**Ba9V3Se15: a novel compound with spin chains**

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J. Phys.: Condens. Matter 30 (2018) 214001 (9pp)

https://doi.org/10.1088/1361-648X/aabdff

Ba9V3Se15: a novel compound with spin chains

Jun Zhang1,3, Min Liu1,3, Xiancheng Wang1 , Kan Zhao1, Lei Duan1,3, Wenmin Li1,3, Jianfa Zhao1,3, Lipeng Cao1, Guangyang Dai1,3, Zheng Deng1,

Shaomin Feng1, Sijia Zhang1, Qingqing Liu1, Yi-feng Yang1,2,3 and Changqing Jin1,2,3

1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

2 Collaborative Innovation Center of Quantum Matter, Beijing 100190, People’s Republic of China

3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

E-mail: [email protected], [email protected] and [email protected] Received 20 December 2017, revised 27 March 2018

Accepted for publication 13 April 2018

Published 30 April 2018

Abstract

In this work, a novel compound Ba9V3Se15 with one-dimensional (1D) spin chains was synthesized under high-pressure and high-temperature conditions. It was systematically characterized via structural, magnetic, thermodynamic and transport measurements.

Ba9V3Se15 crystallizes into a hexagonal structure with a space group of P-6c2 (188) and the lattice constants of a = b = 9.5745(7) Å and c = 18.7814(4) Å. The crystal structure consists of face-sharing octahedral VSe6 chains along c axis, which are trimeric and arranged in a triangular lattice in ab-plane. Ba9V3Se15 is a semiconductor and undergoes complex magnetic transitions. In the zero-field-cooled (ZFC) process with magnetic field of 10 Oe, Ba9V3Se15

sequentially undergoes ferrimagnetic and spin cluster glass transition at 2.5 K and 3.3 K, respectively. When the magnetic field exceeds 50 Oe, only the ferrimagnetic transition can be observed. Above the transition temperature, the specific heat contains a significant magnetic contribution that is proportional to T1/2. The calculation suggests that the nearest neighbor (NN) intra-chain antiferromagnetic exchange J1 is much larger than the next nearest neighbor (NNN) intra-chain ferromagnetic exchange J2. Therefore, Ba9V3Se15 can be regarded as an

effective ferromagnetic chains with effective spin-1/2 by the formation of the V(2)(↓)V(1)(↑) V(2)(↓) cluster.

Keywords: one dimension, spin chain, ferromagnetic chains, specific heat (Some figures may appear in colour only in the online journal)

Introduction

BaVS3 has received a lot of attention because of its rich physical phenomena [1–9], such as metal-insulator (MI) transition driven by Peierls instability [5]. BaVS3 is a spin- 1/2 chain system where the crystal structure consists of face- sharing octahedral VS6 chains. At room temperature BaVS3 crystalizes into hexagonal structure (P63/mmc) with VS6 chains packed in a triangular lattice in ab-plane. The intra-

chain nearest V–V distance is 2.807 Å, much smaller than that of inter-chain (6.713 Å), thereby, presenting a quasi 1D

structure. It undergoes a sequence of phase transitions: struc- tural phase transition to Cmc21 space group at 240 K due to the zigzag deformation of VS6 chains [10], MI transition with TMI ~ 69 K accompanied by another structural phase transition to Im space group [5] and incommensurate antiferromagnetic order (ICAFO) transition at TN ~ 31 K [7]. Far beyond TMI, 1D lattice fluctuations have been revealed, which is responsible for the tetramerization of the VS6 chains and the formation of charge density order, further leading to the MI transition. Between TMI and TN, although the long range magnetic order has not emerged, the presence of long-range and dynamic

1361-648X/18/214001+9$33.00 1 © 2018 IOP Publishing Ltd Printed in the UK

antiferromagnetic correlation has been evidenced, which is analogous with a spin-liquid state [3]. Corresponding to the ICAFO transition, there is no anomaly in the specific heat measurement [2]. In the ICAFO state, the spins are oriented along a axis in the monoclinic structure. The ordering is anti- ferromagnetic in ab-plane and predominantly ferromagnetic with long range modulation along c axis [7].

Applying high pressure to BaVS3 can gradually suppress the MI transition and induce quantum critical point at ~2GPa [9]. Chemical pressure introduced by Sr-doping also can suppress the MI and ICAFO transition, after which a ferromagnetic order appears when Sr-doping level exceeds 0.1 [11]. As an isostruc- tural counterpart of BaVS3, BaVSe3 exhibits similar structural transition from hexagonal to orthorhombic phase at 310 K [12]. However, the important difference is that BaVSe3 is a ferro- magnetic metal with c easy axis and TC ~ 43 K, which behaves like BaVS3 under chemical pressure [13, 14]. Just above TC, BaVSe3 is revealed to undergo a magnetic symmetry change

at 62.5 K from the anisotropy of χc < χ to χc > χ [15]. In the paramagnetic state, the magnetic susceptibility follows the Curie–Weiss form, and the Curie–Weiss temperature (Tθ ~ 44 K) is very close to TC (43 K), which demonstrates less magn-

etic frustration in BaVSe3. Compared with BaVS3, BaVSe3 pre- sents less physical properties associated with spin chains.

How about increasing the distance of adjacent inter-chains in the vanadium chalcogenides? Learning from the 1D struc- ture of Ba9Fe3S15 [16] and Ba9Sn3Te15 [17], we substitute the cation of Fe/Sn with V as well as the anion of S/Te with Se, and successfully synthesize the new compound Ba9V3Se15 under high-pressure and high-temperature conditions. It crystalizes into a hexagonal structure with a space group P-6c2 (188). Similar to BaVS3 and BaVSe3, the structure of Ba9V3Se15 consists of face-sharing VSe6 chains that are packed in a tri- angular lattice in ab-plane. However, the distance of adja-

cent chains (9.5745(7) Å) in Ba9V3Se15 is much larger than BaVS3 and BaVSe3, demonstrating that Ba9V3Se15 further approaches to one dimensionality in the view of crystal struc- ture. Ba9V3Se15 undergoes a ferrimagnetic transition at 2.5 K. At low temperature, there is a significant magnetic specific heat, which is proportional to T1/2. Ba9V3Se15 can be regarded as an effective ferromagnetic chains with effective spin-1/2 by

the formation of the V(2)(↓)V(1)(↑)V(2)(↓) cluster.

Experimental and calculations

A polycrystalline sample of Ba9V3Se15 was synthesized under the conditions of high-pressure and high-temper- ature. The commercially available crystalline powders of V (Alfa, >99.5% pure), Se (Alfa, >99.999% pure) and lumps

of Ba (Alfa, immersed in oil, >99.2% pure) were used as

10 20 30 40 50 60 70 80 90 100 110 120

2Theta (degree)

Figure 1. X-ray powder patterns of Ba9V3Se15 measured at room temperature and the refinement with the space group of P-6c2 (188).

cubic anvil high pressure apparatus. After pressure was slowly raised to 5.5 GPa, the sample was heated to 1400 °C within 4 min and kept for 40 min. After the high-pressure and high- temperature process, the black pure polycrystalline sample of Ba9V3Se15 was obtained.

The powder x-ray diffraction was performed on a Rigaku Ultima VI (3KW) diffractometer using Cu Kα radiation gen- erated at 40 kV and 40 mA. The data was collected at a scan- ning rate of 1° per min with a scanning step length of 0.02°. The Rietveld refinement on the diffraction spectra was carried out by using Gsas software packages. The dc magnetic sus- ceptibility was measured using a superconducting quantum interference device (SQUID). The electronic conductivity, ac susceptibility and specific heat were measured using a phys- ical property measuring system (PPMS).

The electronic structures were obtained by density func- tional theory (DFT) calculations using the full-potential lin- earized augmented plane-wave (LAPW) method [18], with the augmented plane-wave plus local orbitals implemen- tation [19] both in the WIEN2k code [20]. To include the strong correlations in the transition-metal elements, we took the generalized gradient approximation-Perdew, Burke and Ernzerhof (GGA-PBE) exchange correlation potential [21]

with an effective Coulomb repulsion Ueff = 5 eV for V in the GGA + U calculations [22]. The Muffin-tin radii RMT are 2.50

a.u. for Ba, 2.50 a.u. for V, and 2.40 a.u. for Se, respectively.

The maximum modulus for the reciprocal vectors Kmax was chosen such that RMT * Kmax = 8.0 and 1000 k-points meshes were used in the whole Brillouin zone.

Results and discussions

the starting materials. The precursor BaSe was prepared by heating the mixture of Ba blocks and Se powder in an alumina crucible sealed in an evacuated quartz tube at 700 °C for 20 h. The mixture of BaSe, V and Se were homogenously mixed according to a molar ratio 3:1:2 and was pressed into a pellet

with a diameter of 6 mm. The pre-pressed pellet was placed in an h-BN capsule and then put into a furnace of graphite tube. High pressure experiments were performed in a DS6 × 600 T

Figure 1 shows the powder x-ray diffraction patterns of Ba9V3Se15 sample. All the peaks can be indexed in a hexag- onal structure with the lattice parameters of a = b = 9.5745(7)

Å and c = 18.7814(4) Å. The systematic absence of hkl sug-

gests that the space group should be P-6c2 (188). Here, the

structures of Ba9Fe3S15 and newly discovered compounds Ba9Sn3Te15 reported in our previous work were adopted to refine the diffraction data of the Ba9V3Se15 [16, 17]. Using

Table 1. The summary of the crystallographic data at room temperature for Ba9V3Se15.

Compound Ba9V3Se15

Space group: P-6 c 2 (188)—hexagonal

a = b = 9.5745 (7) (Å), c = 18.7814 (4) (Å)

V = 1491.07 (0) (Å3), Z = 2

χ2 = 2.8, wRp = 5.6%, Rp = 4.2%

Atom Label Wyck. x/a y/b z/c SOF U (Å2)

Ba Ba1 12l 0.0144(7) 0.3825(7) 0.0859(4) 1 0.021

Ba Ba2 6k 0.3956(4) 0.3776(8) 0.25000 1 0.023

V V1 2a 0 0 0 1 0.022

V V2 4g 0 0 0.1685(3) 1 0.014

Se Se1 12l 0.2275(8) 0.2208(8) 0.0871(5) 1 0.025

Se Se2 6k 0.0126(2) 0.2336(1) 0.250 00 1 0.031

Se Se3 2c 1/3 2/3 0 1 0.032

Se Se4 4h 1/3 2/3 0.1859(8) 1 0.019

Se Se5 4i 2/3 1/3 0.1658(8) 1 0.004

Se Se6 4i 2/3 1/3 0.0505(6) 0.5 0.023

(a)

(b)

6.9990 Å

(c) (d)

Se

Figure 2. The crystal structures of Ba9V3Se15 and BaVSe3, showing the face-sharing octahedron VSe6 chains. (a) and (c) is the top view with the projection along c axis for Ba9V3Se15 and BaVSe3, respectively; (b) and (d) is the perspective view with the projection along [1 1 0] direction.

Se(3)-Se(4) Chain

Figure 3. The sketch of VSe6 octahedral chains and Se chains in the compound of Ba9V3Se15.

GSAS software packages the refinements were conducted and smoothly converged to χ2 = 2.8, Rp = 4.2% and Rwp = 5.6% for Ba9V3Se15. The summary of the crystallographic data at room temperature is shown in table 1.

Based on the refinement results, the crystal structure of Ba9V3Se15 is sketched in figures 2(a) and (b). For comparison, the structure of BaVSe3 is also shown in figures 2(c) and (d). Both crystal structures of Ba9V3Se15 and BaVSe3 contain face-sharing octahedral VSe6 chains along c axis, which are arranged in a triangular lattice in ab-plane. As for the VSe6 chains, there are three remarkable differences between the two compounds. One is the distance of the adjacent chains, which is given by their lattice constant a, shown in figures 2(a) and

(c) respectively. For Ba9V3Se15, the VSe6 chains are separated by two octahedral SeBa6 chains. Thus, the distance of adjacent chains is significantly enlarged from 6.9990 Å (BaVSe3) to 9.5745 Å, and Ba9V3Se15 presents further approaching to one dimensionality. The second is that the distance of adjacent V atoms within the chains in BaVSe3 are equal (2.93 Å); while the VSe6 chains in Ba9V3Se15 are trimeric, leading to two sites for V atoms. In a trimeric unit, there are one V(1) atom and two V(2) atoms. The distances of adjacent V atoms are 3.01 Å and 3.36 Å, shown in figure 3. The third is the oxidation state of V. For BaVSe3, the valence of V is +4, so that the 3d orbital

is occupied with only one electron. Therefore, BaVSe3 is con-

sidered to be the system with spin-1/2 chains. However, it is a little complex in Ba9V3Se15. Assuming the valence of all the Se anions in Ba9V3Se15 is −2, the oxidation state of V should

be +4 to balance the charge to be neutral. However, this is not

the case. Figure 3 also shows the sketch of Se chains com-

posed of Se(3)-Se(4) and Se(5)-Se(6) atoms in Ba9V3Se15. The distances between the adjacent Se in the chains are 2.69

results of the oxidation state of +2 for V(1) and +3 for V(2) (see the calculations below) and based on the site symmetry and the charge balance, the molecular formula of Ba9V3Se15

can be rewritten as Ba2+9V2+V3+2Se2− Se1−4Se2− .

Figure 4(a) shows the temperature dependence of resistivity of Ba9V3Se15. The resistivity at room temper- ature is about 24 Ω · mm. The resistivity increases with decreasing temperature, thereby demonstrating a semi- conducting behavior. The inset is the curve of lnρ versus

inverse temperature, presenting a straight line. By using the formula of ρ exp(Δg/2kBT), where Δg is the semi- conducting band gap and kB is the Boltzmann’s constant,

the resistivity curve can be well fitted and the band gap Δg is evaluated to be 0.2 eV. Figures 4(b) and (c) shows the temperature dependence of magnetic susceptibility measured with H = 1000 Oe and the magnetic hyster- esis curve, respectively. The M(H) curve is linear at 10 K

and 20 K. When the temperature is cooled down to 5 K, the magnetization M(H) exhibits a negative curvature. At

1.8 K, the saturated magnetic moment is close to 1 µB/f.u.

Figure 4(b) also displays the curve of inverse susceptibility as a function of temperature. By using the Curie–Weiss law 1/χ = T/C − Tθ/C, linearly fitting the curve of high temper- ature region gives the effective magnetic moment µeff ~ 5.3 µB/f.u. and the Curie–Weiss temperature Tθ ~ 31 K. Given

the molecular formula Ba2+9V2+V3+2Se2− Se1−4Se2− , there are three electrons in the 3d orbital for V(1) atoms and two electrons for V(2). In addition, the bellowing calcul-

ations suggest an antiferromagnetic NN intra-chain inter- action, which results in a cluster of V(2)(↓)V(1)(↑)V(2)(↓). Therefore, the theoretical value of the effective moment is gµ 3 × . 3 + 1Σ + 2 × 2 × . 2 + 1Σ ≈ 5.7µ /f.u. and

Ba2SnSe5 and Sr2SnSe5, the Se atoms can form bonds with the bond length ranging from 2.38 Å to 2.44 Å as well as the typical bond angle from106° to 111° [23, 24]. In the Se chains of Ba9V3Se15, the distance of 2.69 Å is very close to

that of bonded Se atoms, suggesting the formation of Se2−

) dimer has also been reported

the saturated moment µsat is 1 µB/f.u., where the Lande

factor g is assigned to be 2. Thus, the values of µeff and µsat deduced from the magnetic measurements agree with the calculations. As will be discussed later, the spin chains are effectively decoupled in the experimental temperature range above the magnetic transition, and can be regarded

2 2

in Ba9Sn3Te15 (Ba9Sn3Se15) [17]. Following the calculated

as an effective ferromagnetic chains with effective spin-1/2

Figure 4. (a) The resistivity as a function of temperature, and the inset shows the ln (ρ) versus inverse temperature. (b) The temperature dependence of susceptibility χ measured with H = 1000 Oe and the inverse susceptibility 1/χ versus T. The inset is the temperature dependence of χT and the fitting curve. (c) The magnetic hysteresis curves measured at different temperatures. (d) The temperature

dependence of magnetization measured under different magnetic fields. The inset is the temperature derivative of magnetization dM/dT. (e) The susceptibility χ measured with H = 10 and 50 Oe. (f) and (g) The ac magnetic susceptibility measured at different frequencies.

by the formation of the V(2)(↓)V(1)(↑)V(2)(↓) cluster. Thus, a better fit for the measured susceptibility may be obtained using the following approximate scaling formula for the fer-

romagnetic spin-1/2 Heisenberg model [25]:

inset of figure 4(b). The deduced value of J is about 53 K, consistent with the Curie–Weiss temperature of 31 K and the estimated value of J2 ~ 47 K derived from our first-principles numerical calculations (see below).

Figure 4(d) displays the temperature dependence of mag-

χT = C

1 1.25S

1 + 0.6J(S + 1) T

netization measured under different magnetic fields. When the field is 7T, the magnetization curve exhibits saturation at low

where S = 1/2 is the spin moment and J = J2 is the inter- cluster interaction. This is indeed the case, as shown in the

temperature. The inset of figure 4(d) is the temperature deriva- tive of magnetization dM/dT, from which the ferrimagnetic

Figure 5. (a) Specific heat data with the temperature down to 0.4 K for Ba9V3Se15; the inset shows the C/T1/2 as a function of T2.5 for Ba9V3Se15. (b) Specific heat measurement for another sample of Ba9V3Se15 in a wide temperature region. The inset is the specific heat subtracted by the lattice contribution, and the fitted line of T0.5 dependence of SH is shown with the red line.

transition temperature can be determined. It can be seen from the inset that the ferrimagnetic transition temperature increases with magnetic field increases, which is a general phenomenon for a ferromagnetic system. Figure 4(e) shows the magnetic susceptibility measured with the magnetic field of 10 Oe and 50 Oe, respectively, where the ZFC curves and FC curves divaricate below 4 K. When the field is 10 Oe, the ZFC curve presents two kinks, corresponding to the ferrimagnetic trans- ition at 2.5 K and spin cluster glass frozen temperature at 3.3 K, respectively. For the field of 50 Oe, the formation process of spin cluster glass cannot be observed and the separation of ZFC and FC curves implies the existence of magnetic hyster- esis. The two phase transitions at low field can be further con- firmed by the ac magnetic susceptibility measurement, which is presented in figures 4(f) and (g). Both the real and imaginary parts exhibit two maximums at 2.5 K and ~3.3 K, respectively. The maximum at 2.5 K is independent on frequency; while the other one shifts towards higher temperature when frequency increases, demonstrating spin cluster glass behavior.

For an ideal 1D spin chain, no long-range magnetic order can exist at finite temperature as implied in the Mermin– Wagner theorem [26]. On the other hand, the inter-chain cou- pling between spin chains may govern the magnetic order although it is in general much weaker than intra-chain cou- plings [27]. In addition, if the 1D spin chains are arranged in a triangular lattice, there also exists magnetic frustration due to the special geometric structure of triangular arrangement and antiferromagnetic inter-chain interaction. A prominent example is ABX3 system where A is alkali metal, B is trans- ition metal and X is a halogen atom [28]. In these materials, there are chains containing atom B (normally magnetic) along the c axis, and the distance of adjacent chains is typically about 7.5 Å. Most of these compounds are antiferromagnetic with a rich magnetic phase diagram due to the magnetic frus- tration, and the magnetic structure can be tuned by magnetic field. While for Ba9V3Se15, the distance of adjacent chains is much larger than ABX3 system, hinting an even weaker inter- chain interaction. The spin cluster glass state should arise

from the spin frustration. A small magnetic field can elimi- nate the spin cluster glass state and orientates the spin to the magnetic direction. Here, we cannot tell the detailed magnetic structure, which deserves to be further studied by neutron dif- fraction measurement.

Figure 5 shows the temperature dependence of specific heat (SH) for two samples of Ba9V3Se15. Figure 5(a) is the data measured in the temperature range from 0.4 K to 10 K. As shown in the figure 5(a), there is a broad maximum centered at about 2.5 K. Although the broad maximum can be usually

expected in an ideal spin chain system [29–31], the broad SH

peak is also a common phenomenon in quasi 1D spin-chain compounds, due to the development of short-range ordering along the chains before 3D magnetic ordering formation [32, 33]. With the applied magnetic field increasing, the SH peak shifts to higher temperature and becomes broader and nearly disappears at 3T. At the same time, the SH curve upshifts, hinting the weight of magnetic contribution moves to higher temperature. The behavior of magnetic SH responding to the applied magnetic field is consistent with that for a ferro- or ferri- magnetic system. As suggested by the following calcul- ations that the NN intra-chain antiferromagnetic exchange J1 is two orders of magnitude larger than NNN intra-chain ferro- magnetic exchange J2, the chains in Ba9V3Se15, therefore, can be regarded as an effective ferromagnetic chains with effec-

tive spin-1/2 by the formation of V(2)(↓)V(1)(↑)V(2)(↓) cluster. It should be noted that, for Ba9V3Se15, there are three energy scales of NN intra-chain exchange J1, NNN intra-chain

exchange J2 and inter-chain exchange J3, which governs the V( 2)(↓)V(1)(↑)V(2)(↓) cluster formation, the development of ferro- magnetic short-range order in the chains and the 3D magnetic transition, respectively. Just above the 3D magnetic transition, the chains are decoupled and the magnetic SH should be dom-

inant by the spin wave excitation arising from the spin chains. As predicted by the spin wave theory, ferromagnetic chains host a quadratic magnon excitation with ω ~ k2, which should lead to a T1/2 magnetic SH at low temperature. Thus, we use the formula of C = αT1/2 + βT3 to analysize the low temper-

ature SH data, where the first term is the magnetic contrib-

ution and the second term is the phonon contribution. The inset of figure 5(a) shows the curve of SH divided by square root temperature C/T1/2 versus T2.5. The magnetic transition temperature can be unambiguously determined by the peak at 2.5 K. Above the transition, the curve of C/T1/2 versus T2.5 is nearly linear in the low temperature region, which can be

fitted using the formula of C/T1/2 = α + βT2.5, where α and β is the coefficient associated with magnetic and phonon SH, respectively. The value of α can be evaluated to be 1096–1458 mJ (mol · K1.5)−1 depending on magnetic field. To confirm the result, we carried out SH measurement on another sample in

a wider temperature range from1.8 K to 20 K with the magn- etic field up to 9T, which is shown in figure 5(b). The curve of C/T1/2 versus T2.5 is slightly deviated from a straight line. Here, the formula of C/T1/2 = α + βT2.5 + ηT4.5, where η is the quintic term coefficient of the phonon SH, can be used to fit

the SH data. The fitted parameters are shown in table 2. After subtracting the lattice contribution, the magnetic SH data of zero magnetic field is shown in the inset of figure 5(b). The

Table 2. The parameters obtained by using the formula

C/T1/2 = α + βT2.5 + ηT4.5 to fit the specific heat data.

α mJ β mJ η mJ

(mol · K1.5)−1 (mol · K4)−1 (mol · K6)−1

0T 1016 10.19 −0.0061

1T 1416 9.67 −0.0053

5T 1214 10.67 −0.0007

9T 1042 10.88 −0.0074

data away from the 3D magnetic transition can be well fitted with a T0.5-dependent line, which demonstrates the magnetic SH of the decoupled chains in Ba9V3Se15 can be described by the spin wave theory.

The electronic and magnetic structures of Ba9V3Se15 were further investigated by the first-principles calculations. To deter- mine the magnetic ground state, GGA and GGA + U spin- polarized calculations were performed for different magnetic structures (see figure 6). Both yield a cluster ferrimagnetic V( 2)(↓)V(1)(↑)V(2)(↓) ground state, in good agreement with exper-

imental analysis. Here, we have used Ueff = 5 eV for V in the

GGA + U calculations, following the common choices in the literature [34]. Other values of Ueff in a wide range around the

above choice have also been tested, and yield the same magn- etic ground state. We obtain a total magnetic moment of 0.999 µB/f.u. with the atomic contributions of V1 and V2 inside the muffin-tin spheres to be 2.592 µB, and −1.998 µB, respectively. These indicate that the local spins on the V1 and V2-ions are approximately S1 = 3/2 and S2 = 1, respectively. The values of

the ionic magnetic moments are slightly reduced from their ideal

values because of the strong hybridization with Se-p orbitals.

The electronic density of states (DOS) and band structures of Ba9V3Se15 from the GGA + U calculation are shown in figure 7. We find an insulating gap of 0.66 eV in the spin up channel and 0.58 eV in the spin down channel. These con- firm the insulating nature of the electronic ground state. The

obtained values are somewhat larger than that derived from experiments, which is, however, not unexpected as GGA + U calculations typically overestimate the insulating gap. Away from the Fermi energy, the bands show a larger dispersion along kz direction (the A-Gamma path) and are flat within

the ab plane (the Gamma-M path), manifesting the quasi 1D structure of Ba9V3Se15. Due to the different distortion of the VSe6 octahedra, we find d3 and d2 configurations for V1 and V2-ions, respectively. As a result, the d orbitals of V1 are half occupied and fully polarized in the spin up channel with a

total spin S = 3/2, while for V2, the two d-electrons occupy the spin down channel with S = 1, consistent with the exper- imental analysis.

To estimate the relative energy scales of the spin chains, we have mapped the total energies of the above magnetic configu- rations into an effective 1D Heisenberg model:

H = E0 Jij−→Si −→Sj

i

Figure 6. Different magnetic structures of Ba9V3Se15.used in the numerical calculations.

Figure 7. The DOS and band structures of Ba9V3Se15 within GGA + U. Se-around denotes the Se-ions around the V-ions on the VSe6 octahedron and Se-chain denotes other Se-ions forming quasi-1D chains.

coupling of the two spins. Here, we only give the intra-chain exchange couplings J1 between the nearest neighboring V1–V2 and J2 for V2–V2 (next nearest neighbors). The inter-chain exchange interactions are negligible because of the very long inter-chain distance. For one formula unit, the total energies associated with different magnetic order can be written as:

E (Fm)= E0 − J1S1S2 − J2S2,

We note the above DFT analysis using decoupled 1D spin chains was only applied to estimate the intra-chain couplings. The real system contains three well-separated energy scales. While J1 is responsible for the formation of the V(2)(↓)V(1)(↑)

V(2)(↓) clusters, which takes place far above the experimental

temperature range, J2 governs the ferromagnetic spin chains

and its magnitude is consistent with the experimental results. In addition, the magnetic interaction between neighboring

E (Afm)= E0 + J1S1S2 + J2S2,

E (Fim)= E0 + J1S1S2 − J2S2.

(1)

spin chains is expected to be very small. However, as indicated in previous work [27], even a small inter-chain coupling could

Here, we use S1 = 3/2 and S2 = 1 for V1 and V2-ions, respec- tively. From the above equations, we obtain the magnetic interactions J1 = −676.28 meV and J2 = 4.09 meV, respec- tively. The resulting antiferromagnetic J1 and ferromagnetic

J2 are in accordance with the ferrimagnetic ground state.

lead to a magnetic transition at finite temperature. This is con- sistent with our observation of the 3D magnetic transitions in Ba9V3Se15. At very low temperatures, one may expect contrib- utions from the 2D triangular lattice. However, above the transition, the system is governed by the spin wave excitations

of the ferromagnetic chains, as indicated by the T1/2 contrib- ution in the specific heat analysis. Detailed calculations based on above model may yield quantitative comparisons with experimental data, but this is beyond the scope of the current work. Nevertheless, our analysis of both the specific heat and susceptibility data seems to agree with the theoretical expec- tation of the ferromagnetic spin-1/2 chain in this temperature range.

Conclusion

In conclusion, the compound of Ba9V3Se15 with spin chains has been synthesized under high-pressure and high-temper- ature conditions. It crystallizes into a hexagonal structure with the space group of P-6c2 (188). In the structure, the trimeric spin chains are along c axis and arranged in a tri- angular lattice in ab-plane. The distance of the adjacent

spin chains is given by the lattice constant a = 9.5745 Å. Ba9V3Se15 is a semiconductor with a band gap ~0.2 eV. It

undergoes complex magnetic transitions. In the ZFC pro- cess with magnetic field of 10 Oe, Ba9V3Se15 sequentially undergoes ferrimagnetic transition and spin cluster glass formation at 2.5 K and 3.3 K, respectively. A small magn-

etic field (>50 Oe) can eliminate the spin cluster glass state and the susceptibility merely presents ferrimagnetic trans-

ition. The specific heat at low temperature obtains a sig- nificant magnetic contribution that is proportional to T1/2. Ba9V3Se15 can be regarded as an effective ferromagnetic chains with effective spin-1/2 by the formation of V(2)(↓)V(

1)(↑)V(2)(↓) cluster. This might be a new route to bypass the

large antiferromagnetic coupling and produce ferromagn-

etic spin chains in the experiment.

Acknowledgments

This work was financially supported by the National Science Foundation of China (NSFC) and the National Basic Research Program of China.

ORCID iDs

Xiancheng Wang https://orcid.org/0000-0001-6263-4963

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