low dimensionality, high density, strong interactions or small $N$. Our scheme instead relies on the engineering of effectively attractive interactions for the spin excitations of two-component (binary) BECs in the ground state, while the actual intracomponent and intercomponent contact interactions remain repulsive. By [*spin excitations*]{}, we mean the out-of-phase excitations of the two components. The interactions are effectively attractive in the sense that spin fluctuations act to decrease the interaction energy. Contrary to the case of true attractive contact interactions [@Bradley1995; @Donley2001], the proposed regime is not vulnerable to collapse of the underlying BEC.

Numerous groups have experimentally realized binary BECs by combining different elements [@Thalhammer2008; @McCarron2011; @Lercher2011; @Pasquiou2013; @Wacker2015; @Wang2016], isotopes [@Papp2008; @Sugawa2011; @FerrierBarbut2014], hyperfine states [@Myatt1997; @Hall1998B; @Matthews1999; @Hoinka2012], and even different spin states [@Maddaloni2000]. There has also been considerable theoretical attention, e.g. see [@Ho1996; @Pu1998; @Ohberg1999; @Trippenbach2000; @Svidzinsky2003; @Kasamatsu2004; @Dutton2005; @Mertes2007; @Ronen2008; @Oles2008; @Anderson2009; @Hofmann2014; @Roy2015; @Liu2016]. In the thermodynamic (TD) limit, a binary condensate is miscible for small intercomponent scattering length $a_{12}$, up until $a_{12}^{\rm c,TD} \equiv \sqrt{a_{11}a_{22}}$, above which it phase separates and becomes immiscible [^1]. Interestingly, at finite temperature ($T$), long-wavelength spin fluctuations tend to diverge on approach to the immiscibility phase transition, while 