Bose-Einstein condensation of triplons in the S=1 tetramer antiferromagnet K2Ni2(MoO4

Abstract

The structure of K2Ni2(MoO4)3 consists of S = 1 tetramers formed by Ni 2+ ions. The magnetic susceptibility χ(T ) and specific heat CP (T ) data on a single crystal show a broad maximum due to the low-dimensionality of the system with shortrange spin correlations. A sharp peak is seen in χ(T ) and CP (T ) at about 1.13 K, well below the broad maximum. This is an indication of magnetic long-range order i.e., the absence of spin-gap in the ground state. Interestingly, the application of a small magnetic field (H > 0.1 T) induces magnetic behavior akin to Bose-Einstein condensation (BEC) of triplon excitations observed in some spin-gap materials. Our results demonstrate that the temperature-field (T − H) phase boundary follows a power-law (T − TN ) ∝ H 1/α with the exponent 1/α close to 2/3, as predicted for BEC scenario. The observation of BEC of triplon excitations in small H infers that K2Ni2(MoO4)3 is located in the proximity of a quantum critical point, which separates the magnetically ordered and spin-gap regions of the phase diagram. PACS numbers:Spin-gap materials exhibit remarkably exotic magnetic phenomena such as the realizations of Bose-Einstein condensation (BEC) and appearance of magnetization plateaus [1][2][3][4][5]. In general, spin-gap materials have a singlet (S = 0) ground state and the triplet excited states are separated from the ground state by an energy gap, called the spin-gap. With increasing magnetic field (which leads to a Zeeman splitting of S = 1 states), at a critical value of the field H c , the lowest sub-state of the triplet (S z = 1) crosses the S = 0 ground state. As a result, a finite concentration of triplets (triplons) populate. This consequently leads to several field-induced magnetic long-range-ordering (LRO) phenomena such as BEC of triplons in the vicinity of T = 0 K and H c [1,2]. In this context, the applied magnetic field (H) acts as a chemical potential in separating the spin-gap region and LRO region of the quantum phase diagram at T → 0 K [6]. Experimentally, the field-induced BEC of triplon behavior has been intensively studied for various spin-gap materials with S = 1/2 dimers TlCuCl 3 [7,8] [18,19]. In the case of Cs 2 CuCl 4 , although the material undergoes a magnetic transition (T N ) at 0.595 K, the gap in the magnon spectrum closes at about 8.51 T and the three dimensional (3D) BEC phase boundary relation T N ∝ (H − H c ) 1/α with an exponent 1/α = 2/3 is observed, similar to other spin-gap materials [7][8][9][10][11][12][13][14][15]. Interestingly, when a spin-gap system is subjected to significant three-dimensional interactions, the triplet states are broadened and thus reduce the size of the spin-gap. In such a case, a small H c is enough to induce BEC of triplon excitations. This class of material offers an ideal ground to explore quantum critical phenomena in the proximity of a Quantum Critical Point (QCP) in view of their collective spin excitations, high homogeneity in boson density, and topological order [1].In this Rapid Communication, we stu...

Gd2Te3: an antiferromagnetic semimetal

“…The inset of figure 6 clearly demonstrates that T * ∝ H 2 3 . The shape and the field-evolution of the M(T) curves bear a striking resemblance to the M H (T) data reported in several spin-gap/spindimer compounds with spin-1 2 including ACuCl 3 (A = K, Tl), Pb 2 V 3 O 9 [17][18][19][20][21], Haldane-gap spin = 1 compounds such as PbNi 2 V 2 O 8 , SrNi 2 V 2 O 8 [22,23] as well as the S = 1 tetramer compound K 2 Ni 2 (MoO 4 ) 3 [24] with a long-range ordered AFM ground state, that exhibit the field-induced (FI) magnon Bose-Einstein condensation (BEC) [25] at a critical magnetic field H c .…”

“…with φ = 3 2 represents the phase boundary between the FI-magnon Bose-Einstein condensate and non-condensate phases in three-dimensional (3D) systems exhibiting the FI-magnon BEC [17][18][19][20][21][22][23][24] or even thermally-excited magnon BEC [25,26]. From the strikingly similar M H (T) and the validity of equation ( 2) in the present case, one may be tempted to conclude that Gd 2 Te 3 is a potential candidate for FI-magnon BEC.…”

Field-induced Bose–Einstein condensation in zigzag spin chain KGaCu(PO4)2

“…As for H//c, below H 1 ≈ 8 T, the M intensity weakens in all three axes as the H increases. However, beyond 8 T, there is a sudden increase in M. As the H continues to increase, the M of the c-axis approaches saturation near H s = 12 T. The magnetization of this system presents a process of the field-induced BEC of triplons, as observed in some other materials [3,[18][19][20][21][22][23]. The lower boundary, H 1 ≈ 8 T, of the BEC in the system is in proximity to the spin gap, ∆ ≈ 12.06 K, ≈ 8 T, determined from the magnetic susceptibility analysis.…”

“…C p /T showed a clear peak at (T max ) Cp/T = 5.29 K, with a maximum value of (C p /T) max = 4.97 J•mol −1 •K −2 . The (T max ) Cp/T is expectedly lower than the T value of the peak at 11.5 K in the χ(T) data, as observed in several low-D spin systems [16][17][18]. For a S = 1/2 AFM uniform Heisenberg chain, the values of (T max ) Cp/T and (C p /T) max can provide a way of estimating the exchange energy couplings in the system using the theoretical equations, (T max ) Cp/T = 0.30716996(2) J/k B [16].…”

Evaluation of field-induced magnetic moments in the spin-12 antiferromagnetic trimerized chain compound Cu3(P2Hase1, Pomjakushin2, Keller3 et al. 2020Phys. Rev. B5010View full textAdd to dashboardCite

“…We believe that it is possible to precisely evaluate exchange interactions in paramagnets with multiple exchange interactions and multiple crystallographic magnetic-ion sites by using field-induced magnetic moments in combination with macroscopic physical quantities because we could precisely evaluate the exchange interactions by using information regarding ordered magnetic moments in conjunction with the magnetic-susceptibility and magnetization results in Cu 2 CdB 2 O 6 [8,9]. This idea is applicable to research of several spin systems such as diamond chain [1][2][3][4][5], spin cluster [20], distorted kagome lattice [21], and three-leg ladder [22,23]. Evaluation of field-induced magnetic moments is also useful in research of magnets containing both transition-metal and rare-earth magnetic ions.…”