PHYSICAL REVIEW B 92, 174421 (2015)

Strongly coupled electronic, magnetic, and lattice degrees of freedom in LaCo5 under pressure

Ryan L. Stillwell,1 Jason R. Jeffries,1 Scott K. McCall,1 Jonathan R. I. Lee,1 Samuel T. Weir,2 and Yogesh K. Vohra3

1Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA2Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA

3Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA(Received 10 August 2015; revised manuscript received 4 November 2015; published 25 November 2015)

We have performed high-pressure magnetotransport and x-ray diffraction measurements on ferromagneticLaCo5, confirming the theoretically predicted electronic topological transition driving the magnetoelastic collapseseen in the related compound YCo5. Our x-ray diffraction results show an anisotropic lattice collapse of the c axisnear 10 GPa that is also commensurate with a change in the majority charge carriers evident from high-pressureHall effect measurements. The coupling of the electronic, magnetic, and lattice degrees of freedom is furthersubstantiated by the evolution of the anomalous Hall effect, which couples to the magnetization of the orderedstate of LaCo5.

DOI: 10.1103/PhysRevB.92.174421 PACS number(s): 75.85.+t, 61.05.cf, 73.43.Lp, 75.47.Np

Coupled degrees of freedom are at the root of the emergentbehaviors of functional materials. Through their intercon-nected responses, lattice, electronic, magnetic, and orbitaldegrees of freedom can manifest physical effects rangingfrom superconductivity to ferroelectricity to magnetocaloricproperties [1–4]. These effects are promising for myriadtechnologies, including energy storage, quantum computing,and magnetic refrigeration, and materials exhibiting theseeffects have been the subject of extensive research anddevelopment. In piezoelectric materials, an electric field(mechanical strain) develops as a result of applied mechanicalstrain (electric field) [5], and this coupling of strain andelectric charge has allowed piezoelectrics to find use assonar sensors, transducers, solar cells, and microantennas [6].Additionally, multiferroic materials are being studied for awide range of applications spanning compact spintronics-based data storage—where magnetic states can be manipu-lated with electric fields—to magnetic refrigeration throughthe magnetocaloric effect—where heat is absorbed througha magnetic-field-driven transition across a magnetic phaseboundary [7,8]. Coupled degrees of freedom clearly presentpromising properties, but a detailed understanding of the subtlecouplings between lattice, electronic, and magnetic degreesof freedom is paramount to the continued development offunctional materials.

While advances in computational models are improvingthe capabilities for predictive materials response, expandingthe promise and potential of functional materials, there isstill a critical need for experiments to validate theoreticalframeworks. These experiments are naturally challenging,requiring capabilities to simultaneously assess seemingly dis-parate degrees of freedom under various conditions. Becauseit is intimately and thermodynamically connected to thevolume of a material, and thus its crystallographic lattice,pressure is an effective tuning parameter for the explorationof functional materials. High pressures not only vary the solidlattice, and any degrees of freedom coupled to it, but modern,high-pressure techniques offer the capacity to interrogate thestructure as well as the electronic and magnetic states arisingfrom structural perturbations.

Pressure has been theoretically shown to genericallycause a magnetoelastic collapse in compounds within the

ferromagnetic RECo5 system (RE = rare earth element includ-ing Y and La) [9], making these systems excellent platformsfor experimentally studying the interplay between crystal,magnetic, and electronic structure. These RECo5 compoundscrystallize in a relatively simple hexagonal structure, and themagnetic RE ions (e.g., not Y, La, or Ce) interact with thecrystalline electric field to orient the RE moment along apreferential crystallographic direction. On-site spin exchangebetween the RE 4f and 5d electrons polarizes the latter, andintersite hybridization between the RE 5d and the Co 3d

states encourages the antiparallel alignment of the RE andCo spins. For the light RE elements, the opposing spin andorbital moments of the RE ion results in a ferromagneticarrangement of the RE and Co magnetic moments [10,11].This general mechanism is responsible for the properties ofsome of the most robust permanent magnet materials availabletoday. A recent study implies that the Sm2Co17 system (aclosely related structure to that of the RECo5 system) shouldnot exhibit a magnetoelastic collapse until pressures near70 GPa [12]. On the other hand, RECo5 compounds composedof nonmagnetic RE are still ferromagnetic, but the absence oflocalized f electrons may provide a less robust magnetic stateand thus a propensity for magnetoelastic collapse at lowerpressure. Indeed, electronic structure calculations predict anisostructural, magnetoelastic collapse in YCo5 and LaCo5 at21 and 23 GPa, respectively [13]. According to the theory, anelectronic topological transition drives this pressure-inducedcollapse when a majority-spin occupied Co 3d band is forcedacross the Fermi level, resulting in a predicted reduction inordered moment as well as a Fermi surface reconstruction [13].While the structural signature of this magnetoelastic collapsehas been observed experimentally in YCo5 [14], no electronicor magnetic signatures of the collapse have been observed ineither YCo5 or LaCo5.

Direct probes of changes in the magnetic moment orelectronic structure are notoriously challenging experimentsat high pressures. While spin-resolved photoemission wouldbe sensitive to the predicted changes in the electronicstructure of LaCo5, the photoelectron energies are far toolow to escape any containment used to generate pressureson the order of 10 GPa. Similarly, bulk magnetization andneutron scattering experiments at these pressures can suffer

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STILLWELL, JEFFRIES, MCCALL, LEE, WEIR, AND VOHRA PHYSICAL REVIEW B 92, 174421 (2015)

from extremely large backgrounds relative to the magneticresponse of the sample. X-ray magnetic circular dichroism(XMCD) measurements at the Co K-edge—which requirespecialized facilities and extensive experimental time—wouldbe sensitive to changes in the ordered Co moment with pressureand also amenable to high-pressure experiments [12,15,16],but quantitative measurement of the Co moment would behampered by the inapplicability of spin-orbit sum rules atthe Co K-edge [17,18]. In a unique application of standardelectrical conductivity measurements enabled through theuse of designer diamond anvils, this paper describes amultifaceted suite of high-pressure measurements on LaCo5

with which we are able to couple not only to the lattice,but also to the electronic and magnetic degrees of freedomat pressures in excess of 10 GPa. While x-ray diffractionmeasurements confirm the predicted isostructural collapsenear 10 GPa, an associated, pressure-dependent magneto-transport study reveals the first experimental signatures ofthe magnetoelastic collapse in the magnetic and electronicchannels.

Polycrystalline samples of LaCo5 were prepared froma stoichiometric mixture of La and Co via arc melt-ing, after which the sample was annealed at 1090 ◦C for28 d. Angle-dispersive x-ray diffraction measurements un-der pressure were performed using beamline 16 BM-D[High Pressure Collaborative Access Team (HPCAT)] ofthe Advanced Photon Source (APS) at Argonne NationalLaboratory. A gas-membrane-driven diamond anvil cell (DAC)was used to generate pressures up to 40 GPa. The samplewas powdered and loaded into the DAC sample chamberalong with a Cu powder pressure calibrant; neon was used asthe pressure-transmitting medium. Electrical transport studiesunder pressure were performed on a small polycrystal ofLaCo5 using an 8-probe designer DAC [19,20] with steatiteas the pressure-transmitting medium and ruby as the pressurecalibrant [21,22]. Longitudinal and transverse resistance mea-surements were performed as a function of temperature andmagnetic field using the AC Transport option in a QuantumDesign Physical Property Measurement System.

LaCo5 crystallizes in the hexagonal CaCu5-type structure(space group P 6/mmm) with one formula unit per unit celland the following atomic positions: La (1a), Co1 (2c), andCo2 (3g) [23]. Our x-ray diffraction results indicate thatthe CaCu5-type crystal structure of LaCo5 persists up to thehighest measured pressures, near 40 GPa. However, whilethere are no structural transformations under pressure, thelattice does display an anomaly in the c axis compression near10 GPa. The diffraction patterns at each pressure were indexedto obtain the lattice parameters of LaCo5 under pressure atambient temperature (Fig. 1). The anomalous behavior inthe c axis compression can be seen in Fig. 1(b) (also see theSupplemental Material, Fig. 1S [24]) and contrasted with theconventional, anomaly-free pressure dependence of the a axisas seen in Fig. 1(a). The contraction is thus highly anisotropic.The c axis contraction is small, amounting to a contractionof about 0.3% at 12 GPa. Because this c axis contraction issmall, the unit cell volume of LaCo5 [Fig. 1(c)] does not showan obvious anomaly, permitting the use of a Birch-Murnaghanequation of state [25] to describe the system under compression(B0 = 104 GPa, B ′ = 4.3). In contrast to the volume, the c/a

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FIG. 1. (Color online) Hexagonal lattice parameters, (a) a and(b) c, as well as (c) the unit cell volume for LaCo5 under pressure atroom temperature. While the a axis compresses relatively smoothly,there is a marked deviation in the pressure dependence of the c axisnear the predicted isomorphic collapse near 10 GPa. Additionally,the pressure dependence of the c/a ratio, inset of (c), flattens near10 GPa, before continuing to increase at higher pressures. Lines in(a), (b), and the inset of (c) are guides to the eye, while the line in (c)is a fit to the Birch-Murnaghan equation of state.

ratio shows a marked change in pressure dependence [insetFig. 1(c)], exhibiting a pronounced flattening between 10 and12.5 GPa.

The pressure-dependent c axis anomaly and the flatteningof the c/a ratio in LaCo5 are very similar to the observedbehavior seen in the isostructural compound YCo5 [13,14].In the case of YCo5, the anomalous structural behavior hasbeen attributed to the effects of an occupied, majority-spin Co3d band crossing the Fermi level. When this d band transectsthe Fermi level, some of the majority-spin antibonding statesare depopulated, resulting in a loss of magnetic moment andan increase in bond energy that contracts the lattice. Usingthe same magnetoelastic coupling scheme for LaCo5, Koudelaet al. predicted a highly anisotropic lattice contraction with a1.2% c axis contraction occurring (within their calculations)at 7.7 GPa in the absence of an “overbinding” correction [13].Our ambient-temperature experimental work is in excellentagreement with the highly anisotropic contraction predictedby density functional theory (DFT), but the magnitude ofthe c axis contraction (0.3 vs 1.2% for experiment vs theory,respectively) and the pressure at which the transition occurs(10 vs 7.7 GPa for experiment vs theory, respectively)show slight quantitative disagreement with predictions, likelyarising from finite-temperature effects. Indeed, measurements

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FIG. 2. (Color online) (a) Hall resistance of LaCo5 as a functionof increasing pressure, showing the increased amplitude of boththe normal and anomalous Hall signals up to the highest pressureof 15.6 GPa. The normal Hall effect is defined as the slope from30–80 kOe, after the saturation field where the ferromagnetic domainshave aligned with the applied field (H ∼ 20 kOe). The Hall slopechanges sign at 9.3 GPa (blue diamonds), also plotted as RH inFig. 3(a). (b) The anomalous contribution is found by subtracting thenormal Hall effect over the entire field range and is plotted as RAHE vsmagnetic field. This plot makes clear that the anomalous contributionalso has an initial decrease, followed by an increase that grows rapidlyfrom 9.3 GPa, concomitant with the isomorphic collapse seen in thex-ray diffraction data shown in Fig. 1.

of YCo5 at ambient temperature show similar discrepancieswith DFT calculations [13]. Altogether, the general agreementbetween previous theoretical predictions and our experimentson LaCo5 lends credence to the magnetoelastic couplingscheme proposed by Koudela et al. and Rosner et al. [13,14].

If the proposed magnetoelastic coupling scheme is a correctdescription of the physics of LaCo5 at high pressure, thenthere should be commensurate changes in the electronic andmagnetic degrees of freedom in LaCo5 in the vicinity of 10 GPaas the Co 3d band crosses the Fermi level. To investigate thishypothesis, we have performed a novel, high-pressure mag-netotransport study enabled by an 8-probe designer diamondanvil (Fig. 2 inset) [20] that affords simultaneous probes ofthe magnetic and electronic channels of LaCo5 through themagnetoelastic collapse. The designer diamond anvil permitsmeasurement of both the longitudinal (Rxx) and transverse(Rxy) resistances versus pressure and magnetic field, and itis Rxy in applied field that couples to both the magnetic andelectronic degrees of freedom of LaCo5.

In the absence of magnetism, Rxy(H) is conventionallylabeled as the Hall resistance after the Hall effect that describesits behavior. The Hall resistance is a function of applied fieldthat is predicated on the electronic structure of a material, andthus any changes in electronic structure (e.g., with appliedpressure) will manifest as changes in the Hall resistance,making it a sensitive probe of the electronic degrees offreedom. In the case of ferromagnetic systems, Rxy(H) willexhibit not only the conventional Hall resistance based onthe electronic structure, but also the anomalous Hall effect(AHE). The AHE is directly coupled to the magnetic degrees offreedom. It is a result of the domains of a ferromagnet aligningwith the applied magnetic field [26], and the magnitude of theAHE is proportional to the magnetization of the system, whichalso means that a nonzero transverse resistance can be realizedin ferromagnets, even in zero applied magnetic field [12].

The total Hall effect in a ferromagnet is the sum of a“conventional” term and an “anomalous” term, such that thetransverse resistance is expressed as

Rxy = RHHz + RsMz,

where RH is the conventional Hall coefficient, which isinversely proportional to the carrier density; Hz is the appliedmagnetic field in the z direction; Rs is the AHE prefactor,which is (generally) proportional to the resistance of thesample; and Mz is the magnetization of the sample. Therehas been great debate on the subject of the proper formof the AHE prefactor [27–33]. All of the theories agreethat Rs is a function of Rxx or the intrinsic band structure,yet the particular mechanisms and regimes where thosemechanisms are dominant are still active areas of research [26].The presence of these multiple scattering mechanisms, eachof which may evolve differently with pressure, can makequantitative interpretation of the AHE signal challenging.

Figure 2(a) shows the antisymmetrized (see SupplementalMaterial for a detailed explanation of the antisymmetrizationprocedure [24]) Rxy versus applied magnetic field up to80 kOe, for pressures ranging from 2.1 to 15.6 GPa. Thecharacteristic nonlinearity of the AHE is evident at low field(<20 kOe), especially at the highest pressures. To isolatethe anomalous part of the Hall effect, we fit the slopeof Rxy over the applied magnetic field range 30–80 kOe,with the assumption that the slope above the saturationfield (H ∼ 20 kOe) is solely due to the normal Hall effect.Subtracting the contribution from the normal Hall effect fromRxy over the entire field yields the component due to the AHE

RAHE = Rxy − RHHz = RsMz,

where RAHE is the combined effect of the changes in the AHEprefactor and magnetization as a function of magnetic field.Figure 2(b) shows the extracted RAHE versus applied magneticfield.

To understand how the electronic structure of LaCo5

changes as it goes through the isomorphic transition near10 GPa, we plot both RH and the average saturation am-plitude of RAHE (for 30 < H < 80 kOe), which we defineas RA, as functions of pressure in Fig. 3. Two interestingconclusions about the effects of pressure on LaCo5 followfrom the trends visible in Fig. 2. First, when the normal Hallcoefficient RH is plotted as a function of increasing pressure

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FIG. 3. (Color online) (a) Hall coefficient RH of LaCo5 plotted vspressure up to 15.6 GPa (error bars: �RH is given as RH ± 1 standarddeviation of the fit to Rxy between 30 < H < 80 kOe, �P = P ±5%). The change in sign of RH at 9.3 GPa shows clearly that there isan electronic topological transition that accompanies the isomorphicstructural transition from the “normal” to “collapsed” structure seenin our high-pressure x-ray diffraction study (Fig. 1). (b) RA plottedas a function of pressure up to 15.6 GPa showing a transition inthe anomalous channel of the Hall signal reflecting changes in themagnetic degrees of freedom.

[Fig. 3(a)], there is a sign change from negative to positive near9.3 GPa, indicating a change in the dominant carrier type fromelectronlike to holelike above this pressure. This change inRH is consistent with a Fermi surface reconstruction. Second,there is a concomitant increase in RA at the same pressure[Fig. 3(b)], demonstrating a change in the magnetic channel(i.e., the product of the magnetization and AHE scatteringprefactor) with pressure.

The simultaneous discontinuities observed in the electronic(RH ), magnetic (RA), and lattice (c axis lattice parameter)degrees of freedom with increasing pressure strongly suggestthat the isostructural collapse of LaCo5 is indeed induced bythe predicted magnetoelastic coupling and its accompanyingFermi surface reconstruction. Within the framework of theircalculations, Koudela et al. predicted a reduction in the mag-netic moment upon entering the collapsed structure [13]; how-ever, this is not obviously borne out in our magnetotransport

experiments, as the magnitude of RA—which is proportionalto the average saturation value of the product of Rs andMz—increases after crossing into the collapsed structure. Ourattempts to isolate the magnetization Mz as a function ofpressure by dividing RA by Rxx(P )(see the SM, Fig. 2S tofor magnetotransport of Rxx versus pressure [24]) and R2

xx(P )did not produce a decreasing trend in RA (shown in the SM,Fig. 3S [24]). This could imply that the theory is incorrect inits calculation of the magnetic moment; but this explanation isunlikely, as the Co moment is already large and in the high-spinstate at ambient conditions. A more likely scenario is thatthe AHE does not simply follow the longitudinal scatteringdependence of the material but reflects the strongly correlatedinterplay between the electronic, magnetic, and lattice degreesof freedom in LaCo5.

In summary, we have confirmed the predicted high-pressureisomorphic transition in LaCo5 using both x-ray diffractionand magnetotransport measurements. The highly anisotropiccollapse of the c axis was observed at 10 GPa, with achange of ∼0.3% at 12 GPa, in very good agreement withprevious zero-temperature DFT calculations that predictedan approximately 1.2% collapse near 8–10 GPa [13]. Thesetheoretical calculations predicted that there would be mag-netic and electronic transitions accompanying the observedanisotropic lattice collapse. Indeed, concomitant changes inthe electronic structure and magnetic response were measuredvia high-pressure magnetotransport, which revealed a changein carrier type and a sharp increase in the amplitude ofthe anomalous Hall effect at 9.3 GPa. Magnetotransportmeasurements show promise as sensitive probes of magnetismunder pressure. Though the measurements of the AHE underpressure could not unambiguously quantify the magneticmoment of LaCo5, further progress into understanding andmodeling the underlying mechanisms responsible for the AHEcould enable routine, quantitative magnetic measurements athigh pressure.

We graciously thank K. Visbeck for assistance with DACpreparation. This paper was performed under LaboratoryDirected Research and Development (LDRD) (Tracking Codes12-ERD-013, 14-ERD-041) and under the auspices of theUS Department of Energy (DOE) by Lawrence LivermoreNational Laboratory (LLNL) under Contract No. DE-AC52-07NA27344. Portions of this paper were performed at HPCAT(Sector 16), APS, Argonne National Laboratory. The HPCAToperations are supported by DOE-National Nuclear SecurityAdministration (NNSA) under Award No. DE-NA0001974and DOE-Basic Energy Sciences (BES) under Award No.DE-FG02-99ER45775, with partial instrumentation fundingby the National Science Foundation (NSF). Beamtime wasprovided by the Carnegie DOE-Alliance Center (CDAC).YKV acknowledges support from DOE-NNSA Grant No.DE-NA0002014.

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