Ba $_2$ YIrO $_6$中磁矩的起源和共振价键态的存在
Origin of magnetic moments and presence of a resonating valence bond state in Ba$_2$YIrO$_6$
摘要：
虽然推测5个$d^4$系统由于强自旋轨道耦合（SOC）而具有非磁性$J$ ~=~0基态，但是到目前为止，所有这样的系统都不可避免地显示出磁矩的存在。一个令人困惑的例子是Ba $_2$ YIrO $_6$，尽管它具有完美的立方结构，其中大部分是分离的Ir $^{5+}$（$d^4$）离子，但始终显示出弱磁矩的存在。此外，我们清楚地表明，从μ子自旋弛豫（$μ$ SR）的测量，在Ba $_2$ YIrO $_6$注入μ子的磁环境的变化发生的温度低于10 K。该观察结果变得违反直觉，因为发现通过用原子$j-j$模型拟合Ba $_2$ YIrO $_6$的RIXS光谱获得的SOC的估计值高达0.39 eV，这意味着该模型内的系统既不期望具有磁矩也不表现出温度依赖性磁响应。因此，我们认为，原子$j-j$耦合的描述是不足以解释这种系统的基态，尽管有很强的SOC，跳频的存在触发离域的空穴，导致自发产生的磁矩。我们的理论计算进一步表明，在Ba $_2$ YIrO $_6$的情况下，这些磁矩有利于自旋轨道单线态的形成，这在低至60 mK的$μ$ SR实验中得到了证实.
英文摘要：
While it was speculated that 5$d^4$ systems would possess non-magnetic $J$~=~0 ground state due to strong Spin-Orbit Coupling (SOC), all such systems have invariably shown presence of magnetic moments so far. A puzzling case is that of Ba$_2$YIrO$_6$, which in spite of having a perfectly cubic structure with largely separated Ir$^{5+}$ ($d^4$) ions, has consistently shown presence of weak magnetic moments. Moreover, we clearly show from Muon Spin Relaxation ($μ$SR) measurements that a change in the magnetic environment of the implanted muons in Ba$_2$YIrO$_6$ occurs as temperature is lowered below 10~K. This observation becomes counterintuitive, as the estimated value of SOC obtained by fitting the RIXS spectrum of Ba$_2$YIrO$_6$ with an atomic $j-j$ model is found to be as high as 0.39~eV, meaning that the system within this model is neither expected to possess moments nor exhibit temperature dependent magnetic response. Therefore we argue that the atomic $j-j$ coupling description is not sufficient to explain the ground state of such systems, where despite having strong SOC, presence of hopping triggers delocalisation of holes, resulting in spontaneous generation of magnetic moments. Our theoretical calculations further indicate that these moments favour formation of spin-orbital singlets in the case of Ba$_2$YIrO$_6$, which is manifested in $μ$SR experiments measured down to 60~mK.
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