Room-temperature structural phase transition in the quasi-2D spin-1/2 Heisenberg antiferromagnet Cu(pz)$_2$(ClO$_4$)$_2$

TL;DR

This study reveals a previously unreported second-order structural phase transition in Cu(pz)$_2$(ClO$_4$)$_2$ at 294 K, characterized by subtle lattice distortions without magnetic ordering, using multiple experimental techniques.

Contribution

The paper uncovers a room-temperature structural phase transition in Cu(pz)$_2$(ClO$_4$)$_2$, combining magnetization, specific heat, NMR, and neutron diffraction data to characterize the transition.

Findings

Evidence of a second-order phase transition at 294 K.

Absence of magnetic ordering across the transition.

Subtle angular distortions of molecular components above the transition.

Abstract

Cu(pz)$_2$(ClO$_4$)$_2$ (with pz denoting pyrazine C$_4$H$_4$N$_2$) is a two-dimensional spin-1/2 square-lattice antiferromagnet with $T_{\mathrm{N}}$ = 4.24 K. Due to a persisting focus on the low-temperature magnetic properties, its room-temperature structural and physical properties caught no attention up to now. Here we report a study of the structural features of Cu(pz)$_2$(ClO$_4$)$_2$ in the paramagnetic phase, up to 330 K. By employing magnetization, specific heat, $^{35}$Cl nuclear magnetic resonance, and neutron diffraction measurements, we provide evidence of a second-order phase transition at $T^{\star}$ = 294 K, not reported before. The absence of a magnetic ordering across $T^{\star}$ in the magnetization data, yet the presence of a sizable anomaly in the specific heat, suggest a structural order-to-disorder type transition. NMR and neutron-diffraction data corroborate our conjecture, by revealing subtle angular distortions of the pyrazine rings and of ClO$^-_4$ counteranion tetrahedra, shown to adopt a configuration of higher symmetry above the transition temperature.

Tables

Table 1. Table 1.: Structural parameters as determined from neutron powder diffraction at T = 295 𝑇 295 T=295  K, using the space groups C ​ 2 / m 𝐶 2 𝑚 C2/m and C ​ 2 𝐶 2 C2 , respectively 3 3 3 The quantities marked with (*) in Table I were constrained to be identical for the same atomic species. The occupation of the D sites was found to be very close to 100%. The occupation of the remaining atomic sites was 100% . For the last group, that is non-centrosymmetric, the origin is floating. For that reason the y 𝑦 y -coordinate of Cu has been fixed to zero, matching the Cu postion in C ​ 2 / m 𝐶 2 𝑚 C2/m . To further facilitate comparisons, the setting for the monoclinic cell was chosen to be the same as in reference Woodward  et al. ( 2007 ) . For every space group the fits were carried out using a single structural model to refine simultaneosly the data recorded at λ = 1.494 𝜆 1.494 \lambda=1.494 and 1.886 Å . The related .cif file with the refinement parameters can be found in the Supplemental Material 4 4 4 The Supplemental Material available at [URL] includes the two structural .cif files used for refining the neutron-diffraction patterns at 295 K, by assuming as valid the space groups C ​ 2 𝐶 2 C2 and C ​ 2 / m 𝐶 2 𝑚 C2/m , respectively. .

$T=295$ K	$𝑪\mathrm{𝟐}/𝒎$ model	$𝑪\mathrm{𝟐}$ model
$a$(Å)	9.78047(9)	9.78070(7)
$b$(Å)	9.77594(9)	9.77589(7)
$c$(Å)	8.16470(9)	8.16488(7)
$\beta {(}^{\circ })$	120.8361(7)	120.8353(6)
Cu $\left(2a\right)/\left(2a\right)$	[0, 0, 0]	[0, 0, 0]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0118(9)	0.0126(9)
Cl $\left(4i\right)/\left(4c\right)$	[0.2402(4), 0, 0.5391(5)]	[0.2599(4), 0.4925(16), 0.4607(5)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.012(3)	0.0292(10)
O1 $\left(8j\right)/\left(4c\right)$	[0.2052(9), 0.1075(9), 0.6031(11)]	[0.3071(18), 0.588(3), 0.388(3)]
$U_{11}\left({\text{Å}}^2\right)$	0.057(5)	0.031(7)
$U_{22}\left({\text{Å}}^2\right)$	0.393(14)	0.48(5)
$U_{33}\left({\text{Å}}^2\right)$	0.128(6)	0.100(13)
$U_{12}\left({\text{Å}}^2\right)$	0.061(6)	$-$0.051(14)
$U_{13}\left({\text{Å}}^2\right)$	$-$0.030(4)	$-$0.035(7)
$U_{23}\left({\text{Å}}^2\right)$	$-$0.195(7)	0.21(2)
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.193(8)	0.20(2)
O1’ $(-)/\left(4c\right)$	–	[0.2713(19), 0.374(3), 0.397(3)]
$U_{11}\left({\text{Å}}^2\right)$	–	0.061(10)
$U_{22}\left({\text{Å}}^2\right)$	–	0.217(16)
$U_{33}\left({\text{Å}}^2\right)$	–	0.176(18)
$U_{12}\left({\text{Å}}^2\right)$	–	0.006(10)
$U_{13}\left({\text{Å}}^2\right)$	–	0.012(11)
$U_{23}\left({\text{Å}}^2\right)$	–	$-$0.173(14)
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.151(15)
O2 $\left(4i\right)/\left(4c\right)$	[0.4010(7), 0, 0.5868(9)]	[0.1025(6), 0.504(2), 0.4146(9)]
$U_{11}\left({\text{Å}}^2\right)$	–	0.015(3)
$U_{22}\left({\text{Å}}^2\right)$	–	0.069(5)
$U_{33}\left({\text{Å}}^2\right)$	–	0.067(5)
$U_{12}\left({\text{Å}}^2\right)$	–	0.005(6)
$U_{13}\left({\text{Å}}^2\right)$	–	0.009(3)
$U_{23}\left({\text{Å}}^2\right)$	–	0.003(7)
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.042(4)	0.047(4)
O3 $\left(4i\right)/\left(4c\right)$	[0.1363(7), 0, 0.3366(8)]	[0.3643(6), 0.503(2), 0.6617(8)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0311(13)	0.0335(13)
C1 $\left(8j\right)/\left(4c\right)$	[0.8968(3), 0.7691(3), 0.1448(4)]	[0.8948(10) 0.2307(14) 0.1506(11)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0145(7)	0.0168(5)∗
C2 $\left(8j\right)/\left(4c\right)$	[0.7985(3), 0.6701(3), 0.1524(4)]	[0.2996(9) 0.8400(15) 0.1504(12)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0190(7)	0.0168(5)∗
C3 $(-)/\left(4c\right)$	–	[0.0997(10), 0.7683(14), 0.8572(11)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.0168(5)∗
C4 $(-)/\left(4c\right)$	–	[0.7037(9), 0.1779(14), 0.8445(12)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.0168(5)∗
D1 $\left(8j\right)/\left(4c\right)$	[1.0197(5), 0.7807(4), 0.2700(6)]	[0.0283(9), 0.2351(14), 0.2558(9)]
Occ	0.978(2)∗	0.961(7)∗
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0428(12)	0.0254(9)∗
D2 $\left(8j\right)/\left(4c\right)$	[0.8379(5), 0.6088(4), 0.2768(5)]	[0.3453(8), 0.9067(14), 0.2672(9)]
Occ	0.978(2)∗	0.961(7)∗
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0372(10)	0.0254(9)∗
D3 $(-)/\left(4c\right)$	–	[0.9892(8), 0.7973(14), 0.7166(10)]
Occ	–	0.961(7)∗
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.0254(9)∗
D4 $(-)/\left(4c\right)$	–	[0.6732(8), 0.1254(14), 0.7153(10)]
Occ	–	0.961(7)∗
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.0254(9)∗
N1 $\left(8j\right)/\left(4c\right)$	[0.6505(2), 0.65082(20), 0.0041(3)]	[0.8503(6), 0.1551(15), 0.9987(8)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	0.0096(4)	0.0141(5)∗
N2 $(-)/\left(4c\right)$	–	[0.1512(6), 0.8534(15), 0.0060(8)]
$U_{\mathrm{iso}}\left({\text{Å}}^2\right)$	–	0.0141(5)∗
$\lambda$( Å)	1.494 1.886	1.494 1.886
${\chi }^2$	5.18 8.54	3.27 5.06
$R_{exp}$	4.50 3.49	4.48 3.48
$R_{wp}$	10.2 10.2	8.10 7.82
$R_p$	9.37 9.14	7.53 7.25
.

Equations

$$K_s=g{A}_{\mathrm{hf}}\chi +K_{\mathrm{orb}},$$

$$M_z(t)=M_0[1-f\cdot (0.9\cdot e^{-(6t/T_1{)}^{\lambda }}+0.1\cdot e^{-(t/T_1{)}^{\lambda }})].$$

Full text

Two-dimensional systems, pressure-dependent phase transitions, antiferromagnetism, nuclear magnetic resonance

I Introduction

As a notable physical realization of a quasi-2D Heisenberg antiferromagnet, Cu(pz)2(ClO4)2 has been a test case for investigating the competition between long-range magnetic order and quantum fluctuations Darriet et al. (1979); Choi et al. (2003). Its structure consists of stacks along the $c$-axis of well-isolated nearly-square layers of Cu2+ ions in the $ab$-plane, rotated by 45∘ with respect to the in-plane primitive vectors, as shown schematically in Fig. I. Along the $c$-axis, each layer is shifted by half a unit cell along the $a$- and $b$-axes. Each Cu2+ ion is bridged to its four nearest-neighbors (NN) by C4H4N2 pyrazine ligands, which provide the intralayer superexchange interaction. Two ClO${}_{4}^{-}$ perchlorate counteranions, linked to Cu2+ ions via one of the oxygen atoms in the O4 tetrahedra, provide a sufficient interlayer separation along the $c$-axis, hence implying a negligible interlayer interaction. Overall, this results in a Cu2+-ion arrangement of nearly-tetragonal symmetry Landee and M.Turnbull (2013). The 3D antiferromagnetism (AFM) of Cu(pz)2(ClO4)2 has been extensively studied by inelastic neutron scattering (INS) Tsyrulin et al. (2010), muon-spin rotation ($\mu$SR) Lancaster et al. (2007), and nuclear magnetic resonance (NMR) Barbero et al. (2016) measurements. It has also been shown that applied magnetic fields along the $c$-axis strengthen the AFM order by suppressing the quantum fluctuations, hence enhancing $T_{\mathrm{N}}$ above its zero-field value of 4.24 K Tsyrulin et al. (2010). On the other hand, external hydrostatic pressure reduces $T_{\mathrm{N}}$ Barbero et al. (2016), most likely by enforcing 1D-type interactions Mermin and Wagner (1966), as suggested by results of density-functional theory (DFT) calculations on similar compounds Vela et al. (2013); Wehinger et al. (2018).

The crystal structure of Cu(pz)2(ClO4)2 was determined at 163 and 293 K from single-crystal x-ray diffraction data Woodward et al. (2007), obtaining a better refinement with the $C2/c$ space group in the first case and with the $C2/m$ space group in the latter. It was also observed that the four pyrazine moieties form two sets at low temperature, each of them characterized by a different tilting angle with respect to the $ab$-plane. The values of these angles are distinct at 163 K, but they become identical (65.8*∘*) at 293 K. Along with x-ray diffraction patterns, Choi et al. Choi et al. (2003) reported also infrared-spectroscopy data, used to track the evolution of the vibrational modes as a function of temperature. Upon heating, the latter measurements indicated a softening of the vibrational modes starting at approximately 180 K, related to the out-of-plane deformations of the pyrazine rings.

In this work, by combining data from NMR, specific-heat and neutron-diffraction experiments, we provide clear evidence for a structural phase transition occurring at $T^{\star}$ = 294(1) K, not reported before in the literature. Our results indicate that the two initially different Cl sites become equivalent above $T^{\star}$ and that the symmetry of the individual pyrazine rings increases upon heating above $T^{\star}$.

After introducing the experimental details in Sec. II, in Sec. III.1 and III.2, we describe the material characterization via magnetization and specific-heat measurements. From these data, we identify the onset of the AFM order at $T_{\mathrm{N}}$ and of the structural transition at $T^{\star}$, respectively. The 35Cl NMR results discussed in Sec. III.3 clearly show the merging of the two lines upon heating, reflecting an increase in structure symmetry and allowing for an evaluation of the isotropic hyperfine coupling. Finally, to precisely identify the variations in bond lengths and angles, we employed neutron powder diffraction measurements, whose results are reported in Sec. III.4. The combined data of our investigations indicate that the second-order structural phase transition is accompanied by subtle transformations in both the ClO${}^{-}_{4}$ tetrahedra and in the C4H4N2 pyrazine ligands.