ca . A . Ru O to the weak interaction between thedilute magnetic impurities. We attempt the same analysis on the magnetization curves inBa Zn . Co . Ru O (the inset of figure 4(a)). They overlap each other at low magnetic ynamical coupling of dilute magnetic impurities with quantum spin liquid state H increases, implying that the magnetic response isaffected by other contributions. A similar trend is found for the Cu-substituted samples (notshown).Now let us discuss a possible origin of the relatively larger Weiss temperature found inBa Zn . A . Ru O . The difference in the magnetic response suggests that the substitutedmagnetic impurities in each host lattice exist under different environments. This would berelated to the magnetism of the Ru ions: the impurities can interact with the Ru ions onlyin the Zn-based compounds. In this context, it is worth noting that the low T upturn of thesusceptibility due to the impurities is strongly suppressed below θ imp in Ba Zn . A . Ru O .This feature is reminiscent of the low-temperature susceptibility in Kondo systems [38,39], inwhich localized spins are screened by conduction electrons via an antiferromagnetic couplingbetween them. Therefore, we propose that the large Weiss temperature observed in thesubstituted Ba ZnRu O is the implication of such screening effect on the impurity spins,which results from the magnetic coupling of these spins and the Ru spins. If that were thecase, the spin fluctuation rates of impurity spins should be enhanced, leading to the magneticmoment instability [40]. In this sense, the Weiss temperature is interpreted as a measure of thedegree of the spin fluctuations. The screening effect would also be suggested from the absenceof a Curie tail in the parent Ba ZnRu O despite unwanted magnetic impurities should exist,as in Ba CaRu O .Unlike Kondo systems, there are no conduction electrons in the title compound.Nevertheless, QSL candidates are believed to possess a kind of quasiparticles as fermionicelementary excitations, because a gapless T -linear term of the specific heat has been generallyobserved [10, 25, 41, 42]. Thus, one possible explanation of the screening effect is that amagnetic impurity couples with the quasiparticles. However, this scenario is incompatiblewith the S imp dependence of θ imp in our system because the Weiss temperature exhibits theopposite S imp dependence in the framework of the Kondo model [43]. As another possiblescenario, we suggest that the enhancement of the spin fluctuation rates is caused by thequantum fluctuations originating from the Ru O dimers. In our previous study [25], we havepointed out that the spin state of the Ru O dimers dynamically changes in the range between S tot = 0 and S tot = 2 for the title compound, where S tot is the total spin. In such a situation,a magnetic coupling of the magnetic impurities with the Ru O dimers will be dynamical andproduces a fluctuating internal field at each impurity site. The increase in S imp would imply astronger exchange coupling between them, resulting in the observed S imp dependence of θ imp .The NMR and neutron scattering measurements are indispensable to examine this scenariothrough direct observation of the spin fluctuation.
4. Summary
We have investigated the effect of the magnetic impurity on the magnetic properties of thequantum spin liquid candidate Ba ZnRu O through the comparison with the spin gappedcompound Ba CaRu O . The magnetic ground state of these systems is robust against the 2%impurity substitution, and the introduced magnetic impurities behave as paramagnetic spins. ynamical coupling of dilute magnetic impurities with quantum spin liquid state O dimers. Acknowledgments
We gratefully acknowledge Y. Hara, T Matsushita, and N. Wada at Nagoya University for thecollaboration in the magnetic and thermodynamic measurements at very low temperatures.This work was partly supported by Grants-in-Aid for Scientific Research (18H01173). Oneof the authors (T. D. Y.) was supported by the Program for Leading Graduate Schools”Integrative Graduate Education and Research in Green Natural Sciences”, MEXT, Japanand a Grant-in-Aid for JSPS Research Fellow (No. 17J04840), MEXT, Japan.
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