Suppression of ferromagnetism in the La(V x Cr 1−x )Sb 3 system
Xiao Lin, Valentin Taufour, Sergey L. Bud'ko, Paul C. Canfield
aa r X i v : . [ c ond - m a t . m t r l - s c i ] N ov September 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A
Philosophical Magazine
Vol. 00, No. 00, 00 Month 2013, 1–22
Suppression of ferromagnetism in the La(V x Cr − x )Sb system Xiao Lin a , Valentin Taufour a , Sergey L. Bud’ko a , b , and Paul C. Canfield a , ba Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011,U.S.A. ; b Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames,Iowa 50011, U.S.A ( Received 00 Month 200x; final version received 00 Month 200x )To explore the possibility of quantum phase transitions and even quantum criticality inLaCrSb based compounds, we performed measurements under pressure as well as a vana-dium substitution study. The Curie temperature of LaCrSb was found to be invariant underpressure. Although pressure was not able to suppress the ferromagnetism, chemical substitu-tion was used as another parameter to tune the magnetism. We grew La(V x Cr − x )Sb ( x =0 – 1.0) single crystals, and studied the series by measurements of temperature and field de-pendent magnetic susceptibility, magnetization, resistivity, and specific heat. Ferromagnetismhas been observed for x ≤ .
22, and the system manifests a strong anisotropy in its orderedstate. The Curie temperature decreases monotonically as the V concentration increases. For0 . ≤ x ≤ .
73, the system enters a new magnetic state at low temperatures, and no mag-netic ordering above 1.8 K can be observed for x ≥ .
88. The effective moment µ eff /Cr variesonly slightly as the V concentration increases, from 3.9 µ B for x = 0 to 2.9 µ B for x =0.88. Features related to quantum criticality have not been observed in the La(V x Cr − x )Sb system. Keywords: ferromagnetism; pressure; chemical substitution
1. Introduction
The study of ferromagnetic materials has long been a focus of research in con-densed matter physics. The suppression of an itinerant ferromagnetic transitiontemperature to zero is of specific interest, since it may lead to the discovery of aquantum critical point (QCP) [1–6] which exhibits exotic physical properties, suchas non-Fermi liquid behavior and even superconductivity. The Stoner model hasbeen developed to describe a mechanism of an itinerant ferromagnetic system, andis based on the premise that the magnetic properties of the itinerant ferromagnetsoriginate from de-localized electrons [7]. In particular these de-localized electronsbecome part of the conduction band and influence the density of state (DOS) atthe Fermi level. Based on the Stoner criterion,
U D ( ε F ) >
1, where U and D ( ε F ) areCoulomb repulsion and the DOS at the Fermi level respectively, itinerant ferromag-netism can be suppressed by tuning U and/or D ( ε F ). The suppression of itinerantferromagnetism not only results in the decrease of the ordering temperature, but isalso accompanied by decrease of the effective and saturated moments per magneticspecies. On the other hand, ferromagnetic ordering can also arise from the interac-tions of local magnetic moments [8, 9]. As the exchange interaction favors parallelspin alignments, the materials show spontaneous magnetization. Suppressing theferromagnetism by diluting the local moments, does not reduce the size of effectiveor saturated moments (per moment bearing ion) and, does not necessarily lead toa QCP [10, 11]. New magnetic states, such as spin glass, may also emerge in the ISSN: 1478-6435 print/ISSN 1478-6443 onlinec (cid:13) eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A2
Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield diluted magnetic system [12, 13]. Therefore, the suppression of ferromagnetism bysubstitution may offer an opportunity to approach a QCP, or may result a glassystate, and in doing so, sheds light onto the nature of the ordering mechanism of aspecific ferromagnetic system.LaCrSb has been reported to order ferromagnetically below T C ∼
125 – 142 K,with the differences arising from the sample preparation methods [14–18]. LaCrSb crystallizes in an orthorhombic structure (space group P bcm ), where Cr occupiesone single crystallographic site 4 c [19]. Extensive investigations into LaCrSb havebeen undertaken, and the compound is found to have a rich magnetic phase diagram[18, 20–23]. LaCrSb exhibits unconventional magnetic behavior with a cantedferromagnetism in bc -plane. A spin-reorientation transition can be observed in the bc -plane at ∼
95 K, and can be suppressed by a small applied magnetic field ∼ is an itinerant ferromagnet [17, 18],the nature of its magnetic moments is still under debate. A neutron scatteringstudy suggests a coexistence of localized and itinerant spins in LaCrSb [20]. AsLa is not moment-bearing, the Cr ion plays the primary role in the magnetism ofLaCrSb . Band structure calculations and the X-ray photoelectron spectroscopystudies find that the 3 d electrons of the Cr exhibit a large DOS peak at/near theFermi level in the paramagnetic state [22–24], which, based on the Stoner criterion,has a possibility of inducing the ferromagnetic instability.An itinerant magnetic system can often be perturbed by applying pressure orvia chemical substitution. Take MnSi [25], UGe [4] and La(V x Cr − x )Ge [26] asexamples; in each, the ferromagnetic state disappears as pressure is applied. Thus,pressure might be able to suppress the ferromagnetic phase and lead to a QCPor quantum phase transition (QPT) in LaCrSb . Also the DOS can be changedby chemical substitutions for the Cr atoms. LaVSb , which is an isostructuralcompound to LaCrSb , has no magnetic ordering down to 2 K [18, 19, 27]. It isfound that the Fermi level in LaVSb is shifted away from the highest peak ofthe DOS [23]. Thus, the ferromagnetism in LaCrSb may also be suppressed bysubstituting V for Cr atom.Previous work on polycrystalline samples showed that V substitution does sup-press the ferromagnetic transitions, and claimed that the mechanism of the ferro-magnetic ordering can not be explained by a simple localized magnetic momentmodel [28]. Only the temperature dependence of magnetization was measured onthe V-doped polycrystalline samples. The nominal V substitution reached only upto 20%, and the precise stoichiometry of this doped system was not analyzed ex-perimentally. It is also not clear at which concentration the ferromagnetism wasfully suppressed. In order to better understand the effects of V substitution on themagnetic state of this system, detailed measurements of the transport and ther-modynamic properties of systematically substituted single crystals are necessary.In this work, we report the synthesis of single crystalline La(V x Cr − x )Sb ( x =0 – 1.0) samples, and present a systematic study of their transport and thermody-namic properties. In addition, measurements of magnetization under pressure wereperformed on the LaCrSb sample. Whereas the Curie temperature is essentiallyinvariant under pressure, the ferromagnetic ordering is systematically suppressedas the V concentration increases from x = 0 to x = 0.36. For 0 . ≤ x ≤ . x ≥ .
88, the samples stay in theparamagnetic state down to 2 K. The magnetic anisotropy also changes with theV substitution. Although the effective moment per Cr varies slightly as the V con-centration increases, possibly suggesting a valence change of Cr ion induced byV substitution, there is no indication of µ eff decreasing toward zero and the Cr eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine
20 40 60 8005001000 I n t en s i t y ( c oun t s ) measured LaCrSb Si [ ] [ ] [100] La(V x Cr )Sb x = 0.13 Figure 1. Powder X-ray diffraction pattern of La(V x Cr − x )Sb ( x = 0.13). Inset: photo of a single crys-talline sample ( x = 0.06) on a millimeter grid. moment appears to be robust and fundamentally local-moment like in nature. Noexperimental features expected in the vicinity of a QCP have been observed byeither applied pressure or chemical substitution.
2. Experimental Details
Single crystalline La(V x Cr − x )Sb samples were synthesized via high-temperaturesolution method with excess Sb as self-flux [18, 27, 29, 30]. High purity ( > x : 8- x : 84, wereplaced in a 2 mL alumina crucible and sealed in a fused silica tube under a partialpressure of high purity argon gas. The ampoule containing the growth materialswas heated up to 1180 ◦ C over 3 h and held at 1180 ◦ C for another 3 h. The growthwas then cooled to 750 ◦ C over ∼
85 h at which temperature the excess liquid wasdecanted using a centrifuge [29, 30]. Single crystals of La(V x Cr − x )Sb grew asrectangular plates, with shiny surfaces that had a few drops of residual Sb-richflux on them. An example of such a crystal is shown in the inset of fig 1. The sizesof crystals increase as the V-concentration increases, varying from ∼ × × for LaCrSb to being crucible limited, ∼ × × for LaVSb .Powder X-ray diffraction data were collected at room temperature on a RigakuMiniFlex II diffractometer with Cu K α radiation. Samples with rod-like shape wereselected for measurement. Data collection was performed with the counting timeof 2 s for every 0.02 degree. The refinement was conducted using the programRietica [31]. Error bars associated with the values of the lattice parameters weredetermined by statistical errors, and a Si powder standard was used as an internalreference. To identify the crystallographic orientation, real-time back-scatteringLaue diffraction measurements were performed with Mo source ( λ ∼ . A ).The structural solutions were refined by the Cologne Laue Indexation Program[32].Elemental analysis of the samples was performed using wavelength-dispersiveX-ray spectroscopy (WDS) in a JEOL JXA-8200 electron probe microanalyzer.Only clear and shiny surface regions were selected for determination of the samplestoichiometry, i.e. regions with residual Sb flux droplets were avoided. For eachcomposition, the WDS data were collected from multiple points on the same sam-ple. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A4 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield (d)
La(V x Cr )Sb c ( ¯ ) x (a) La(V x Cr )Sb x W D S x nominal (c) La(V x Cr )Sb b ( ¯ ) x La(V x Cr )Sb a ( ¯ ) x (b) Figure 2. (a) x WDS vs. x nominal . The lattice parameters of single crystalline La(V x Cr − x )Sb compoundsas a function of the V-concentration are shown in (b) a vs. x , (c) b vs. x , and (d) c vs. x . Note: the measured, x WDS were used to indicate the composition of the compounds in this series.
Table 1. The WDS data for La(V x Cr − x )Sb . N is the number of points measured on one sample, x nominal isthe nominal concentration, x WDS is the average x value measured, and 2 σ is two times the standard deviationof the N values measured. N
12 12 12 12 12 12 12 12 12 12 12 12 12 x nominal x WDS σ Measurements of field and temperature dependent magnetization were performedin a Quantum Design, Magnetic Property Measurement System (MPMS) super-conducting quantum interference device (SQUID) magnetometer. The ac resistivitywas measured by a standard four-probe method in a Quantum Design, PhysicalProperty Measurement System (PPMS). Samples were polished into long rectan-gular bars. Platinum wires were attached to the sample using Epo-tek H20E silverepoxy, with the current flowing along the c -axis. The absolute values of resistivityare accurate to ±
15% due to the accuracy of measurements of electrical contacts’positions. The residual resistivity ratio is defined as RRR = ρ (300 K)/ ρ (2.0 K).Temperature dependent specific heat data were measured in the PPMS usingthe relaxation technique in zero field for representative samples. The specific heatof LaVSb was used to estimate the non-magnetic contribution to the specificheat of LaCrSb . The magnetic contribution to specific heat from the Cr ions wascalculated by the relation of C M = C p (LaCrSb )- C p (LaVSb ).The temperature dependent field-cooled magnetization of a single crystal underpressure was measured in the MPMS magnetometer in a magnetic field of 100 Oeapplied along the c-axis. Pressures of up to 5.3 GPa were achieved with a moissaniteanvil cell [33]. The body of the cell is made of Cu-Ti alloy and the gasket is madeof Cu-Be. Daphne 7474 was used as a pressure transmitting medium [34], and thepressure was determined at 77 K by the ruby fluorescence technique. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine H b H c M / H ( e m u / m o l e ) T (K)
H = 50 Oe
LaCrSb Figure 3. Anisotropic field-cooled (FC) magnetization as a function of temperature for LaCrSb at 50Oe.
3. Results and Analysis3.1.
Crystal Stoichiometry and Structure
The stoichiometry of the La(V x Cr − x )Sb samples was inferred from WDS mea-surements. Table 1 summarizes the atomic percent of each element determinedfrom the weight percent obtained from the analyses. The error bar is taken astwice the standard deviation σ . As shown in fig. 2 (a), the actual V-concentration x WDS follows the initial stoichiometry x nominal systematically, ranging from 0 to 1,and the small 2 σ -value suggests that the samples are homogeneous, at least on thelength scale probed by the WDS measurements ∼ µ m. In the following, the mea-sured, x WDS , rather than x nominal values will be used to indicate the compositionof the compounds in this series.The crystal structure and orientation were confirmed by back-scattering Lauediffraction. Consistent with the reported data [18, 19, 27], this series of compoundsform in an orthorhombic structure, P bcm (No. 57). As shown in the inset of fig. 1,the a -axis was verified to be perpendicular to the rectangular plate, and the c -axisis parallel to the longest side, consistent with the reported data [27]. Powder X-raydiffraction patterns were collected on ground single crystals from each compound.Fig. 1 gives powder X-ray diffraction pattern for x = 0.13 as an example. The mainphase can be refined with LaCrSb ’s reflection pattern ( P bcm structure), consistentwith the Laue diffraction. No clear trace of Sb residue or other secondary solidifi-cation can be detected, and similar results (
P bcm structure) were obtained for therest of the series. The lattice parameters obtained by the analysis of the powderX-ray diffraction data are presented in fig. 2 (b) – (d). The lattice parameters a , b and c all manifest systematic changes as the x increases, which is consistent withthe reported data [18, 19]. Crystallographically, the transition metal elements inLaCrSb and LaVSb occupy the same unique site 4 c [19]. Physical properties of La(V x Cr − x )Sb ( x = 0 and 1.0) The anisotropic, temperature-dependent, field-cooled (FC) magnetization ofLaCrSb is shown in fig. 3. The measurements were performed with the applied fieldparallel to b - and c -axes at 50 Oe. As is shown, the magnetization rises sharply near130 K for both H k b and H k c , indicating a transition to a low-temperature fer- eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A6 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield
Figure 4. Anisotropic magnetic susceptibility as a function of temperature of LaVSb measured at 1 kOe. ( c m ) T (K)La(V x Cr )Sb x = 1.0 x = 0 Figure 5. The electrical resistivity ρ as a function of temperature for La(V x Cr − x )Sb ( x = 0 and 1.0). romagnetic state. A second anomaly can be observed in both directions at around100 K, which can be associated with spin reorientation, as suggested by previousstudies [18, 20]. Below roughly look, the magnetization data in both directionsremain almost constant as temperature is lowered.The anisotropic magnetic susceptibility of LaVSb was measured at 1 kOe, asshown in fig. 4. It is clear that the magnetic susceptibility has weakly positivevalues in all three directions, and M ( T ) /H is essentially temperature independent.It is evident that LaVSb follows Pauli magnetic behavior, and is consistent withthe reported data [18, 27].Figure 5 presents the electrical resistivity data of La(V x Cr − x )Sb ( x = 0 and1.0) as a function of temperature. To within 15%, the room temperature resistivityvalues ρ (300 K) are about 105 µ Ω cm for x = 0 and 87 µ Ω cm for x = 1 . x = 0, a dramatic anomaly occursat about 132 K, which is most likely due to the loss of spin disorder scattering andcan be associated with the ferromagnetic transition. For x = 1 .
0, no anomaly wasobserved for temperatures above 1.8 K. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A
Philosophical Magazine La(V x Cr )Sb x = 1.0 x = 0 C p ( J / K m o l e ) T (K) x = 0 C p ( J / K m o l ) T (K)
Figure 6. Temperature-dependent of specific heat of La(V x Cr − x )Sb ( x = 0 and 1). Inset: magneticcontributions to the specific heat △ C p as a function of temperature for x = 0. The dashed line indicatesthe ordering temperature. The temperature-dependent specific heat data for the La(V x Cr − x )Sb ( x = 0and 1) are presented in fig. 6. The specific heat can be estimated by the relation C p ( T ) = C e + C ph + C M , where C e is the conduction electron contribution, C ph is the phonon contribution, and C M is the magnetic contribution. C e + C ph canbe roughly approximated by the C p data of LaVSb . Thus, the magnetic contribu-tion C M was, to the specific neat of LaCrSb , evaluated as △ C p = C p (LaCrSb )- C p (LaVSb ). A cusp can be seen in △ C p , as shown in the inset of fig.6. This is thefirst time that the ferromagnetic transition of LaCrSb has been observed in thespecific heat data. This anomaly can be associated with the ferromagnetic transi-tion. The ordering temperature T C obtained from △ C p data for x = 0 is about 132K, as indicated by the dash line in the inset of fig. 6. Effects of pressure on the magnetic properties of LaCrSb In an attempt to suppress the ferromagnetism in LaCrSb , hydrostatic pressuresup to 5.3 GPa were applied. Figure 7 (a) shows the temperature dependence ofthe filed-cooled magnetization of LaCrSb under different pressures. At lower pres-sures, the ferromagnetic transition is revealed by a rather sharp increase of themagnetization. Defined here as a minimum point in dM ( T ) /dT (as seen in fig. 7(b)), the Curie temperature, T C , is plotted as a function of applied pressure in fig.7 (c). T C changes only very slightly with applied pressure with dT C /dp ≈ . ± . c -axis (fig. 7 (a) andfig. 3). A decrease of the magnetization is still observed for pressure of 0.6 and1 GPa, although the plateau can not be observed. The decrease of magnetizationcannot be detected above 3 GPa. Effects of chemical substitution on the physical properties ofLa(V x Cr − x )Sb Given that accessible pressures appear to have little or no effect on the ferromag-netic transition temperature of LaCrSb , we decided to study the effects of chemicalsubstitution on the physical properties of the La(V x Cr − x )Sb series. The electrical eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A8 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield
T (K) M ( a . u . ) -6
30 2010 040
LaCrSb H = 100 Oe FCH c
LaCrSb (c) T C ( K ) Pressure (GPa) dT C /dp 0.1 0.3 K/GPa (b) d M / d T ( a . u . ) T (K) T C Figure 7. (a) Temperature dependence of the FC magnetization for LaCrSb under different pressureswith H = 100 Oe, H k c . Note: The values of the magnetization are shifted for clarity. (b) d M /d T vs. T : the arrow indicates the Curie temperature. (c) Pressure dependence of T C for LaCrSb , where T C isdetermined by the minimum point in dM ( T ) /dT . resistivity data, as a function of temperature for La(V x Cr − x )Sb are presented infig. 8 (a) and (b). The room temperature resistivity values ρ (300 K) of all com-pounds are in the range of 80 – 140 µ Ω cm. For low x -value samples, the distinctdrop in the resistivity below 150 K is probably associated with the ferromagnetictransition. This anomaly moves to lower temperatures and is broadened as the Vconcentration increases up to 0.36 (seen in fig. 8 (a)). For x ≥ T C — the peak position inthe dρ/dT indicated by the arrow, and the inferred T C values are summarized inTable 2 (below). With current along c -axis, samples for x = 1.0 and 0 have RRRof ≃ x -valuecompounds are due to increased site disorder caused by the substitution.Based on the resistivity and specific heat data, a T – x phase diagram wasassembled. As shown in fig. 9, the Curie temperature decreases systematically asthe V concentration increases. For lower V-doped compounds, x < eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine x = 0 0.06 0.13 0.18 0.22 0.33 0.36 La(V x Cr )Sb ( c m ) T (K)
I c (a) (T) d /dT
T (K) ( c m ) x = 0.06 d / d T ( a . u . ) T C (b) La(V x Cr )Sb ( c m ) T (K)
Figure 8. The electrical resistivity ρ as a function of temperature for La(V x Cr − x )Sb . (a) x = 0 –0.36. Inset: ρ ( T ) and dρ/dT for x = 0.06. The arrow indicates the criterion used to determine the Curietemperature T C . (b) x = 0.42 – 1.0.Figure 9. x -dependent transition temperatures for La(V x Cr − x )Sb determined by ρ ( T ) and C p ( T ) mea-surements.eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A10 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield possess a paramagnetic state at high temperatures, and transits into a magneticallyordered state at low temperatures. For higher V-doped compounds, x > M ( T ) for selected compounds. Figure 10 (a) shows the anisotropic, ZFC, magne-tization isotherms for LaCrSb measured at T = 2 K. The magnetization showsclear ferromagnetic behavior – spontaneous spin alignment in both b and c direc-tions as the applied field increases from zero. At T = 2 K, in the ordered state, themagnetization is anisotropic, with M b > M c > M a . The value of the magnetizationmeasured at 50 kOe in the b direction is taken as the saturated moment ( µ S ). For x = 0, µ S is about 1.61 µ B per Cr, consistent with the reported value [18, 20].Figure 10 (b) shows the hysteresis loop of LaCrSb measured at 2 K for H k b . Thespontaneous spin alignment can be clearly seen, whereas hysteresis can hardly beobserved. This probably suggests that LaCrSb is a soft ferromagnet. Comparedto the V-doped compounds (see below), LaCrSb exhibits negligible pinning effectthat is associated with the disorder induced by substitution.Similar magnetization isotherms can be observed for x = 0.22, see in fig. 11(a). The b -axis can still be identified as the easy axis and M a has the lowestvalue of all three directions, however, the differences in magnetization betweendifferent directions becomes slightly less obvious. The saturated moment is 1.37 µ B /Cr for H k b . The hysteresis loop for x = 0.22 is shown in fig. 11 (b). Clearhysteresis can be observed, and the coercivity is about 1.63 kOe. At low fields, themagnetization in the virgin curve, instead of showing spontaneous spin alignment,rises slowly with the applied field. This is probably caused by domain pinningeffects. In addition, a discrepancy can be seen in the low-field magnetization for H k b between fig. 11 (a) and fig. 11 (b). It is possibly due to the remnant fieldin a superconducting magnet giving rise to different virgin curve starting points.Based on the behavior of the field-dependent magnetization, it is evident thatLa(V x Cr − x )Sb ( x = 0.22) possesses a ferromagnetic state at low temperatures.Figure 11 (c) shows the ZFC and FC magnetization as a function of temperature.The measurements were performed at 50 and 100 Oe with H k b . As can beseen, the FC M/H increases dramatically upon cooling and continuously rising atlow temperatures, indicating the existence of a ferromagnetic state. The complexfeature in the ZFC M ( T ) /H at low temperatures is probably due to domain pinningeffects. Hence, with increasing V substitution up till x = 0.22, the La(V x Cr − x )Sb series maintains a ferromagnetic state at low temperatures.Starting from x = 0.33, two major differences can be found in the magnetizationisotherms, as shown in fig. 12 (a) and fig. 13 (a). First of all, a spontaneous spinalignment can not be observed for any direction of applied field measured. Themagnetization for H k b rises much slower as field increases (compared with thecase of x = 0), whereas M a and M c seem to show rather broad shoulders. With theincreased V concentration, even M b shows a shoulder-like feature, and no saturationcan be observed. These data might suggest that the magnetic state for x ≥ x Cr − x )Sb series is no longer ferromagnetic. The second difference foundis the change of anisotropy. Although the b -axis is still the easy axis, M a is largerthan M c for x ≥ x = 0.33 and 0.52, asshown in fig. 12 (b) and fig. 13 (b). However the coercivity decreases as the Vconcentration increases. It drops to 1.47 kOe for x = 0.33 and 0.58 kOe for x =0.52. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine H k b for the LaCrSb . The applied magnetic field changes fromzero to 50 kOe, to -50 kOe, and then up to 50 kOe again. Figures 12 (c) and 13 (c) also present the ZFC and FC magnetization as afunction of temperature measured at 50 and 100 Oe with H k b . Besides theinitial increase in both ZFC and FC M ( T ) /H upon cooling, a local maximumcan be observed in both of the ZFC and FC curves. This feature is more obviousfor the higher V-doped compound, x = 0.52 (fig. 13 (c)). As is shown, the ZFCand FC M ( T ) /H are split at low temperatures, and the ZFC curves exhibit adramatic decrease as T decreases. These might imply some degree of frustrationwhich leads to some form of cluster or spin-glass state [12]. It is possible that withthe continuous suppression of ferromagnetism, the magnetic state in this seriesevolves into a new magnetic state, which is often observed in the local magneticmoment systems [12, 35].As vanadium content increases, the moment along a -axis continuously gets closerto M b . As shown in fig. 14 (a), M a and M b becomes almost identical for x = 0.73. At2 K, the magnetization gradually increases with the increasing field, exhibiting nofeature of spontaneous spin alignment. No saturation or hysteresis can be observedfor x = 0.73 (fig. 14 (b)). It is evident that La(V x Cr − x )Sb series does not possessa ferromagnetic order above 2.0 K for x > b -axis shows typical ferromagnetic behavior eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A12 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield
Figure 11. (a) Zero-field-cooled (ZFC) anisotropic field-dependent magnetization isotherms taken at 2K. (b) Hysteresis loop measured at 2 K with H k b . The applied magnetic field changes from zero to 50kOe, to -50 kOe, and then up to 50 kOe again. The arrows indicate the directions of the field sweeping.(c) Zero-field-cooled (ZFC) and field-cooled (FC) temperature dependence of the magnetic susceptibilitytaken at 50 and 100 Oe with H k b for the La(V x Cr − x )Sb ( x = 0.22).eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine H k b . The applied magnetic field changes from zero to 50kOe, to -50 kOe, and then up to 50 kOe again. The arrows indicate the directions of the field sweeping.(c) Zero-field-cooled (ZFC) and field-cooled (FC) temperature dependence of the magnetic susceptibilitytaken at 50 and 100 Oe with H k b for the La(V x Cr − x )Sb ( x = 0.33).eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A14 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield
Figure 13. (a) Zero-field-cooled (ZFC) anisotropic field-dependent magnetization isotherms taken at 2K. (b) Hysteresis loop measured at 2 K with H k b . The applied magnetic field changes from zero to5 kOe, to -5kOe, and then up to 5 kOe again. The arrows indicate the directions of the field sweeping.(c) Zero-field-cooled (ZFC) and field-cooled (FC) temperature dependence of the magnetic susceptibilitytaken at 50 and 100 Oe with H k b for the La(V x Cr − x )Sb ( x = 0.52). for the lower V-doped compounds, and given that the b -axis is the easy axis inalmost the whole x range (0 ≤ x ≤ . x Cr − x )Sb system is presented with themagnetization data along b -axis. The temperature-dependent FC magnetizationcurves of the La(V x Cr − x )Sb ( x = 0.06 – 0.73) series, with H k b at 50 Oe areshown in fig. 15 (a) and (b). Magnetization for x = 0.06 – 0.36 shows the expected eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine -4 -2 0 2 4-0.4-0.20.00.20.4 (b) M ( B / C r) H (kOe)
H ll b
La(V x Cr )Sb T = 2 Kx = 0.73 M ( B / C r) H (kOe) H a H b H c (a)x = 0.73 Figure 14. (a) Zero-field-cooled (ZFC) anisotropic field-dependent magnetization isotherms taken at 2 K.(b) Hysteresis loop measured at 2 K with H k b for the La(V x Cr − x )Sb ( x = 0.73). The applied magneticfield changes from zero to 50 kOe, to -50 kOe, and then up to 50 kOe again. rapid increase of the magnetization as well as the saturation at low temperatures(fig. 15 (a)). The Curie temperature decreases as V concentration increases, andthe transition shifts to lower temperature, as can be clearly seen in fig. 15 (b).With increasing amounts of V substituted for Cr, from x = 0.42, the temperature-dependent magnetic susceptibility starts deviating from the ferromagnetic behavior(fig.15). As the temperature decreases, the magnetization rises in a much slowermanner compared with the lower V-doped compounds, and a local maximum at lowtemperatures can be observed. It can be inferred that instead of the ferromagneticstate, a new magnetic state may emerge for higher V-doped compounds.The Curie temperature can be estimated by d ( M/H ) /dT for low values of appliedfield ( H = 50 Oe in this case), as indicated by the arrow in fig. 16 (a), where thetransition temperature T is determined by the sharp anomaly in d ( M/H ) /dT . Theobtained T -values are listed in Table 2. The transition temperature systematicallydecrease to lower temperatures as the V-concentration increases, from 133 K for x = 0 to 24 K for x = 0.36 with H k b . On the other hand, for higher V-dopedcompounds ( x > d ( M/H ) /dT . Besides theminimum point, the maximum point in d ( M/H ) /dT is chosen as the criterion tocharacterize the transition temperature of a potential new magnetic state (shownin fig.15 (b)). Again the obtained transition temperatures T and T are listed inTable 2.The polycrystalline average of M/H measured at 1 kOe is shown in fig. 17. It is eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A16
Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield (b) x = 0 0.06 0.13 0.18 0.22 0.33 0.36 0.42 0.52 0.59 0.73
La(V x Cr )Sb M / H ( e m u / m o l e ) T (K) x = 0.06 0.13 0.18 0.22 0.33 0.36 0.42 0.52 0.59 0.73
La(V x Cr )Sb M / H ( e m u / m o l e ) T (K)
H b H = 50 OeFC (a)
Figure 15. (a) FC magnetization as a function of temperature for La(V x Cr − x )Sb ( x = 0.06 – 0.73) at50 Oe with H k b . (b) FC magnetization as a function of temperature for x = 0 – 0.73 presented in asemi-log plot. obtained by χ ave = ( χ a + χ b + χ c ). A modified Curie-Weiss law with inclusionof a temperature-independent term χ : χ ave = χ + C/ ( T − θ poly ), was used to fitthe magnetic susceptibility, where θ poly is the Curie-Weiss temperature estimatedby the polycrystalline averaged data and C is the Curie constant. Considering theaccuracy of measuring sample’s mass, the values of the effective moments in thisseries are accurate to ± χ and the calculated µ eff and θ poly are summarized in Table 2. For x = 0, µ eff is found to be about 3.9 µ B /Cr,close to the calculated value for Cr : 3.8 µ B , and is consistent with the reportedvalue [18]. As shown in Table 2, the effective moment gradually decreases as the Vconcentration increases. However, µ eff does not approach zero for some critical x value, or even as x gets close to 1, unlike the ferromagnetic system dominated bysolely itinerant moments [36]. Instead, µ eff falls to 2.9 µ B /Cr for x = 0.88, whichis close to Cr : 2.8 µ B . It is possible that the Cr ion in the La(V x Cr − x )Sb compounds has a valence changed in compounds with higher V substitution. Inaddition, it is found that the Curie-Weiss temperature, θ poly in this series are allpositive, indicating the ferromagnetic interaction as the dominant interaction inthese compounds. Also the fact that θ poly decreases as x increases implies theferromagnetic interaction is weakened by the V substitution.We have been able to suppress the ferromagnetism in the La(V x Cr − x )Sb se-ries via chemical substitution. The ordering temperatures inferred from low fieldmagnetization, resistivity and specific heat measurements are summarized in Table2. A phase diagram of x -dependent transition temperature for La(V x Cr − x )Sb is eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine (b) T (K) M / H ( e m u / m o l e ) T M/H d(M/H)/dT d ( M / H ) / d T ( a . u . ) T x = 0.52 T (K) M / H ( e m u / m o l e ) d ( M / H ) / d T ( a . u . ) T M/H d(M/H)/dT x = 0.13 (a)
Figure 16. (a) The temperature dependence of the magnetization and d ( M/H ) /dT for x = 0.13, andthe arrow indicates the criterion used to determine the transition temperature T . (b) The temperaturedependence of the magnetization and d ( M/H ) /dT for x = 0.52, and the arrow indicates the criteria usedto determine the transition temperature T and T . M / H ( e m u / m o l e ) T (K) x = 0 0.22 0.33 0.52 0.73 0.88
La(V x Cr )Sb H = 1 kOe H / M ( O e / e m u m o l e ) T (K)
Figure 17. Polycrystalline averaged
M/H vs. T for La(V x Cr − x )Sb ( x = 0, 0.22, 0.33, 0.52, 0.73 and0.88) measured at H = 1 kOe. Inset: inverse magnetic susceptibility as a function of temperature.eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A18 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield T , H b T , H c T , H b T , H c (T) C p (T) T ( K ) x FM CMSI
Figure 18. x -dependent transition temperatures for La(V x Cr − x )Sb determined by anisotropic M ( T ), ρ ( T ) and C p ( T ) measurements. The dashed lines outline three potential regions of the low temperaturemagnetic behavior: ferromagnetic state (FM), complex magnetic state I (CMSI) and complex magneticstate II (CMSII). assembled in fig. 18. For x x > x Cr − x )Sb series, ferromagnetism can be clearly observed for x up to 0.22, and the ferromagnetic transition temperature is suppressed mono-tonically by the V substitution: T C = 133 K for x = 0, and T C = 52 K for x =0.22 (based on the low field M ( T ) data with H k b ). If T is used as a criterionfor determining the transition to a low-temperature magnetic state for the wholeseries, it seems that the magnetic transition temperature gets gradually suppressedby V substitution and drops below our base-temperature of 2.0 K. If T is used asthe criterion for higher V-doped samples, then considering the features observed in M ( H ), M ( T ) /H and ρ ( T ) for x = 0.33 and 0.36, it seems that x = 0.33 – 0.36 is aregion for the system to transition from the ferromagnetic state to a new magneticstate. Similar phenomena have also been observed in the LiHo x Y − x F family: for0.25 ≤ x ≤ ≤ x ≤ ≤ x ≤ x ≥ M ( T ) exhibits a local maximum at low temperature, andii) field-cooled and zero-field-cooled M ( T ) deviate from each other, it is possiblethat this new magnetic ground state is a complex glassy state. As the V concen-tration reaches even higher, x ≥ .
88, no magnetic ordering can be observed andthe system shows paramagnetic behavior down to our base temperature of 2.0 K.Based on our data, the La(V x Cr − x )Sb system has a phase diagram consis-tent with dominantly local moment like behavior of Cr. The progression from welldefined magnetic ordering to complex magnetic state, to something that may beglassy state and gradually has a freezing temperature drop toward zero is similarto what has been found for local moment systems such as (Tb x Y − x )Ni Ge [13].At no point were features consistent with a quantum critical point observed. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A Philosophical Magazine Table 2. Summarized effective moment µ eff , saturated moment µ B , polycrystalline averaged Curie-Weiss temperature θ poly , transition temperatures T , T estimated from low field M(T) measurements with H k b and H k c , and Curietemperature T C estimated from ρ ( T ) and C p ( T ) measurements for La(V x Cr − x )Sb ( x = 0 – 0.88). x T C T T T T T C θ poly χ µ eff µ S (K) (K) (K) (K) (K) (K) (K) (10 − emu/mole) ( µ B /Cr) ( µ B /Cr) dρ/dT H k b H k b H k c H k c C p ( T )0 132 133 132 132 141 -40 3.9 1.610.06 95 98 980.13 80 82 830.18 59 62 660.22 45 54 58 90 0 3.7 1.370.33 23 24 14 32 12 70 -5 3.20.36 24 24 12 32 130.42 18 10 20 100.52 14 8 20 6 52 1 3.10.59 12 5 13 50.73 6 3 34 6 2.90.88 0.1 8 2.9Figure 19. The Curie-Weiss temperature θ poly and the effective moment µ eff per Cr as a function of x for La(V x Cr − x )Sb .
4. Discussion and Conclusions
Our efforts to suppress ferromagnetism in LaCrSb started with applications ofpressures up to 5.3 GPa. As seen in fig. 7, the ferromagnetic ordering temperature, T C , is essentially insensitive to p < compoundby applying pressure, we evaluated the potential for quantum critical behavior byusing chemical substitution as an alternative tuning parameter. The growth of sin-gle crystalline La(V x Cr − x )Sb samples has allowed for the detailed study of theanisotropic properties, the determination of the easy axis as well as the estimateof the effective moment. In addition, careful chemical analysis was performed todetermine the precise concentration of this doped system. This offers a certainunderstanding of chemical substitution effect on the suppression of the ferromag-netism and the evolution of the magnetic state in this system.The estimated Curie-Weiss temperature θ poly and the effective moment µ eff perCr as a function of the V-concentration x are plotted in fig. 19. It is clearly seenthat θ poly decreases monotonically from about 141 K to almost zero as x increases,implying that the ferromagnetic interaction is suppressed by the V substitution.The effective moment also decreases as x increases, but in a more subtle way. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A20 Xiao Lin, Valentin Taufour, Sergey L. Bud’ko and Paul C. Canfield
La(V x Cr )Sb S ( B / C r) x La(V x Cr )Ge Figure 20. The saturated moment µ S as a function of x for the La(V x Cr − x )Ge and La(V x Cr − x )Sb series. Note: for La(V x Cr − x )Sb compounds with x > b -axis. Data on La(V x Cr − x )Ge are from Ref. [26].Figure 21. The Rhodes-Wohlfarth ratio µ c / µ S as a function of Curie temperature T C for theLa(V x Cr − x )Ge and La(V x Cr − x )Sb series. Data on La(V x Cr − x )Ge are from Ref. [26]. Instead of quickly approaching to zero as seen in the suppression of ferromagnetismin the itinerant ferromagnets [1–4], µ eff per Cr varies slightly as x increases, from3.9 µ B for x = 0 to 2.9 µ eff for x = 0.88. Whereas the former value is close to thetheoretical effective moment of Cr , the latter one is close to Cr . Hence, thedecrease of µ eff is more likely as a consequence of the valence change due to the Vsubstitution than manifesting an itinerant-moment behavior.The saturated moment values for the La(V x Cr − x )Sb compounds are presentedin fig. 20. µ S shows a slight decrease with the increase of the V concentration, from1.61 µ B /Cr for x = 0 to 1.37 µ B /Cr for x = 0.22. For higher V-doped compounds( x > x Cr − x )Sb systems does not have a ferromagnetic state atlow temperatures, hence, µ S is replaced by the value of magnetization at 50 kOewith field along the b -axis. The arrows in fig. 20 imply that M ( H = 50 kOe) is thelower limit of the possible saturated moment of the higher V-doped compounds. Itis clear that Cr’s moment stays well above zero as the V concentration approachesto 1. eptember 18, 2018 10:5 Philosophical Magazine LaVCrSb3˙101313A REFERENCES To learn more about Cr’s magnetic moment, we can compare the saturated mo-ments of both La(V x Cr − x )Ge and La(V x Cr − x )Sb series (as shown in fig. 20).It can be clearly seen that µ S of the La(V x Cr − x )Ge compounds quickly decreasesas the V concentration increase, that is associated with the itinerant magnetism[26]. For the La(V x Cr − x )Sb series, µ S has a slower decreasing rate as the V con-centration increases. This possibly implies that the magnetic moment associatedwith Cr in the La(V x Cr − x )Sb compounds is mainly of local character. Based onthe values of µ eff and µ S obtained, one can calculate the Rhodes-Wolfarth ratio(RWR) [36], seen in fig. 21. According to Rhodes and Wolfarth, RWR = µ c / µ S ,where µ c is related to the number of moment carriers, and can be obtained from µ c ( µ c +1)= µ . While RWR = 1 is an indication of localized magnetism, largerRWR values suggest the existence of itinerant ferromagnetism. In our case, RWRequals to ≃ x = 0 and ≃ x = 0.22. Although this seems suggestingthe ferromagnetism is itinerant, the change of RWR as a function of T C shows verydifferent behavior compared with the La(V x Cr − x )Ge system [26] (seen in fig. 21)and the original Rhodes-Wohlfarth plot [36]. Therefore, unlike La(V x Cr − x )Ge ,La(V x Cr − x )Sb is less likely to be dominated solely by itinerant magnetic mo-ments. Probably the magnetism in this family is of predominantly local character. Acknowledgements
We thank W. E. Straszheim for his assistance with the elemental analysis of thesamples. We appreciate help of E. Colombier and A. Kaminski in setting up theruby fluorescence system. We also would like to thank H. Hodovanets for assist-ing in Laue diffraction measurement. This work was carried out at the Iowa StateUniversity and supported by the AFOSR-MURI grant No. FA9550-09-1-0603 (X.Lin, V. Taufour and P. C. Canfield). S. L. Bud’ko was supported by the U.S. De-partment of Energy, Office of Basic Energy Science, Division of Materials Sciencesand Engineering. Part of this work was performed at Ames Laboratory, US DOE,under Contract No. DE-AC02-07CH11358.
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100 200 3000246 (b)
La(V x Cr )Sb M / H ( - e m u / m o l e ) T (K)
H = 1 kOex = 1.0
H a H b H c M / H ( e m u / m o l e ) T (K)
H a H b H c